integration of solid oxide fuel cells and ... - Ea Energianalyse
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INTEGRATION OF<br />
SOLID OXIDE FUEL CELLS AND<br />
ABSORPTION COOLING UNITS<br />
MASTER THESIS<br />
Casper Frimodt<br />
Kim Frithj<strong>of</strong> Mygind<br />
JULY 5, 2010<br />
DTU - MECHANICAL ENGINEERING<br />
IN COOPERATION WITH TOPSOE FUEL CELL<br />
SUPERVISORS:<br />
BRIAN ELMEGAARD, MASOUD ROKNI & THOMAS PETERSEN
Empty line<br />
Lyngby July 5, 2010<br />
Casper Frimodt (s042506)<br />
Casper Frimodt (s042506)<br />
Kim Mygind (s030689)<br />
Kim Mygind (s030689)
Abstract<br />
It is investigated whether it is feasible to integrate a <strong>solid</strong> <strong>oxide</strong><br />
<strong>fuel</strong> cell (SOFC) <strong>and</strong> an absorption (ABS) air conditioner (AC).<br />
First a market investigation based on rough economical calculations<br />
shows that the SOFC-ABS system fits two market segments -<br />
Auxiliary Power Unit (APU) for ships <strong>and</strong> Distributed Generation<br />
(DG) for hotels. The latter is the best suited example <strong>of</strong> an application<br />
<strong>and</strong> will constitute the basis in this project.<br />
A thermodynamical zero-dimensional steady state model <strong>of</strong><br />
the SOFC-ABS system is developed in order to demonstrate the<br />
performance <strong>of</strong> the integrated system. The thermodynamical model<br />
is mainly based on theory but also partly on empirical knowledge<br />
from the industry.<br />
More system configurations are modeled showing that the<br />
double stage absorption cycle is the best choice if the inlet air for<br />
the SOFC is additionally preheated by the heat from the exhaust<br />
gas remaining after the ABS. A wet cooling tower is necessary for<br />
the double stage ABS unit if the surrounding temperature is above<br />
20 ◦ C - otherwise the desorber temperature will have to exceed the<br />
normal limit <strong>of</strong> 150 ◦ C.<br />
The system is simulated with a st<strong>and</strong>ard parameter configuration,<br />
changing one parameter at a time in order to determine its influence<br />
on the system performance. Additionally a sensitivity analysis<br />
is made in order to determine how crucial the exact values <strong>of</strong><br />
the estimated parameters are. From these results an optimized parameter<br />
configuration is found.<br />
In a climate with a temperature <strong>of</strong> 30 ◦ C <strong>and</strong> relative humidity <strong>of</strong><br />
40% a <strong>fuel</strong> input (methane gas) <strong>of</strong> 100kW gives 50kW <strong>of</strong> electricity,<br />
59kW <strong>of</strong> cooling <strong>and</strong> 3kW <strong>of</strong> hot water.<br />
Three case studies <strong>of</strong> hotels in different locations show that the<br />
SOFC-ABS system can cope with very hot climates if they are dry.<br />
For humid climates the ABS unit can not run at too high ambient<br />
temperatures.<br />
The thermodynamical model shows that it is feasible to integrate<br />
a SOFC <strong>and</strong> an ABS unit, <strong>and</strong> the economical calculations indicate<br />
that it could be an economical advantage as well.
Dansk resumé<br />
Det vil blive undersøgt, om det er muligt at integrere en Solid<br />
Oxide BrændselsCelle (SOFC) med et absorptionsairconditionanlæg<br />
(ABS).<br />
Først laves en markedsundersøgelse på baggrund af økonomiske<br />
overslagsberegninger. Denne viser, at SOFC-ABS-systemet passer<br />
godt til to markedssegmenter - Auxiliary Power Unit (APU) til<br />
skibe og Distributed Generation (DG) til et hotel. Hotellet konkluderes<br />
at være det mest egnede til SOFC-ABS-kombinationen, og<br />
denne case danner derfor grundlag for resten af projektet.<br />
En termodynamisk nul-dimensional steady state model af SOFC-<br />
ABS-systemet udvikles for at beregne ydelsen af det integrerede<br />
system. Den termodynamiske model er hovedsageligt baseret på<br />
teori men også delvist på empirisk viden fra industrien.<br />
Flere forskellige systemkonfigurationer modelleres. Det viser<br />
sig, at dobbelteffekt absorptionskredsløbet giver den bedste ydelse.<br />
I hvert fald hvis luften til brændselscellen forvarmes af den<br />
spildvarme, der er tilbage i udstødningsgassen efter ABS-anlægget.<br />
Et vådkøletårn er nødvendigt, hvis dobbelteffekt-ABS-anlægget<br />
skal bruges i omgivelser med en temperatur på over 20 ◦ C - ellers<br />
kommer desorbertemperaturen over de 150 ◦ C, der normalt anses<br />
for at være den øvre grænse.<br />
Systemet er simuleret med en st<strong>and</strong>ardparameterkonfiguration,<br />
hvorefter en parameter ændres ad gangen for at fastlægge, hvordan<br />
den influerer på systemets ydelse. Derudover laves en følsomhedsanalyse<br />
for at vise, hvor følsomt systemet er over for den præcise<br />
værdi af de skønnede parametre. Ud fra disse undersøgelser findes<br />
en optimal parameterkonfiguration.<br />
I et klima med en temperatur på 30 ◦ C og en relativ fugtighed<br />
på 40%, vil det optimerede system, ved et brændselsinput (af<br />
metan) på 100kW, give ca. 50kW elektricitet, 59kW køling og 3kW<br />
v<strong>and</strong>opvarmning.<br />
Tre cases med hoteller i forskellige egne viser, at SOFC-ABSsystemet<br />
er passende til meget varme klimaer, der samtidigt har<br />
lav luftfugtighed. Hvis der derimod er høj luftfugtighed, kan<br />
absorptionsanlægget ikke køre ved høje omgivelsestemperaturerer.<br />
Simuleringerne og beregningerne viser, at det er muligt at<br />
integrere en SOFC-brændselscelle med et absorptionskøleanlæg og<br />
tyder desuden på, at det også kunne være en økonomisk fordel.
Preface<br />
This report is documentation <strong>of</strong> our master thesis <strong>of</strong> 2 times 30 ECTS<br />
points carried out in the period from February to June in 2010. The projet<br />
is conducted under DTU Mechanical Engineering in corporation with<br />
Topsoe Fuel Cell.<br />
ix
Acknowledgment<br />
Thanks to:<br />
Brian Elmegaard<br />
Thomas F. Petersen<br />
Masoud Rokni<br />
Topsoe Fuel Cell for hospitality<br />
Arne Hansen for printing this report<br />
xi
CONTENTS<br />
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .<br />
Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .<br />
ix<br />
xi<br />
Nomenclature<br />
xxi<br />
Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi<br />
Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii<br />
Greek (<strong>and</strong> other) Symbols . . . . . . . . . . . . . . . . . . . . . . . . xxiii<br />
Latin Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiv<br />
Subscripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv<br />
1 Introduction 1<br />
1.1 Project outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1<br />
1.2 General formalities . . . . . . . . . . . . . . . . . . . . . . . . . . 3<br />
1.3 General introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3<br />
1.3.1 Distributed generation . . . . . . . . . . . . . . . . . . . 3<br />
1.3.2 Fuel <strong>cells</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4<br />
1.3.3 Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . 4<br />
1.3.4 Dem<strong>and</strong> for cooling . . . . . . . . . . . . . . . . . . . . . 5<br />
1.4 SOFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6<br />
1.4.1 SOFC Waste heat . . . . . . . . . . . . . . . . . . . . . . . 6<br />
1.4.2 Topsoe Fuel Cell . . . . . . . . . . . . . . . . . . . . . . . 7<br />
1.4.3 APU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7<br />
1.4.4 Micro CHP . . . . . . . . . . . . . . . . . . . . . . . . . . 7<br />
1.4.5 DG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7<br />
1.5 Heat driven cooling . . . . . . . . . . . . . . . . . . . . . . . . . 8<br />
1.5.1 Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . 9<br />
1.5.2 Carré cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 9<br />
1.5.3 Platen Munters cycle . . . . . . . . . . . . . . . . . . . . 14<br />
1.5.4 Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . 15<br />
1.6 Problem delimitation . . . . . . . . . . . . . . . . . . . . . . . . 17<br />
1.7 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . 18<br />
2 Market investigation 19<br />
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19<br />
2.2 Auxiliary Power Unit (APU) . . . . . . . . . . . . . . . . . . . . 21<br />
xii
Contents<br />
2.2.1 Truck APU . . . . . . . . . . . . . . . . . . . . . . . . . . 21<br />
2.2.2 Ship APU . . . . . . . . . . . . . . . . . . . . . . . . . . . 22<br />
2.3 Micro Combined Heat <strong>and</strong> Power (µCHP) . . . . . . . . . . . 25<br />
2.3.1 Micro CHP - Air condition . . . . . . . . . . . . . . . . . 25<br />
2.3.2 Micro CHP - Refrigerators . . . . . . . . . . . . . . . . . 26<br />
2.4 Distributed Generation (DG) . . . . . . . . . . . . . . . . . . . . 29<br />
2.4.1 Three solutions . . . . . . . . . . . . . . . . . . . . . . . . 30<br />
2.4.2 Hot vs Normal climate . . . . . . . . . . . . . . . . . . . 31<br />
2.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32<br />
2.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 38<br />
2.5 Conclusion <strong>of</strong> the whole market investigation . . . . . . . . . 39<br />
3 Component description 41<br />
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41<br />
3.1.1 EES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41<br />
3.1.2 Components . . . . . . . . . . . . . . . . . . . . . . . . . 42<br />
3.2 Absorber - ABSO . . . . . . . . . . . . . . . . . . . . . . . . . . . 45<br />
3.3 Blower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48<br />
3.4 Burner - BURN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49<br />
3.5 Condenser - COND . . . . . . . . . . . . . . . . . . . . . . . . . 50<br />
3.6 Desorber - DES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53<br />
3.7 Evaporator - EVAP . . . . . . . . . . . . . . . . . . . . . . . . . . 55<br />
3.8 Heat Exchanger - HEX . . . . . . . . . . . . . . . . . . . . . . . . 57<br />
3.9 Mixer - MIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60<br />
3.10 Pre Reformer - PR . . . . . . . . . . . . . . . . . . . . . . . . . . . 61<br />
3.11 Pump - PUMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63<br />
3.12 Solid Oxide Fuel Cell - SOFC . . . . . . . . . . . . . . . . . . . . 64<br />
3.12.1 Chemical reactions . . . . . . . . . . . . . . . . . . . . . 65<br />
3.13 Splitter - SP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70<br />
3.14 Cooling Tower - TOWER . . . . . . . . . . . . . . . . . . . . . . 71<br />
3.14.1 Dry Cooling Tower - TOWERd . . . . . . . . . . . . . . 72<br />
3.14.2 Wet Cooling Tower - TOWERw . . . . . . . . . . . . . . 73<br />
3.15 Expansion valve - VA/VB . . . . . . . . . . . . . . . . . . . . . 76<br />
3.15.1 Expansion valve for refrigerant - VA . . . . . . . . . . 76<br />
3.15.2 Expansion valve for LiBr solution - VB . . . . . . . . . 76<br />
4 System description 79<br />
4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79<br />
4.2 SOFC subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . 81<br />
4.2.1 Fuel pretreatment <strong>and</strong> recirculation . . . . . . . . . . . 81<br />
4.2.2 Air inlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83<br />
xiii
CONTENTS<br />
4.2.3 SOFC stack . . . . . . . . . . . . . . . . . . . . . . . . . . 84<br />
4.2.4 Exhaust gas . . . . . . . . . . . . . . . . . . . . . . . . . . 85<br />
4.3 Absorption Single Stage . . . . . . . . . . . . . . . . . . . . . . . 86<br />
4.3.1 Refrigerant cycle . . . . . . . . . . . . . . . . . . . . . . . 87<br />
4.3.2 Solution cycle . . . . . . . . . . . . . . . . . . . . . . . . . 87<br />
4.3.3 Pumping factor . . . . . . . . . . . . . . . . . . . . . . . . 88<br />
4.4 Absorption Double Stage . . . . . . . . . . . . . . . . . . . . . . 89<br />
4.5 Absorption Double Stage, Dual Heat . . . . . . . . . . . . . . . 92<br />
4.6 Cooling Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94<br />
4.6.1 Wet Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . 95<br />
4.6.2 Dry Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . 95<br />
4.6.3 Hot Water . . . . . . . . . . . . . . . . . . . . . . . . . . . 95<br />
4.7 System calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 97<br />
4.7.1 Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . 97<br />
4.8 Verification <strong>of</strong> Model . . . . . . . . . . . . . . . . . . . . . . . . . 100<br />
4.8.1 Energy balance . . . . . . . . . . . . . . . . . . . . . . . . 100<br />
4.8.2 Check <strong>of</strong> heat exchangers . . . . . . . . . . . . . . . . . 100<br />
4.9 Validation <strong>of</strong> Model . . . . . . . . . . . . . . . . . . . . . . . . . 101<br />
4.9.1 SOFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101<br />
4.9.2 Absorption cycle . . . . . . . . . . . . . . . . . . . . . . . 102<br />
5 Simulation <strong>and</strong> Results 105<br />
5.1 Basic absorption cooling . . . . . . . . . . . . . . . . . . . . . . 105<br />
5.1.1 Changing the desorber temperature . . . . . . . . . . . 106<br />
5.1.2 Changing condenser temperature . . . . . . . . . . . . 109<br />
5.1.3 Changing evaporator temperature . . . . . . . . . . . . 111<br />
5.1.4 Changing absorber temperature . . . . . . . . . . . . . 112<br />
5.1.5 Summing up the general behavior <strong>of</strong> the absorption<br />
cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113<br />
5.2 System configurations . . . . . . . . . . . . . . . . . . . . . . . . 114<br />
5.2.1 Single, Double, Dual Heat (+/- Air Preheat) . . . . . . 115<br />
5.2.2 Wet vs Dry cooling <strong>and</strong> ambient temperature . . . . . 117<br />
5.2.3 ∆T min,Tower . . . . . . . . . . . . . . . . . . . . . . . . . . 119<br />
5.3 Partial optimization <strong>of</strong> st<strong>and</strong>ard parameters . . . . . . . . . . 120<br />
5.3.1 Outer conditions . . . . . . . . . . . . . . . . . . . . . . . 120<br />
5.3.2 Desorber temperatures . . . . . . . . . . . . . . . . . . . 123<br />
5.3.3 SOFC subsystem . . . . . . . . . . . . . . . . . . . . . . . 125<br />
5.3.4 Closest Approach Temperature Differences (∆T min ) . 135<br />
5.3.5 ∆T for external circuits . . . . . . . . . . . . . . . . . . . 140<br />
5.3.6 Hot Water . . . . . . . . . . . . . . . . . . . . . . . . . . . 140<br />
5.4 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 142<br />
xiv
Contents<br />
5.4.1 Closest Approach Temperature Difference . . . . . . . 142<br />
5.4.2 Pressure Losses . . . . . . . . . . . . . . . . . . . . . . . . 143<br />
5.4.3 Heat Losses . . . . . . . . . . . . . . . . . . . . . . . . . . 145<br />
5.4.4 (Other) Key Parameters . . . . . . . . . . . . . . . . . . 146<br />
5.5 Total optimization <strong>of</strong> system . . . . . . . . . . . . . . . . . . . . 149<br />
5.5.1 Absorption subsystem . . . . . . . . . . . . . . . . . . . 149<br />
5.5.2 Current density . . . . . . . . . . . . . . . . . . . . . . . 152<br />
5.5.3 Future: ∆T SOFC = 120 ◦ C . . . . . . . . . . . . . . . . . . 153<br />
6 Cases <strong>and</strong> Economics 155<br />
6.1 Air conditioning <strong>of</strong> hotels . . . . . . . . . . . . . . . . . . . . . . 155<br />
6.2 High humidity climate . . . . . . . . . . . . . . . . . . . . . . . 156<br />
6.2.1 Seychelles . . . . . . . . . . . . . . . . . . . . . . . . . . . 156<br />
6.2.2 Bangkok . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157<br />
6.3 Low humidity climate . . . . . . . . . . . . . . . . . . . . . . . . 160<br />
6.3.1 Las Vegas . . . . . . . . . . . . . . . . . . . . . . . . . . . 160<br />
6.3.2 Water consumption . . . . . . . . . . . . . . . . . . . . . 161<br />
6.4 Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163<br />
7 Discussion 165<br />
7.1 The thermodynamical model . . . . . . . . . . . . . . . . . . . 165<br />
7.1.1 Accuracy <strong>and</strong> sensitivity . . . . . . . . . . . . . . . . . . 167<br />
7.2 Economical considerations . . . . . . . . . . . . . . . . . . . . . 168<br />
7.2.1 Auxillary Power Unit (APU) . . . . . . . . . . . . . . . 168<br />
7.2.2 Micro Combined Heat <strong>and</strong> Power (µCHP) . . . . . . . 169<br />
7.2.3 Distributed Generation (DG) . . . . . . . . . . . . . . . 171<br />
7.3 Other considerations . . . . . . . . . . . . . . . . . . . . . . . . . 176<br />
8 Conclusion 177<br />
9 Further work 181<br />
Bibliography 183<br />
Appendices 187<br />
A Market investigation 189<br />
A.1 Market Investigation Appendix - Introduction . . . . . . . . . 190<br />
A.2 APU appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191<br />
A.2.1 Ship APU appendix . . . . . . . . . . . . . . . . . . . . . 191<br />
A.3 CHP appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196<br />
A.3.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 196<br />
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CONTENTS<br />
A.4 DG appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202<br />
A.5 Absorption cooling unit prices . . . . . . . . . . . . . . . . . . . 219<br />
A.6 Gas <strong>and</strong> electricity prices . . . . . . . . . . . . . . . . . . . . . . 224<br />
B Diagrams <strong>and</strong> plots 227<br />
B.1 GAX diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228<br />
B.2 Double stage diagram . . . . . . . . . . . . . . . . . . . . . . . . 229<br />
B.3 Closed adsorption cycle . . . . . . . . . . . . . . . . . . . . . . . 230<br />
B.4 Property plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231<br />
B.4.1 Phase diagram <strong>of</strong> water-LiBr-solution . . . . . . . . . 231<br />
B.4.2 p-T diagram <strong>of</strong> water-LiBr-solution . . . . . . . . . . . 232<br />
C EES 233<br />
C.1 Parameter configuration . . . . . . . . . . . . . . . . . . . . . . 233<br />
C.2 Results - St<strong>and</strong>ard parameter configuration . . . . . . . . . . 242<br />
C.3 Results - Optimized parameter configuration . . . . . . . . . 250<br />
C.4 Results - Uncertainty propagation (STD) . . . . . . . . . . . . 258<br />
C.4.1 ∆T min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258<br />
C.4.2 Miscellaneous parameters . . . . . . . . . . . . . . . . . 261<br />
C.4.3 ∆p for SOFC subsystem . . . . . . . . . . . . . . . . . . 263<br />
C.4.4 ∆p for absorption subsystem . . . . . . . . . . . . . . . 266<br />
C.4.5 ˙Q loss for absorption subsystem . . . . . . . . . . . . . . 268<br />
C.5 Guide to EES files . . . . . . . . . . . . . . . . . . . . . . . . . . . 269<br />
D Other 271<br />
D.1 Explanation <strong>of</strong> chosen Parameters . . . . . . . . . . . . . . . . 271<br />
D.2 Spider diagram parameter interval choice . . . . . . . . . . . 272<br />
D.3 Water consumption . . . . . . . . . . . . . . . . . . . . . . . . . . 273<br />
E Optimization graphs 275<br />
E.1 Simulations <strong>and</strong> Results . . . . . . . . . . . . . . . . . . . . . . . 276<br />
E.1.1 All 12 Configurations . . . . . . . . . . . . . . . . . . . . 276<br />
E.1.2 ∆T for external circuits . . . . . . . . . . . . . . . . . . . 277<br />
E.1.3 Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280<br />
E.2 Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283<br />
E.2.1 Extreme low relative humidity . . . . . . . . . . . . . . 283<br />
F Literature 285<br />
F.1 Sc<strong>and</strong>inavian Energy Group Aps. . . . . . . . . . . . . . . . . . 285<br />
G System diagram 293<br />
xvi
LIST OF FIGURES<br />
1.1 Individual air conditioning . . . . . . . . . . . . . . . . . . . . . . . 5<br />
1.2 Diagram <strong>of</strong> single stage absorption cycle . . . . . . . . . . . . . . 10<br />
1.3 Diagram <strong>of</strong> Platen Munters cycle . . . . . . . . . . . . . . . . . . . 14<br />
2.1 Ship: Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . 23<br />
2.2 Ship: Pay Back Time . . . . . . . . . . . . . . . . . . . . . . . . . . . 24<br />
2.3 Refrigerator: Pay Back Time . . . . . . . . . . . . . . . . . . . . . . 27<br />
2.4 Refrigerator: Sensitivity analysis . . . . . . . . . . . . . . . . . . . 28<br />
2.5 Hotel: Pay Back Time AC . . . . . . . . . . . . . . . . . . . . . . . . 34<br />
2.6 Hotel: Pay Back Time BC . . . . . . . . . . . . . . . . . . . . . . . . 35<br />
2.7 Hotel: Annuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36<br />
2.8 Hotel: Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . 37<br />
3.1 Absorber component . . . . . . . . . . . . . . . . . . . . . . . . . . . 45<br />
3.2 QT-diagram for absorber . . . . . . . . . . . . . . . . . . . . . . . . 46<br />
3.3 Blower component . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48<br />
3.4 Burner component . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49<br />
3.5 Condenser component . . . . . . . . . . . . . . . . . . . . . . . . . . 50<br />
3.6 QT-diagram for Condenser . . . . . . . . . . . . . . . . . . . . . . . 51<br />
3.7 Desorber component . . . . . . . . . . . . . . . . . . . . . . . . . . . 53<br />
3.8 QT-diagram for Desorber . . . . . . . . . . . . . . . . . . . . . . . . 54<br />
3.9 Evaporator component . . . . . . . . . . . . . . . . . . . . . . . . . 55<br />
3.10 QT-diagram for evaporator . . . . . . . . . . . . . . . . . . . . . . . 55<br />
3.11 HEX component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57<br />
3.12 QT-diagram for HEXes . . . . . . . . . . . . . . . . . . . . . . . . . 57<br />
3.13 Pre Reformer component . . . . . . . . . . . . . . . . . . . . . . . . 61<br />
3.14 Solution pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63<br />
3.15 SOFC component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64<br />
3.16 Cooling Tower component . . . . . . . . . . . . . . . . . . . . . . . 71<br />
3.17 QT-diagram for TOWERd . . . . . . . . . . . . . . . . . . . . . . . . 72<br />
3.18 Ix-diagram for TOWERw . . . . . . . . . . . . . . . . . . . . . . . . 74<br />
3.19 Expansion valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76<br />
4.1 System diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80<br />
4.2 Diagram <strong>of</strong> SOFC subsystem . . . . . . . . . . . . . . . . . . . . . . 81<br />
xvii
LIST OF FIGURES<br />
4.3 Diagram <strong>of</strong> single stage absorption subsystem . . . . . . . . . . . 86<br />
4.4 Diagram <strong>of</strong> double stage absorption subsystem . . . . . . . . . . 89<br />
4.5 Diagram <strong>of</strong> double stage, dual heat absorption subsystem . . . 92<br />
4.6 Diagram <strong>of</strong> cooling system <strong>and</strong> hot water production . . . . . . 94<br />
5.1 Diagram <strong>of</strong> single stage absorption cycle . . . . . . . . . . . . . . 105<br />
5.2 ∆T DES vs COP ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107<br />
5.3 ∆T DES vs COP ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108<br />
5.4 ∆T COND vs COP ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110<br />
5.5 ∆T EV AP vs COP ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111<br />
5.6 ∆T ABSO vs COP ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112<br />
5.7 Comparison <strong>of</strong> system configurations . . . . . . . . . . . . . . . . 116<br />
5.8 T amb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118<br />
5.9 T EV AP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120<br />
5.10 φ air at T DES2 = 150 ◦ C . . . . . . . . . . . . . . . . . . . . . . . . . . . 121<br />
5.11 φ air at T DES2 = 160 ◦ C . . . . . . . . . . . . . . . . . . . . . . . . . . . 122<br />
5.12 T DES2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124<br />
5.13 T DES1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125<br />
5.14 ∆T SOFC 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126<br />
5.15 ∆T SOFC 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127<br />
5.16 T SOFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128<br />
5.17 α 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129<br />
5.18 i d without bypass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131<br />
5.19 U f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132<br />
5.20 i d when bypassing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133<br />
5.21 ∆T minW W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136<br />
5.22 ∆T minCOND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137<br />
5.23 ∆T minW G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138<br />
5.24 ∆T minGG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139<br />
5.25 ∆T minW G Hot water . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140<br />
5.26 Spider diagram ∆T min . . . . . . . . . . . . . . . . . . . . . . . . . . 143<br />
5.27 Spider diagram pressures . . . . . . . . . . . . . . . . . . . . . . . . 144<br />
5.28 Spider diagram ˙Q loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 146<br />
5.29 Spider diagram other parameters . . . . . . . . . . . . . . . . . . . 147<br />
5.30 NTU vs ɛ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150<br />
5.31 Optimized parameters, i d . . . . . . . . . . . . . . . . . . . . . . . . 151<br />
5.32 Bar diagram Optimized parameters . . . . . . . . . . . . . . . . . 153<br />
6.1 Weather data for Port Victoria, Seychelles . . . . . . . . . . . . . . 156<br />
6.2 Hotel in high humidity climate (φ = 0,8). . . . . . . . . . . . . . . 157<br />
6.3 Weather data for Bangkok, Thail<strong>and</strong> . . . . . . . . . . . . . . . . . 158<br />
xviii
List <strong>of</strong> Figures<br />
6.4 Hotel in high humidity climate (φ = 0,9). . . . . . . . . . . . . . . 159<br />
6.5 Weather data for Las Vegas, USA . . . . . . . . . . . . . . . . . . . 160<br />
6.6 Hotel in low humidity climate (φ = 0,4). . . . . . . . . . . . . . . . 161<br />
6.7 Hotel vs OPTI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163<br />
B.1 Diagram <strong>of</strong> GAX cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 228<br />
B.2 Diagram <strong>of</strong> double stage absorption cycle . . . . . . . . . . . . . . 229<br />
B.3 Diagram <strong>of</strong> closed adsorption cycle . . . . . . . . . . . . . . . . . . 230<br />
B.4 Phase diagram <strong>of</strong> water-LiBr . . . . . . . . . . . . . . . . . . . . . . 231<br />
B.5 p-T diagram <strong>of</strong> water-LiBr . . . . . . . . . . . . . . . . . . . . . . . 232<br />
E.1 Comparison <strong>of</strong> system configurations . . . . . . . . . . . . . . . . 276<br />
E.2 T EV AP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277<br />
E.3 T DES1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278<br />
E.4 T DES2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279<br />
E.5 T TOW ERd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280<br />
E.6 T TOW ERw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281<br />
E.7 T TOW ERw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282<br />
E.8 Hotel in extreme low humidity climate. . . . . . . . . . . . . . . . 283<br />
xix
NOMENCLATURE<br />
Acronyms<br />
Acronym<br />
ABS<br />
AC<br />
APU<br />
CATD<br />
CCHP<br />
CHP<br />
DG<br />
ECH<br />
EES<br />
HEX<br />
LiBr<br />
LPG<br />
NP<br />
NPV<br />
NTU<br />
OPTI<br />
STD<br />
VAT<br />
WGS<br />
Description<br />
Absorption chiller<br />
Air Conditioning<br />
Auxiliary Power Unit<br />
Closest Approach Temperature Difference<br />
Combined Cooling, Heating, <strong>and</strong> Power<br />
Combined Heating <strong>and</strong> Power<br />
Distributed Generation<br />
Electrical driven Chiller<br />
Engineering Equation Solver<br />
Heat EXchanger<br />
Lithium Bromide<br />
Liquified Petroleum Gas<br />
Net Payment<br />
Net Present Value<br />
Number <strong>of</strong> Transfer Units<br />
Optimized<br />
St<strong>and</strong>ard<br />
Value Added Tax<br />
Water Gas Shift reaction
NOMENCLATURE<br />
Components<br />
Component<br />
ABSO<br />
BLOW<br />
BURN<br />
COND<br />
DES<br />
EVAP<br />
FAN<br />
GGHEX<br />
MIXL<br />
MIXG<br />
MIXR<br />
PR<br />
PUMP<br />
SOFC<br />
SPL<br />
SPG<br />
SPR<br />
TOFC<br />
TOWER<br />
VA<br />
VB<br />
WGHEX<br />
Description<br />
Absorber<br />
Blower, air<br />
Burner<br />
Condenser<br />
Desorber<br />
Evaporator<br />
Fan, air<br />
Gas-Gas Heat Exchanger<br />
Mixer, LiBr solution<br />
Mixer, gas<br />
Mixer, refrigerant<br />
Pre Reformer<br />
Pump, water<br />
Solid Oxide Fuel Cell<br />
Splitter, LiBr solution<br />
Splitter, gas<br />
Splitter, refrigerant<br />
Topsoe Fuel Cell<br />
Cooling tower<br />
Expansion valve for refrigerant<br />
Expansion valve LiBr solution<br />
Water-gas heat exchanger<br />
xxii
Greek (<strong>and</strong> other) Symbols<br />
Greek (<strong>and</strong> other) Symbols<br />
Symbol Unit Description<br />
α [−] mass fraction in splitters<br />
∆ [−] change (increase)<br />
∆ T,min [K] minimum temp. difference between streams in HEX<br />
ɛ [−] effectiveness <strong>of</strong> HEX<br />
η [−] efficiency<br />
λ [−] air excess number<br />
ρ<br />
o<br />
[ ] kg<br />
m 3<br />
[−]<br />
density<br />
st<strong>and</strong>ard pressure (100 kPa)<br />
xxiii
NOMENCLATURE<br />
Latin Symbols<br />
Symbol Unit Description<br />
A<br />
[<br />
m<br />
2 ] Area<br />
ASR [Ωm] Area Specific Resistance<br />
[<br />
Ċ<br />
kW<br />
]<br />
Heat capacity flow rate<br />
K<br />
COP<br />
[<br />
[−]<br />
] Coefficient Of Performance<br />
C kJ<br />
p<br />
heat Capacity, constant pressure<br />
kgK<br />
F R [−] Fraction <strong>of</strong> gas Reformed in prereformer<br />
FW [−] Fraction <strong>of</strong> gas in Water gas shift reaction<br />
PF [−] Mass flow ratio <strong>of</strong> the weak solution <strong>and</strong> the refrigerant<br />
h<br />
[<br />
kJ<br />
kg<br />
]<br />
mass specific enthalpy<br />
Ḣ [kW] enthalpy flow rate<br />
I [A] current<br />
i d<br />
[<br />
A<br />
m 2 ]<br />
current density<br />
K W GS [−] reaction constant for Water Gas Shift<br />
LG r atio [<br />
[−]<br />
] Liquid-Gas ratio<br />
kg<br />
ṁ<br />
s<br />
mass flow rate<br />
n [−] number<br />
[<br />
ṅ<br />
kmol<br />
]<br />
mole flow rate<br />
s<br />
OC r atio [−] Oxygen-Carbon ratio<br />
p [kPa] pressure<br />
˙Q [kW] heat flow rate<br />
qu<br />
[<br />
[−]<br />
] quality <strong>of</strong> steam in the two phase region<br />
s<br />
kJ<br />
kgK<br />
mass specific entropy<br />
T [ ◦ C] Temperature<br />
U f [<br />
[−]<br />
] <strong>fuel</strong> Utilization factor<br />
v<br />
m 3<br />
mass specific volume<br />
kg<br />
V<br />
[<br />
[V]<br />
] electric potential (voltage)<br />
˙V<br />
m 3<br />
s<br />
volume flow rate<br />
w [−] concentration <strong>of</strong> LiBr in water solution<br />
Ẇ [kW] power<br />
W Q r atio [−] power-heat flow rate ratio<br />
x [−] mass fraction<br />
y [−] mole fraction<br />
xxiv
Subscripts<br />
Subscripts<br />
Subscript<br />
2P<br />
air<br />
ABS<br />
amb<br />
ano<br />
av<br />
c<br />
cat<br />
cell<br />
chill<br />
chk<br />
el<br />
g<br />
h<br />
HW<br />
i<br />
inver t<br />
i s<br />
mp<br />
o<br />
over all<br />
r<br />
re f<br />
s<br />
sat<br />
SC<br />
SH<br />
ss<br />
st ack<br />
tr ans<br />
w<br />
ws<br />
Description<br />
two Phase<br />
atmospheric air<br />
Absorption cycle<br />
ambient<br />
anode<br />
average<br />
cold side <strong>of</strong> heat exchanger<br />
cathode<br />
cell, SOFC<br />
chilling fluid<br />
checking state: sub cooled OR two phase<br />
electric<br />
gas<br />
hot side <strong>of</strong> heat exchanger<br />
Hot Water<br />
in<br />
inverter (DC to AC)<br />
isentropic process<br />
mid point (in heat exchangers)<br />
out<br />
the entire system<br />
refrigerant<br />
reference<br />
solution <strong>of</strong> LiBr<br />
saturated<br />
Sub Cooled<br />
Super Heated<br />
strong solution <strong>of</strong> LiBr<br />
SOFC stack <strong>of</strong> n <strong>cells</strong><br />
transfer<br />
water<br />
weak solution <strong>of</strong> LiBr<br />
xxv
C H A P T E R<br />
1<br />
INTRODUCTION<br />
1.1 Project outline<br />
In this report the <strong>integration</strong> <strong>of</strong> a Solid Oxide Fuel Cell (SOFC) <strong>and</strong> a heat<br />
driven chiller will be investigated.<br />
Chapter 1, Introduction<br />
The SOFC technology <strong>and</strong> some <strong>of</strong> its applications are briefly described<br />
<strong>and</strong> the principles <strong>of</strong> heat driven chilling <strong>and</strong> different technologies are<br />
introduced. In the end <strong>of</strong> the chapter the problem statement <strong>of</strong> this<br />
project will be shown.<br />
Chapter 2, Market investigation<br />
In order to see if there is any potential in combining a SOFC with a heat<br />
driven chiller a short market investigation is carried out. Economical<br />
calculations are made to check if the SOFC-absorption system (SOFC-<br />
ABS) can provide an economical advantage over the more traditional<br />
cooling technologies. At this point no thermodynamical model has been<br />
made yet, so the efficiencies will merely be estimated.<br />
Chapter 3, Component description<br />
The individual components <strong>of</strong> the thermodynamical model <strong>of</strong> the SOFC-<br />
ABS system are described in details.<br />
1
1. INTRODUCTION<br />
Chapter 4, System description<br />
This chapter is divided into two parts:<br />
a. The system configuration is described i.e. the way in which the<br />
components are arranged relative to each other.<br />
b. The chosen values <strong>of</strong> the parameters for the components are described.<br />
Chapter 5, Simulation <strong>and</strong> Results<br />
The model is used to simulate the general behavior <strong>of</strong> an absorption<br />
chiller <strong>and</strong> the behavior <strong>of</strong> the system as a whole under different<br />
conditions. The most important parameters are examined <strong>and</strong> their<br />
impact on the system performance is illustrated.<br />
Chapter 6, Cases <strong>and</strong> Economics<br />
Three different case studies <strong>of</strong> hotels in different climates are described.<br />
Economics <strong>and</strong> other issues are considered.<br />
Chapter 7, Discussion<br />
The results are discussed <strong>and</strong> evaluated. The model is compared to<br />
commercial products, <strong>and</strong> the uncertainty <strong>and</strong> assumptions <strong>of</strong> the model<br />
are assessed.<br />
Chapter 8, Conclusion<br />
The results <strong>of</strong> the entire project <strong>and</strong> the discussion is summed up, <strong>and</strong><br />
the questions <strong>of</strong> the problem statement are answered.<br />
Chapter 9, Further work<br />
Ideas for further work include new areas which could be investigated<br />
<strong>and</strong> things that could be done to improve the accuracy <strong>of</strong> the model <strong>and</strong><br />
calculations.<br />
2
1.2. General formalities<br />
1.2 General formalities<br />
Decimal separator<br />
The European decimal separator, decimal comma, is used throughout the<br />
report. Dot is used as thous<strong>and</strong> separator.<br />
Dot notation<br />
In this report the dot notation is applied, i.e. ẋ is the time derivative <strong>of</strong><br />
the variable x.<br />
1.3 General introduction<br />
Climate changes, security <strong>of</strong> energy supply, <strong>and</strong> high oil prices are all<br />
arguments for finding alternatives to the worlds energy sources which<br />
today primarily are based on fossil <strong>fuel</strong>s like oil, coal <strong>and</strong> natural gas. The<br />
increasing dem<strong>and</strong> for energy has a major impact on the environment<br />
especially due to emission <strong>of</strong> CO 2 which contributes to the green house<br />
effect <strong>and</strong> thereby increases the average temperature <strong>of</strong> the <strong>Ea</strong>rth 1 . This<br />
is one <strong>of</strong> the most extensive challenges for mankind in our time <strong>and</strong><br />
probably in the future as well. Energy efficiency also play an important<br />
role in reducing the primary energy consumption - in all parts <strong>of</strong> the<br />
supply chain starting from primary energy to end-use services.<br />
The consumption <strong>of</strong> primary energy can be split up in sectors<br />
like ”electricity <strong>and</strong> heat production” (energy conversion), ”industry”,<br />
”business <strong>and</strong> service”, ”residential” <strong>and</strong> ”transport”. Some examples <strong>of</strong><br />
how energy could be saved within these sectors are briefly described in<br />
the following sections.<br />
1.3.1 Distributed generation<br />
Distributed generation (DG) <strong>of</strong> electricity <strong>and</strong> heat is an opportunity<br />
for reducing the energy losses in the ”electricity <strong>and</strong> heat” sector.<br />
Traditionally most power is produced by large scale power stations <strong>and</strong><br />
1 According to IPCC - Intergovernmental Panel on Climate Change<br />
3
1. INTRODUCTION<br />
the electricity <strong>and</strong> heat 2 is distributed via grids to the end-user which<br />
introduces transmission <strong>and</strong> distribution losses. These can to some<br />
extend be eliminate by moving the generation <strong>of</strong> electricity close to the<br />
end-user (covers three <strong>of</strong> the sectors mentioned above).<br />
Combined Heat <strong>and</strong> Power (CHP) generation is advantageous, since<br />
the waste heat can be utilized locally for process heating (industrial<br />
sector), space heating, <strong>and</strong> hot water. This means that the losses are<br />
reduced significantly.<br />
Distributed generation could be applied in several places e.g. in the<br />
manufacturing industry (large scale), hospitals <strong>and</strong> malls, but also for<br />
private homes (very small scale).<br />
1.3.2 Fuel <strong>cells</strong><br />
Fuel <strong>cells</strong> are one <strong>of</strong> several DG technologies. One <strong>of</strong> the strengths <strong>of</strong> <strong>fuel</strong><br />
cell systems is that the efficiency is relatively high <strong>and</strong> depends very little<br />
on system size which is an important property for this purpose.<br />
The <strong>fuel</strong> <strong>cells</strong> are still in the developing phase <strong>and</strong> only market niches<br />
exist. It is though expected that the market share will grow in the future<br />
as the price <strong>of</strong> <strong>fuel</strong> <strong>cells</strong> decrease (the current price <strong>of</strong> <strong>fuel</strong> <strong>cells</strong> is still far<br />
to high to compete with other technologies on the market).<br />
1.3.3 Transport<br />
The transports sector today is very dependent on fossil <strong>fuel</strong> especially oil.<br />
The primary energy consumption within this sector is enormous due to<br />
high dem<strong>and</strong> <strong>and</strong> due to relatively poor energy efficiency <strong>of</strong> combustion<br />
engines (especially during part load) 3 . In addition the growth rate <strong>of</strong><br />
transport dem<strong>and</strong> is large.<br />
The <strong>fuel</strong> <strong>cells</strong> can be used to generate electricity for propulsion, but<br />
another option is to use it as an auxiliary power unit (APU) which<br />
supplies electricity when the grid is not accessible or e.g. the main engine<br />
<strong>of</strong> a truck is turned <strong>of</strong>f.<br />
2 Some countries utilize the waste heat from the electricity generation via district<br />
heating networks, but it is most common to reject the heat to the surroundings.<br />
3 Large engines e.g. in ships have a much better efficiency than combustion engines<br />
in general though - up to more than 50% [2]<br />
4
1.3. General introduction<br />
1.3.4 Dem<strong>and</strong> for cooling<br />
The dem<strong>and</strong> for cooling (air conditioning) is one <strong>of</strong> the large end-use<br />
energy services. The growing wealth in the world leads to an increased<br />
dem<strong>and</strong> for this service in many countries (especially those with a hot<br />
climate). The most common way to meet this dem<strong>and</strong> is by means<br />
<strong>of</strong> individual electrically driven air conditioning units (see figure 1.1),<br />
which in many cases is not the most energy efficient way to deliver this<br />
service.<br />
Figure 1.1: Individual air conditioning units on facade. Edited picture taken from [15].<br />
5
1. INTRODUCTION<br />
1.4 SOFC<br />
The <strong>fuel</strong> cell technology is a c<strong>and</strong>idate for the future energy system.<br />
Basically it is a converter <strong>of</strong> chemical to electrical energy <strong>and</strong> it has an<br />
efficiency which is higher than the most <strong>of</strong> competing technologies <strong>of</strong><br />
today 4 . Additionally the efficiency is almost not affected by the size<br />
<strong>of</strong> the system. Solid Oxide Fuel Cells (SOFC) are operated at high<br />
temperature (700-800 ◦ C) which enable them to accept a lot <strong>of</strong> different<br />
<strong>fuel</strong>s e.g. diesel, natural gas or biogas. This is an advantage because it<br />
makes the technology more flexible.<br />
1.4.1 SOFC Waste heat<br />
The high temperature at which the Solid Oxide Fuel Cells (SOFCs) are<br />
operated gives them an important advantage compared to other (low<br />
temperature) <strong>fuel</strong> <strong>cells</strong>: The waste heat is rejected at a much higher<br />
temperature <strong>and</strong> that is an advantage if the waste heat is to be utilized<br />
for certain purposes.<br />
The waste heat can be turned into useful energy when it is used for<br />
e.g. space heating or water heating. These are normally low temperature<br />
applications. But in some cases this heating service is not needed.<br />
So another options is to utilize the waste heat in a heat driven heat<br />
pump/chiller which will reduce the consumption <strong>of</strong> primary energy 5 .<br />
Especially heat driven chilling is interesting since the dem<strong>and</strong> for<br />
cooling (air conditioning) <strong>of</strong>ten increases when the outside temperature<br />
is high while the dem<strong>and</strong> for (space) heating decreases. It is also possible<br />
to produce both cooling <strong>and</strong> heating simultaneously in a Combined<br />
Cooling, Heating <strong>and</strong> Power (CCHP) unit.<br />
Thus it would be interesting to investigate how a <strong>fuel</strong> cell could be<br />
integrated with a heat driven chiller.<br />
4 The electrical efficiency <strong>of</strong> a <strong>fuel</strong> cell system <strong>fuel</strong>ed with methane is about 55%<br />
today [31].<br />
5 Assuming that the produced heating/cooling replaces an energy services which<br />
require primary energy.<br />
6
1.4. SOFC<br />
1.4.2 Topsoe Fuel Cell<br />
Topsoe Fuel Cell (TOFC) (subsidiary company <strong>of</strong> Haldor Topsøe A/S)<br />
has developed SOFC <strong>cells</strong> <strong>and</strong> stacks in corporation with Risø DTU since<br />
1989. TOFC has a small scale production facility <strong>of</strong> SOFC <strong>cells</strong> <strong>and</strong> stacks<br />
which are primarily use for development <strong>and</strong> demonstration purposes.<br />
The business plan <strong>of</strong> TOFC is to be a subcontractor to <strong>fuel</strong> cell system<br />
manufacturers (e.g. Wärtsilä in Finl<strong>and</strong> <strong>and</strong> Dantherm in Denmark). The<br />
product is a Topsoe PowerCore TM consisting <strong>of</strong> the <strong>fuel</strong> cell stack <strong>and</strong><br />
other high temperature components in a integrated unit. The focus will<br />
be on three markets which are described in the following.<br />
1.4.3 APU<br />
The Auxiliary Power Unit (APU) is an alternative to small diesel<br />
generators which supply electricity when the electricity grid is not<br />
accessible. The present APU delivers 2,3kW e (electricity) with an<br />
efficiency <strong>of</strong> 40%. Applications for APU’s include heavy duty trucks,<br />
recreational vehicles <strong>and</strong> yachts. The most important advantages <strong>of</strong> a<br />
<strong>fuel</strong> cell for this purpose are silent operation <strong>and</strong> high efficiency 6 [30].<br />
1.4.4 Micro CHP<br />
The micro Combined Heat <strong>and</strong> Power (µCHP) unit is an alternative to<br />
traditional oil <strong>and</strong> gas burners for residential use. It presently has a<br />
power output <strong>of</strong> 1kW e <strong>and</strong> an electrical efficiency <strong>of</strong> 45%. The overall<br />
efficiency (electricity <strong>and</strong> heat) is 85%. Acceptable <strong>fuel</strong>s are natural gas,<br />
diesel, biogas, bio diesel <strong>and</strong> synthetic <strong>fuel</strong> [32].<br />
1.4.5 DG<br />
Distributed Generation (DG) means that power <strong>and</strong> heat is produced<br />
close to the consumer. TOFC plans to <strong>of</strong>fer a product in the range <strong>of</strong> 10-<br />
250kW e (<strong>and</strong> higher) with an efficiency <strong>of</strong> 55%. The <strong>fuel</strong> can be natural<br />
gas, bio gas <strong>and</strong> in the future bio <strong>fuel</strong>s. Another benefit is the elimination<br />
<strong>of</strong> NO x <strong>and</strong> SO x [31].<br />
6 Compared to a large idling truck diesel engine.<br />
7
1. INTRODUCTION<br />
1.5 Heat driven cooling<br />
The most common principle <strong>of</strong> producing cooling is the vapor compression<br />
cycle (reverse Rankine cycle) which is driven by mechanical work<br />
(normally an electric motor).<br />
An alternative is to produce the cooling by a sorption cycle. ”Sorption”<br />
covers absorption <strong>and</strong> adsorption cycles which are mainly operated by heat<br />
as energy source [18].<br />
The sorption cycle is in principle like the vapor compression cycle<br />
with a condenser, an expansion valve <strong>and</strong> an evaporator. The main<br />
difference is how the refrigerant is pressurized after the evaporator:<br />
for the vapor compression cycle it is a mechanical compression, e.g.<br />
a reciprocation or a screw compressor, which compresses evaporated<br />
refrigerant. In the sorption cycle it is a ”heat driven compressor” 7 . How<br />
this work will be explained in the next section.<br />
The heat ratio, COP ABS , <strong>of</strong> a sorption cycle is the ratio between cooling<br />
load <strong>and</strong> driving heat 8 .<br />
COP ABS =<br />
˙Q cooling load<br />
˙Q dr i ving heat<br />
(1.1)<br />
This COP is not comparable to the COP <strong>of</strong> the vapor compression<br />
cycle because the inputs have different value (heat at the relatively low<br />
temperature has a lower exergy than mechanical or electric work) [18].<br />
The medium in sorption cycles is a pair consisting <strong>of</strong> a refrigerant <strong>and</strong><br />
a ”sorbent”. For the absorption cycle the refrigerant is absorbed by the<br />
absorbent (which is either a liquid or a dissolved salt), i.e. a solution,<br />
whereas for the adsorption cycle the refrigerant is adsorbed on the surface<br />
<strong>of</strong> the adsorbent. The two cycles can be divided into subcategories which<br />
are described in following sections.<br />
7 Actually the physical pressurization is done by a mechanical pump.<br />
8 The small amount <strong>of</strong> electric or mechanical energy used for driving pumps in some<br />
variants is not included. For systems larger than 1 MW <strong>of</strong> cooling the consumption <strong>of</strong><br />
electrical energy <strong>of</strong> the pump is about one per thous<strong>and</strong> <strong>of</strong> cooling power<br />
8
1.5. Heat driven cooling<br />
1.5.1 Absorption<br />
There are two major types <strong>of</strong> absorption cycles:<br />
• Carré cycle which is used for cooling <strong>and</strong> air conditioning (as well<br />
as heat pumps) in the range <strong>of</strong> 15 kw to megawatts.<br />
• Platen Munters cycle which is used for small (household size)<br />
refrigerators/freezers.<br />
The two cycles are in principle almost identical, but in practice they<br />
differ a lot - hence the very different applications. In the following<br />
sections, the two types will be described.<br />
1.5.2 Carré cycle<br />
The basic principle <strong>of</strong> the absorption cycle is developed by the French<br />
scientist Ferdin<strong>and</strong> Carré about 1860.<br />
Working media.<br />
The fluid in the absorption cycle consists <strong>of</strong> a pair <strong>of</strong> a refrigerant <strong>and</strong><br />
an absorption medium which is capable to absorb the refrigerant. More<br />
than 40 refrigerants <strong>and</strong> 200 absorption media exist [35].<br />
The most common pairs are ammonia-water (N H 3 − H 2 O) <strong>and</strong> waterlithium<br />
bromide (H 2 O − LiBr ). Ammonia is the refrigerant in the N H 3 −<br />
H 2 O solution (ammonia has a lower boiling point than water), whereas<br />
water is the refrigerant in the H 2 O − LiBr solution.<br />
Ammonia-water is usable for small as well as large scale units<br />
working at various temperatures, e.g. air conditioning or industrial<br />
cooling/freezing (evaporator temperatures down to -60 ◦ C).<br />
Water-lithium bromide has a limited temperature range due to the<br />
freezing point <strong>of</strong> water, <strong>and</strong> in practical applications the chilled water<br />
should never be lower than 6 ◦ C [27]. Thus this pair is feasible for<br />
applications such as production <strong>of</strong> chilled water or air conditioning.<br />
9
1. INTRODUCTION<br />
Cycle description.<br />
As mentioned, the absorption cycle is very similar to the vapor<br />
compression cycle - the mechanical compressor is just replaced by a<br />
”thermal compressor”. This consists <strong>of</strong> a desorber 9 (DES), an absorber<br />
(ABSO), a solution heat exchanger (SHEX), an expansion valve (VB), <strong>and</strong><br />
a pump as seen in figure 1.2.<br />
COND<br />
1<br />
HEAT<br />
DES<br />
COOLING<br />
9<br />
7<br />
2<br />
SHEX<br />
3<br />
VA<br />
EVAP<br />
4<br />
11<br />
12<br />
VB<br />
ABSO<br />
PUMP<br />
6<br />
5<br />
CHILLED WATER<br />
COOLING<br />
Figure 1.2: Diagram <strong>of</strong> single stage absorption cycle<br />
The principle <strong>of</strong> the absorption cycle will now be described.<br />
numbering refers to the state points appearing in figure 1.2.<br />
The<br />
1 → 2: Superheated refrigerant at high pressure is condensed to<br />
saturated liquid in the condenser (COND). The heat is removed by<br />
an external cooling circuit.<br />
2 → 3: The pressure <strong>of</strong> the liquid refrigerant is reduced from the<br />
high to the low working pressure by the expansion valve (VA).<br />
9 This is some time called a generator, but the phrase desorber will be used throughout<br />
this report.<br />
10
1.5. Heat driven cooling<br />
3 → 4: The refrigerant is evaporated in the evaporator (EVAP).<br />
Heat is transferred at a low temperature from an external circuit <strong>of</strong><br />
water or a brine which is thereby being chilled.<br />
4 → 5: The refrigerant is absorbed by the strong absorption<br />
solution (rich in absorption medium) entering at point 12. This<br />
process is exothermic due to both condensing <strong>of</strong> refrigerant <strong>and</strong><br />
mixing <strong>of</strong> refrigerant <strong>and</strong> solution. The heat is removed by an<br />
external cooling circuit.<br />
5 → 6: The liquid weak solution (poor in absorption media) is<br />
pressurized by a pump in order to reach the high pressure.<br />
6 → 7: The solution is preheated in the solution heat exchanger.<br />
7 → 9: The weak solution is heated by an external high temperature<br />
heat source which makes the refrigerant boil <strong>of</strong>.<br />
9 → 11: The strong solution is sent through the solution heat<br />
exchanger <strong>and</strong> heat is recovered by the weak solution.<br />
11 → 12: The high pressure <strong>of</strong> the strong solution is reduced to the<br />
low pressure by an expansion valve before it enters the absorber.<br />
In cycles using the ammonia-water solution (or similar solution) it<br />
is necessary to install a rectifier (”water separator”) after the desorber<br />
(DES in figure 1.2) to ensure that only refrigerant (ammonia) is sent to<br />
the condenser ([18]). If the refrigerant is not free <strong>of</strong> absorption medium,<br />
it will decrease the performance <strong>of</strong> the system.<br />
Cycle configurations<br />
The performance <strong>of</strong> the single stage cycle 10 described previously is quite<br />
limited (COP is in the range <strong>of</strong> 0,6 to 0,8). To increase the performance,<br />
various configurations have been developed. In the following some <strong>of</strong><br />
these alternative cycles <strong>of</strong> ammonia-water <strong>and</strong> water-lithium bromide<br />
are listed <strong>and</strong> their respective COP’s are indicated to compare the<br />
performance <strong>of</strong> the different configurations:<br />
10 In the literature the phrase single effect cycle is <strong>of</strong>ten for describing the same thing.<br />
11
1. INTRODUCTION<br />
Ammonia-water<br />
The COP values come from figure 6 in [20] at a heat rejection temperature<br />
<strong>of</strong> 35 ◦ C. The details about how the cycles work will not be explained here<br />
but a complete diagram is shown in appendix B.1 page 228.<br />
Basic single stage cycle, COP = 0,6<br />
Same cycle as described in previous section <strong>and</strong> in figure 1.2 (plus<br />
a rectifier between desorber <strong>and</strong> condenser).<br />
Single stage cycle with pre cooler, COP = 0,65<br />
The same as the above. A pre cooler (the same as a suction line heat<br />
exchanger) is added (transferring heat from point 2 to point 4 in<br />
figure 1.2).<br />
Absorber heat exchanger, COP = 0,9<br />
The same as the above. Two extra solution heat exchangers - one in<br />
the desorber <strong>and</strong> one in the absorber, are added.<br />
Desorber absorber heat exchange, COP = 1,3<br />
The same as the above. Another extra heat exchange (done by an<br />
external circuit) between absorber <strong>and</strong> desorber is added. This<br />
configuration is normally called GAX - Generator-Absorber-heat<br />
eXchanger.<br />
These configurations show that it is possible to double up the performance<br />
<strong>of</strong> the system by adding extra heat exchangers etc.<br />
Water-lithium bromide<br />
For the double, triple <strong>and</strong> quadruple stage, the mentioned COP’s are<br />
taken from figure 4 in [20] <strong>and</strong> the temperature in parenthesis is<br />
the heat supply temperature. For the three mentioned configurations<br />
the temperature <strong>of</strong> heat rejection <strong>and</strong> chilled water is 29 ◦ C <strong>and</strong> 7 ◦ C<br />
respectively.<br />
12<br />
Basic single stage cycle, COP = 0,7<br />
Same cycle as described in previously section <strong>and</strong> shown in figure<br />
1.2 (COP is taken from table 4 in [35]).<br />
Double stage cycle, parallel flow, COP = 1,3 (150 ◦ C)<br />
An extra cycle consisting <strong>of</strong> a pump, solution heat exchanger,
1.5. Heat driven cooling<br />
desorber, expansion valve <strong>and</strong> condenser is added to the single<br />
stage cycle (PUMP2, SHEX2, DES2, VB2 <strong>and</strong> COND2, see diagram<br />
in appendix B.2 page 229).<br />
The desorber (DES1) is now supplied with waste heat from the<br />
upper cycle condenser (COND2). The upper cycle desorber (DES2)<br />
is the only one receiving heat from an external source.<br />
The two cycles are coupled in parallel, which requires further three<br />
components - one splitter <strong>and</strong> two mixers (SPL, MIXL <strong>and</strong> MIXR).<br />
Triple stage cycle, parallel flow, COP = 1,7 (200 ◦ C)<br />
This is the same as above, but with yet another cycle on top <strong>of</strong> the<br />
two. This configuration is also called double condenser coupled.<br />
Quadruple stage cycle, parallel flow, COP = 2,0 (275 ◦ C)<br />
This is the same as above, but with yet another cycle on top <strong>of</strong> the<br />
three.<br />
Alternatively the water lithium bromide can be configured with series<br />
flow. According to [21] the parallel configuration has a higher COP than<br />
the series configuration at the same operation conditions.<br />
The above mentioned configurations are just a few examples, but<br />
it will be out <strong>of</strong> the scope <strong>of</strong> this report to mention all possible<br />
configurations.<br />
The examples show that it is possible to enhance the performance<br />
<strong>of</strong> an absorption cycle substantially, but it does make the system more<br />
<strong>and</strong> more complex <strong>and</strong> expensive. It also appears that cycles with water<br />
lithium bromide has a slightly higher COP than cycles with ammonia<br />
water.<br />
Heat source<br />
Another way to categorize absorptions units is by looking at how the heat<br />
is supplied. Direct fired units use gas-fired combustors whereas indirect<br />
fired units have the heat supplied by hot water or steam. The double (<strong>and</strong><br />
triple/quadruple) stage system use either gas-fired combustors or steam<br />
since the input temperature has to be higher than for single stage[29].<br />
13
1. INTRODUCTION<br />
1.5.3 Platen Munters cycle<br />
To some extend the Platen Munters cycle is similar to the Carré cycle with<br />
the ammonia/water working media pair. One important difference is<br />
that the total pressure in the Platen Munters cycle is the same throughout<br />
the whole system. This is possible because a third working medium, an<br />
inert gas (hydrogen), is used together with the refrigerant (ammonia) <strong>and</strong><br />
the absorbing medium (water).<br />
Figure 1.3: Diagram <strong>of</strong> Platen Munters cycle. The generator is the same as a desorber. Diagram<br />
downloaded from [26].<br />
The following description refers to the diagram in figure 1.3. The<br />
temperature in the condenser where pure ammonia vapor condenses<br />
determines the pressure <strong>of</strong> the system, e.g. 12 bars at approximately<br />
30 ◦ C. The condensed ammonia is sent to the evaporator (point 2). In<br />
the evaporator the liquid ammonia is mixed with hydrogen (point 4) <strong>and</strong><br />
the partial pressure <strong>of</strong> ammonia drops which makes it evaporate.<br />
The gas mixture <strong>of</strong> ammonia <strong>and</strong> hydrogen is sent to the absorber<br />
(point 3). The ammonia is absorbed by a poor ammonia water solution<br />
(poor in ammonia, entering at point 6) <strong>and</strong> the hydrogen is sent back to<br />
the evaporator (point 4).<br />
14
1.5. Heat driven cooling<br />
The rich solution (rich in ammonia) from the absorber (point 5) is sent<br />
to the desorber (generator). Heat from an external source (Q G ) evaporates<br />
some <strong>of</strong> the ammonia which is then sent to the condenser (point 1) <strong>and</strong><br />
the cycle starts over.<br />
In theory the Platen Munters cycle could reach the same COP as the<br />
Carré single stage cycle. But since it is difficult to build a large plant, a<br />
COP <strong>of</strong> only 0,2 to 0,3 is what is achieved in practise [18].<br />
1.5.4 Adsorption<br />
An adsorbent is a material which attracts water vapor. Zeolite is an<br />
adsorbent which has a surface area <strong>of</strong> 1000 m2 . Another example <strong>of</strong> a<br />
g<br />
adsorbent is silica-gel/water.<br />
Closed loop<br />
The closed loop is similar to the Carré cycle described previously, but a<br />
significant difference is the intermitted operation.<br />
The adsorber, which contains refrigerant (water vapor), is heated<br />
by an external source while it is isolated from (not connected to) the<br />
evaporator <strong>and</strong> condenser. This makes both temperature <strong>and</strong> pressure<br />
increase. When the pressure reaches the condensation pressure <strong>of</strong> the<br />
refrigerant the adsorber is connected to the condenser while heating <strong>of</strong><br />
the adsorber continues.<br />
The condenser <strong>and</strong> adsorber are disconnected. The condensed<br />
refrigerant is exp<strong>and</strong>ed through a valve <strong>and</strong> sent to the evaporator.<br />
The adsorber is cooled down to the initial temperature. When this<br />
temperature is reached the adsorber is connected to the evaporator.<br />
The evaporating refrigerant is adsorbed by the adsorber. Finally the<br />
adsorber <strong>and</strong> evaporator are disconnected <strong>and</strong> the adsorber is heated.<br />
The cycle start over.<br />
The cycle can be upgraded to a quasi-continuous cycle by applying an<br />
extra adsorber bed. The two-bed adsorption cycle is shown in appendix<br />
B.3 page 230. In practise the COP can reach 0,7 if the adsorber is supplied<br />
with heat at 90 ◦ C [35].<br />
15
1. INTRODUCTION<br />
Open loop<br />
In an open loop the air which should be cooled (or dehumidified) is in<br />
direct contact with the adsorption material. The ”Lizzy” system is an<br />
example <strong>of</strong> a desiccant cooling system which is <strong>of</strong>ten used in connection<br />
with sorption chillers or traditional AC’s [35]. It has one drying process,<br />
one heat exchange process <strong>and</strong> one humidifying process [18]. The cycle<br />
seems to have a potential COP which is below one [35] <strong>and</strong> will not be<br />
examined further in this report.<br />
16
1.6. Problem delimitation<br />
1.6 Problem delimitation<br />
Topsoe Fuel Cell (TOFC) manufactures <strong>solid</strong> <strong>oxide</strong> <strong>fuel</strong> cell (SOFC) stacks<br />
integrated with other high temperature components in a PowerCore TM .<br />
TOFC develops three different products with focus on three market<br />
segments: Auxiliary Power Unit (APU), Distributed Generation (DG)<br />
<strong>and</strong> micro Combined Heat <strong>and</strong> Power (µCHP). The latter two generates<br />
heat (hot water) besides electricity.<br />
The waste heat from a SOFC has a relative high temperature which<br />
might be an opportunity for producing heat driven cooling instead <strong>of</strong> (or<br />
in combination with) hot water.<br />
TOFC wants to know whether it is technically feasible to integrate<br />
SOFC <strong>and</strong> heat driven cooling <strong>and</strong> which market segments that are<br />
suited for such a product - is there a match between generation <strong>and</strong><br />
dem<strong>and</strong> for electricity, cooling <strong>and</strong> heat<br />
The absorption cycle (ABS) with water-lithium bromide solution is<br />
chosen as the heat driven cooling technology, because it seems to have<br />
most advantages for this purpose. As described in previous section it<br />
has one <strong>of</strong> the best performances <strong>and</strong> many possibilities to enhance it,<br />
<strong>and</strong> it is more simple than the ABS cycle with ammonia-water. Although<br />
there is the drawback that the application can only operate above zero<br />
degree Celsius to avoid water freezing.<br />
To determine whether <strong>integration</strong> <strong>of</strong> SOFC <strong>and</strong> ABS is feasible <strong>and</strong><br />
whether there is a match between electric power, cooling <strong>and</strong> heating<br />
dem<strong>and</strong>s, it is necessary to make a thermodynamic model, which can<br />
simulate the interplay <strong>of</strong> such components. Practical experiments could<br />
be an alternative approach but it is both a very expensive <strong>and</strong> time<br />
consuming task, which is less feasible for a master thesis like this.<br />
17
1. INTRODUCTION<br />
1.7 Problem statement<br />
In order to determine if the SOFC-ABS combination is at all economically<br />
feasible, some rough economical calculations will be made for each <strong>of</strong> the<br />
three <strong>of</strong> TOFCs intended market segments, APU, DG <strong>and</strong> µCHP.<br />
The next step will be to develop a thermodynamic model to simulate<br />
the interaction <strong>of</strong> the essential components <strong>of</strong> a SOFC-ABS system such<br />
as SOFC stack, absorption chiller unit, heat exchangers etc. The behavior<br />
<strong>of</strong> these components must be simulated <strong>and</strong> then efficiencies (electrical,<br />
cooling, heating <strong>and</strong> overall) will be determined <strong>and</strong> compared for<br />
different system configurations.<br />
The model should be so general that it is capable <strong>of</strong> simulating a<br />
range <strong>of</strong> different applications with different temperatures <strong>and</strong> powers,<br />
flows, ambient conditions etc. The purpose <strong>of</strong> the model should be to<br />
make an estimation <strong>of</strong> whether the combination <strong>of</strong> SOFC-ABS is a good<br />
thermodynamical match, <strong>and</strong> to investigate if <strong>and</strong> how the electrical <strong>and</strong><br />
thermal output <strong>of</strong> the system can be increased.<br />
An example <strong>of</strong> an application will be simulated in order to demonstrate<br />
the capabilities <strong>of</strong> the model.<br />
The following questions will be answered in this report.<br />
• For which market segments is there a good match between SOFC<br />
<strong>and</strong> absorption cooling<br />
• Which <strong>of</strong> the system components are especially critical for obtaining<br />
a good performance<br />
• Which system configuration gives the best CCHP performance<br />
• How does climate influence the performance <strong>of</strong> the CCHP system<br />
• How does the relation between generated electricity, cooling, <strong>and</strong><br />
heating match the dem<strong>and</strong>, <strong>and</strong> can this be improved<br />
18
C H A P T E R<br />
2<br />
MARKET INVESTIGATION<br />
2.1 Introduction<br />
Introduction to the cases<br />
Before looking into the thermodynamical aspects <strong>of</strong> combining a SOFC<br />
with an absorption cooling unit, a short economical analysis is made in<br />
order to see if there is a market / economical potential for this. Three<br />
different market segments are examined: APU (Auxiliary Power Unit),<br />
CHP (Combined Heat <strong>and</strong> Power), <strong>and</strong> DG (Distributed Generation).<br />
Many <strong>of</strong> the input parameters in the economical model (COPs, prices<br />
etc) have been obtained by contacting several distributers <strong>of</strong> absorption<br />
<strong>and</strong> adsorption cooling units asking for preliminary <strong>of</strong>fers. The prices resulting<br />
from this can be seen in appendix A.5 page 219. Other parameters<br />
have been estimated by searching for prices on the internet <strong>and</strong> reading<br />
reports from agencies such as the ”Energy Information Administration”.<br />
Some data which was not available (e.g. usage time/full load hours for<br />
a given application) has been estimated by the authors. So the results <strong>of</strong><br />
the calculations in this section are merely guidelines meant to show if the<br />
synergetic effects <strong>of</strong> a given application can add up to an amount equal<br />
to or bigger than the extra cost <strong>of</strong> buying the extra equipment. Sensitivity<br />
analyses have however been made to see how the different input parameters<br />
affect the outcome.<br />
Some general assumptions about the input parameters are described in<br />
19
2. MARKET INVESTIGATION<br />
appendix A.1 page 190.<br />
All the prices in the calculations are made up in real prices (as in<br />
opposition to nominal prices). So the approximation that the electricity<br />
prices <strong>and</strong> gas prices will only increase with the rate <strong>of</strong> the inflation<br />
means that the price <strong>of</strong> a kWh will be the same each year (in real prices).<br />
In all the cases a discount factor <strong>of</strong> 5% (in real prices) has been used,<br />
corresponding to 7-8% in nominal prices, since inflation is generally 2-<br />
3%. This means that an investment will be regarded favorable if it yields<br />
an average return <strong>of</strong> 5% (plus inflation) per year or more. This value is<br />
intentionally set a little low, since it is assumed that economical gains<br />
will only be part <strong>of</strong> the reason for choosing this option. The reduction<br />
<strong>of</strong> energy consumption will also be good for the image <strong>of</strong> the company,<br />
since a green image is becoming more <strong>and</strong> more important, <strong>and</strong> it is also<br />
likely that the price <strong>of</strong> CO 2 quotas will increase in the coming years [12].<br />
The economical calculations have been made by calculating the NPV<br />
(Net Present Value) for the net payment (NP) each year:<br />
NPV i = NP · (1 + R D ) −t<br />
Then the accumulated NPV has been found for each year by:<br />
NPV akk,i = Σ i 1 NPV i<br />
Finally the annuity has been found as:<br />
Annui t y i = NPV akk,i · R D /(1 − (1 − R D ) −t )<br />
Since only the expenses have been viewed 1 , it has been chosen to let the<br />
values be positive for expenses. So the smaller the NPV akk <strong>and</strong> annuities,<br />
the cheaper the solution is.<br />
The full calculations in Excel can be seen in appendix A.2, A.3, <strong>and</strong> A.4<br />
page 191 to 202.<br />
In the next section the three different market segments will be examined<br />
one by one.<br />
1 The application has a certain need <strong>of</strong> cooling (<strong>and</strong> electricity), <strong>and</strong> as long as it<br />
is provided at the correct temperature <strong>and</strong> rate it has the same value regardless <strong>of</strong> the<br />
process used to create it.<br />
20
2.2 Auxiliary Power Unit (APU)<br />
2.2.1 Truck APU<br />
2.2. Auxiliary Power Unit (APU)<br />
Large trucks normally idle their main engine when they are parked in<br />
order to generate air conditioning for cooling the cabin <strong>and</strong> electricity<br />
for equipment such as microwave ovens, TV, DVD player etc. Idling<br />
the engine for this is, however, quite inefficient, since a diesel engine<br />
efficiency is quite small at low loads. One solution for this problem could<br />
be to mount a SOFC on the truck to generate electricity when parked, <strong>and</strong><br />
then use the waste heat to drive an absorption air condition. But there<br />
are two problems:<br />
1. The air conditioning need is in the order <strong>of</strong> 3kW reference [22], <strong>and</strong><br />
the electricity need (excluding electric air condition) seems to be<br />
no higher than 2kW. So if a SOFC should generate the electricity, it<br />
would probably suffice with a unit <strong>of</strong> 2kWe combined with some<br />
batteries to take care <strong>of</strong> peak load. And the approximately 2kW<br />
<strong>of</strong> waste heat would not be nearly enough to generate sufficient<br />
cooling, since the COP <strong>of</strong> the smallest (4kW cooling) absorption<br />
unit is only 0,4.<br />
2. Even the smallest (4kW cooling) heat driven AC sorption units<br />
weighs 216kg excl HEXes, <strong>and</strong> takes up a lot <strong>of</strong> space. This is<br />
disadvantageous on a truck since it is desired to have as much space<br />
as possible cleared for the cargo. Furthermore the extra weight<br />
slightly reduces the maximum cargo load.<br />
Hence the SOFC/ABS AC is not a good match for a truck.<br />
21
2. MARKET INVESTIGATION<br />
2.2.2 Ship APU<br />
Large ships are usually equipped with a separate diesel engine to<br />
generate electricity for light, air conditioning <strong>and</strong> other auxiliary<br />
equipment. A possibility could be to replace this secondary engine with<br />
a <strong>fuel</strong> cell which would increase the electrical efficiency, reduce the NO x<br />
<strong>and</strong> particle emission <strong>and</strong> lower the noise. If that is done it might be<br />
possible to use the waste heat from the SOFC to drive an absorption air<br />
condition.<br />
An economical estimation <strong>of</strong> the feasibility has been made by<br />
comparing a ship with a SOFC <strong>and</strong> a conventional 20kW air conditioning<br />
(electrically driven chiller), relative to a SOFC with a 20kW absorption air<br />
conditioning. The assumptions are as follows:<br />
Assumptions<br />
• Full load usage time fraction = 0,5 (4380 hours per year)<br />
• SOFC electrical efficiency = 0,5<br />
• Absorption cooling power = 20kW<br />
• COP elec.ac = 3,6<br />
• Electrical AC price: 20 kW = 61,000DKK<br />
• Absorption AC price: 20 kW = 200,000DKK (incl HEX’es)<br />
The pay back time is approximately 1,7 years when the absorption air<br />
conditioning runs half the time (approximately 4400 full load hours per<br />
year). During a 10 year lifetime, a total NPV <strong>of</strong> 520.000DKK can be<br />
saved by using the ABS including the higher purchase price, which is<br />
200.000DKK vs 60.000DKK. The full economical calculations can be seen<br />
in appendixA.2 page 191.<br />
Sensitivity analysis<br />
The biggest impact on the pr<strong>of</strong>itability comes from the usage time<br />
fraction, the diesel price, <strong>and</strong> the SOFC efficiency. A 10% increase <strong>of</strong> these<br />
variables gives 12% change in the annuity after 10 years. The purchase<br />
22
2.2. Auxiliary Power Unit (APU)<br />
Sensitivity analysis <strong>of</strong> Ship ABS vs ECH<br />
15<br />
10<br />
Annuity increase [%]<br />
5<br />
0<br />
-10 -5 0 5 10<br />
-5<br />
-10<br />
Purchase price ABS<br />
Purchase price EAC<br />
Diesel price<br />
Efficiency SOFC<br />
Usage time fraction<br />
Discount rate<br />
-15<br />
Increase in variables [%]<br />
Figure 2.1: The percentage increase in annuity gain is shown for a 10% increase <strong>of</strong> the input<br />
parameters. The annuity is for a lifespan <strong>of</strong> 10 years. The purchase price <strong>of</strong> the ABS unit is<br />
200.000DKK. With the chosen parameters the gained annuity is 75.000DKK/y (incl purchase).<br />
price <strong>of</strong> the ABS unit, however, gives only a 3,5% decrease <strong>of</strong> the annuity<br />
for a 10% increased price, <strong>and</strong> the ECH price <strong>and</strong> discount rate gives even<br />
smaller changes. So the lack <strong>of</strong> exact knowledge about the price turns out<br />
not to be so critical after all.<br />
The reason for the huge influence from SOFC efficiency <strong>and</strong> diesel<br />
price is that these factors are determining the price <strong>of</strong> the electricity<br />
generated for the electrical chiller.<br />
Pay Back Time vs. usage time fraction<br />
As long as the usage time fraction is above 30%, the investment seems to<br />
be quite beneficial (pay back time less than 3 years), but if the usage time<br />
fraction comes below 20%, the pay back time starts to increase quickly.<br />
So for a usage time fraction <strong>of</strong> 10%, the pay back time is just under 10<br />
years, which is far too long for many companies.<br />
23
2. MARKET INVESTIGATION<br />
Pay Back Time for ABS unit on ship<br />
Usage time fraction [-]<br />
1,0<br />
0,9<br />
0,8<br />
0,7<br />
0,6<br />
0,5<br />
0,4<br />
0,3<br />
0,2<br />
0,1<br />
0,0<br />
0 2 4 6 8 10 12<br />
Pay Back Time [years]<br />
Figure 2.2: The x-axis shows the pay back time for a given usage time fraction (how big a<br />
fraction <strong>of</strong> the time the Absorption unit runs). The Pay Back Time is for an ABS unit mounted<br />
on an existing SOFC without the cost/gain <strong>of</strong> the SOFC itself.<br />
Conclusion<br />
If the ABS unit is in use more than about 30% <strong>of</strong> the time there seems<br />
to be a relatively good economical potential in adding an absorption air<br />
conditioning unit on ships where an SOFC is installed. It has, however,<br />
not been investigated whether the SOFC in itself is pr<strong>of</strong>itable to begin<br />
with. Furthermore one <strong>of</strong> the producers <strong>of</strong> absorption air conditioning<br />
units claim that they are fairly sensitive to the inclination <strong>of</strong> the floor [7],<br />
so the rocking motion <strong>of</strong> ships might pose a problem. This has not been<br />
investigated further though.<br />
24
2.3. Micro Combined Heat <strong>and</strong> Power (µCHP)<br />
2.3 Micro Combined Heat <strong>and</strong> Power (µCHP)<br />
2.3.1 Micro CHP - Air condition<br />
If a SOFC is installed in private homes to generate electrical power,<br />
the waste heat can be utilized for domestic hot water as well as space<br />
heating. The space heating, however, is not so relevant during summer<br />
in hot climates, although hot water is still necessary for showering etc.<br />
Many places (e.g. the US or in most asian countries) air conditioners are<br />
employed during most <strong>of</strong> the summer. So it would be beneficial if the<br />
excessive heat from the SOFC could be used in an absorption cooling<br />
unit to create air conditioning.<br />
By contacting the majority <strong>of</strong> the producers <strong>of</strong> ABS units it was<br />
discovered that the smallest available heat driven air conditioning unit<br />
had a cooling power <strong>of</strong> 4kW, which is in the right range for cooling a<br />
one family house 2 . But the heat dem<strong>and</strong> <strong>of</strong> the absorption unit was<br />
12.5kW 3 which was far more than the maximum approximately 1kW<br />
heat which would in average be supplied by the SOFC for a 1kW <strong>of</strong><br />
electricity production 4 .<br />
Of course the absorption cooling unit could be run at part load, but<br />
the low COP combined with fact that some <strong>of</strong> the waste heat was to<br />
be used to heat up the hot water, <strong>and</strong> that some part <strong>of</strong> the waste heat<br />
can not be extracted due to heat exchanger efficiency below 1, made the<br />
absorption unit a very bad match for the SOFC. Furthermore the small<br />
absorption chillers are fairly expensive per kW, so they have to have a lot<br />
<strong>of</strong> full load hours in order to make for a reasonable pay back time.<br />
Conclusion<br />
This all meant that there seems not to be a potential for using an<br />
absorption air conditioning unit together with SOFCs in private homes.<br />
2 Assuming a well insulated house or that the climate is not too hot.<br />
3 the small 4kW absorption unit had a COP <strong>of</strong> only 0,4 whereas most <strong>of</strong> the larger<br />
single cycle units experienced COPs <strong>of</strong> around 0,7<br />
4 assuming an electrical efficiency <strong>of</strong> the SOFC <strong>of</strong> approximately 0,5 <strong>and</strong> an expected<br />
electrical power consumption <strong>of</strong> a single family house <strong>of</strong> 1kW [32]<br />
25
2. MARKET INVESTIGATION<br />
2.3.2 Micro CHP - Refrigerators<br />
The refrigerators used in hotel rooms are <strong>of</strong> the absorption type, but<br />
they use the Platen cycle, which means that the COP is only around 0,25<br />
In addition the heat must be supplied at relatively high temperatures<br />
- in the range <strong>of</strong> 120-180 ◦ C [18]. In hotels the driving heat is typically<br />
provided by an electric heating element which gives quite a high energy<br />
consumption, but this is tolerated since the refrigerator is very quiet. For<br />
other applications like mobil homes LPG is used as energy source.<br />
In theory there might be a potential in combining a SOFC with an<br />
absorption refrigerator for private homes. There is enough waste heat,<br />
since the average waste heat consumption would be in the order <strong>of</strong> 200W<br />
for the absorption refrigerator (see calculations in Appendix A.3 on page<br />
196).<br />
Assumptions<br />
The following assumptions have been used to calculate the cost (Net<br />
Present Value <strong>and</strong> annuity) <strong>of</strong> an electrical <strong>and</strong> an absorption refrigerator<br />
(all seen from the consumer view point - including taxes <strong>and</strong> VAT):<br />
• Compressor refrigerator price = 4,000DKK 5 [8]<br />
• Absorption refrigerator price = 11,000DKK 6 [1]<br />
• Compressor refrigerator electricity consumption = 208kWh/y<br />
• Electricity price 2 DKK/kWh (Danish prices)<br />
After 10 years, the annuity cost is 1420 DKK for the absorption <strong>and</strong><br />
930DKK for the electrical unit including investment <strong>and</strong> electricity but<br />
no extra piping or heat exchanger for transferring the SOFC waste heat.<br />
So with a lifespan <strong>of</strong> 10 years, the absorption unit is estimated to be<br />
about 50% more expensive than the conventional refrigerator including<br />
electricity consumption <strong>and</strong> purchase price but no piping. The pay back<br />
time will be around 50 years strongly dependent on the discount factor,<br />
which is assumed to be 5%. The full calculations can be seen in appendix<br />
A.3 page 196.<br />
5 Bosch KGV 36X27 225 liter refrigerator <strong>and</strong> 91 liter freezer.<br />
6 RGE 400 from Åbybro camping og fritid 224 liter refrigerator + 76 liter freezer.<br />
26
Pay Back Time vs. refrigerator price<br />
2.3. Micro Combined Heat <strong>and</strong> Power (µCHP)<br />
12000<br />
Pay Back Time for absorption refrigerator<br />
ABS refrigerator Purchase<br />
Price [DKK]<br />
10000<br />
8000<br />
6000<br />
4000<br />
2000<br />
0<br />
0 5 10 15 20 25<br />
Pay Back Time [years]<br />
Figure 2.3: The x-axis shows the pay back time for a given purchase price <strong>of</strong> the absorption<br />
refrigerator (i.e. how long time does it take before the ABS refrigerator becomes cheaper than a<br />
regular electrical refrigerator.<br />
The price <strong>of</strong> the normal refrigerator used for comparing is 4,000DKK,<br />
so if the absorption refrigerator could be made for the same price 7 , the<br />
pay back time would be zero years. If the lifetime <strong>of</strong> both types <strong>of</strong><br />
refrigerators is 10 years, the price <strong>of</strong> the absorption unit should be no<br />
more than 7,000DKK if the investment is to become favorable within the<br />
expected 10 year lifespan. Already with a price <strong>of</strong> 10,000DKK, the pay<br />
back time exceeds 25 years.<br />
Sensitivity analysis<br />
It appears that the most important factor influencing the pr<strong>of</strong>itability <strong>of</strong><br />
the ABS refrigerator is the purchase price <strong>of</strong> the unit itself. If this is<br />
increased by 10%, the deficit <strong>of</strong> the absorption solution is increased by<br />
30%.<br />
The electricity price, annual electricity consumption <strong>and</strong> the purchase<br />
price <strong>of</strong> the electrical refrigerators, are all approximately equally<br />
7 with no significant costs to installation <strong>and</strong> piping from the SOFC exhaust gas<br />
27
2. MARKET INVESTIGATION<br />
Sensitivity analysis <strong>of</strong> refrigiator ABS vs ECH<br />
30<br />
20<br />
Annuity increase [%]<br />
10<br />
0<br />
-10 -5 0 5 10<br />
-10<br />
Purchase price ABS<br />
Purchase price El-unit<br />
-20<br />
Electricity price<br />
Anual electricity consump<br />
-30<br />
Discount rate<br />
Increase in variables [%]<br />
Figure 2.4: The annuity is already negative to begin with (suggesting that the ABS unit is more<br />
expensive than the electrical counterpart), so an increase in y-value means that using the ABS<br />
unit becomes an even bigger disadvantage.<br />
influential. A 10% increase in their value reduces the deficit <strong>of</strong> the<br />
absorption refrigerator around 10%.<br />
The discount rate does at first glance not appear so influential, but<br />
since its value can easily differ 50% from the estimated/chosen value, it<br />
is a significant source <strong>of</strong> uncertainty.<br />
Conclusion<br />
From an economical view point, using SOFC waste heat for refrigerators<br />
doesn’t seem so advantageous. But it does depend very much on<br />
the purchase price <strong>of</strong> the absorption unit, so if this can be reduced<br />
by 1/3 from the current levels, it starts to make sense economically,<br />
although piping <strong>and</strong> installation might change the picture somewhat in a<br />
disadvantageous direction. Furthermore the CO 2 savings have not been<br />
assigned any value in these calculations.<br />
Another factor to consider is if it is inconvenient to place the<br />
refrigerator right next to the <strong>fuel</strong> cell, since you normally prefer to have<br />
the refrigerator in the kitchen <strong>and</strong> the SOFC in the basement near the hot<br />
water storage.<br />
28
2.4 Distributed Generation (DG)<br />
2.4. Distributed Generation (DG)<br />
As described in chapter 1 distributed generation has many applications.<br />
Hotels are appropriate for a case study since they are <strong>of</strong>ten placed in<br />
areas with a hot climate <strong>and</strong> since the guests expect comfort, hotels are<br />
normally equipped with air conditioning. There is also a substantial<br />
dem<strong>and</strong> for electricity (for misc appliances) <strong>and</strong> hot water (primarily for<br />
showering). It could be expected that the dem<strong>and</strong> for the three end-use<br />
products (electricity, cooling <strong>and</strong> hot water) have a good match.<br />
Since traveling still increases both for business <strong>and</strong> pleasure, more<br />
hotels are being build <strong>and</strong> these require air conditioning, meaning an<br />
increasing dem<strong>and</strong> for cooling <strong>and</strong> thus a potential increase <strong>of</strong> the market<br />
for DG.<br />
So it is examined if a Hotel could use a combination <strong>of</strong> a SOFC <strong>and</strong><br />
an ABS (Absorption cooling) unit to provide electricity, cooling, <strong>and</strong> heat<br />
for domestic hot water in an economical way. The input parameters <strong>and</strong><br />
assumptions are as follows:<br />
Input/assumptions<br />
• 230 room hotel (18.000m 2 )<br />
• 2 different climates - normal (hot summer, cold winter) vs hot all<br />
year<br />
• COP E AC = 4,0<br />
• COP ABS = 1,3<br />
• η SOFC = 0,5<br />
• Gas price 0,20DKK/kWh (see appendix A.6 page 224) [17]<br />
• Electricity price = 0,75DKK/kWh (see appendix A.6 page 224) [10]<br />
+ [11]<br />
• SOFC price 2.650 DKK/kW (=$500/kW) [16]<br />
• ABS price 3.700DKK/kW 8<br />
8 Derived from the market investigation in appendix A.5 page 221<br />
29
2. MARKET INVESTIGATION<br />
• ECH price 1.800DKK/kW 9<br />
• ABS electricity consumption neglected<br />
• Discount factor 5%<br />
2.4.1 Three solutions<br />
In order to examine which part <strong>of</strong> a pr<strong>of</strong>itability that arrives from the<br />
SOFC in itself <strong>and</strong> which part that arrives from adding the absorption<br />
chiller, three configurations are now considered <strong>and</strong> compared:<br />
(A) Grid + ECH. All electricity is bought from the grid, <strong>and</strong> the air<br />
conditioning is purely electrical (ECH). Hot water <strong>and</strong> space heating<br />
is done with natural gas (efficiency 1,0). So this is the normal<br />
configuration <strong>of</strong> a hotel.<br />
(B) SOFC + HotWater + ECH. A SOFC is installed <strong>and</strong> the waste<br />
heat is used to heat up all the hot water for the hotel, but the air<br />
conditioning is still made by an electrical unit. The size <strong>of</strong> the SOFC<br />
is made so the net production <strong>of</strong> electricity equals the total electricity<br />
dem<strong>and</strong> <strong>of</strong> the hotel including the electrical air condition when the<br />
SOFC runs at full load 24/7. This means importing electricity from<br />
the grid during peak load hours, while electricity will be sold to the<br />
grid during hours with less electricity consumption in the hotel. It<br />
is assumed that the buying <strong>and</strong> selling price for the electricity is the<br />
same 10 . Space heating is done by natural gas.<br />
(C) SOFC + HotWater + ABS + ECH. A SOFC is installed <strong>and</strong> the waste<br />
heat is used to heat up all the hot water as well as running an<br />
absorption air conditioner. Due to heat exchanger efficiency it is<br />
assumed that only 80% <strong>of</strong> the waste heat can be extracted from the<br />
exhaust gas. The water heating is done entirely with waste heat, <strong>and</strong><br />
the rest <strong>of</strong> the waste heat energy is used int the absorption cooling 11 .<br />
9 Derived from the market investigation in appendix A.5 page 221<br />
10 This is a somewhat crude assumption, even though the net export <strong>of</strong> electricity is<br />
zero but again these calculations are only approximations, meant to show the overall<br />
trends.<br />
11 in praxis the absorption cooling unit will <strong>of</strong> course be the physically first unit to use<br />
some <strong>of</strong> the waste heat, since it needs higher temperatures than the hot water heating.<br />
But the ABS is allowed no more waste energy than what will leave enough waste heat<br />
for the water heating.<br />
30
2.4. Distributed Generation (DG)<br />
In the hot climate, the absorption unit is set to run all year, whereas<br />
it only runs during the summer in the normal climate (50% <strong>of</strong> the<br />
time). Since there is not enough waste heat to cover all <strong>of</strong> the air<br />
conditioning dem<strong>and</strong>, an electrical air conditioner must be used to<br />
supply the rest <strong>of</strong> the cooling service. Space heating is in all cases<br />
done by natural gas.<br />
2.4.2 Hot vs Normal climate<br />
The climate must be expected to have a big effect on the advantage <strong>of</strong><br />
absorption chillers, since a hot climate will facilitate a bigger cooling<br />
dem<strong>and</strong>. Hence the following two climate-cases are considered:<br />
Normal climate<br />
Electricity consumption <strong>and</strong> hot water need is assumed evenly distributed<br />
throughout the year (the consumption <strong>of</strong> electricity, air conditioning, domestic<br />
water heating <strong>and</strong> space heating taken from [13] 12 ). The entire<br />
cooling energy dem<strong>and</strong> is assumed to be evenly distributed throughout<br />
the 6 month <strong>of</strong> the summer. The air conditioning units (ABS <strong>and</strong> electrical)<br />
are designed <strong>and</strong> sized for summer use, <strong>and</strong> in winter time they<br />
just shut down completely. The space heating will also correspond to the<br />
average dem<strong>and</strong> <strong>of</strong> the USA <strong>and</strong> is provided by natural gas.<br />
Hot climate<br />
In the hot climate, a cooling dem<strong>and</strong> is assumed to be present all year,<br />
<strong>and</strong> hence the needed cooling energy per year is assumed to be double<br />
that <strong>of</strong> the normal climate cooling need. But the space heating is assumed<br />
to fall to zero since it is hot all year.<br />
The electricity <strong>and</strong> hot water consumption will be exactly the same as<br />
in the normal climate (showering etc. is still needed in hot climates).<br />
12 The normal climate is assumed to be close the average <strong>of</strong> the three climates<br />
investigated in [13], which is: Anaheim (Mild climate), Las Vegas (Hot climate), <strong>and</strong><br />
Minneapolis (Cold climate)<br />
31
2. MARKET INVESTIGATION<br />
2.4.3 Results<br />
The full results <strong>and</strong> input can be seen in appendix A.4 page 202. First<br />
<strong>of</strong> all it turns out, that the waste heat from the SOFC is not at all<br />
enough to cover the entire cooling dem<strong>and</strong> even though a double stage<br />
absorption chiller is used (with a COP <strong>of</strong> 1,3). In the normal climate<br />
the ABS chiller supplies ¼ <strong>of</strong> the yearly cooling dem<strong>and</strong> <strong>and</strong> in the<br />
hot climate, it supplies 1/3 because the SOFC system must be larger in<br />
order to generate additional electricity for the supplementary electrical<br />
air conditioner. This does, however, mean that the small ABS chiller can<br />
run as base load, <strong>and</strong> hence have a lot <strong>of</strong> full load hours per year since<br />
the daily variation <strong>of</strong> cooling dem<strong>and</strong> is probably not so big that it falls<br />
below 1/3 <strong>of</strong> the average daily cooling dem<strong>and</strong>. But <strong>of</strong> course both ECH<br />
<strong>and</strong> ABS will have to be shut <strong>of</strong>f during wintertime in the normal climate.<br />
If the lifetime <strong>of</strong> all the components in the system is 10 years, the total<br />
cost (Net Present Value) for system components, natural gas or electricity<br />
imported from the net is calculated to be the following:<br />
Hot Climate<br />
Case A: 27mil. DKK (-SOFC, -Absorption unit)<br />
Case B: 15mil. DKK (+SOFC, -Absorption unit)<br />
Case C: 14mil. DKK (+SOFC, +Absorption unit)<br />
With an estimated SOFC price <strong>of</strong> around 2500DKK/kW, the investment<br />
cost <strong>of</strong> the SOFC will be just above 1mil. DKK. And hereby a yearly electricity<br />
consumption <strong>of</strong> 3,0mil. DKK can be exchanged with a gas consumption<br />
<strong>of</strong> 1,4mil. DKK. So if the lifetime is 10 years, 13mil. DKK can<br />
be saved in <strong>fuel</strong> (with a discount rate <strong>of</strong> 5%), <strong>and</strong> the total surplus will<br />
then become 12mil. DKK.<br />
If an ABS unit is used, the additional investment (compared to a purely<br />
electrical air conditioner) will be 0,4 mil. DKK 13 , <strong>and</strong> the savings in<br />
<strong>fuel</strong>/electricity will be around 1,9 mil. DKK. So adding an absorption<br />
13 If no ABS unit is used, the electrical chiller will cost 1,5mil. DKK. If the ABS is<br />
used, the unit in itself will costs around 1,0mil. DKK <strong>and</strong> the supplementary electrical<br />
air conditioner will cost 0,9mil. DKK.<br />
32
2.4. Distributed Generation (DG)<br />
air conditioner will give a total saving <strong>of</strong> around 1,5 mil. DKK 14 . So the<br />
investment seems to be quite pr<strong>of</strong>itable.<br />
Normal Climate<br />
For this climate the numbers are a little closer:<br />
Case A: 26mil. DKK (-SOFC, -Absorption unit)<br />
Case B: 16mil. DKK (+SOFC, -Absorption unit)<br />
Case C: 16mil. DKK (+SOFC, +Absorption unit)<br />
For this climate the savings <strong>of</strong> using an SOFC is slightly decreased from<br />
12 to 10mil. DKK. But the gain <strong>of</strong> using the ABS unit is significantly<br />
reduced from around 1,5mil. DKK to 0,4mil. DKK. So it still looks<br />
pr<strong>of</strong>itable although not as good as for the hot climate.<br />
Pay Back Time for the entire system (case A vs case C)<br />
Figure 2.5 shows how long time it takes before case C becomes cheaper<br />
than case A when running a hotel i.e. how long does the entire<br />
SOFC+ABS system has to live in order to be cheaper than just purchasing<br />
the electricity from the electrical grid <strong>and</strong> use an electrical air conditioner<br />
for cooling. It is seen that if the purchase price <strong>of</strong> the SOFC is around<br />
the expected 2500DKK/kW, the pay back time for the entire system will<br />
be around 1 year for both climate cases. And even if the SOFC price<br />
is as high as 10.000DKK/kW the payback time is less than 3 years, but<br />
at this price it is seen that the SOFC+ABS investment is slightly more<br />
advantageous for the hot climate.<br />
So if the SOFC price can just be lowered to around 10.000DKK/kW it<br />
could become pr<strong>of</strong>itable for at hotel to purchase the SOFC + ABS system.<br />
But the comparison <strong>of</strong> case A <strong>and</strong> C says nothing about whether it is<br />
the addition <strong>of</strong> the absorption chiller or the SOFC in itself which makes<br />
the investment pr<strong>of</strong>itable. Hence in the following case B <strong>and</strong> C will be<br />
compared to see what effect the addition <strong>of</strong> the absorption chiller has on<br />
the economics (assuming that the SOFC is used either way).<br />
14 The NPV values <strong>of</strong> case B <strong>and</strong> C for the hot climate stated above have been rounded<br />
<strong>of</strong>f from 15,27mil. DKK <strong>and</strong> 13,78mil. DKK respectively<br />
33
2. MARKET INVESTIGATION<br />
16000<br />
14000<br />
Pay Back Time: Entire System (SOFC+ABS)<br />
SOFC Price [DKK/kW]<br />
12000<br />
10000<br />
8000<br />
6000<br />
4000<br />
2000<br />
0<br />
Normal Climate<br />
Hot Climate<br />
0 1 2 3 4 5<br />
Time [years]<br />
Figure 2.5: The x-axis shows the pay back time for a system consisting <strong>of</strong> a SOFC + ABS +<br />
Hot water heating compared to pure electricity import from the electrical grid + electrical air<br />
conditioner. The varied parameter (y-axis) is the purchase price <strong>of</strong> the SOFC.<br />
Pay Back time for the ABS unit (case B vs case C)<br />
From figure 2.6 it can be seen how long it takes for the ABS unit to repay<br />
itself. As expected the pay back time is much shorter for the hot climate<br />
than for the normal climate. This is mainly because the number <strong>of</strong> full<br />
load hours for the ABS is much bigger for the hot climate, where it runs<br />
all year, so more electricity is saved. With the current prices for the ABS<br />
<strong>of</strong> just below 4000Dkk/kW the pay back time is 1,5 years <strong>and</strong> 4 years for<br />
the hot <strong>and</strong> normal climate respectively. It is seen, however, that the pay<br />
back time is fairly sensitive to the purchase price <strong>of</strong> the ABS. And if the<br />
purchase price goes below approximately 2000DKK/kW the ABS unit<br />
becomes pr<strong>of</strong>itable from day one since this is the same as an electrical air<br />
conditioner would cost.<br />
34
2.4. Distributed Generation (DG)<br />
ABS Price [DKK/kW]<br />
10000<br />
9000<br />
8000<br />
7000<br />
6000<br />
5000<br />
4000<br />
3000<br />
2000<br />
1000<br />
0<br />
Pay Back Time: Absorption Cooling Unit (ABS)<br />
Normal Climate<br />
Hot Climate<br />
0 2 4 6 8 10 12<br />
Time [years]<br />
Figure 2.6: The x-axis shows the pay back time if an ABS is added to a system already featuring<br />
a SOFC system. The varied parameter (y-axis) is the purchase price <strong>of</strong> the ABS unit.<br />
Annuity for all three cases (A vs B vs C)<br />
The pay back time only says how long it takes for the system to become<br />
pr<strong>of</strong>itable, not how much money will be spend or saved. So now the<br />
annuity (average annual cost) is viewed.<br />
The three different solutions (A,B,C) are now compared by looking<br />
at their annuity 15 , assuming a life time for all <strong>of</strong> the components <strong>of</strong> 5<br />
years, 10 years <strong>and</strong> 15 years respectively. In the hot climate (figure 2.7A)<br />
it appears that by far the biggest amount <strong>of</strong> the savings are achieved by<br />
purchasing the SOFC unit - this reduces the annual price by a little more<br />
than 40% <strong>of</strong> the present costs. Adding the ABS reduces the price further<br />
about 10% compared to when the SOFC is used alone.<br />
For the normal climate (figure2.7B) the SOFC still reduces the price<br />
by a little less than 40%. The effect <strong>of</strong> the ABS is however a lot smaller<br />
than for the hot climate so only 2-3% <strong>of</strong> the yearly costs can be saved by<br />
using an ABS unit.<br />
It should be noted that the pr<strong>of</strong>itability <strong>of</strong> the SOFC as well as<br />
15 the annuity includes gas, electricity, <strong>and</strong> purchase <strong>of</strong> SOFC, ABS <strong>and</strong> ECH<br />
35
2. MARKET INVESTIGATION<br />
Annuity price [DKK/y]<br />
4'000'000<br />
3'500'000<br />
3'000'000<br />
2'500'000<br />
2'000'000<br />
1'500'000<br />
1'000'000<br />
500'000<br />
HOT climate.<br />
Annual price for all energy equipment + gas <strong>and</strong> electricity use<br />
Annuity_5<br />
Annuity_10<br />
Annuity_15<br />
Annuity price [DKK/y]<br />
4'000'000<br />
3'500'000<br />
3'000'000<br />
2'500'000<br />
2'000'000<br />
1'500'000<br />
1'000'000<br />
500'000<br />
Normal climate.<br />
Annual price for all energy equipment + gas <strong>and</strong> electricity use<br />
Annuity_5<br />
Annuity_10<br />
Annuity_15<br />
0<br />
EL SOFC+WH SOFC+WH+ABS<br />
0<br />
EL SOFC+WH SOFC+WH+ABS<br />
Figure 2.7: The annuity (yearly cost) is examined for an expected lifespan <strong>of</strong> the SOFC, ABS,<br />
<strong>and</strong> ECH unit <strong>of</strong> 5, 10, <strong>and</strong> 15 years respectively. A: Hot climate. B:Normal climate.<br />
SOFC+ABS does not depend so much on their lifetime because the<br />
purchase price <strong>of</strong> the SOFC <strong>and</strong> ABS unit is quite small relative to the<br />
yearly cost <strong>of</strong> natural gas <strong>and</strong> electricity. The SOFC cost is approximately<br />
equal to the yearly savings in <strong>fuel</strong> (1,0 to 1,2 mil. DKK). The cost <strong>of</strong> the<br />
ABS unit is around 1mil. DKK, but at the same time the price <strong>of</strong> the<br />
supplementary air conditioning unit decreases from 1,4mil. DKK to 0,9<br />
mil. DKK. 16<br />
Sensitivity analysis<br />
Since there are three setups (A, B <strong>and</strong> C), all in both hot <strong>and</strong> normal<br />
climate, a sensitivity analysis could be made for a lot <strong>of</strong> different setups.<br />
Here it has however been chosen to look only at case B vs C for the<br />
hot climate. I.e. the investigated parameter is the Net Present Value<br />
<strong>of</strong> the difference in cost between using a SOFC system with an ABS air<br />
conditioner vs a SOFC system with a normal electrical air conditioner.<br />
16 The reason that the annuity <strong>of</strong> the case with pure electricity import from the grid<br />
(left bars) changes with the component lifetime is that it has been assumed that the ECH<br />
has the same lifetime as the ABS <strong>and</strong> SOFC unit (either 5, 10 or 15 years). Their lifetime<br />
could have been changed individually, but this would generate even more graphs.<br />
36
2.4. Distributed Generation (DG)<br />
Net Present Value increase [%]<br />
Sensitivity analysis: SOFC+HW+ABS vs SOFC+WH<br />
30<br />
20<br />
10<br />
0<br />
-10 -5 0 5 10<br />
-10<br />
-20<br />
ECH price<br />
COP_ABS<br />
Electricity price<br />
COP_ECH<br />
Discount rate<br />
Gas price<br />
eta_SOFC<br />
SOFC price<br />
ABS price<br />
-30<br />
Increase in variables [%]<br />
Figure 2.8: The y-axis shows the increase in total savings (Net Present value) by using a<br />
SOFC system with ABS instead <strong>of</strong> importing electricity from the grid <strong>and</strong> using an electrical air<br />
conditioner in the hot climate. The lifetime <strong>of</strong> the system has been set to 10 years.<br />
If all prices are as assumed, <strong>and</strong> the life time <strong>of</strong> all components is 10<br />
years, then the NPV <strong>of</strong> the savings by using the ABS with the SOFC (case<br />
C) rather than only using the SOFC, is 1,5 mil. DKK as mentioned earlier.<br />
A positive value <strong>of</strong> e.g. 10% on the y-axis on figure 2.8 means that the<br />
savings by using the ABS is 10% bigger (i.e. 1,65 mil. DKK)<br />
The efficiency <strong>of</strong> the <strong>fuel</strong> cell is seen to have by far the biggest<br />
influence on the result. A bigger SOFC efficiency makes the ABS less<br />
pr<strong>of</strong>itable because <strong>of</strong> a higher efficiency leaving less waste heat for the<br />
ABS, <strong>and</strong> because the electricity for the ECH (produced by the SOFC)<br />
becomes cheaper.<br />
The gas price <strong>and</strong> the COP <strong>of</strong> the two types <strong>of</strong> chillers are also quite<br />
influential. And the influence <strong>of</strong> the gas price is even more important<br />
than the figure might indicate, since it changes significantly over time<br />
(price can easily change +/-50% from the estimated value), whereas the<br />
COP <strong>of</strong> the ABS <strong>and</strong> ECH is a lot more stable <strong>and</strong> predictable (the real<br />
COP is likely to be within +/- 10% <strong>of</strong> the estimated value).<br />
37
2. MARKET INVESTIGATION<br />
2.4.4 Conclusion<br />
In general both the SOFC <strong>and</strong> the ABS seem to have an economical<br />
potential. The SOFC pr<strong>of</strong>itability depends a lot on the purchase<br />
price, <strong>and</strong> ABS pr<strong>of</strong>itability depends a lot on the gas price <strong>and</strong> SOFC<br />
efficiency. Furthermore it seems that hot climates make the ABS far more<br />
advantageous because <strong>of</strong> the increased usage fraction.<br />
The general tendency is that the addition <strong>of</strong> the SOFC (Case B vs<br />
A) is very pr<strong>of</strong>itable, since the electricity generated by the SOFC is<br />
only 0,4DKK/kWh - about half the price <strong>of</strong> the electricity form the grid<br />
(0,75DKK/kWh). So the total cost is almost cut in halves, <strong>and</strong> 12mil.<br />
DKK is saved over a 10 year period with an original investment <strong>of</strong><br />
around 1,0mil. DKK for the SOFC system. This does however require the<br />
<strong>fuel</strong> cell system to last 10 years, so stack degradation has to be minimized<br />
from today’s level.<br />
But since the yearly savings <strong>of</strong> electricity is 3,0mil. DKK <strong>and</strong> the extra<br />
cost <strong>of</strong> natural gas is 1,5mil. DKK, the purchase price <strong>of</strong> the SOFC (1,0-<br />
1,2mil. DKK) will be earned back within the first year!<br />
If an ABS unit is used, the additional investment (compared to a purely<br />
electrical air conditioner) will be 0,4 mil. DKK, <strong>and</strong> the electricity savings<br />
in 10 years are around 1,9mil. DKK for the hot climate, so this looks very<br />
pr<strong>of</strong>itable with a pay back time or around 1,5 years).<br />
It must, however, be noted that there are a lot <strong>of</strong> assumptions <strong>and</strong> simplifications<br />
in the calculations, such as neglected installation costs, piping,<br />
maintenance, equal selling <strong>and</strong> buying prices <strong>of</strong> electricity <strong>and</strong> nonfluctuation<br />
cooling <strong>and</strong> electricity consumption during the day (the latter<br />
might be solved by a storage <strong>of</strong> cold water <strong>and</strong> electricity).<br />
38
2.5. Conclusion <strong>of</strong> the whole market investigation<br />
2.5 Conclusion <strong>of</strong> the whole market<br />
investigation<br />
From the economical investigations it has been concluded that the two<br />
areas appearing to have the biggest advantage <strong>of</strong> using an absorption<br />
cooling unit in conjunction with a SOFC is the ship APU <strong>and</strong> the hotel<br />
DG. In both these cases it looks like there is a definite market potential<br />
with the pay back time being just below 2 years (although various<br />
assumptions <strong>and</strong> neglecting <strong>of</strong> maintenance, installation costs etc. can<br />
have made the outcome a little too optimistic).<br />
But it seems that the idea <strong>of</strong> combining the two technologies has a<br />
potential, so it has been decided to carry on with the project <strong>and</strong> create a<br />
thermodynamical model <strong>of</strong> the combined system.<br />
39
C H A P T E R<br />
3<br />
COMPONENT DESCRIPTION<br />
3.1 Introduction<br />
3.1.1 EES<br />
The model <strong>of</strong> the SOFC system <strong>and</strong> the absorption cycle is carried<br />
out in Engineering Equation Solver (EES) which is a program that<br />
solves algebraic as well as differential equations. One advantages <strong>of</strong><br />
this program is that the equations can be stated r<strong>and</strong>omly. Another<br />
advantage is that EES provides fluid property functions for a lot <strong>of</strong><br />
different species.<br />
Structure<br />
It is attempted to build up the model by a structure <strong>of</strong> subroutines in<br />
order to have an overview <strong>of</strong> the entire system <strong>and</strong> to reuse components<br />
<strong>and</strong> functions as much as possible. <strong>Ea</strong>ch component in the model<br />
corresponds to a physical unit or a part <strong>of</strong> it. E.g. the evaporator <strong>and</strong><br />
the absorber are modeled as to separate components, but physically they<br />
are integrated as one unit.<br />
Most components are modeled as modules which are placed in<br />
separate files. The equations in a module are called from the main system<br />
file <strong>and</strong> solved simultaneously with equations in other modules, just like<br />
the equation were put all together.<br />
41
3. COMPONENT DESCRIPTION<br />
The helping procedures, on the other h<strong>and</strong>, are solve in a chronological<br />
sequence like normal programming languages. This reduces the time for<br />
solving these equations.<br />
3.1.2 Components<br />
In section 3.2 to 3.14 each component will be described in detail, but first<br />
common properties <strong>of</strong> the components will be described in the following<br />
All <strong>of</strong> the components are modeled as zero dimensional components i.e. the<br />
system can be scaled to any size keeping all extensive variable at the<br />
same ratio. Thus it is necessary to change a lot <strong>of</strong> parameters if the size<br />
<strong>of</strong> the system should have any affect on the system performance. For<br />
instance, the blower efficiency would in reality change a little if the size<br />
<strong>of</strong> the system is changed, but this does not happen automatically in the<br />
model - it can only be done manually by changing the blower efficiency<br />
parameter.<br />
<strong>Ea</strong>ch component has one or more inlets <strong>and</strong> outlets (points) each with<br />
a unique name, e.g. ”DES2 ss,i ” which can be interpreted as ”desorber<br />
number two: strong solution, inlet”. All <strong>of</strong> these points are associated<br />
with a state number. If two different points (normally from two different<br />
components) are associated with the same state number, it means that<br />
those two components are connected through the respective in- <strong>and</strong><br />
outlets. This feature also make it relative easy to build up the system<br />
or reconfigure components in the system. This is described further in<br />
chapter 4.<br />
Fluid properties<br />
It is assumed that the fluid properties does not change in between<br />
components, i.e. that losses in the piping system are neglected.<br />
The entire system consists <strong>of</strong> seven different fluid streams (each<br />
composed <strong>of</strong> one or more species) which are indicated by a specific color<br />
to make it easy to distinguish those from each other, see figure 4.1 page<br />
80 or in appendix G page 293. Some streams might be variants <strong>of</strong> the<br />
same fluid.<br />
42
3.1. Introduction<br />
The seven stream are indicated by their corresponding color in the<br />
following list:<br />
1. Flue gas (including atmospheric air <strong>and</strong> <strong>fuel</strong> input).<br />
2. External heat transfer loops.<br />
3. Domestic hot water.<br />
4. Atmospheric air.<br />
5. Absorption cycle: Refrigerant.<br />
6. Absorption cycle: Weak solution <strong>of</strong> LiBr water.<br />
7. Absorption cycle: Strong solution <strong>of</strong> water-LiBr.<br />
The flue gas stream is used in the components around the SOFC<br />
component (SOFC sub-system) <strong>and</strong> in the heat exchangers connecting it<br />
to the ABS cycles <strong>and</strong> Hot Water heating. These components have been<br />
modeled to accept seven different chemical species: C H 4 , CO, CO 2 , H 2 ,<br />
H 2 O, N 2 <strong>and</strong> O 2 . All seven species are assumed to behave like ideal<br />
gases, i.e. the enthalpy is independent <strong>of</strong> pressure (<strong>and</strong> there are no<br />
phase changes). This can be assumed since the pressure change in the<br />
components is relatively small.<br />
The reference pressure <strong>and</strong> temperature for enthalpy <strong>of</strong> these gasses<br />
are 100 kPa <strong>and</strong> 25 ◦ C respectively. The enthalpy <strong>of</strong> formation is included<br />
in the chemical compounds.<br />
A mixture <strong>of</strong> the species is assumed to be ideal, which means that the<br />
physical property <strong>of</strong> a mixture is the sum <strong>of</strong> properties <strong>of</strong> each species in<br />
the mixture.<br />
The enthalpy flow rate Ḣ at state point ”j” is calculated as the sum <strong>of</strong><br />
mass flow rate times enthalpy <strong>of</strong> species ”k”:<br />
Ḣ j =<br />
7∑<br />
ṁ j,k h j,k (3.1)<br />
k=1<br />
The fluid in the external heat transferring loops <strong>and</strong> domestic hot water is<br />
sub cooled water. A real water fluid property function is applied in these<br />
streams. To keep the water sub cooled, an sufficiently high pressure is<br />
applied.<br />
43
3. COMPONENT DESCRIPTION<br />
The components in the Absorption cycle operate with LiBr <strong>and</strong>/or water.<br />
The Absorption cycle can be split up into two sub cycles: a refrigeration<br />
cycle <strong>and</strong> a solution cycle. The water used in the refrigeration cycle is a<br />
real fluid since the fluid undergo phase transition.<br />
The water-LiBr solution in the solution cycle is also calculated by a<br />
real fluid function ”LiBrH2O”. The function is valid for saturated liquid<br />
only, e.g. the quality qu = 0. Several properties, e.g. pressure <strong>and</strong> heat<br />
capacity are calculated from input <strong>of</strong> temperature <strong>and</strong> the mass fraction<br />
<strong>of</strong> LiBr, w, which must be in the range <strong>of</strong> 0 to about 0,75 1 (can be seen in<br />
phase diagram in appendix B.4.1 page 231).<br />
Since the function only work for saturated liquid, just two state<br />
variables are necessary to define the state. The properties for both<br />
refrigerant <strong>and</strong> the cooling water are determined by the internal EES real<br />
fluid function ”Water”.<br />
General assumptions<br />
All heat flow rates ˙Q <strong>and</strong> power Ẇ are calculated as positive quantities.<br />
It is assumed that the components don’t leak any fluid to the surroundings:<br />
ṁ o = ṁ i (3.2)<br />
Potential <strong>and</strong> kinetic energy is neglected for all components. The<br />
energy required to circulate water in the external heat transferring loops<br />
(including domestic hot water) has been neglected as well. The heat<br />
loss from the components to the surroundings is assumed to be zero if<br />
nothing else is stated, but can be given by a heat loss parameter for each<br />
single component.<br />
Wherever it is feasible, the heat exchangers are assumed to be<br />
configured in counterflow.<br />
1 Very dependent on temperature <strong>and</strong> pressure. The range is valid for the normal<br />
operation <strong>of</strong> an absorption cycle.<br />
44
3.2. Absorber - ABSO<br />
3.2 Absorber - ABSO<br />
In the absorber the strong water-LiBr solution absorbs the refrigerant<br />
which is water. The absorption process is exothermic. The heat from<br />
this process is removed by an external cooling circuit, which is water, see<br />
figure 3.1.<br />
When the weak solution (ws,o) leaves the absorber it is assumed to be<br />
saturated liquid. The strong solution is either a liquid (can be sub cooled)<br />
or in the two phase region. The refrigerant can be either in the two phase<br />
region, saturated vapor, or super heated.<br />
Figure 3.1: Absorber component. Strong solution (ss,i) (rich in LiBr), is absorbed by the<br />
refrigerant (r,i) <strong>and</strong> sent out as weak solution (ws,o). The absorption process is cooled by a<br />
fluid (c,i) <strong>and</strong> (c,o).<br />
At the inlet <strong>of</strong> the absorber, water vapor (at low temperature) <strong>and</strong><br />
strong LiBr solution (at a higher temperature) is mixed. It is quite<br />
difficult to determine whether the water vapor <strong>and</strong> strong LiBr solution<br />
are perfectly mixed just after the inlets, before they become cooled, or<br />
if the mixing happens during the cooling - <strong>and</strong> this is very difficult<br />
to calculate in a Zero dimensional model. In reality there must be<br />
some temperature distribution throughout the absorber, but finding this<br />
temperature distribution is not an easy task, <strong>and</strong> it is not required for<br />
the energy balance, mass balance, state variables (at inlets/outlet) etc.<br />
to work. It is only relevant for designing the heat exchanger part <strong>of</strong><br />
the absorber <strong>and</strong> setting the parameters associated with it. So finding<br />
the temperature distribution has been accomplished by the following<br />
reasoning:<br />
Since the cooling circuit removes energy from the solution, the<br />
temperature around the inlet <strong>of</strong> the solution <strong>and</strong> refrigerant (T st ar t ) must<br />
be larger than (or at least equal to) the outlet temperature (T ws,o ). (This is<br />
confirmed by [20], page 537).<br />
∆T minws,o = T ws,o − T c,o (3.3)<br />
45
3. COMPONENT DESCRIPTION<br />
T [° C ]<br />
T ss , i<br />
T c ,o<br />
T start<br />
ΔT min ,ws , o<br />
T ws ,o<br />
T c ,i<br />
˙Q[kW ]<br />
Figure 3.2: ABSO: The temperature <strong>of</strong> the hot fluid into the absorber is not known fore sure, so<br />
the heat exchanger part is made as co-flow to make sure that no approach temperature difference<br />
is smaller that the one given by ∆T min .<br />
So by modeling the heat transfer in the absorber as a co-flow heat exchanger<br />
(figure 3.2) there should be no doubt that the smallest approach<br />
temperature difference (∆T min ) occurs between the solution outlet <strong>and</strong><br />
the cooling circuit outlet: Due to lack <strong>of</strong> knowledge about the temperature<br />
distribution the effectiveness <strong>of</strong> the heat transfer is not determined<br />
(it is not known which flow has the smaller heat capacity flow, since the<br />
temperature distribution <strong>of</strong> the solution is not known), so for this component,<br />
only ∆T min is calculated.<br />
The amount <strong>of</strong> heat to be removed by the cooling circuit is calculated<br />
by the energy balance, which includes a loss to the surroundings ( ˙Q loss ),<br />
which should be zero (adiabatic component) or positive (heat loss to the<br />
surroundings).<br />
Ḣ ss,i + Ḣ r,i + Ḣ c,i = Ḣ ws,o + Ḣ c,o + ˙Q loss (3.4)<br />
A mass balance <strong>of</strong> H 2 O as well as LiBr is needed, but since the absorber<br />
is connected in a closed loop, they are not given explicitly (in one <strong>of</strong><br />
the components in a closed loop, the mass balance must be omitted to<br />
avoid over specification). So the following two mass balances are given<br />
46
3.2. Absorber - ABSO<br />
implicitly through the desorber:<br />
ṁ ws,o = ṁ ss,i + ṁ r,i (3.5)<br />
ṁ ws,o · w ws,o = ṁ ss,i · w ss,i (3.6)<br />
The pressure losses (given as a negative pressure increases) are defined<br />
as three different ∆P parameters:<br />
p ws,o = p r,i + ∆p r (3.7)<br />
p ws,o = p ss,i + ∆p ss (3.8)<br />
p c,o = p c,i + ∆p c (3.9)<br />
47
3. COMPONENT DESCRIPTION<br />
3.3 Blower<br />
Figure 3.3: Blower component. ”i” is the inlet <strong>and</strong> ”o” is the outlet. Ẇ is the blower power.<br />
It is assumed that no chemical reaction takes place in the blower, so<br />
the mass flow <strong>of</strong> each species out <strong>of</strong> the blower is equal to its mass flow<br />
into the blower. All species have been modeled as ideal gasses. They are<br />
hence in gas phase all the time, <strong>and</strong> the enthalpy only depends on the<br />
temperature, while the entropy also depends on the pressure. The blower<br />
uses an isentropic efficiency to determine the enthalpy <strong>and</strong> temperature<br />
(i=inlet, 2=state just after the compression).<br />
η i s = Ḣ2,i s − Ḣ i<br />
Ḣ 2 − Ḣ i<br />
(3.10)<br />
The blower work is then determined as the enthalpy flow difference<br />
during the compression.<br />
Ẇ = (Ḣ 2 − Ḣ 1 ) (3.11)<br />
The energy balance then includes the parameter ˙Q loss which is the<br />
amount <strong>of</strong> heat lost to the surroundings (assumed to happen after the<br />
compression). So the outlet temperature is determined from the enthalpy<br />
flow in the outlet (o) which will be:<br />
Ḣ o = Ḣ i +Ẇ − ˙Q loss (3.12)<br />
48
3.4. Burner - BURN<br />
3.4 Burner - BURN<br />
Figure 3.4: Catalytic burner component. The <strong>fuel</strong> <strong>and</strong> air inlets are ”i,1” <strong>and</strong> ”i,2” respectively.<br />
Additional <strong>fuel</strong> (C H 4 ) can be added directly at ”CH4,add,i”. ”o” is the exhaust gas outlet.<br />
The burner makes all the combustibles at the inlets react 100% with<br />
oxygen to produce water <strong>and</strong> carbon di<strong>oxide</strong> by the following three<br />
reactions:<br />
C H 4 + 2O 2 → CO 2 + 2H 2 O<br />
CO + 1 2 O 2 → CO 2<br />
H 2 + 1 2 O 2 → H 2 O<br />
∆H o c<br />
∆H o f<br />
∆H o f<br />
= +890,00<br />
kJ<br />
mol<br />
= −282,62<br />
kJ<br />
mol<br />
= −241,82<br />
kJ<br />
mol<br />
(3.13)<br />
(3.14)<br />
(3.15)<br />
The release <strong>of</strong> chemical energy is then translated into temperature <strong>of</strong> the<br />
gasses <strong>and</strong> a heat loss to the surroundings which is set manually:<br />
Ḣ i − Ḣ u − ˙Q loss = 0 (3.16)<br />
The pressure loss over the burner is set manually by the pressure increase<br />
∆p (which will always be negative):<br />
p o = p i + ∆p (3.17)<br />
49
3. COMPONENT DESCRIPTION<br />
3.5 Condenser - COND<br />
Figure 3.5: Condenser component. Refrigerant enters at ”r,i” <strong>and</strong> leaves at ”r,o”. ”c,i” <strong>and</strong><br />
”c,o” are the cooling water in- <strong>and</strong> outlet respectively.<br />
In the Condenser the refrigerant (H 2 O) comes in as either superheated<br />
gas, saturated gas or in the two-phase region. The cooling water facilitates<br />
a phase change <strong>of</strong> the refrigerant which comes out <strong>of</strong> the condenser<br />
as a liquid. (The refrigerant can not be subcooled, since the outlet enthalpy<br />
is found by the stem quality (<strong>and</strong> pressure)).<br />
In case the refrigerant comes in as saturated steam or in the two phase region,<br />
the calculation <strong>of</strong> closest approach temperature difference <strong>and</strong> heat<br />
exchanger effectiveness will be straight forward. But if the refrigerant<br />
comes in as superheated steam (which is the case in this model), things<br />
become a little more complicated:<br />
By far the most likely point for ∆T min to appear is where the<br />
refrigerant becomes saturated steam, but in theory ∆T min could also<br />
appear at the refrigerant inlet (se figure 3.6). So to make sure that the<br />
(closest) approach temperature difference is not specified at a wrong<br />
point, ∆T min is calculated in both inlet, outlet, <strong>and</strong> midpoint (saturated<br />
gas) 2 .<br />
∆T minr,i = T r,i − T c,o (3.18)<br />
∆T minr,o = T r,o − T c,i (3.19)<br />
∆T minmp = T r,mp − T c,mp (3.20)<br />
The effectiveness is equally complicated. Since the closest approach<br />
temperature difference occurs at the midpoint, the effectiveness must<br />
either be specified between the refrigerant inlet <strong>and</strong> the midpoint or<br />
between the refrigerant outlet <strong>and</strong> the midpoint.<br />
2 In reality ∆T minmp should be specified, but EES crashes when this is attempted, so<br />
instead ∆T minr,o is given (a little too high), so that ∆T minmp reaches the relevant value.<br />
∆T minr,i should not be given explicitly, since it depends very much on the degree <strong>of</strong><br />
superheating at the refrigerant inlet.<br />
50
3.5. Condenser - COND<br />
T [° C ]<br />
ΔT min ,r ,i<br />
T r ,o<br />
ΔT min ,r ,o<br />
ΔT min ,mp T c ,o<br />
T c ,i<br />
T r ,i<br />
˙Q[kW ]<br />
Figure 3.6: Condenser: Approach temperature differences are calculated both in the ends <strong>and</strong> at<br />
the middle to make sure that the one being given as a parameter actually is the smallest <strong>of</strong> them.<br />
The problem can be viewed as having two heat exchangers - one<br />
for the superheated region, <strong>and</strong> one for the two-phase region. Both<br />
effectiveness are calculated, <strong>and</strong> the larger <strong>of</strong> them is the one to be<br />
specified (if not the closest approach temperature difference is specified<br />
instead):<br />
ɛ SH = T r,i − T r,mp<br />
T r,i − T c,mp<br />
(3.21)<br />
ɛ 2P = T c,mp − T c,i<br />
T r,mp − T c,i<br />
(3.22)<br />
Where SH = Super Heated region, <strong>and</strong> 2P = Two-Phase region.<br />
The refrigerant midpoint temperature (T r,mp ) is calculated from the<br />
saturation temperature at the given pressure. The cooling water<br />
midpoint temperature (T c,mp ) is calculated from an energy balance<br />
between refrigerant inlet <strong>and</strong> midpoint:<br />
(h c,o − h c,mp ) · ṁ c = (h r,i − h r,mp ) · ṁ r (3.23)<br />
The amount <strong>of</strong> heat to be removed by the cooling circuit is calculated<br />
by the energy balance, which includes a loss to the surroundings ( ˙Q loss ),<br />
which should be zero (adiabatic component) or positive (heat loss to the<br />
51
3. COMPONENT DESCRIPTION<br />
surroundings).<br />
Ḣ r,i + Ḣ c,i = Ḣ r,o + Ḣ c,o + ˙Q loss (3.24)<br />
The mass balance is specified for the refrigerant as well as the coolant.<br />
ṁ r,o = ṁ r,i (3.25)<br />
ṁ c,o = ṁ c,i (3.26)<br />
The pressure losses (given as a negative pressure increases) are defined<br />
as two different ∆p parameters:<br />
p r,o = p r,i + ∆p r (3.27)<br />
p c,o = p c,i + ∆p c (3.28)<br />
52
3.6. Desorber - DES<br />
3.6 Desorber - DES<br />
In the desorber the weak water-LiBr solution enters (either sub cooled or<br />
saturated liquid) <strong>and</strong> is mixed with the solution in the desorber, which<br />
is heated up by the heating water circuit. Hereby the refrigerant (water)<br />
is evaporated, <strong>and</strong> strong solution LiBr (which is saturated) is returned<br />
towards the absorber. See figure 3.7.<br />
Figure 3.7: Desorber component. Weak solution (ws,i) enters the desorber <strong>and</strong> is heated by the<br />
heating water (h,i <strong>and</strong> h,o). Refrigerant in gas phase (r,o) is sent out through an outlet at the<br />
top, while the strong solution (ss,o) leaves at the bottom <strong>of</strong> the desorber.<br />
The desorber is made up by a reservoir <strong>of</strong> solution in which some<br />
heat exchanger tubes with the warm heating water run. On top there is a<br />
gas phase <strong>of</strong> refrigerant. In the model it is assumed that the temperature<br />
is the same throughout the liquid phase <strong>and</strong> the gas phase. So when<br />
the weak LiBr solution enters the reservoir, it instantly becomes perfectly<br />
mixed with the rest <strong>of</strong> the liquid phase.<br />
It is also assumed that the outlet temperature <strong>of</strong> the refrigerant<br />
(superheated steam) is the same as the outlet temperature <strong>of</strong> the solution,<br />
after all, the water has been evaporated from the solution (at which point<br />
they must have the same temperature), <strong>and</strong> no heating or cooling is<br />
assumed to happen to the gas after the evaporation (hence T ss,o = T r,o ),<br />
see figure 3.8.<br />
Since it is assumed that the temperature <strong>of</strong> the solution is the same<br />
throughout the desorber, only the heating water changes temperature.<br />
Hence the closest approach temperature difference appears between<br />
the outlet temperature <strong>of</strong> the heating water (T h,o ) <strong>and</strong> the mutual<br />
temperature <strong>of</strong> the refrigerant <strong>and</strong> solution (T ss,o = T r,o ):<br />
∆T minr,o = T h,o − T ss,o (3.29)<br />
Since only the heating water changes temperature during the heat<br />
exchange process, the effectiveness will be based on the heating water<br />
53
3. COMPONENT DESCRIPTION<br />
T [° C ]<br />
T h , i<br />
T h , o<br />
ΔT min ,r ,o<br />
T ss , o<br />
T r ,o<br />
T ws ,i<br />
˙Q[kW ]<br />
Figure 3.8: Desorber: The solution/gas temperature is assumed to be constant throughout the<br />
desorber. So the closest approach temperature difference will be between the heating water outlet<br />
<strong>and</strong> the common solution temperature.<br />
heat capacity flow:<br />
ɛ = T h,i − T h,o<br />
T h,i − T ss,o<br />
(3.30)<br />
The amount <strong>of</strong> heat to be added by the heating circuit is calculated by<br />
the energy balance, which includes a loss to the surroundings ( ˙Q loss ),<br />
which should be zero (adiabatic component) or positive (heat loss to the<br />
surroundings).<br />
Ḣ ws,i + Ḣ h,i = Ḣ r,o + Ḣ ss,o + Ḣ h,o + ˙Q loss (3.31)<br />
A mass balance is made for H 2 O as well as LiBr (total inlet = total outlet):<br />
ṁ r,o + ṁ ss,o = ṁ ws,i (3.32)<br />
ṁ ss,o · w ss,o = ṁ ws,i · w ws,i (3.33)<br />
were w is the concentration <strong>of</strong> LiBr in the solution. The pressure losses<br />
(given as a negative pressure increases) are defined as three different ∆P<br />
parameters:<br />
p r,o = p ws,i + ∆p r (3.34)<br />
p ss,o = p ws,i + ∆p ss (3.35)<br />
p h,o = p h,i + ∆p h (3.36)<br />
54
3.7. Evaporator - EVAP<br />
3.7 Evaporator - EVAP<br />
Figure 3.9: The evaporator has two sets <strong>of</strong> inlet <strong>and</strong> outlet: refrigerant (r,i <strong>and</strong> r,o) <strong>and</strong> chilled<br />
water (chill,i <strong>and</strong> chill,o).<br />
In the evaporator heat is transferred from an external circuit <strong>of</strong><br />
chilling water to the refrigerant. It is assumed that the refrigerant is in<br />
the two-phase region when it enters the evaporator. The refrigerant in<br />
the outlet can either be saturated gas or in the two-phase region.<br />
The closest approach temperature difference is defined as the temperature<br />
difference between the chilled water outlet <strong>and</strong> the refrigerant inlet,<br />
see figure 3.10.<br />
T [° C ]<br />
T chill , o<br />
T r ,i<br />
ΔT min ,r ,i<br />
T chill ,i<br />
T r ,o<br />
EVAP<br />
˙Q[kW ]<br />
Figure 3.10: Evaporator: The closest approach temperature difference is at the refrigerant inlet.<br />
∆T minr,i = T chill,o − T r,i (3.37)<br />
The effectiveness is determined by the chilled water because it has the<br />
lowest heat capacity flow; both media are water, but the refrigerant<br />
55
3. COMPONENT DESCRIPTION<br />
undergoes a phase transition which by far gives a higher heat capacity<br />
flow.<br />
ɛ = T chill,i − T chill,o<br />
T chill,i − T r,i<br />
(3.38)<br />
The chilling power <strong>of</strong> the evaporator is calculated by the enthalpy<br />
change <strong>of</strong> the chilling water. This change is determined by the energy<br />
balance. The heat ingress from the surroundings defined by the<br />
parameter ˙Q loss , should be either zero or a negative number.<br />
˙Q = Ḣ chill,i − Ḣ chill,o (3.39)<br />
Ḣ r,i + Ḣ chill,i = Ḣ r,o + Ḣ chill,o + ˙Q loss (3.40)<br />
The mass balance is specified for the refrigerant as well as the chilling<br />
water cycle.<br />
ṁ r,o = ṁ r,i (3.41)<br />
ṁ chill,o = ṁ chill,i (3.42)<br />
The pressure losses (given as a negative pressure increases) are defined<br />
as two different ∆P parameters:<br />
p r,o = p r,i + ∆p r (3.43)<br />
p c,o = p c,i + ∆p chill (3.44)<br />
56
3.8. Heat Exchanger - HEX<br />
3.8 Heat Exchanger - HEX<br />
Beside the heat exchangers implicitly appearing in the absorber, condenser<br />
<strong>and</strong> evaporator, three different heat exchanger components (HEXes)<br />
exist:<br />
• Gas-Gas HEX appearing in the SOFC subsystem.<br />
• Water-Gas HEX for transferring heat from the exhaust gas to<br />
heating circuits.<br />
• Solution HEX for internal heat exchange between strong <strong>and</strong> weak<br />
LiBr solution.<br />
Figure 3.11: Heat exchangers (all counter flow). Types: Gas-Gas, Water-Gas, <strong>and</strong> Solution<br />
heat exchangers<br />
T [° C ]<br />
T hot , i<br />
ΔT min ,hot ,i<br />
T hot , o<br />
T cold ,o<br />
ΔT min ,hot ,o<br />
T cold ,i<br />
HEX<br />
˙Q[kW ]<br />
Figure 3.12: Heat Exchangers: Closest approach temperature difference can appear in either<br />
end.<br />
57
3. COMPONENT DESCRIPTION<br />
The general working principle is the same for all <strong>of</strong> them - only the media<br />
differ. None <strong>of</strong> the media experience phase changes, so the definition <strong>of</strong><br />
approach temperature differences <strong>and</strong> efficiencies are straight forward.<br />
The effectiveness is calculated in both ends, <strong>and</strong> the larger <strong>of</strong> them is<br />
the valid one. Approach temperature differences are also calculated in<br />
both ends, <strong>and</strong> the smaller <strong>of</strong> them is the closest approach temperature<br />
difference.<br />
The indices are different for the three heat exchanger types, but the<br />
general way <strong>of</strong> determining approach temperature difference <strong>of</strong> a hot<br />
<strong>and</strong> a cold stream is:<br />
∆T mincold,i = T hot,o − T cold,i (3.45)<br />
∆T mincold,o = T hot,i − T cold,o (3.46)<br />
The effectiveness for the cold <strong>and</strong> the hot stream respectively are defined<br />
as:<br />
ɛ cold = T cold,o − T cold,i<br />
T hot,i − T cold,i<br />
(3.47)<br />
ɛ hot = T hot,o − T hot,i<br />
T cold,i − T hot,i<br />
(3.48)<br />
An energy balance is specified for each heat exchanger, including the<br />
possibility for specifying a heat loss to the surroundings ( ˙Q loss ):<br />
Ḣ cold,i + Ḣ hot,i = Ḣ cold,o + Ḣ hot,o + ˙Q loss (3.49)<br />
For the Gas-Gas HEX <strong>and</strong> Water-Gas HEX, the specific enthalpies are<br />
calculated from the temperature <strong>and</strong> pressure, but for the Solution Hex,<br />
the enthalpy function is only valid for saturated liquid. So in the latter,<br />
the specific heat capacity has been calculated (at the saturated state) for<br />
the given temperature <strong>and</strong> concentration. It has then been assumed that<br />
c p doesn’t change with temperature in the sub cooled area:<br />
h j = h(T = T j , p = p j ) (GGHE X & W GHE X ) (3.50)<br />
∆h i→o = c p (T = T sat , w = w i ) · (T o − T i ) (SHE X ) (3.51)<br />
The mass balance is specified for the two flows.<br />
ṁ cold,o = ṁ cold,i (3.52)<br />
ṁ hot,o = ṁ hot,i (3.53)<br />
58
3.8. Heat Exchanger - HEX<br />
The pressure losses (given as a negative pressure increases) are defined<br />
as two different ∆P parameters:<br />
p cold,o = p cold,i + ∆p cold (3.54)<br />
p hot,o = p hot,i + ∆p hot (3.55)<br />
59
3. COMPONENT DESCRIPTION<br />
3.9 Mixer - MIX<br />
There are three mixer components:<br />
• one for exhaust gas (from the SOFC)<br />
• one for the LiBr solution (in the ABS)<br />
• one for the water/steam (in the ABS)<br />
They all work the same basic way, just with different species.<br />
No chemical reaction takes place in the mixer, so the mass flow <strong>of</strong> each<br />
species (j) out is the sum <strong>of</strong> the two mass flows <strong>of</strong> that species into the<br />
component.<br />
ṁ o,j = ṁ i ,1,j + ṁ i ,2,j (3.56)<br />
The mixer is adiabatic, but since the temperature in the two inlets can be<br />
different, an energy balance is applied to calculate the temperature in the<br />
outlet.<br />
Ḣ o = Ḣ i ,1 + Ḣ i ,2 (3.57)<br />
The pressure at the two inlets can be different (due to other components<br />
in the system), so the component includes two different pressure loss<br />
parameters (<strong>of</strong> which none may be positive).<br />
p o = p i ,1 + ∆p 1 (3.58)<br />
p o = p i ,2 + ∆p 2 (3.59)<br />
60
3.10. Pre Reformer - PR<br />
3.10 Pre Reformer - PR<br />
Figure 3.13: Pre Reformer component<br />
The most important function <strong>of</strong> the pre reformer is to break down<br />
large carbon chains into methane, hydrogen, <strong>and</strong> carbon <strong>oxide</strong>s. All the<br />
components in the model have, however, only been made to accept 7<br />
different species (not including other hydro carbons than C H 4 ). So in this<br />
model, the pre reformer only reforms methane into carbon <strong>oxide</strong>s <strong>and</strong><br />
hydrogen by the ”Reforming” <strong>and</strong> ”Water Gas Shift” process:<br />
C H 4 + H 2 O → CO + 3H 2<br />
CO + H 2 O ⇋ CO 2 + H 2<br />
∆H ◦ f<br />
∆H ◦ f<br />
kJ<br />
= +206,10<br />
mol<br />
kJ<br />
= −41,16<br />
mol<br />
(3.60)<br />
(3.61)<br />
The degree to which these two reactions occur, is set by the two<br />
parameters ´´FR´´ (Fraction <strong>of</strong> Reforming) <strong>and</strong> ”FW” (Fraction <strong>of</strong> Water<br />
gas shift). FR determines how many times the reforming process runs<br />
per molecule <strong>of</strong> C H 4 that is sent into the pre reformer:<br />
F R =<br />
ṙre f<br />
ṅ C H4 ,i<br />
(3.62)<br />
FW determines how many times the water gas shift reaction runs per<br />
molecule <strong>of</strong> CO present after the reforming process<br />
FW =<br />
ṙ W GS<br />
ṙ re f + ṅ CO,i<br />
(3.63)<br />
Since reforming is endothermic while water gas shift is exothermic, the<br />
temperature can either raise or fall during reformation, depending on<br />
how large FW <strong>and</strong> FR are relative to each other. The pressure loss is<br />
given by the parameter ∆p.<br />
p o =p i + ∆p (3.64)<br />
61
3. COMPONENT DESCRIPTION<br />
The energy balance includes the heat loss to the surroundings, which is<br />
set manually by the parameter ˙Q loss :<br />
Ḣ 2 = Ḣ 1 − ˙Q loss (3.65)<br />
62
3.11. Pump - PUMP<br />
3.11 Pump - PUMP<br />
Figure 3.14: LiBr solution pump<br />
The pump increases the pressure <strong>of</strong> the LiBr solution which is<br />
assumed incompressible. The enthalpy <strong>of</strong> the corresponding isentropic<br />
process is calculated from the density at the inlet <strong>and</strong> the pressure<br />
difference:<br />
∆h i s = ∆p<br />
ρ i<br />
(3.66)<br />
The actual enthalpy change is determined by the isentropic efficiency <strong>of</strong><br />
the pump:<br />
∆h = ∆h i s<br />
η<br />
(3.67)<br />
The heat capacity, which is evaluated at the inlet is used to determine the<br />
temperature at the outlet where the solution is sub cooled (which means<br />
that the LiBr function is incapable <strong>of</strong> evaluating the temperature):<br />
T o = T i + ∆h<br />
c p,i<br />
(3.68)<br />
The pumping power is calculated from the actual enthalpy change:<br />
Ẇ = m˙<br />
i ∆h (3.69)<br />
The enthalpy flow at the outlet is calculated from the pumping power<br />
<strong>and</strong> the heat losses to the surroundings by the energy balance:<br />
Ḣ o = Ḣ i +Ẇ − ˙Q loss (3.70)<br />
The mass is conserved <strong>and</strong> the composition remains the same:<br />
ṁ o = ṁ i (3.71)<br />
w o = w i (3.72)<br />
63
3. COMPONENT DESCRIPTION<br />
3.12 Solid Oxide Fuel Cell - SOFC<br />
Figure 3.15: SOFC component<br />
The SOFC is modeled as a number <strong>of</strong> stacks (n st ack ) each consisting <strong>of</strong><br />
a number <strong>of</strong> <strong>cells</strong> (n cell ). Electricity wise the <strong>cells</strong> are connected in series.<br />
This means that the voltage <strong>of</strong> the stack will be n cell times bigger than<br />
the cell voltage. The total power <strong>of</strong> the SOFC is just the number <strong>of</strong> stacks<br />
times the power <strong>of</strong> each stack:<br />
Ẇ SOFC = n st ack ·Ẇ st ack (3.73)<br />
Ẇ st ack = n cell I cell V cell (3.74)<br />
Gas flow wise the stacks can be connected in parallel or in series. If<br />
the stacks are in series, they can use a higher percentage <strong>of</strong> the <strong>fuel</strong>,<br />
since cell number two will be fed with the exhaust from the first cell.<br />
In parallel connection, however, the power will be bigger, since each cell<br />
gets its own gas. And since SOFCs are still quite expensive, the extra <strong>fuel</strong><br />
utilization <strong>of</strong> the series connection is probably not enough to compensate<br />
for the lower electricity generation per kg <strong>fuel</strong> cell. So in the model the<br />
stacks are coupled in parallel.<br />
The model has an anode side, where all the <strong>fuel</strong>, water <strong>and</strong> CO 2 is<br />
sent in, <strong>and</strong> a cathode side, where the air is sent in. The air is modeled as<br />
consisting <strong>of</strong> 79% Nitrogen <strong>and</strong> 21% Oxygen (volume fraction).<br />
Some <strong>of</strong> the heat generated by the chemical reactions in the SOFC can<br />
be set to be lost to the surroundings ( ˙Q loss ), whereas the rest will lead<br />
to a temperature increase <strong>of</strong> the gasses at the outlet. In reality the outlet<br />
temperature <strong>of</strong> the anode side is different from that <strong>of</strong> the cathode side,<br />
but since the model is zero dimensional the temperature distribution in<br />
the cell has not been calculated, <strong>and</strong> the outlet temperatures have instead<br />
been set equal to each other.<br />
64
3.12. Solid Oxide Fuel Cell - SOFC<br />
The temperature into the SOFC must be in the region 650 ◦ C to 700 ◦ C<br />
since the catalyst must be hot enough for the electrochemical reaction to<br />
take place. At the same time the temperature must not be too high either,<br />
since that will significantly increase the degradation <strong>of</strong> the cell. So the<br />
exhaust temperature must be around 750 ◦ C to 800 ◦ C.<br />
When calculating certain variables in the cell, such as ASR <strong>and</strong> Gibbs free<br />
energy, the mean temperature <strong>of</strong> the cell must be used. This has been set<br />
to 30 ◦ C below the outlet temperature <strong>of</strong> the cell, since this seems to give<br />
data consistent with that <strong>of</strong> the Topsoe Fuel Cell models.<br />
3.12.1 Chemical reactions<br />
The <strong>fuel</strong> cell can run on three different <strong>fuel</strong>s: C H 4 , CO, <strong>and</strong> H 2 . When<br />
recycling <strong>and</strong>/or pre reforming is used, all <strong>of</strong> those will be present at the<br />
inlet <strong>of</strong> the SOFC (anode side).<br />
Three chemical reactions take place. First all the C H 4 is transformed by<br />
internal steam reforming (which is an endothermal reaction):<br />
C H 4 + H 2 O → CO + 3H 2<br />
∆H ◦ f<br />
= +206,10<br />
kJ<br />
mol<br />
(3.75)<br />
In the Water Gas Shift reaction (WGS) the Carbon mon<strong>oxide</strong> <strong>and</strong> water<br />
is turned into Carbon di<strong>oxide</strong> <strong>and</strong> Hydrogen (which is an exothermal<br />
reaction):<br />
CO + H 2 O ⇋ CO 2 + H 2<br />
∆H ◦ f<br />
= −41,16<br />
kJ<br />
mol<br />
(3.76)<br />
The electrochemical reaction transforms hydrogen <strong>and</strong> oxygen into<br />
water, <strong>and</strong> is the only reaction generating electricity in the <strong>fuel</strong> cell.<br />
H 2 + 1 2 O 2 ⇋ H 2 O<br />
∆H ◦ f<br />
= −241,82<br />
kJ<br />
mol<br />
(3.77)<br />
At the same time a chemical equilibrium is assumed to exist in the<br />
cell between the species in the WGS reaction (CO, CO 2 , H 2 , <strong>and</strong><br />
H 2 O). The equilibrium constant (K W GS is determined from the average<br />
65
3. COMPONENT DESCRIPTION<br />
cell temperature <strong>and</strong> the free Gibbs energy <strong>of</strong> the species in the<br />
electrochemical reaction.<br />
K W GS = ṅCO 2 ṅ H2<br />
ṅ CO ṅ H2 O<br />
(3.78)<br />
K W GS = e −∆g<br />
RTav (3.79)<br />
∆g = (g CO2 + g H2 ) − (g CO + g H2 O) (3.80)<br />
One more equation comes from the assumption that the C H 4 is not present<br />
at the outlet (meaning that reforming runs 100%).<br />
The last equation is given by the <strong>fuel</strong> Utilization factor U f , which is an<br />
input parameter. This factor states how much H 2 is used in the electrochemical<br />
reaction (ṙ Elk ) divided by the much H 2 that would be available<br />
for the electrochemical reaction, if all the C H 4 <strong>and</strong> CO in the anode inlet<br />
was reformed <strong>and</strong> water gas shifted into H 2 :<br />
U f =<br />
ṙ Elk<br />
4ṅ C H4,i + ṅ CO,i + ṅ H2,i<br />
(3.81)<br />
Together with the conservation <strong>of</strong> mass (for each element), this is enough<br />
to determine composition <strong>of</strong> the outlet gas. Nitrogen <strong>and</strong> oxygen leaves<br />
the SOFC at the cathode side, whereas all other species leaves on the<br />
anode side.<br />
OC ratio<br />
If the concentration <strong>of</strong> Carbon atoms at the anode side <strong>of</strong> the SOFC<br />
becomes too large relative to the concentration <strong>of</strong> Oxygen atoms on<br />
the anode side, there is a risk that Carbon will deposit in the cell (this<br />
includes the O- <strong>and</strong> C- content in all the different species at the anode<br />
side). So it is desirable that there is at least twice as much Oxygen as<br />
Carbon [25].<br />
The ratio is controlled by altering the degree <strong>of</strong> anode recycling, since<br />
more recycling means more Oxygen atoms into the anode side (from CO,<br />
CO 2 , <strong>and</strong> H 2 O). So it is desired that OC r atio ≧ 2:<br />
ṅ C H4 ,ai + ṅ CO,ai + ṅ CO2 ,ai<br />
OC r atio =<br />
ṅ CO,ai + 2ṅ CO2 ,ai + 2ṅ H2 O,ai + 2ṅ O2 ,ai<br />
(3.82)<br />
66
3.12. Solid Oxide Fuel Cell - SOFC<br />
The electrochemical process<br />
Equation 3.77 is a redox-reaction which can be split op into to halfreactions<br />
for anode (oxidation) <strong>and</strong> cathode (reduction) respectively.<br />
H 2 +O 2− → H 2 O + 2e − (anode) (3.83)<br />
1<br />
2 O 2 + 2e − → O 2− (cathode) (3.84)<br />
”The free Gibbs energy” or ”the chemical potential” is an expression for<br />
the maximum possible ”non-expansion work” (e.g. electrical work) a<br />
chemical reaction can give. The (free) Gibbs energy can be expressed as:<br />
g = h − Ts (3.85)<br />
where ”h” is the molar specific enthalpy, ”T ” is the absolute temperature,<br />
<strong>and</strong> ”s” is the molar specific entropy. The Gibbs energy is only<br />
determined for the electrochemical reaction (equation 3.77), since this<br />
is the only reaction creating electrical power in the cell (the reforming<br />
<strong>and</strong> WGS does not contribute to the electrical power generation). The<br />
Gibbs energy must be evaluated at the actual (average) temperature in<br />
the cell according to [33]. As mentioned earlier, the average temperature<br />
is assumed to be a little (30 ◦ C) below the exhaust temperature <strong>of</strong> the cell.<br />
The Gibbs energy per mole <strong>of</strong> H 2 is found as:<br />
∆g c = g H2 O(T av ) − g H2 (T av ) − 1 2 g O 2<br />
(T av ) (3.86)<br />
The temperature in the parentheses state the temperature which the<br />
Gibbs energy is evaluated at. The ideal theoretical voltage that can be<br />
obtained by the cell is given by the Nernst potential (V Ner nst ), which<br />
depends on Faraday’s constant (F = 96485,3 C ), the number <strong>of</strong> electrons<br />
mol<br />
per reaction (two), the Gibbs free energy <strong>of</strong> the reaction, <strong>and</strong> the partial<br />
pressure <strong>of</strong> the three species participating in the electrochemical reaction.<br />
The bigger the concentration <strong>of</strong> the reactants, <strong>and</strong> the smaller the<br />
concentration <strong>of</strong> the products, the bigger the Nernst potential will be.<br />
⎛<br />
V Ner nst = − ∆g c<br />
2F − RT<br />
2F ln ⎜<br />
⎝<br />
p H2<br />
p 0<br />
p H2 O<br />
p 0<br />
√<br />
pO2<br />
p 0<br />
⎞<br />
⎟<br />
⎠ (3.87)<br />
67
3. COMPONENT DESCRIPTION<br />
Losses<br />
There are always losses in real processes, <strong>and</strong> the actual voltage <strong>of</strong> the<br />
cell will hence be smaller than the theoretical Nernst voltage. The real<br />
cell voltage becomes:<br />
V cell = V Ner nst − i d · ASR (3.88)<br />
With i d being the current density (current per cell area) A/m 2 <strong>and</strong> ASR<br />
being the Area Specific Resistance Ωm 2 . The ASR is meant to include the<br />
four kinds <strong>of</strong> losses which appear in the <strong>fuel</strong> cell [23]:<br />
• Ohmic resistance: There is a certain resistance in the electrodes,<br />
which will decrease when the temperature <strong>of</strong> the cell is increased.<br />
• Fuel cross over <strong>and</strong> internal currents: If there is a leakages a little<br />
part <strong>of</strong> the <strong>fuel</strong> might be wasted by passing through the electrolyte<br />
so the chemical reaction occurs at the cathode side whereby no<br />
electricity is generated from its reaction. Since the electrolyte has<br />
a finite electrical resistance a small current can pass through it.<br />
• Activation losses: It takes a certain amount <strong>of</strong> energy (electrochemical<br />
potential) to make the electrochemical reaction happen. The rate<br />
<strong>of</strong> the reaction on the surface <strong>of</strong> the catalyst depends on the current<br />
density <strong>and</strong> the temperature. A high temperature will result in low<br />
activation loss.<br />
• Concentration loss: There is a resistance against diffusion <strong>of</strong> the<br />
reactants (H 2 <strong>and</strong> O 2 ) as well as the product H 2 O [33], which<br />
depends on their concentrations. The more reactants, <strong>and</strong> the less<br />
products, the smaller the concentration loss will be.<br />
So in reality the ASR depends on the Temperature <strong>of</strong> the cell, the<br />
current density <strong>and</strong> the concentrations. In this report is does, however<br />
only depend on the temperature <strong>of</strong> the cell. The ASR function has<br />
been constructed by fitting an exponential curve to measurements from<br />
Topsoe Fuel Cell <strong>and</strong> multiplying it with a factor a little different from 1,<br />
in order to prevent classified data from being published.<br />
ASR = 0,0280e −0,0083·T SOFC ,av<br />
Ωm 2 (3.89)<br />
So if the current draw is large, the cell voltage will be low <strong>and</strong> visa versa.<br />
68
3.12. Solid Oxide Fuel Cell - SOFC<br />
Current <strong>and</strong> power<br />
The electric current will be proportional to the mole flow <strong>of</strong> the reacted<br />
Hydrogen, the number <strong>of</strong> electrons per mole Hydrogen, <strong>and</strong> Faraday’s<br />
constant. And the current becomes:<br />
I SOFC =ṅ H2 ,c 2F (3.90)<br />
i d = I SOFC<br />
A cell<br />
(3.91)<br />
The electrical gross power <strong>of</strong> the cell will then be:<br />
Ẇ SOFC = V SOFC I SOFC (3.92)<br />
A control volume is put around the SOFC component, <strong>and</strong> the first law<br />
<strong>of</strong> thermodynamics is applied on this. Potential <strong>and</strong> kinetic energy is<br />
neglected, so the energy balance becomes as follows:<br />
Ḣ i − Ḣ o −Ẇ SOFC − ˙Q loss = 0 (3.93)<br />
Ḣ i <strong>and</strong> Ḣ o are the total enthalpy flow rates for in- <strong>and</strong> out-lets (cathode<br />
plus anode). Hereby the enthalpy <strong>and</strong> hence temperature at the outlet<br />
can be determined. ˙Q loss is the heat lost directly to the surroundings.<br />
Pressure losses<br />
The pressure losses in the anode <strong>and</strong> cathode can be different, <strong>and</strong> are set<br />
by the parameters ∆p a <strong>and</strong> ∆p c .<br />
p a,o =p a,i + ∆p SOFC ,a (3.94)<br />
p c,o =p c,i + ∆p SOFC ,c (3.95)<br />
69
3. COMPONENT DESCRIPTION<br />
3.13 Splitter - SP<br />
There are three splitter components:<br />
• one for exhaust gas (from the SOFC)<br />
• one for the LiBr solution (in the ABS)<br />
• one for the water/steam (in the ABS)<br />
They all work the same basic way, just with different species.<br />
No chemical reaction takes place in the splitter, so the mass flow <strong>of</strong> each<br />
species (j) into the component is the sum <strong>of</strong> the two mass flows <strong>of</strong> that<br />
species out the component. The fraction <strong>of</strong> the inlet flow which goes to<br />
the first outlet is termed α (<strong>and</strong> the fraction for the other outlet then becomes<br />
(1-α)):<br />
ṁ o,1,j = ṁ i ,j α (3.96)<br />
ṁ o,2,j = ṁ i ,j (1 − α) (3.97)<br />
The mixer is adiabatic <strong>and</strong> hence the temperature <strong>of</strong> the two outlet are<br />
equal to the inlet temperature:<br />
T o,1 = T i (3.98)<br />
T o,2 = T i (3.99)<br />
The pressure at the two outlets can be different (due to other<br />
components in the system), so the splitter includes two different pressure<br />
loss parameters (<strong>of</strong> which none may be positive).<br />
p o,1 = p i + ∆p 1 (3.100)<br />
p o,2 = p i + ∆p 2 (3.101)<br />
70
3.14 Cooling Tower - TOWER<br />
3.14. Cooling Tower - TOWER<br />
Removing heat (at a temperature not too far from the ambient temperature)<br />
to the surrounding air can be somewhat difficult, expensive <strong>and</strong><br />
energy consuming (<strong>and</strong> perhaps water consuming). Three popular solutions<br />
exist:<br />
air,o<br />
air,o<br />
air,o<br />
DRY<br />
WET<br />
SEMI<br />
w,add<br />
w,add<br />
w,o<br />
FAN<br />
air,mp<br />
air,i<br />
w,i<br />
w,o<br />
FAN<br />
air,mp<br />
air,i<br />
w,i<br />
w,o<br />
FAN<br />
air,mp<br />
air,i<br />
w,i<br />
Figure 3.16: The three variants <strong>of</strong> the Cooling Tower component. w = water, i = inlet, o = outlet,<br />
mp = midpoint (after fan at the air side) <strong>and</strong> w.add = water addition.<br />
• A Dry Cooling Tower, which only consumes power for driving<br />
a fan to send ambient air over tubes containing the fluid to be<br />
cooled. A dry cooler can, however only cool down the fluid to a<br />
temperature above the ambient temperature.<br />
• A Wet Cooling Tower, which utilizes the enthalpy <strong>of</strong> evaporation<br />
<strong>of</strong> water for cooing the fluid. The water <strong>and</strong> air is in direct contact,<br />
which increases the heat transfer. Furthermore, by using this<br />
component it is possible to cool down the fluid to below ambient<br />
temperature. A wet tower has the advantage, that it consumes<br />
(less) power for driving a fan than a dry tower, since a smaller air<br />
flow is needed, but on the downside it has a water consumption to<br />
make up for the water lost in evaporation.<br />
• A semi-wet Cooler mixing the two types above by spraying a water<br />
mist over the tubes <strong>of</strong> the dry cooling tower to use the enthalpy <strong>of</strong><br />
evaporation. This has the advantage that more water can be added<br />
during hot weather, while the cooler can run in dry cooling mode<br />
during cold weather. But since the fluid inside the tubes <strong>and</strong> the air<br />
71
3. COMPONENT DESCRIPTION<br />
is not in direct contact there will be a temperature difference (over<br />
the tubes), <strong>and</strong> the outlet temperature <strong>of</strong> the fluid will be higher<br />
than for the Wet Cooling Tower.<br />
In this project only the Dry Cooling Tower <strong>and</strong> the Wet Cooling<br />
Tower will be investigated <strong>and</strong> modeled since they constitute the two<br />
extremities.<br />
3.14.1 Dry Cooling Tower - TOWERd<br />
The heat transmission <strong>of</strong> the dry tower works exactly as the general heat<br />
exchanger component (see section 3.8 page 57). The only new thing is<br />
that the cold fluid is humid air with a humidity at the inlet equal to that<br />
<strong>of</strong> the ambient air, while the outlet air has the same absolute humidity as<br />
inlet air (i.e. the relative humidity changes).<br />
T [° C ]<br />
T w ,o<br />
T w ,i<br />
ΔT min ,w , i<br />
ΔT min ,w , o<br />
T air , o<br />
T air ,i<br />
TOWERd<br />
˙Q[kW ]<br />
Figure 3.17: Dry Tower: ∆T min,w,o (left side) specifies how much larger the water outlet<br />
temperature is than the (ambient) air inlet temperature. ∆T min,w,i (right side) specifies how<br />
much colder the outlet air is relative to the water inlet temperature<br />
.<br />
The electricity consumption <strong>of</strong> the fan in the tower is calculated by<br />
the volume flow <strong>of</strong> the air times the (explicitly given) pressure loss in the<br />
72
3.14. Cooling Tower - TOWER<br />
tower divided by the efficiency <strong>of</strong> the fan:<br />
Ẇ f an = ∆p · ˙V air,i<br />
η f an<br />
(3.102)<br />
The energy balance <strong>of</strong> the component includes the fan power (since<br />
it must be assumed that all <strong>of</strong> the power sent into the fan will be<br />
transformed into heat in the air):<br />
Ḣ air,i + Ḣ w,i +Ẇ f an = Ḣ air,o + Ḣ w,o (3.103)<br />
The variable (W Q r atio ) expresses how much power the fan consumes relative<br />
to how big a cooling service the tower delivers to the water circuit,<br />
since this provides an easy way to compare the power consumption to<br />
that <strong>of</strong> commercial dry coolers.<br />
W Q r atio =<br />
Ẇ f an<br />
˙Q cool<br />
(3.104)<br />
˙Q cool = Ḣ w,i − Ḣ w,o (3.105)<br />
3.14.2 Wet Cooling Tower - TOWERw<br />
The Wet Tower also has air at ambient temperature <strong>and</strong> humidity coming<br />
in at the inlet, but since water is evaporated, the outlet temperature<br />
<strong>of</strong> water <strong>and</strong> air is lower than for the Dry Tower (for a given ambient<br />
temperature).<br />
The tower is made in three steps:<br />
1. Compression <strong>of</strong> the inlet air<br />
2. Evaporation <strong>of</strong> water.<br />
3. Addition <strong>of</strong> water to make up for the evaporation water loss.<br />
1. First the fan slightly compresses the air (to produce the air flow), which<br />
increases the pressure <strong>and</strong> temperature <strong>of</strong> the air (while the absolute<br />
humidity is kept constant):<br />
Ẇ f an = ∆p · ˙V air,i<br />
η f an<br />
(3.106)<br />
73
3. COMPONENT DESCRIPTION<br />
air,mp<br />
air,i<br />
ΔTmin,a,o<br />
w,i<br />
w,o<br />
wb<br />
air,o<br />
w,o<br />
Figure 3.18: WET Tower: The fan increases the temperature <strong>of</strong> the air (air,i → air,mp), this<br />
process has been exaggerated on the figure, since the temperature increase in reality is quite<br />
small. The water outlet temperature lays at a point ɛ wb down from air,mp to wb. The air does<br />
not follow the path <strong>of</strong> the arrow from air,mp to wb on its way to saturation. The arrow only<br />
shows how the water outlet temperature is found. The air becomes saturated at the temperature:<br />
T air,o = T w,i − ∆T min,a,o , which should be in the range T w,o
3.14. Cooling Tower - TOWER<br />
The air could ideally come out at a temperature equal to the water inlet<br />
temperature, but due to resistances, heat transports, mixing etc. the real<br />
outlet temperature <strong>of</strong> the air is expected to be somewhat lower. This is<br />
modeled by means <strong>of</strong> the approach temperature difference ∆T minair,o :<br />
∆T minair,o = T w,i − T air,o (3.108)<br />
3. Since some <strong>of</strong> the water in the water circuit has been lost to the air<br />
during the evaporation process, some new water is added (ṁ add ).<br />
A mass balance is made for each <strong>of</strong> the steps for both the water flow<br />
<strong>and</strong> air flow. The overall mass balances becomes:<br />
ṁ w,o = ṁ w,i (3.109)<br />
ṁ air,o = ṁ air,i + ṁ w,add (3.110)<br />
An energy balance is also added for each step:<br />
Ḣ air,i +Ẇ f an = Ḣ air,mp pressurizing (3.111)<br />
Ḣ air,mp + Ḣ w,i = Ḣ air,o + Ḣ w,mp evaporation (3.112)<br />
Ḣ w,mp + Ḣ w,add = Ḣ w,o water side refill (3.113)<br />
The variable (W Q r atio ) expresses how much power the fan consumes<br />
relative to how big a cooling service the tower delivers to the water<br />
circuit.<br />
W Q r atio =<br />
Ẇ f an<br />
˙Q cool<br />
(3.114)<br />
˙Q cool = Ḣ w,i − Ḣ w,o (3.115)<br />
75
3. COMPONENT DESCRIPTION<br />
3.15 Expansion valve - VA/VB<br />
Figure 3.19: The expansion valve has a single inlet <strong>and</strong> outlet.<br />
The expansion valve reduces the pressure <strong>of</strong> the incoming fluid. If the<br />
heat loss to the surroundings is zero, the process is isenthalpic.<br />
Ḣ 2 = Ḣ 1 − ˙Q loss (3.116)<br />
The mass is conserved <strong>and</strong> the composition remains the same.<br />
ṁ o = ṁ i (3.117)<br />
w o = w i (3.118)<br />
The pressure difference is governed by other components, <strong>and</strong> thus no<br />
pressure loss is defined for the valves.<br />
There are two different types <strong>of</strong> valves - one for refrigerant (water)<br />
<strong>and</strong> one for water-LiBr solution. The latter has two variants. The<br />
difference <strong>of</strong> the three valves will be described in the following<br />
subsections.<br />
3.15.1 Expansion valve for refrigerant - VA<br />
This valve h<strong>and</strong>les pure water only <strong>and</strong> hence it can be assumed that<br />
the outlet <strong>of</strong> the valve will always end up inside the two-phase region as<br />
long as the entering fluid is saturated liquid.<br />
3.15.2 Expansion valve for LiBr solution - VB<br />
Calculating the enthalpy at the outlet is always straight forward, since<br />
the only enthalpy change in the component comes from ˙Q loss (which will<br />
<strong>of</strong>ten be set to zero). But the temperature at the outlet can be difficult to<br />
find, since the LiBr function only works for saturated liquid.<br />
The fluid in the LiBr solution circuit will not always be saturated<br />
liquid when entering the expansion valves. Thus there are three<br />
76
3.15. Expansion valve - VA/VB<br />
possibilities - the fluid can either end up as sub cooled liquid, as saturated<br />
liquid, or in the two-phase region. In order to h<strong>and</strong>le this, two different<br />
variants <strong>of</strong> valves have been modeled. (If the fluid outlet is saturated<br />
liquid, both models are valid).<br />
Sub cooled outlet<br />
First the saturation temperature at the outlet pressure (<strong>and</strong> concentration)<br />
is found. Then the heat capacity (evaluated at the saturated state) is<br />
used in order to calculated the actual temperature at the outlet:<br />
T o = T sat + h o − h sat<br />
c p,sat<br />
(3.119)<br />
In order to make sure that this variant is the one to use, it is necessary to<br />
check that the outlet state is in fact subcooled. This is done by ∆h chk,SC<br />
which is defined as:<br />
∆h chk,SC = h sat − h o (3.120)<br />
If ∆h chk,SC is positive the outlet is sub cooled <strong>and</strong> the component variant<br />
is valid. If ∆h chk,SC is negative, the other variant <strong>of</strong> VB must be used.<br />
Two-phase outlet<br />
This variant is to be used if the enthalpy at the outlet is larger than the<br />
saturation enthalpy at the outlet pressure <strong>and</strong> concentration. ∆h chk,2P is<br />
used to check this (notice that it is defined oppositely <strong>of</strong> ∆h chk,SC ):<br />
∆h chk,2P = h o − h sat (3.121)<br />
If ∆h chk,2P is positive this component variant is valid <strong>and</strong> the outlet<br />
temperature is set equal to the saturation temperature at the outlet<br />
pressure:<br />
T o = T sat (3.122)<br />
77
C H A P T E R<br />
4<br />
SYSTEM DESCRIPTION<br />
4.1 General<br />
The components described in the previous chapter have been assembled<br />
in order to make a model <strong>of</strong> SOFC system integrated with an absorption<br />
cooling unit, see figure 4.1. The system can be divided into subsystems:<br />
SOFC subsystem, absorption subsystem <strong>and</strong> cooling tower.<br />
The absorption cycle can be either a Singe Stage or a Double Stage. In<br />
addition it is possible to supply the double stage cycle with heat input in<br />
two different points - this is called Dual Heat. Enlarged layout diagrams<br />
<strong>of</strong> all three system configurations are seen in appendix G page 293.<br />
<strong>Ea</strong>ch <strong>of</strong> the subsystems will be described in the following sections as<br />
well as the three different system configurations. Also the value <strong>of</strong> the<br />
most important parameters <strong>and</strong> assumptions will be stated.<br />
In general all heat losses <strong>of</strong> the components to the surroundings are<br />
assumed to be zero 1 .<br />
The closest approach temperature difference for heat exchangers<br />
is estimated to be 5 ◦ C for liquid-liquid, 10 ◦ C for Condensers (which<br />
are liquid-liquid/gas), 15 ◦ C for liquid-gas <strong>and</strong> 25 ◦ C for gas-gas heat<br />
exchangers.<br />
The fluid in the external heat transfer circuits is water <strong>and</strong> the<br />
1 The wet/dry cooling towers are an exception - their purpose is to reject heat to the<br />
surroundings.<br />
79
4. SYSTEM DESCRIPTION<br />
8<br />
SPG 10<br />
20<br />
1 1-α<br />
WGHEX<br />
1<br />
α 7<br />
43<br />
CH4, add, in<br />
6<br />
GGHEX1 9<br />
GGHEX2<br />
0<br />
42 41<br />
COND2<br />
71<br />
70<br />
78<br />
2 MIXG 3<br />
4<br />
5 ANODE<br />
DES2<br />
1<br />
33 34<br />
21<br />
1 PR<br />
10<br />
79<br />
SOFC<br />
BURN<br />
18<br />
22<br />
CH4, in<br />
SPG α<br />
SHEX<br />
2<br />
CATHODE 2<br />
WGHEX<br />
80 77<br />
12 13<br />
14 15 16<br />
72<br />
2<br />
1-α<br />
GGHEX4<br />
GGHEX3<br />
81<br />
76<br />
BLOW<br />
11<br />
1<br />
17<br />
MIXG<br />
34<br />
Air, in<br />
2<br />
PUMP<br />
22 20 19<br />
VA2<br />
VB2<br />
19<br />
31<br />
2<br />
21<br />
23<br />
82<br />
73 75<br />
1-α<br />
32<br />
28<br />
MIXR<br />
α<br />
SPL<br />
1<br />
WGHEX<br />
50<br />
1<br />
58<br />
3<br />
DES1<br />
57<br />
59<br />
MIXL<br />
27 24 Flue gas, out<br />
COND1<br />
1<br />
51<br />
82<br />
35 36<br />
SHEX<br />
Domestic Hot Water<br />
60 1 57<br />
Saturated air<br />
47<br />
52<br />
61<br />
56<br />
VA1<br />
VB1<br />
PUMP<br />
1<br />
Water add<br />
38<br />
TOWER<br />
46<br />
53<br />
49<br />
EVAP<br />
48<br />
54<br />
62<br />
ABSO<br />
36 37<br />
55<br />
39<br />
37<br />
FAN<br />
45<br />
Atmospheric air<br />
Chilled Water<br />
Figure 4.1: Diagram <strong>of</strong> SOFC-ABS system in Double Stage, Dual Heat configuration. The<br />
SOFC subsystem is located in the upper left corner. The ABS subsystem is located at the<br />
righth<strong>and</strong> side. The names <strong>of</strong> the components are listed in the nomenclature page xxii.<br />
pressure in all <strong>of</strong> them is assumed to be 2000 kPa (to ensure liquid phase).<br />
A complete list <strong>of</strong> parameters is given in appendix C.1 page 233. Further<br />
explanation regarding the choice <strong>of</strong> parameters can be seen in D.1 page<br />
271.<br />
80
4.2. SOFC subsystem<br />
4.2 SOFC subsystem<br />
4.2.1 Fuel pretreatment <strong>and</strong> recirculation<br />
At point 1 the <strong>fuel</strong> which is methane (C H 4 ) 2 is fed into a heat exchanger<br />
(GGHEX1) where it is preheated, see figure 4.2.<br />
Normally the <strong>fuel</strong> is natural gas coming from a supply grid or<br />
pressurized storage, so it is assumed that the pressure <strong>of</strong> the gas is<br />
sufficiently high to overcome the pressure losses in the system. It<br />
is assumed that the temperature <strong>of</strong> the <strong>fuel</strong> is equal to the reference<br />
temperature <strong>of</strong> 25 ◦ C. The mass flow rate <strong>of</strong> methane corresponds to an<br />
enthalpy flow <strong>of</strong> 100kW 3 .<br />
8<br />
GGHEX1<br />
9<br />
SPG<br />
1<br />
α<br />
10<br />
1-α<br />
7<br />
GGHEX2<br />
6<br />
CH4, add, in<br />
0<br />
1<br />
CH4, in<br />
Air, in<br />
2<br />
11<br />
MIXG<br />
1<br />
BLOW<br />
1<br />
3<br />
PR<br />
4<br />
ANODE<br />
SOFC<br />
SPG α<br />
CATHODE 2<br />
12 13<br />
14 15 16<br />
1-α<br />
GGHEX4<br />
GGHEX3<br />
23<br />
22<br />
20<br />
5<br />
19<br />
10<br />
BURN<br />
17<br />
18<br />
MIXG<br />
2<br />
19<br />
Figure 4.2: Diagram <strong>of</strong> SOFC subsystem (zoom <strong>of</strong> figure 4.1) which consists <strong>of</strong> gas-gas heat<br />
exchangers (GGHEX), a pre reformer (PR), mixers (MIXG), splitters (SPG), a Solid Oxide Fuel<br />
Cell stack (SOFC) <strong>and</strong> a catalytic burner (BURN).<br />
At point 2, the <strong>fuel</strong> is mixed with the recirculated gas coming from<br />
point 9 in the mixer component (MIXG) before it enters the pre reformer<br />
(PR) in point 3.<br />
2 Natural gas contains mainly methane but also higher order hydrocarbons. For<br />
simplicity it has been assumed that only methane is present.<br />
3 Based on lower heating value<br />
81
4. SYSTEM DESCRIPTION<br />
Pre reformer<br />
Since there is not chemical equilibrium in the pre reformer [25], the degree<br />
to which reforming <strong>and</strong> water gas shift happens in the pre reformer<br />
can not be calculated easily <strong>and</strong> is hence determined by two parameters,<br />
which have been set to give partial pressures <strong>of</strong> the different species at<br />
the outlet approximately equal to the values <strong>of</strong> the TOFC model.<br />
The parameter ”F R” (fraction <strong>of</strong> reforming) determines how much <strong>of</strong> the<br />
incoming methane (at point 3) which is reformed (see equation 3.62 page<br />
61).<br />
”FW ” (fraction <strong>of</strong> water gas shift reaction) determines how much <strong>of</strong><br />
the CO after the reforming reaction 4 which reacts in the water gas shift<br />
reaction, see equation 3.65 page 62.<br />
F R is set to 0,14, while FW is set to 0,6. With these values the<br />
following happens to the volume flow from the pre reformer inlet (point<br />
3) to the outlet (point 4):<br />
1) H 2 is approximately doubled.<br />
2) CO is reduced by 50%.<br />
3) CO 2 is increased by 15%.<br />
These numbers are all quite close to the TOFC model.<br />
After the pre reformer (point 4) the <strong>fuel</strong> heated to 690 ◦ C by GGHEX2<br />
before it enters the SOFC stack in point 5.<br />
Recirculation<br />
The exhaust gas from the SOFC anode (point 6) is sent back to the hot<br />
side <strong>of</strong> both GGHEX2 (point 7) <strong>and</strong> GGHEX1 (point 8) for heat recovery.<br />
In order to make the model more flexible when parameters are varied, the<br />
effectiveness (ɛ) <strong>of</strong> these two heat exchangers are set equal to each other<br />
instead <strong>of</strong> giving the closest approach temperature difference (∆T min ) for<br />
one <strong>of</strong> them.<br />
The splitter (SPG1) is controlled by the parameter α SPG1 dictating the<br />
4 In reality the two reactions occur simultaneously, but it is assumed that the<br />
reforming reaction run to end before the water gas shift reaction starts<br />
82
4.2. SOFC subsystem<br />
fraction which is recirculated to point 9. The st<strong>and</strong>ard value for α SPG1 is<br />
set to 0,62 (62% recirculation) since this corresponds to an OC ratio just<br />
above 2. The OC ratio is the ratio <strong>of</strong> oxygen <strong>and</strong> carbon molecules at the<br />
SOFC anode inlet (point 5) (see equation 3.82 page 66).<br />
Normally a blower is needed to recirculate the exhaust gases from the<br />
SOFC anode (the pressure is higher in point 3 than in point 9), but to<br />
simplify the system this blower has been neglected. This is done by allowing<br />
a positive 5 pressure loss in MIXG1 from point 9 to point 3.<br />
4.2.2 Air inlet<br />
Atmospheric air (79% N 2 <strong>and</strong> 21% O 2 , by volume) at reference temperature<br />
<strong>and</strong> pressure (T re f =25 ◦ C <strong>and</strong> p re f =100kPa) enter the blower (BLOW1) at<br />
point 11.<br />
The blower has an isentropic efficiency 6 <strong>of</strong> 60%. This value is<br />
dependent on the size <strong>of</strong> the blower, especially small scale blowers have<br />
a low efficiency. However, this has been neglected since only larger<br />
systems are considered <strong>and</strong> it is assumed that blowers in this scale has<br />
the same isentropic efficiency independent <strong>of</strong> the system size.<br />
In the blower the pressure <strong>of</strong> the air is only slightly increased<br />
to a pressure corresponding to the pressure losses in the successive<br />
components (the absolute pressure after the blower is 122kPa). The<br />
pressure loss <strong>of</strong> each component is an estimate based on data from TOFC.<br />
Since all the gasses in the model are ideal the losses in the gas system only<br />
influence the blower power. All pressure losses are listed in appendix C.1<br />
page 233.<br />
Air pre heating<br />
The air must be preheated before it enters the SOFC stack to obtain an<br />
inlet temperature <strong>of</strong> 690 ◦ C. This is done by heat recovery <strong>of</strong> the exhaust<br />
gases. The system has the opportunity to do this air preheating in two<br />
steps:<br />
First the air is preheated by the low temperature exhaust gas<br />
via GGHEX4 from point 12 to point 13. This is an extra feature<br />
5 The pressure loss is defined as a negative value<br />
6 See definition in equation 3.10 page 48<br />
83
4. SYSTEM DESCRIPTION<br />
which increases system performance <strong>and</strong> therefore called Additional Air<br />
Preheating.<br />
Afterwards the air is preheated by high temperature exhaust gas by<br />
GGHEX3 to a temperature <strong>of</strong> 690 ◦ C before it enters the SOFC cathode<br />
inlet point 14.<br />
4.2.3 SOFC stack<br />
The specified cell area <strong>of</strong> 0,0228 m 2 makes the SOFC the only component<br />
in the model having a physical size. The number <strong>of</strong> <strong>cells</strong> per stack has<br />
been set to 60. However these value does not affect system efficiency or<br />
system size - the number <strong>of</strong> stacks in the system is variable <strong>and</strong> will depend<br />
on the enthalpy flow <strong>of</strong> the <strong>fuel</strong> input 7 . So the cell area <strong>and</strong> number<br />
<strong>of</strong> <strong>cells</strong> are only specified to have some kind <strong>of</strong> relation to real systems.<br />
The <strong>fuel</strong> utilization factor (U f ) is set 70% which is a typical value for <strong>fuel</strong><br />
cell systems [25]. Together with the <strong>fuel</strong> input <strong>of</strong> 100kW <strong>and</strong> recirculation<br />
factor <strong>of</strong> 0,62 this gives the current <strong>of</strong> the system. Instead <strong>of</strong> the <strong>fuel</strong> input<br />
<strong>of</strong> 100kW the current draw could have been specified, but when the <strong>fuel</strong><br />
input is kept constant, the cooling <strong>and</strong> heating powers become easier to<br />
evaluate during the parameter investigations in chapter5.3.<br />
The current density (i d ) is a parameter which determines how much<br />
the SOFC is loaded (regulation). The value <strong>of</strong> 3000 A/m 2 is an estimate<br />
based on data from TOFC. The <strong>fuel</strong> input determines the size <strong>of</strong> the system<br />
(100kW <strong>fuel</strong> input). These two factors give the number <strong>of</strong> stacks,<br />
which becomes 20,15. Instead <strong>of</strong> the current density the number <strong>of</strong> stacks<br />
n st ack ) could be specified, but it is impractical to have more than one extensive<br />
parameter.<br />
The two inlets at the SOFC are assumed to have equal temperature, <strong>and</strong><br />
the two outlets have the same temperature. ∆T min,SOFC determines the<br />
temperature increase from inlet (point 5 <strong>and</strong> 14) to the outlet (point 6<br />
<strong>and</strong> 15). ∆T min,SOFC has a value <strong>of</strong> 90 ◦ C which is a typical value <strong>of</strong> <strong>fuel</strong><br />
<strong>cells</strong> today [25]. It is important that the limits <strong>of</strong> minimum temperature<br />
at the inlet <strong>and</strong> maximum temperature at the outlet are not violated, as<br />
described in section 3.12 page 64.<br />
7 Alternatively the current draw could have be specified or the number <strong>of</strong> stacks<br />
(since the current density is also given)<br />
84
4.2. SOFC subsystem<br />
The air utilization factor is defined as the fraction <strong>of</strong> the oxygen input<br />
at the cathode side <strong>of</strong> the SOFC component which is consumed:<br />
U air = ṅSOFC ,cat,i ,O 2<br />
− ṅ SOFC ,cat,o,O2<br />
ṅ SOFC ,cat,i ,O2<br />
= ṅ14,O 2<br />
− ṅ 15,O2<br />
ṅ 14,O2<br />
(4.1)<br />
4.2.4 Exhaust gas<br />
The air which is not consumed in the SOFC stack (point 15) is split by<br />
SPG2. α SPG2 defines how much <strong>of</strong> the air is sent to the burner inlet, point<br />
16. The exhaust gas (containing excess <strong>fuel</strong>) from the SOFC is sent to the<br />
burner <strong>fuel</strong> inlet point 10.<br />
It is also possible to bypass the pretreatment <strong>of</strong> the <strong>fuel</strong> <strong>and</strong> the SOFC<br />
by adding <strong>fuel</strong> to the burner directly at point 0 if more heat <strong>and</strong> less<br />
electricity is wanted. The parameter FuelBP Ratio determines the fraction<br />
<strong>of</strong> the total <strong>fuel</strong> input which is sent directly to the burner circumventing<br />
the rest <strong>of</strong> the SOFC system. This option, though, is only used for a<br />
single simulation, so normally FuelBP Ratio = 0. More details are given<br />
in section 5.3.3 page 130.<br />
λ BURN ,i is the air excess ratio <strong>of</strong> the burner inlet (point 0, 10 <strong>and</strong> 16)<br />
defined as:<br />
λ BURN ,i = 2ṅ i ,C H 4<br />
+ 0,5ṅ i ,H2 + 0,5ṅ i ,CO<br />
ṅ i ,O2<br />
(4.2)<br />
λ BURN ,i is set to 1,5 which is common for combustors. This implicitly<br />
sets the value <strong>of</strong> α SPG2 such that the right amount <strong>of</strong> air is bypassed the<br />
burner (point 17). The bypassing air is mixed with the exhaust gas from<br />
the burner (point 18) in MIXG2. The gas is returned to the hot side <strong>of</strong><br />
GGHEX3 (point 19) before it leaves the SOFC subsystem in point 20.<br />
After some <strong>of</strong> the energy in the exhaust gas has been utilized in the<br />
absorption cycle, the gas is returned to the SOFC subsystem entering at<br />
point 22. Heat is transferred via GGHEX4 to the inlet air <strong>and</strong> the exhaust<br />
gas leaves at point 23.<br />
85
4. SYSTEM DESCRIPTION<br />
4.3 Absorption Single Stage<br />
The exhaust gas from the SOFC subsystem enters the water-gas heat<br />
exchanger (WGHEX2) in point 21 <strong>and</strong> leaves in point 22, see figure 4.3.<br />
Heat is transferred by a closed loop <strong>of</strong> water to the desorber (DES1)<br />
heating inlet point 31. The temperature T 31 is set to 85 ◦ C (parameter<br />
for the single stage only). The temperature change in the heating loop<br />
(∆T h,DES1 ) is 5 ◦ C corresponding to a temperature in point 32 <strong>of</strong> 80 ◦ C for<br />
the single stage.<br />
22<br />
21<br />
WGHEX<br />
2<br />
32<br />
31<br />
50<br />
DES1<br />
58<br />
59<br />
52<br />
35<br />
COND1<br />
36<br />
51<br />
60<br />
61<br />
SHEX<br />
1<br />
57<br />
56<br />
VA1<br />
VB1<br />
PUMP<br />
1<br />
53<br />
49<br />
EVAP<br />
48<br />
54<br />
62<br />
36<br />
ABSO<br />
37<br />
55<br />
Chilled Water<br />
Figure 4.3: Diagram <strong>of</strong> single stage absorption subsystem (zoom <strong>of</strong> full diagram in appendix<br />
G page 293) composed <strong>of</strong> an absorber (ABSO), a condenser (COND1), a desorber (DES1), an<br />
evaporator (EVAP), a pump, a solution heat exchanger (SHEX), a water-gas heat exchanger<br />
(WGHEX2), <strong>and</strong> two valves (VA1 <strong>and</strong> VB1).<br />
In reality the WGHEX2 <strong>and</strong> DES1 would have been integrated as one<br />
unit since the water circuit was only introduced due to flexibility in the<br />
modeling work. So in reality there would only be one (Water-Gas)HEX<br />
<strong>and</strong> hence only one ∆T min between the exhaust gas <strong>and</strong> fluid in DES2. So<br />
∆T min,DES1,r,o has been set to zero. This way ∆T min,W GHE X 2,w,i = 15 covers<br />
the overall closest approach temperature difference.<br />
86
4.3. Absorption Single Stage<br />
4.3.1 Refrigerant cycle<br />
The superheated refrigerant in point 51 is condensed in COND1 until<br />
a condition <strong>of</strong> saturated liquid is reached (qu COND1,r,o = 0) in point 52.<br />
The high pressure in the condenser is determined by the cooling water<br />
temperature <strong>and</strong> the ∆T min <strong>of</strong> the condenser.<br />
The evaporation temperature is given by the temperature <strong>of</strong> the<br />
cooling circuit <strong>and</strong> ∆T min,COND1,r,o = 10 ◦ C 8 .<br />
The refrigerant is led through expansion valve VA1 to point 53. The<br />
low pressure in the evaporator (EVAP) is set so the temperature <strong>of</strong> the<br />
chilled water obtains the desired temperature (T 49 = 6 ◦ C) for the given<br />
closest approach temperature difference (between T 49 <strong>and</strong> T 53 ), which<br />
is ∆T min,EV AP,r,i = 5 ◦ C. The temperature difference <strong>of</strong> the chilled water<br />
leaving the evaporator (point 49) <strong>and</strong> the returned water in point 48<br />
(∆T chill,EV AP ) is assumed to be 5 ◦ C 9 .<br />
4.3.2 Solution cycle<br />
When the refrigerant leaves the evaporator in point 54 as saturated<br />
gas (qu EV AP,r,o = 1) it is absorbed by the strong LiBr solution (rich in<br />
LiBr) entering at point 62 in the absorber. The heat is removed by the<br />
cooling water entering at point 36 <strong>and</strong> leaving at point 37. Together<br />
with the pressure, T 37 determines the concentration <strong>of</strong> the weak solution<br />
which leaves at point 55, via the closest approach temperature difference<br />
∆T min,ABSO,s,o = 5 ◦ C (Difference between T 55 <strong>and</strong> T 37 ).<br />
The weak solution is pressurized by a canned pump (PUMP1) which<br />
is assumed to have an efficiency <strong>of</strong> 0,5 (point 56). Next the solution<br />
is preheated in SHEX1 before entering DES1 in point 57. The strong<br />
solution leaving the desorber in point 59 transfers heat to the weak<br />
solution in SHEX1 (point 60-61) <strong>and</strong> exp<strong>and</strong>s in VB1 before entering the<br />
absorber.<br />
8 EES has problems running if ∆T min,COND1,r,o is given explicitly, so in praxis<br />
∆T min,COND1,r,o is given to 12,5 ◦ C in the st<strong>and</strong>ard parameter configuration, <strong>and</strong><br />
monitored <strong>and</strong> changed during investigations, so that ∆T min,COND1,r,o remains at 10 ◦ C<br />
9 It is assumed that the water is sent to a cold water storage with a temperature <strong>of</strong><br />
10 ◦ C <strong>and</strong> that the air temperature for the air coming out <strong>of</strong> an air conditioning should<br />
be about 15 ◦ C. Similar temperatures are used in [19] <strong>and</strong> [34].<br />
87
4. SYSTEM DESCRIPTION<br />
4.3.3 Pumping factor<br />
The pumping factor is defined as the mass flow ratio <strong>of</strong> the weak solution<br />
<strong>and</strong> the refrigerant[18]:<br />
PF = ṁ55<br />
ṁ 51<br />
(4.3)<br />
For the st<strong>and</strong>ard configuration PF = 12,75. This number should not be<br />
too high since it increases the amount <strong>of</strong> LiBr solution circulated per kW<br />
<strong>of</strong> cooling which increases desorber heating, absorber cooling <strong>and</strong> pump<br />
power.<br />
88
4.4 Absorption Double Stage<br />
4.4. Absorption Double Stage<br />
The double stage absorption cycle is similar to the single stage cycle<br />
described in previous section. Thus only the additional components <strong>and</strong><br />
changes <strong>of</strong> parameters will be described in this section. All state points<br />
refers to figure 4.4.<br />
20<br />
WGHEX<br />
1<br />
43<br />
COND2<br />
71<br />
33 34<br />
21<br />
70<br />
79<br />
42<br />
DES2<br />
41<br />
78<br />
72<br />
80<br />
81<br />
SHEX<br />
2<br />
77<br />
76<br />
52<br />
35<br />
COND1<br />
36<br />
51<br />
PUMP<br />
VA2<br />
VB2<br />
2<br />
82<br />
73 75<br />
1-α<br />
32 31<br />
MIXR<br />
α<br />
SPL<br />
1<br />
50<br />
1<br />
58<br />
MIXL<br />
1<br />
59<br />
82<br />
60<br />
61<br />
DES1<br />
SHEX<br />
1<br />
57<br />
56<br />
57<br />
VA1<br />
VB1<br />
PUMP<br />
1<br />
53<br />
49<br />
EVAP<br />
48<br />
54<br />
62<br />
36<br />
ABSO<br />
37<br />
55<br />
Chilled Water<br />
Figure 4.4: Diagram <strong>of</strong> double stage absorption subsystem (zoom <strong>of</strong> full diagram in appendix G<br />
page 293). It is similar to the single stage cycle with addition <strong>of</strong> an extra condenser (COND2),<br />
desorber (DES2), two mixers (MIXR <strong>and</strong> MIXL), a pump, a splitter (SPL) <strong>and</strong> two valves (VA2<br />
<strong>and</strong> VB2).<br />
The exhaust gas is sent through WGHEX1 (point 20 <strong>and</strong> point 21).<br />
As for the single stage cycle, WGHEX1 <strong>and</strong> DES2 are modeled as two<br />
components (but considered as one) which means that ∆T min,DES2,r,o = 0.<br />
89
4. SYSTEM DESCRIPTION<br />
The temperature difference between point 41 <strong>and</strong> point 42 (∆T h,DES2 ) is<br />
5 ◦ C like for DES1. The temperature <strong>of</strong> DES2 is 150 ◦ C (point 70 <strong>and</strong> 79).<br />
The high pressure refrigerant is sent to COND2 inlet (point 71). Like<br />
for COND1 in the single stage cycle configuration, the refrigerant is both<br />
de-superheated <strong>and</strong> condensed in COND2. Thus the closest approach<br />
temperature difference is found somewhere between point 71 <strong>and</strong> point<br />
72. Due to limitations in the model it is not possible to set this parameter<br />
directly <strong>and</strong> instead ∆T min,COND2,r,o is set to 12,5 ◦ C. This corresponds to<br />
∆T min,COND2,mp being 10 ◦ C.<br />
The heat from COND2 is removed by the heat transferring loop (point<br />
31 to point 34) <strong>and</strong> supplied to low temperature desorber DES1. The loop<br />
is modeled as a water circuit, but in a real double stage unit, COND2 <strong>and</strong><br />
DES1 would be integrated as one component.<br />
The saturated liquid refrigerant (qu 72 = 0) is exp<strong>and</strong>ed in VA2 point<br />
72 before it is mixed with superheated refrigerant from DES1 point 50 in<br />
MIXR1. The quality <strong>of</strong> the refrigerant outlet is between zero <strong>and</strong> one in<br />
point 51.<br />
Unlike COND2, the refrigerant entering COND1 is not superheated.<br />
Thus the closest approach temperature difference exists at the inlet in<br />
point 51 (compared to the temperature in point 36) but the value is still<br />
10 ◦ C. The heat from COND2 is removed by the cooling circuit (point 35<br />
<strong>and</strong> point 36)<br />
The refrigerant is exp<strong>and</strong>ed in VA1 (point 53), then evaporated (point<br />
54), <strong>and</strong> absorbed in the absorber exactly the same way as in the single<br />
stage cycle. The difference occurs after the weak solution is preheated in<br />
SHEX1 in point 57. In the double stage system only some <strong>of</strong> the solution<br />
is sent to DES1 but the remaining part is pressurized further by PUMP2<br />
(point 76) <strong>and</strong> preheated in SHEX2 (point 77) before it enters DES2 (point<br />
78). The strong solution is cooled in SHEX2 (point 80 to 81), exp<strong>and</strong>ed in<br />
VB2 <strong>and</strong> mixed with the strong solution coming from DES1 in MIXL1.<br />
Since the temperature in point 50 is not set as a parameter (as it is the<br />
case for the single stage cycle), another relation is given:<br />
ṁ 70<br />
ṁ 78<br />
= ṁ50<br />
ṁ 58<br />
(4.4)<br />
This relation determines the fraction <strong>of</strong> solution which is sent to the<br />
DES2. It also implies that concentration <strong>of</strong> the weak <strong>and</strong> strong solution<br />
will be the same for the two solutions in the two circuits (w 55 = w 75<br />
90
4.4. Absorption Double Stage<br />
<strong>and</strong> w 59 = w 79 ). This has been done for two reasons. First <strong>of</strong> all it<br />
gives a value <strong>of</strong> T 50 = 78 ◦ C which is quite close to optimum. Secondly<br />
if other parameters like the temperature <strong>of</strong> the high pressure desorber<br />
is increased then T 50 will increase as well <strong>and</strong> thereby remain near<br />
optimum for the given T 70 .<br />
91
4. SYSTEM DESCRIPTION<br />
4.5 Absorption Double Stage, Dual Heat<br />
20<br />
WGHEX<br />
1<br />
43<br />
72<br />
COND2<br />
71<br />
33 34<br />
22<br />
34<br />
WGHEX<br />
2<br />
21<br />
42<br />
70<br />
79<br />
80<br />
81<br />
DES2<br />
SHEX<br />
2<br />
41<br />
77<br />
76<br />
78<br />
52<br />
35<br />
COND1<br />
36<br />
VA2<br />
31<br />
VB2<br />
73<br />
82<br />
75<br />
MIXR<br />
32<br />
α<br />
1<br />
51<br />
MIXL<br />
1<br />
50<br />
59<br />
82<br />
60<br />
61<br />
DES1<br />
SHEX<br />
1<br />
57<br />
56<br />
58<br />
57<br />
PUMP<br />
2<br />
1-α<br />
SPL<br />
1<br />
VA1<br />
VB1<br />
PUMP<br />
1<br />
53<br />
49<br />
EVAP<br />
48<br />
54<br />
62<br />
36<br />
ABSO<br />
37<br />
55<br />
Chilled Water<br />
Figure 4.5: Diagram <strong>of</strong> double stage absorption subsystem with dual heat (zoom <strong>of</strong> full diagram<br />
in appendix G page 293). The cycle is similar to the double stage cycle - the difference is that<br />
heat is transferred from the exhaust gas to the absorption cycle at two points (via WGHEX1 <strong>and</strong><br />
WGHEX2).<br />
Another attempt to increase the production <strong>of</strong> cooling is to make a<br />
configuration which is a combination <strong>of</strong> the single <strong>and</strong> the double stage<br />
cycle, see figure 4.5. Basically it is a double stage cycle where heat is<br />
transferred from the exhaust gas to the absorption cycle twice (dual heat).<br />
In the configuration without Air Preheat, the exhaust gas from<br />
WGHEX1 in point 21 is 165 ◦ C so only some <strong>of</strong> the heat from the exhaust<br />
gas is used for the cooling cycle. So in order to use more <strong>of</strong> the heat from<br />
92
4.5. Absorption Double Stage, Dual Heat<br />
the exhaust gas it is sent through WGHEX2 (hot side) so it is cooled down<br />
to around 90 ◦ C at point 22. This extra heat is sent into DES1 through the<br />
external circuit (point 31, 32, 33 <strong>and</strong> 34) 10 . In this way more <strong>of</strong> the heat <strong>of</strong><br />
the exhaust gas can be used, although part <strong>of</strong> it goes directly into the low<br />
temperature desorber <strong>and</strong> hence doesn’t benefit from the Double Stage<br />
setup.<br />
10 In a real application these three components could be integrated as one <strong>and</strong> the<br />
heat could be transferred in parallel rather than in series, which would change the<br />
involved temperatures a little, but this has not been investigated further.<br />
93
4. SYSTEM DESCRIPTION<br />
4.6 Cooling Tower<br />
28<br />
WGHEX<br />
3<br />
23<br />
MIXR<br />
1<br />
50<br />
32<br />
DES1<br />
31<br />
27<br />
Domestic Hot Water<br />
24<br />
Saturated air<br />
47<br />
Flue gas, out<br />
52<br />
35<br />
COND1<br />
36<br />
51<br />
MIXL<br />
1<br />
59<br />
82<br />
60<br />
61<br />
SHEX<br />
1<br />
57<br />
56<br />
VA1<br />
VB1<br />
PUMP<br />
1<br />
Water add<br />
38<br />
TOWER<br />
46<br />
53<br />
49<br />
EVAP<br />
48<br />
54<br />
62<br />
36<br />
ABSO<br />
37<br />
55<br />
39<br />
37<br />
FAN<br />
45<br />
Atmospheric air<br />
Chilled Water<br />
Figure 4.6: Diagram <strong>of</strong> cooling system <strong>and</strong> hot water production (zoom <strong>of</strong> figure 4.1). The<br />
cooling tower removes waste heat from the absorber (ABSO) <strong>and</strong> the condenser (COND1). The<br />
remaining heat in the exhaust gas is used for hot water production.<br />
As described in section 4.3, heat must be removed from the condenser<br />
(COND1) <strong>and</strong> the absorber (ABSO) by a heat transferring fluid (water).<br />
It has been decided to connect COND1 <strong>and</strong> ABSO in series. According<br />
to Sc<strong>and</strong>inavian Energy Group [27] the condenser is normally ”before” the<br />
absorber for cooling units (for heat pumps it is always the opposite). This<br />
corresponds to the series connection <strong>of</strong> COND1 <strong>and</strong> ABSO (point 35, 36<br />
<strong>and</strong> 37) in figure 4.6.<br />
The temperature difference <strong>of</strong> the Tower inlet (point 37) <strong>and</strong> outlet<br />
(point 39) is estimated to be ∆T c,TOW ER1 = 5 ◦ C. In praxis this is<br />
controlled by the water mass flow in the external circuit. The COP<br />
generally increases if ∆T c,TOW ER1 is reduced (the absorber <strong>and</strong> condenser<br />
becomes colder), but since the water flow increases, pumping work<br />
<strong>and</strong> component geometry is enlarged which requires more energy <strong>and</strong><br />
increases the price <strong>of</strong> the condenser <strong>and</strong> absorber.<br />
The water is cooled by the ambient air (at T amb ) which enters the<br />
tower at point 45, is pressurized by the FAN (point 46) <strong>and</strong> then<br />
94
4.6. Cooling Tower<br />
discharged in point 47. The cooling tower is either a dry tower (dry<br />
cooler) or a wet tower, as described in section 3.14 page 71.<br />
The parameter configuration for these two towers are different <strong>and</strong><br />
will be described separately in the next two paragraphs.<br />
4.6.1 Wet Tower<br />
The ambient air has a temperature <strong>of</strong> 30 ◦ C when the wet tower is used.<br />
Since the water <strong>and</strong> air is mixed this allows a much lower CATD than for<br />
a tube heat exchanger <strong>and</strong> it is thus estimated to be ∆T min,TOW ER1,a,o,wet =<br />
3 ◦ C. This way the temperature <strong>of</strong> the discharged air (T 47 ) is almost in the<br />
middle <strong>of</strong> the water outlet temperature (T 39 ) <strong>and</strong> water inlet temperature<br />
(T 37 ).<br />
According to [14] the ”wet bulb” Tower efficiency is typically around<br />
0,75, so this has been assumed also to be the case here giving a water<br />
outlet temperature <strong>of</strong> 22 ◦ C when the inlet air is 30 ◦ C <strong>and</strong> the relative<br />
humidity is 40%.<br />
4.6.2 Dry Tower<br />
Ideally the dry tower should use the same ambient temperature as the<br />
wet tower (30 ◦ C), but this gives a condenser <strong>and</strong> absorber temperature<br />
so high that the model can not run at all. So it has been necessary to use a<br />
lower ambient temperature for the dry tower although it gives a slightly<br />
unfair advantage when comparing it to the wet tower. A temperature <strong>of</strong><br />
18 ◦ C has been chosen, since this is just below where COP ABS,f uel starts<br />
to decrease rapidly (at 20 ◦ C the system will barely run), so the unfair<br />
temperature advantage is minimized as much as possible.<br />
The Approach Temperature Difference between water inlet (T 37 ) <strong>and</strong><br />
air outlet (T 47 ) is estimated to be: ∆T min,TOW ER1,a,o,dr y = 8 ◦ C.<br />
4.6.3 Hot Water<br />
Most <strong>of</strong> the energy in the exhaust gas is utilized in the absorption cycle<br />
<strong>and</strong> for air preheating (eventually additional air preheating is used in<br />
GGHEX4). In point 23 temperature <strong>of</strong> the exhaust gas is rather low<br />
95
4. SYSTEM DESCRIPTION<br />
(below 100 ◦ C), but high enough for heating domestic hot water.<br />
exhaust gas is discharged to the surroundings at point 24.<br />
The<br />
Fresh water is entering the water-gas heat exchanger (WGHEX3) in<br />
point 27. It is assumed that the water comes from a supply line which<br />
has the same temperature as the surroundings 11 (T amb ). This water is<br />
heated to a temperature <strong>of</strong> 65 ◦ C 12 in point 28.<br />
It is assumed that the consumption follows the production <strong>of</strong> hot<br />
water or that the water can be stored in a thermal stratification heat<br />
storage, so the water inlet temperature <strong>of</strong> WGHEX3 remains constant.<br />
11 for buried pipes the temperature could be much lower.<br />
12 Recommended maximum temperature to avoid scald <strong>and</strong> high enough to avoid<br />
bacteria growth in storage tanks.<br />
96
4.7. System calculation<br />
4.7 System calculation<br />
Most calculations are done in the respective component modules as<br />
described in chapter 3, but calculations concerning more than one<br />
component (or just very simple components - merely consisting <strong>of</strong> an<br />
efficiency) have been places in the main system file. These calculations<br />
will be described in the following sections.<br />
Inverter<br />
The power produced by the SOFC (Ẇ SOFC ) is delivered by direct current<br />
(DC), but for many applications alternating current (AC) is more desirable.<br />
It is assumed that the other components in the system (blower, fan <strong>and</strong><br />
pumps) are driven by AC power.<br />
An inverter converts DC to AC which introduces a power loss. The<br />
efficiency <strong>of</strong> the inverter is specified by η inver t which is estimated to 95%.<br />
4.7.1 Efficiencies<br />
When looking at the system it is convenient to know how much energy<br />
that is available in each point <strong>of</strong> the gas stream (<strong>fuel</strong>, air <strong>and</strong> exhaust gas).<br />
For this the ”energy flow rate”, ∆Ḣ, is used 13 . It is defined as how much<br />
enthalpy the gas contains in a given point relative to when it is totally<br />
combusted at the reference temperature (T re f = 25 ◦ C, in non-condensed<br />
state):<br />
∆Ḣ j = Ḣ j − Ḣ f ull y combusted at Tre f<br />
(4.5)<br />
∆Ḣ is calculated in point 0 to 24 (figure 4.1 page 80). The sum <strong>of</strong> all<br />
incoming gases to the system (point 0, 1 <strong>and</strong> 11) is called ∆Ḣ i .<br />
SOFC<br />
The gross AC <strong>and</strong> the net AC power delivered by the SOFC stack (without<br />
deductions for ABS pump or cooling tower fan) is calculated respectively<br />
13 Caution! This has another reference than the normal enthalpy flow rate Ḣ as<br />
defined in equation 3.1 page 43<br />
97
4. SYSTEM DESCRIPTION<br />
as:<br />
Ẇ AC = Ẇ SOFC · η inver t (4.6)<br />
Ẇ SOFC ,SOLO = Ẇ AC −Ẇ BLOW 1 (4.7)<br />
The electrical efficiency <strong>of</strong> the SOFC subsystem alone - disregarding<br />
electricity consuming components in the rest <strong>of</strong> the components in the<br />
system - then becomes:<br />
η SOFC ,el,SOLO = ẆSOFC ,SOLO<br />
∆Ḣ i<br />
(4.8)<br />
Absorption chiller<br />
The performance <strong>of</strong> the absorption cycle (per kW heat consumption) is<br />
determined as:<br />
COP ABS =<br />
˙Q Chill,EV AP<br />
˙Q tr ans,W GHE X 1 + ˙Q tr ans,W GHE X 2<br />
(4.9)<br />
where ˙Q tr ans,W GHE X is the amount <strong>of</strong> heat transferred into the absorption<br />
cycle (through WGHEX1 <strong>and</strong> WGHEX2). This COP is comparable to<br />
COP’s found in the literature <strong>of</strong> absorption system.<br />
System<br />
The electrical net efficiency <strong>of</strong> the entire system takes the power<br />
consumption <strong>of</strong> all components into account:<br />
Ẇ sys,net = Ẇ AC −Ẇ BLOW 1 −Ẇ PU MP1 −Ẇ PU MP2 −Ẇ F AN (4.10)<br />
η sys,el ,net =<br />
Ẇ sys,net<br />
∆Ḣ i<br />
(4.11)<br />
The chilling Coefficient Of Performing is defined as kW chilling power<br />
output per kW <strong>fuel</strong> (methane) input into the entire system:<br />
COP ABS,f uel = ˙Q Chill,EV AP<br />
∆Ḣ i<br />
(4.12)<br />
98
4.7. System calculation<br />
This definition has the advantage that the COP implicitly takes into<br />
account how much heat the absorption unit receives from the exhaust<br />
gas (more heat means more cooling power). So it tells how much cooling<br />
power per <strong>fuel</strong> input the system generates, which is the important thing<br />
from a system perspective, where the ”regular” COP ABS only tells part <strong>of</strong><br />
the story).<br />
The hot water efficiency is defined as kW water heating per kW <strong>fuel</strong><br />
(methane) input into the entire system:<br />
η HW = ˙Q tr ans,W GHE X 3<br />
∆Ḣ i<br />
(4.13)<br />
The total ”efficiency” 14 is found as the sum <strong>of</strong> useful power (electrical,<br />
heating <strong>and</strong> cooling) or the sum <strong>of</strong> two efficiencies <strong>and</strong> COP:<br />
Ẇ sys,net + ˙Q Chill,EV AP + ˙Q tr ans,W GHE X 3<br />
η sys,tot =<br />
(4.14)<br />
∆Ḣ i<br />
η sys,tot = η sys,el ,net +COP ABS,f uel + η HW (4.15)<br />
Since η sys,el ,net <strong>and</strong> η HW are defined as positive quantities for energy<br />
going out <strong>of</strong> the system, whereas COP ABS,f uel is positive for energy going<br />
into the system, η sys,tot can be above 1 <strong>and</strong> should hence be used with<br />
caution. (If one imagine that ∆Ḣ i = 100kW <strong>and</strong> ˙Q Chill,EV AP is 50kW, then<br />
the system will contain 150kW, which could be used for generating up<br />
to maximum 150kW <strong>of</strong> electricity <strong>and</strong> hot water. This would give an<br />
electrical efficiency <strong>of</strong> η sys,el,net = 50kW+150kW<br />
100kW<br />
= 2).<br />
14 Since energy input at low temperature (the chilling power) is not included in the<br />
denominator, η sys,tot can be above one <strong>and</strong> therefore by definition is not an efficiency<br />
although this name will be used in lack <strong>of</strong> better.<br />
99
4. SYSTEM DESCRIPTION<br />
4.8 Verification <strong>of</strong> Model<br />
All variables in the model have been assigned units. EES has a feature<br />
to check units automatically. This has been carried out <strong>and</strong> no unit<br />
problems were found 15 .<br />
4.8.1 Energy balance<br />
The conservation <strong>of</strong> energy must be fulfilled for all energy systems. In<br />
order to verify the model, an energy balance around the entire system<br />
has been made:<br />
EB tot =∆Ḣ i − ∆Ḣ W GHE X 3,g ,o − Ḣ air,i − Ḣ air,o + ˙Q Chill,EV AP (4.16)<br />
− ˙Q HW + Ḣ w,add +Ẇ BLOW +Ẇ F AN +Ẇ PU MP1<br />
+Ẇ PU MP2 −Ẇ SOFC = 0<br />
where ∆Ḣ W GHE X 3,g ,o is the enthalpy flow <strong>of</strong> discharged exhaust gas,<br />
Ḣ air,i <strong>and</strong> Ḣ air,o is the enthalpy flow <strong>of</strong> the air into the cooling tower<br />
<strong>and</strong> out <strong>of</strong> it, <strong>and</strong> Ḣ w,add is the enthalpy <strong>of</strong> the fresh water added to the<br />
cooling tower.<br />
4.8.2 Check <strong>of</strong> heat exchangers<br />
Most <strong>of</strong> the heat exchangers are defined by a Closest Approach Temperature<br />
Difference. This can however introduce an error if the chosen parameter<br />
for the approach temperature difference is not the closest one - in that<br />
case the real closest approach temperature can then become negative<br />
(whereby ɛ exceeds one).<br />
To avoid this error a variable ”ɛ M AX ” has been introduced. It simply<br />
finds the largest effectiveness <strong>of</strong> all the heat exchangers in the system.<br />
This way it is not necessary to monitor the effectiveness <strong>of</strong> all the heat<br />
exchangers during simulation as long as ɛ M AX does not exceed 1,0.<br />
15 Due to a bug in the external function ”CP_LiBrH2O.LIB” (the unit <strong>of</strong> c p is set<br />
to kJ<br />
kg <strong>and</strong> not kJ<br />
kgK<br />
), so the unit check feature finds 15 unit problems - all related to<br />
CP_LiBrH2O.LIB. These have been checked manually <strong>and</strong> no error was found.<br />
100
4.9. Validation <strong>of</strong> Model<br />
4.9 Validation <strong>of</strong> Model<br />
During the development <strong>of</strong> the model, the output (results) has been<br />
compared to other models as well as measured data. Rules <strong>of</strong> thumb<br />
have also been taken into account. In some cases additional variables<br />
have been introduced in order to validate the model <strong>and</strong> will be<br />
described in the following.<br />
4.9.1 SOFC<br />
In the st<strong>and</strong>ard parameter configuration the increase <strong>of</strong> the temperature<br />
from the inlet to the outlet <strong>of</strong> the <strong>fuel</strong> cell (∆T SOFC ) is 90 ◦ C. The <strong>fuel</strong><br />
utilization factor U f is 0,7 <strong>and</strong> the current density isi d = 3000 A . The<br />
m 2<br />
fraction <strong>of</strong> reforming in the pre reformer (F R) is 0,14. The air utilization<br />
factor (U air ) which is dependent on ∆T SOFC , U f <strong>and</strong> F R is calculated to<br />
0,16 which is quite close to that <strong>of</strong> the TOFC models [25].<br />
Recycling<br />
The fraction <strong>of</strong> anode recycling α SPG1 is 0,62. This deviates less than<br />
5% from an equivalent SOFC system modeled by TOFC. And the gas<br />
composition at the SOFC anode outlet matches the TOFC model.<br />
Blower power<br />
A rule <strong>of</strong> thumb says that the blower consumes 10% <strong>of</strong> the produced<br />
power [25]. Ẇ Blower is 5,5kW which corresponds to 10% <strong>of</strong> Ẇ SOFC ,SOLO<br />
(see definition in equation 4.6 <strong>and</strong> 4.7 page 98), while the TOFC models<br />
the fraction is in the range <strong>of</strong> only 5-8% <strong>of</strong> the net power.<br />
Since the SOFC system in this project is integrated with an absorption<br />
cooling unit, more heat exchangers are applied <strong>and</strong> hence it is expected<br />
that the total pressure loss <strong>of</strong> the exhaust gases must be higher. Taking<br />
this into account the blower power consumption seems to be reasonable.<br />
101
4. SYSTEM DESCRIPTION<br />
SOFC net efficiency<br />
The net electrical efficiency <strong>of</strong> the SOFC subsystem, η SOFC ,el,SOLO (the<br />
definition is shown in equation 4.8 page 98) is 54% which is a bit higher<br />
than that <strong>of</strong> the TOFC models. This might partly be due to a higher<br />
current density in the model <strong>of</strong> this project.<br />
4.9.2 Absorption cycle<br />
Some general recommendation (rules <strong>of</strong> thumb) about operation <strong>of</strong><br />
absorption cycles are given by SEG (Sc<strong>and</strong>inavian Energy Group) [27].<br />
These are valid for a single cycle only, but have been used in order<br />
to validate the components in the absorption cycle (under single stage<br />
configuration).<br />
∆T EV AP,ABSO is the temperature difference <strong>of</strong> the absorber cooling<br />
water outlet (T 37 ) <strong>and</strong> the evaporator chilling outlet (T 49 ). ∆T COND,DES<br />
is the temperature difference <strong>of</strong> the condenser (COND1) cooling water<br />
outlet (T 36 ) <strong>and</strong> the desorber (DES1) solution outlet (T 59 ).<br />
∆T EV AP,ABSO = T 37 − T 49 (4.17)<br />
∆T COND,DES = T 36 − T 59 (4.18)<br />
∆T CFG,C HK = ∆T COND,DES − ∆T EV AP,ABSO (4.19)<br />
∆T CFG,C HK must be a positive quantity <strong>and</strong> is typically approximately<br />
20 ◦ C. At the st<strong>and</strong>ard parameter configuration in single cycle mode<br />
(using additional reheating <strong>and</strong> wet tower cooling) ∆T CFG,C HK is 35 ◦ C<br />
(∆T EV AP,ABSO = 21 ◦ C <strong>and</strong> ∆T COND,DES = 56 ◦ C) which is higher than the<br />
typical value.<br />
Part <strong>of</strong> the reason can be the relatively low condenser <strong>and</strong> absorber<br />
temperatures provided by the wet cooling tower. If these temperatures<br />
are increased by 5 ◦ C, ∆T CFG,C HK will decrease to 26 ◦ C. But no matter<br />
how the temperature <strong>of</strong> DES1, COND1, EVAP or ABSO is set in the<br />
model, ∆T CFG,C HK can not be brought to reach 20 ◦ C. This however is very<br />
likely caused by the chosen values <strong>of</strong> CATD in the desorber, condenser,<br />
evaporator <strong>and</strong> absorber.<br />
102
4.9. Validation <strong>of</strong> Model<br />
Distribution <strong>of</strong> heat rejection<br />
The heat from the absorption cycle is removed by the condenser <strong>and</strong> the<br />
absorber <strong>and</strong> according to [27] the distribution should be as follows:<br />
˙Q ABSO = 56%<br />
˙Q COND = 44%<br />
For the single cycle at st<strong>and</strong>ard parameter configuration with<br />
additional air pre heat <strong>and</strong> wet tower the heat removed by the absorber<br />
<strong>and</strong> the condenser is ˙Q ABSO = 31,1kW (53%) <strong>and</strong> ˙Q COND = 27,7kW (47%)<br />
respectively.<br />
So in the model a slightly bigger fraction <strong>of</strong> the heat is removed by the<br />
condenser. The reason is the same as described in the previous section<br />
- low condenser/absorber temperature. If this is increased by 5 ◦ C, COP<br />
will drop to about 0,7 <strong>and</strong> the fraction <strong>of</strong> the heat rejected by the absorber<br />
will be 56%.<br />
COP<br />
According to [27], COP ABS should be between 0,70 <strong>and</strong> 0,75 almost independent<br />
<strong>of</strong> the temperatures (<strong>and</strong> load). At the st<strong>and</strong>ard configuration,<br />
the model gives a COP ABS <strong>of</strong> 0,80 which is a little higher than expected.<br />
But this can be due to the assumptions that the heat losses as well as<br />
pressure losses <strong>of</strong> the components have been neglected. Also the low<br />
condenser/absorber temperature will increase the COP ABS .<br />
Taking the above into consideration it is concluded that the temperature<br />
levels <strong>of</strong> the absorption cycle <strong>and</strong> the general behavior <strong>of</strong> the absorption<br />
model seems to be reasonable.<br />
103
C H A P T E R<br />
5<br />
SIMULATION AND RESULTS<br />
5.1 Basic absorption cooling<br />
COND<br />
1<br />
HEAT<br />
DES<br />
COOLING<br />
9<br />
7<br />
2<br />
SHEX<br />
3<br />
VA<br />
EVAP<br />
4<br />
11<br />
12<br />
VB<br />
ABSO<br />
PUMP<br />
6<br />
5<br />
CHILLED WATER<br />
COOLING<br />
Figure 5.1: Diagram <strong>of</strong> single stage absorption cycle<br />
In this section the single stage absorption cycle will be simulated<br />
in order to demonstrate the general behavior <strong>of</strong> an absorption cycle,<br />
independently <strong>of</strong> the rest <strong>of</strong> the system. Therefore the cooling tower is<br />
105
5. SIMULATION AND RESULTS<br />
eliminated by choosing ”manual” in the control panel <strong>of</strong> the EES model.<br />
Instead, inlet temperatures <strong>and</strong> temperature differences <strong>of</strong> the condenser<br />
<strong>and</strong> absorber are given explicit. The basic parameter configuration is<br />
though the same as for the st<strong>and</strong>ard single cycle with cooling tower in<br />
order to make it easier to compare.<br />
The four temperatures <strong>of</strong> the desorber, condenser, evaporator <strong>and</strong><br />
absorber will be varied one at the time <strong>and</strong> presented in four separate<br />
figures. These temperatures correspond to point 1, 2, 4 <strong>and</strong> 5 in figure<br />
5.1. They temperatures will be shown in upper x-axis <strong>of</strong> the graphs.<br />
A temperature change with reference to the st<strong>and</strong>ard parameter<br />
configuration for each <strong>of</strong> the four temperatures is introduced <strong>and</strong> shown<br />
on the lower x-axis on four graphs. As far as possible the four<br />
temperatures will be varied 10 ◦ C up <strong>and</strong> down.<br />
COP ABS (equation 1.1, page 8) is the most important indicator <strong>of</strong> how<br />
the st<strong>and</strong> alone cycle performs. In each figure COP ABS , the pressures<br />
(high <strong>and</strong> low) <strong>and</strong> the concentrations <strong>of</strong> the strong <strong>and</strong> weak LiBr<br />
solution will be plotted (w ss <strong>and</strong> w ws ).<br />
5.1.1 Changing the desorber temperature<br />
The desorber temperature is equivalent to the temperature at which heat<br />
is supplied to the absorption cycle 1 . Changing the desorber temperature<br />
does not affect the high or the low pressure, see figure 5.2A.<br />
On the other h<strong>and</strong>, the concentration <strong>of</strong> the strong solution (strong in<br />
LiBr) flowing from the absorber to the desorber (see figure 5.1) is affected<br />
by T DES . Since the high pressure is constant <strong>and</strong> the temperature <strong>of</strong><br />
the desorber is changed, it implies that the concentration <strong>of</strong> the strong<br />
solution must change as well in order to keep the solution <strong>and</strong> vapor in<br />
equilibrium (saturated liquid).<br />
When the desorber temperature drops, w ss decreases as well, see<br />
figure 5.2A. If the temperature decreases 10 ◦ C (corresponding to a<br />
desorber temperature <strong>of</strong> 70 ◦ C) w ss becomes almost equal to w ws .<br />
This means that the pumping factor (mass flow <strong>of</strong> LiBr solution in<br />
the absorber-desorber cycle relative to the flow <strong>of</strong> generated refrigerant)<br />
1 To avoid change in the amount <strong>of</strong> heat supplied, ˙Q HE AT,DES is given explicit for this<br />
particular simulation. T min,W GHE X 2,w,i is set free.<br />
106
5.1. Basic absorption cooling<br />
Figure 5.2: A: T DES is the desorber temperature. ∆T DES is the change <strong>of</strong> the desorber<br />
temperature relative to the st<strong>and</strong>ard parameter configuration (80 ◦ C). w ss <strong>and</strong> w ws is the<br />
concentration <strong>of</strong> the strong <strong>and</strong> weak LiBr-solution on mass basis. p Hi g h <strong>and</strong> p Low is the<br />
pressure at the condenser <strong>and</strong> evaporator respectively B: PF is the Pumping factor, which is<br />
the ratio between the mass flow <strong>of</strong> the weak solution (ṁ ws ) <strong>and</strong> refrigerant (ṁ r ).<br />
becomes very large as seen in figure 5.2B. This is the reason why COP ABS<br />
drops rapidly at the left h<strong>and</strong> side <strong>of</strong> the graph <strong>of</strong> figure 5.2A.<br />
There is no clear optimum for the desorber temperature with respect<br />
to COP ABS - the curve is rather flat. So it seems there is no reason to<br />
raise the desorber temperature above 80 ◦ C for the chosen parameter<br />
configuration. In the following it will be examined why the COP<br />
has a flat optimum at so low a temperature (rather than continuously<br />
increasing with temperature like so many other thermodynamic cycles<br />
do).<br />
Changing the solution heat exchanger<br />
At the st<strong>and</strong>ard parameter configuration ∆T min,SHE X = 5 ◦ C (ɛ SHE X = 0,9).<br />
To find out why the COP optimum is flat it is now investigated what<br />
happens if SHEX is either not present (ɛ SHE X = 0) or if the heat is ideally<br />
transferred (∆T min,SHE X = 0). In figure 5.3A COP ABS is plotted as function<br />
<strong>of</strong> ∆T DES for the three cases mentioned above.<br />
107
5. SIMULATION AND RESULTS<br />
Figure 5.3: A: Comparison <strong>of</strong> COP ABS for 1: a system without solution heat exchanger, 2:<br />
at st<strong>and</strong>ard parameter configuration (∆T min,SHE X = 5 ◦ C) <strong>and</strong> 3: with ideal heat exchanging<br />
(∆T min,SHE X = 0). B: The curves with dotted markers show the heat capacity flow <strong>of</strong> the weak<br />
<strong>and</strong> strong solution. The curves with triangular markers show ∆T min at each end <strong>of</strong> the SHEX.<br />
No SHEX<br />
If the SHEX is not present, COP ABS will increase as long as T DES increases,<br />
only limited by the maximum concentration <strong>of</strong> w ss (which is about 75%,<br />
see appendix B.4 page 231). The explanation is that before evaporation<br />
can take place, each kg <strong>of</strong> solution entering the desorber from the<br />
absorber has to be heated up from 31 ◦ C (T ABSO ) to T DES which requires<br />
energy without creating refrigerant. So it is an advantage to evaporate<br />
as much water per kg <strong>of</strong> LiBr solution as possible. And this is done by<br />
having a large difference in concentration between ws <strong>and</strong> ss (i.e. a high<br />
desorber temperature).<br />
Ideal SHEX<br />
For the ideal SHEX (∆T min,SHE X = 0) COP ABS will have an optimum at<br />
T DES = 72 ◦ C. At this point the difference in concentration <strong>of</strong> the strong<br />
<strong>and</strong> weak solution is very small, which leads to a very large pumping<br />
factor (PF), see figure 5.2B.<br />
108<br />
The reason why the SHEX makes a lower temperature more advanta-
5.1. Basic absorption cooling<br />
geous seems to be the following:<br />
When the desorber temperature is 72 ◦ C (optimum) the concentration<br />
<strong>of</strong> the strong solution is only slightly higher than that <strong>of</strong> the weak<br />
solution so the mass flow <strong>of</strong> the two flows is almost identical. This means<br />
that the heat capacity flow (Ċ = ṁ · c p ) becomes almost equal as seen in<br />
figure 5.3B<br />
Now that Ċ is almost the same for both flows, ∆T min,SHE X will be<br />
around zero in both ends <strong>of</strong> the SHEX as seen in figure 5.3B. This means<br />
that when the weak solution comes out <strong>of</strong> the SHEX <strong>and</strong> enters the<br />
desorber, it is already at the same temperature as the rest <strong>of</strong> the desorber<br />
(72 ◦ C). This way all <strong>of</strong> the heat supplied to the desorber can be used to<br />
evaporate refrigerant (water) from the solution instead <strong>of</strong> ”wasting” part<br />
<strong>of</strong> it on heating up the weak solution entering the desorber.<br />
If the desorber temperature was now increased to 80 ◦ C the weak<br />
solution would only be 75 ◦ C when entering the desorber since the ∆T min<br />
at the strong solution inlet would be 5 ◦ C even though the ∆T min at the<br />
weak solution inlet is 0 ◦ C. So in that case some <strong>of</strong> the heat supplied to<br />
the desorber would be needed for heating up the incoming solution to<br />
80 ◦ C before evaporation could begin. Hence the desorber temperature<br />
should not be too high.<br />
Conclusion on Desorber Temperature<br />
The investigations show that when the SHEX is omitted, a high desorber<br />
temperature is an advantage since it minimizes the energy required for<br />
heating up refrigerant into the desorber before evaporation can begin.<br />
But the better the SHEX is, the more advantageous it becomes to use<br />
a lower desorber temperature, since the SHEX can then do all <strong>of</strong> the ”pre<br />
heating” <strong>of</strong> the weak solution whereby all energy input into the desorber<br />
can be used for evaporating the refrigerant.<br />
5.1.2 Changing condenser temperature<br />
When the temperature <strong>of</strong> the condenser increases, the pressure increases<br />
as well because the condensation mainly takes place in the two phase<br />
region where pressure <strong>and</strong> temperature are dependent, see figure 5.4.<br />
Since the temperature <strong>of</strong> the desorber is kept constant <strong>and</strong> the<br />
pressure is equal to the condenser pressure, the concentration <strong>of</strong> the<br />
109
5. SIMULATION AND RESULTS<br />
Figure 5.4: T COND is the condenser temperature (upper x-axis). ∆T COND is the change <strong>of</strong> the<br />
condenser temperature (lower x-axis). w ss <strong>and</strong> w ws is the concentration <strong>of</strong> the strong <strong>and</strong> weak<br />
LiBr-solution on mass basis. p Hi g h <strong>and</strong> p Low is the pressure at the condenser <strong>and</strong> evaporator<br />
respectively (right y-axis)<br />
strong LiBr-solution (w ss ) must decrease in order to keep the solution<br />
at equilibrium, see appendix B.4.2 page 232.<br />
As w ss decreases it approaches w ws as seen in figure 5.4. If T COND<br />
increases to 42 ◦ C the concentration <strong>of</strong> the strong <strong>and</strong> weak solution<br />
becomes equal <strong>and</strong> COP ABS drops rapidly since no refrigerant is sent to<br />
the condenser.<br />
COP ABS has no optimum with respect to ∆T COND within the simulated<br />
range - the condenser temperature should just be as low as possible.<br />
But since the curve is almost flat on the left h<strong>and</strong> side <strong>of</strong> the graph, it<br />
can be concluded that a condenser temperature <strong>of</strong> about 30 to 35 ◦ C is<br />
sufficiently low for the given parameter configuration (<strong>of</strong> the single cycle<br />
configuration).<br />
110
5.1.3 Changing evaporator temperature<br />
5.1. Basic absorption cooling<br />
Figure 5.5: T EV AP is the evaporator temperature (upper x-axis) which must be above 0 ◦ C to<br />
avoid freezing <strong>of</strong> the refrigerant (water). ∆T EV AP is the change <strong>of</strong> the evaporator temperature<br />
(lower x-axis). w ss <strong>and</strong> w ws is the concentration <strong>of</strong> the strong <strong>and</strong> weak LiBr-solution on mass<br />
basis. p Hi g h <strong>and</strong> p Low is the pressure at the condenser <strong>and</strong> evaporator respectively (right y-axis)<br />
The evaporator temperature is proportional to the temperature at<br />
which the chilling is supplied. It has a lower limit since the refrigerant is<br />
water. This allows the st<strong>and</strong>ard evaporator temperature to be decreased<br />
by only 1 ◦ C relative to the st<strong>and</strong>ard parameter configuration - the gray<br />
area in figure 5.5 indicates the non-valid area.<br />
When the evaporator temperature (T EV AP ) increases, the low pressure<br />
(p low ) increases as well since T EV AP <strong>and</strong> p low are dependent in the two<br />
phase region (see figure 5.5).<br />
The pressure in the absorber is determined by the pressure in the<br />
evaporator. An increase <strong>of</strong> p low thus decreases the concentration <strong>of</strong> the<br />
weak solution (w ws ) because the temperature <strong>of</strong> the absorber is kept<br />
constant while the solution must be in equilibrium.<br />
111
5. SIMULATION AND RESULTS<br />
COP ABS does not reach an optimum in the investigated temperature<br />
range. It is evident that the performance increases with increasing<br />
evaporator temperature, but the cooling also becomes less valuable as<br />
the temperature increases. At 19 ◦ C the COP ABS reaches 0,88, but at<br />
this temperature chilling could almost be provided by the cooling tower<br />
directly, which would be much cheaper.<br />
5.1.4 Changing absorber temperature<br />
Figure 5.6: T ABSO is the absorber temperature (upper x-axis). ∆T ABSO is the change <strong>of</strong> the<br />
evaporator temperature relative to the st<strong>and</strong>ard absorber temperature (lower x-axis). w ss <strong>and</strong><br />
w ws is the concentration <strong>of</strong> the strong <strong>and</strong> weak LiBr-solution on mass basis. p Hi g h <strong>and</strong> p Low<br />
is the pressure at the condenser <strong>and</strong> evaporator respectively (right y-axis)<br />
The heat from the absorber must be removed at a temperature<br />
which is not too high. T ABSO does not affect the high or low pressure<br />
which are constant, see figure 5.6. But an increase <strong>of</strong> T ABSO will affect<br />
the concentration <strong>of</strong> the weak solution (w ws ) which will increase until<br />
it reaches w ss at T ABSO = 41 ◦ C. At this temperature COP ABS drops<br />
dramatically. The reasons for the shape <strong>of</strong> COP ABS is mainly the same<br />
112
5.1. Basic absorption cooling<br />
as described in section 5.1.1 about the desorber (now it is just the<br />
strong solution concentration which is constant, <strong>and</strong> the weak solution<br />
concentration which is changed).<br />
So T ABSO <strong>and</strong> T DES should be adjusted relative to each other to give<br />
the optimum performance. One should remember that since the heat<br />
is rejected to the surroundings, T ABSO is to a certain extend determined<br />
by the ambient temperature, so the concentration difference is probably<br />
easiest to adjust by changing T DES . This would in praxis be done by<br />
changing the flow rate <strong>of</strong> the LiBr solution relative to the heat input into<br />
the desorber.<br />
5.1.5 Summing up the general behavior <strong>of</strong> the<br />
absorption cycle<br />
In table 5.1 the characteristics <strong>of</strong> the absorption cycle is summed up. ↑<br />
symbols an increase for the current variable. The ↕ for COP ABS in line one<br />
indicates that the optimum is near the st<strong>and</strong>ard parameter configuration<br />
value <strong>of</strong> T DES .<br />
Table 5.1: General behavior <strong>of</strong> a single stage absorption cycle.<br />
Temperature Pressure Concentration Performance<br />
T DES ↑ ⇒ - ⇒ w ss ↑ ⇒ COP ABS ↕<br />
T COND ↑ ⇒ p COND ↑ ⇒ w ss ↓ ⇒ COP ABS ↓<br />
T EV AP ↑ ⇒ p EV AP ↑ ⇒ w ws ↓ ⇒ COP ABS ↑<br />
T ABSO ↑ ⇒ - ⇒ w ws ↑ ⇒ COP ABS ↓<br />
113
5. SIMULATION AND RESULTS<br />
5.2 System configurations<br />
In the previous section with the single cycle mostly COP ABS was used<br />
(i.e. the ratio <strong>of</strong> cooling power <strong>and</strong> high temperature heat input into the<br />
absorption cycle). This was typically around <strong>of</strong> 0,8 for Single Stage <strong>and</strong><br />
around 1,4 for Double Stage.<br />
In the following sections primarily COP ABS,f uel will be used since this<br />
shows how much cooling power the system provides per kW <strong>of</strong> <strong>fuel</strong> into<br />
the system (which remains constant at 100kW). This is done because the<br />
important thing for system optimization is how much cooling the system<br />
produces in the end (it doesn’t help that COP ABS is increased by<br />
a certain tweak if the heat flow into the absorption unit is at the same<br />
time reduced by a greater factor, so that the cooling power as a total<br />
drops). COP ABS,f uel will typically be around 0,4-0,5 corresponding to<br />
40kW-50kW <strong>of</strong> cooling per 100kW <strong>of</strong> <strong>fuel</strong> input.<br />
Three different aspects will be examined regarding the overall system<br />
configuration:<br />
• Single Stage (SS) vs Double Stage (DS) vs Double Stage with Dual<br />
Heat (DH).<br />
• Air Preheating (AP) vs No Air Preheat (-).<br />
• Dry Cooling Tower (d) vs Wet Cooling Tower (w).<br />
First SS, DS, <strong>and</strong> DH will be compared for AP <strong>and</strong> ”-AP” (all using a wet<br />
cooling tower 2 ). Once the best <strong>of</strong> these six combinations has been chosen,<br />
the two types <strong>of</strong> cooling towers will be compared. A figure with all 12<br />
combinations can be seen in appendix E.1.1 (page 276).<br />
For each figure in the following, the color convention will be as follows:<br />
Blue represents COP ABS,f uel : the amount <strong>of</strong> cooling power generated<br />
per <strong>fuel</strong> input (kW/kW).<br />
Black represents η el ,sys,net : the amount <strong>of</strong> net electricity generated per<br />
<strong>fuel</strong> input (kW/kW).<br />
2 The same tendencies are observed when the dry tower is used, just with<br />
COP ABS,f uel at a lower level<br />
114
5.2. System configurations<br />
Red represents η HW : the amount <strong>of</strong> energy used for hot water heating<br />
per <strong>fuel</strong> input (kW/kW).<br />
Since the <strong>fuel</strong> input is 100kW, each percent point <strong>of</strong> efficiency is equivalent<br />
to 1kW.<br />
5.2.1 Single, Double, Dual Heat (+/- Air Preheat)<br />
No Air Preheat<br />
From figure 5.7A it can be seen that if no air preheat is used, a pure<br />
double stage cycle doesn’t deliver more cooling than a single cycle. This<br />
is because <strong>of</strong> two opposite tendencies.<br />
• The COP based on the heat flow into the desorber <strong>of</strong> the absorption<br />
unit increases from 0,8 to 1,4.<br />
• The heat flow itself is reduced since less energy can be extracted<br />
from the exhaust gas <strong>of</strong> the SOFC (SS: T 22 =95 ◦ C, DS: T 22 =165 ◦ C,<br />
while T 20 =246 ◦ C in both cases). So the Single Stage receives 29kW,<br />
whereas the Double Stage receives only 16kW.<br />
The two tendencies happen to almost exactly counterweigh each<br />
other at the given parameter configuration (the cooling power is 23,3kW<br />
for SS <strong>and</strong> 22,7kW for DS).<br />
So the pure Double Stage doesn’t <strong>of</strong>fer any more cooling power than<br />
the Single Stage, although it does leave more energy in the exhaust gas,<br />
which can be used for hot water production (23kW vs 10kW).<br />
When the Dual Heat configuration is applied, DES2 still receives the<br />
same amount <strong>of</strong> heat as for the Double Stage (16kW) by cooling down<br />
the exhaust gas to 165 ◦ C. But now the exhaust gas is cooled down further<br />
(to 95 ◦ C) in WGHEX2, so an additional 13kW is sent into DES1. This<br />
significantly raises COP ABS,f uel which becomes 0,34. So the Dual Heat<br />
input raises the cooling by 11kW, although the hot water production is<br />
reduced from 23kW to 10kW. Since cooling, however, is assumed to be<br />
115
5. SIMULATION AND RESULTS<br />
more valuable than hot water 3 , the Dual Heat configuration is the best<br />
solution when no air preheat is used.<br />
eta | COP<br />
1.1<br />
1.0<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.10<br />
No Air Preheat<br />
0.23<br />
0.23 0.23<br />
0.10<br />
0.34<br />
0.53 0.53 0.52<br />
eta_HW<br />
COP_ABS,<strong>fuel</strong><br />
eta_sys,el,net<br />
eta | COP<br />
1.1<br />
1.0<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
With Air Preheat<br />
0.06<br />
0.26<br />
0.07<br />
0.46<br />
0.07<br />
0.38<br />
0.53 0.52 0.52<br />
eta_HW<br />
COP_ABS,<strong>fuel</strong><br />
eta_sys,el,net<br />
0.1<br />
0.1<br />
0.0<br />
SSw- DSw- DHw-<br />
0.0<br />
SSwA DSwA DHwA<br />
Figure 5.7: A+B: Comparison <strong>of</strong> system configurations. SS = Single Stage, DS = Double Stage,<br />
DH = Dual Heat. w = Wet cooling tower, d = Dry cooling tower. A = with Air preheat, - = no<br />
air preheat<br />
Air Preheat<br />
Figure 5.7B: When Air Preheat is applied (by adding GGHEX4) much <strong>of</strong><br />
the energy remaining in the exhaust gas after the absorption unit can be<br />
used to heat up the inlet air for the SOFC. This reduces the need for heat<br />
transmission in GGHEX3 <strong>and</strong> hence T 20 is increased. So this way more<br />
energy can be transferred to DES2 (DES1 for Single Stage).<br />
The COP ABS,f uel doesn’t change so much for Single Stage, since it already<br />
uses much <strong>of</strong> the exhaust gas energy to begin with.<br />
Dual Stage, however, benefits very much from the air preheating, since<br />
T 20 is increased from 246 ◦ C to 326 ◦ C. So now DES2 receives 33kW instead<br />
<strong>of</strong> only 16kW when no Air Preheat is used.<br />
3 why else use the Absorption cooling unit in the first place - if hot water was more<br />
valuable, all the waste heat should just be used for hot water production<br />
116
5.2. System configurations<br />
Dual Heat also receives 33kW, but only 19kW is sent in through DES2<br />
while the other 14kW goes directly into DES1 which is much less efficient<br />
than DES2.<br />
Conclusion about Air Preheat<br />
When Air Preheat is not used, the Dual Heat configuration is superior.<br />
But when Air Preheat is used, the pure Double Stage becomes even better<br />
than Dual Heat.<br />
Using the Air Preheat means that one more gas-gas heat exchanger<br />
(GGHEX4) is needed, which will increase the price <strong>of</strong> the system. But<br />
when GGHEX4 is added, GGHEX3 can be made somewhat smaller, since<br />
it doesn’t have to supply so much heat. So this will partially compensate<br />
for the extra cost <strong>of</strong> GGHEX4. Furthermore by using Double Stage rather<br />
than Dual Heat, WGHEX2 can be omitted. So the price <strong>of</strong> DSwA <strong>and</strong><br />
DHw- will probably not be too far apart.<br />
Hence it has been chosen solely to look at Double stage with Air<br />
Preheat from now on.<br />
5.2.2 Wet vs Dry cooling <strong>and</strong> ambient temperature<br />
In the rest <strong>of</strong> the optimization/investigation process in this chapter, a<br />
figure will be shown with the electrical efficiency (black), the absorption<br />
cycle COP (blue) <strong>and</strong> the hot water efficiency (red). Sometimes another<br />
figure will be presented to the right <strong>of</strong> this to help explain the observed<br />
behavior.<br />
It is examined in which interval <strong>of</strong> the ambient temperature the<br />
absorption process will run, <strong>and</strong> how the ambient temperature affects<br />
the performance <strong>of</strong> the system:<br />
COP ABS,f uel<br />
First it should be noticed from figure 5.8A that when the system uses the<br />
dry tower it will only run when the ambient temperature is below 20 ◦ C,<br />
<strong>and</strong> it is only effective when the temperature is below 18 ◦ C. If, on the<br />
other h<strong>and</strong>, the wet tower is used, the system can be run at temperatures<br />
up to 39 ◦ C (figure 5.8B).<br />
117
5. SIMULATION AND RESULTS<br />
Figure 5.8: Efficiencies <strong>and</strong> COP for Double Stage system with st<strong>and</strong>ard parameter<br />
configuration. A: Dry Tower. The grey area is where the system is not able to run. B: Wet<br />
Tower<br />
So there is very little idea in using the absorption cooling unit in<br />
conjunction with a dry tower - the ambient temperature has to be so low<br />
for this to work, that the cooling service could probably just as well be<br />
provided by blowing the ambient air over the product which needed the<br />
cooling service. Furthermore air conditioning is rarely needed when the<br />
ambient temperature is below 20 ◦ C, so a dry tower does not seem to be<br />
usable for the double stage ABS unit 4<br />
When the wet tower it used, the cooling COP increases somewhat<br />
when the ambient temperature is decreased (see blue curve in figure<br />
5.8B), but not at all as much as would have been the case for an electrical<br />
air conditioner. But in very hot climates, the limit at around 38-40 ◦ C<br />
could be a problem. It might be rare for so high a temperature to occur,<br />
but when it does, air conditioning would be absolutely crucial.<br />
Further investigations, however, show that if the temperature <strong>of</strong><br />
the high pressure desorber is increased, the condenser <strong>and</strong> absorber<br />
temperature can be increased, whereby the system will be able to operate<br />
4 A single stage ABS unit would be better as using a dry tower since the desorber<br />
temperature <strong>of</strong> this is normally around 80 ◦ C, so it could be raised without any problem -<br />
thereby making it possible to use a higher absorber <strong>and</strong> condenser temperature as well.<br />
118
5.2. System configurations<br />
in a hotter climate. If T DES2 is increased from 150 ◦ C to 190 ◦ C the limit <strong>of</strong><br />
the ambient temperature is increased from around 40 ◦ C to 50 ◦ C for the<br />
wet tower. For the dry tower, the limit is increased from 20 ◦ C to 30 ◦ C.<br />
But in order to avoid corrosion in the desorber, 150 ◦ C is generally<br />
considered to be the maximum allowed desorber temperature [27]. So<br />
for the very hot climate applications (>40 ◦ C) an option could be to use<br />
more expensive more corrosion resistant desorber materials <strong>and</strong> increase<br />
its temperature, or a single cycle could be used, which <strong>of</strong> course would<br />
be cheaper but less efficient. The same tendencies go for the dry tower.<br />
η sys,el ,net<br />
For the dry tower, the electrical efficiency (black curve in figure 5.8A) is<br />
quite steady except when the ambient temperature becomes high, which<br />
leads to an efficiency increase due to lower cooling tower fan power since<br />
the tower needs less cooling when the evaporator cooling production<br />
decreases.<br />
For the wet tower (figure 5.8B) the electrical efficiency increases<br />
steadily with the ambient temperature. This is because <strong>of</strong> the following:<br />
when the air temperature is high (<strong>and</strong> the relative humidity constant<br />
at 40%), one kg <strong>of</strong> air can absorb a bigger amount <strong>of</strong> water since the<br />
absolute humidity difference between the air inlet <strong>and</strong> the (saturated)<br />
outlet becomes larger. This means that the air flow through the cooling<br />
tower is lower at high ambient temperatures thereby reducing the fan<br />
power consumption.<br />
η HW<br />
The hot water heating(η HW , red curve in figure 5.8) is bigger for low<br />
ambient temperatures than for high ambient temperatures. But this is<br />
because the temperature <strong>of</strong> the water to be heated up is assumed to be the<br />
same as the ambient temperature. So when the ambient temperature is<br />
low, the exhaust gas can be cooled down to a lower temperature whereby<br />
more energy is transferred to the water.<br />
5.2.3 ∆T min,Tower<br />
The influence <strong>of</strong> the closest approach temperature difference on the two<br />
different types <strong>of</strong> towers is examined in appendix E.1.3.1 page 280.<br />
119
5. SIMULATION AND RESULTS<br />
5.3 Partial optimization <strong>of</strong> STD parameters<br />
In this section the st<strong>and</strong>ard (STD) parameters <strong>of</strong> the DSwA system<br />
configuration (Double Stage, Wet Tower + Air Preheat) are partial<br />
optimized.<br />
5.3.1 Outer conditions<br />
Evaporator temperature<br />
The temperature level <strong>of</strong> the evaporator outlet (T EV AP ) is now investigated.<br />
In a normal electrical air conditioner, the COP is strongly depen-<br />
Figure 5.9: The outlet temperature <strong>of</strong> the cooling water (point 49) is 6 ◦ C in the st<strong>and</strong>ard<br />
parameter configuration, <strong>and</strong> since ∆T min = 5 ◦ C this gives a temperature inside the evaporator<br />
<strong>of</strong> 1 ◦ C. When T EV AP,w,o is increased, the temperature inside the evaporator increases by the same<br />
amount.<br />
dent on the evaporator temperature. But for the absorption unit it has<br />
a much smaller effect (figure 5.9). When the evaporator outlet temperature<br />
is increased from 5 ◦ C to as much as 30 ◦ C (the ambient temperature),<br />
COP ABS,f uel is only increased 21% (9,5 percent points). So from<br />
120
5.3. Partial optimization <strong>of</strong> st<strong>and</strong>ard parameters<br />
this it can be concluded that an absorption cooling unit should preferably<br />
be used to cool down things to low temperatures where electrical<br />
units loose a bigger fraction <strong>of</strong> their COP - it is not good for just cooling<br />
things a few degrees. But since the refrigerant is water, it is impossible to<br />
get much lower than 5 ◦ C for a water-LiBr absorption unit (otherwise the<br />
water freezes), so there is a quite sharp lower limit.<br />
Relative humidity<br />
The influence <strong>of</strong> the relative air humidity is now examined. The ambient<br />
temperature is kept at 30 ◦ C:<br />
Figure 5.10: A): The COP <strong>and</strong> efficiencies are shown together with the water consumption <strong>of</strong><br />
the cooling tower. B (right side): The green curves show the temperature <strong>of</strong> the air in <strong>and</strong> out <strong>of</strong><br />
the cooling tower. The blue curves show the temperature <strong>of</strong> the water in <strong>and</strong> out <strong>of</strong> the tower.<br />
As can be seen from the dark blue curve in figure 5.10B, the model<br />
<strong>of</strong> the cooling tower predicts a decrease <strong>of</strong> the water outlet temperature<br />
when the relative humidity is decreased. This is because the wet bulb<br />
temperature is reduced.<br />
Figure 5.10A shows that from a COP perspective, it is most beneficial<br />
if the ambient air is as dry as possible since the water can thereby<br />
121
5. SIMULATION AND RESULTS<br />
be cooled down to a lower temperature. But the water consumption<br />
(kg/s per kW <strong>fuel</strong> input) raises considerably when the relative humidity<br />
decreases. This is mainly because the water is cooled down to a lower<br />
temperature which increases the need <strong>of</strong> heat removal by evaporation.<br />
The slight increase in η sys,el,net for an increase in humidity comes from<br />
a lower FAN power consumption (less cooling for the ABSO <strong>and</strong> COND1<br />
is needed <strong>and</strong> less air is sent through the tower).<br />
Furthermore with the st<strong>and</strong>ard parameter configuration the system<br />
becomes very ineffective at generating cooling when the relative humidity<br />
exceeds 0,7 (at 30 ◦ C ambient temperature). So in hot damp climates it<br />
could be a problem to run the system.<br />
Figure 5.11: The curves with the triangles show what happens if the temperature <strong>of</strong> the high<br />
pressure desorber is increased from 150 ◦ C (STD parameter config.) to 160 ◦ C which is seen to be<br />
an advantage for high humidity only<br />
But it turns out that increasing the desorber temperature can remedy<br />
this problem. So if the desorber temperature is just increased from 150<br />
to 160 ◦ C, the maximum limit for the relative humidity is increased from<br />
70% to 90% as seen in figure 5.11. The electrical efficiency <strong>and</strong> hot water<br />
efficiency remains virtually unaffected by the desorber temperature.<br />
122<br />
Raising the desorber temperature is however only an advantage for
5.3. Partial optimization <strong>of</strong> st<strong>and</strong>ard parameters<br />
damp or hot conditions - if the relative humidity is below 45% at an<br />
ambient temperature <strong>of</strong> 30 ◦ C then the lower desorber temperature gives<br />
a better COP.<br />
5.3.2 Desorber temperatures<br />
The temperature inside each desorber is assumed to be uniform i.e. the<br />
outlet temperature <strong>of</strong> the refrigerant <strong>and</strong> the strong solution is the same<br />
since the temperature is uniform everywhere inside the desorber.<br />
The desorber temperatures influences the saturation concentration <strong>of</strong><br />
the LiBr-solution, <strong>and</strong> hence the temperatures can only be altered in a<br />
certain interval for the model to work - one constraint is that the strong<br />
solution has to be stronger than the weak solution.<br />
The temperature <strong>of</strong> the high pressure desorber will be described first,<br />
since this is more simple than the low pressure desorber.<br />
Desorber 2<br />
In most thermodynamic cycles a system will perform best when the<br />
supplied heat is at a temperature as high as possible. So one would<br />
expect that it would be beneficial to use a desorber temperature as high<br />
as possible. But this turns out not to be the case. In fact the COP has<br />
a maximum for a desorber temperature around 150 ◦ C (for the chosen<br />
parameter configuration!) as can be seen in figure 5.12A. This is actually<br />
quite fortunate since it fits very well with the limit <strong>of</strong> 150 ◦ C due to the<br />
corrosion rate in the desorber.<br />
There are several reasons for this. First <strong>of</strong> all the concentration <strong>of</strong><br />
the weak <strong>and</strong> strong LiBr solution should be neither too close neither<br />
too far apart as explained in section 5.1. Secondly the amount <strong>of</strong> heat<br />
being reused from COND2 to DES1 can be seen to have an optimum<br />
around 150 ◦ C <strong>and</strong> a drastic decrease below 130 ◦ C (see orange curve in<br />
figure 5.12B). The heat flow into DES2 is constant though, since a higher<br />
T DES2 will increase T 22 , thereby preheating the SOFC inlet air even more<br />
in GGHEX4 so that GGHEX3 will take less energy from the exhaust gas.<br />
And this way T 20 will increase just as much as T 22 (purple <strong>and</strong> red curve).<br />
123
5. SIMULATION AND RESULTS<br />
Figure 5.12: A: Efficiencies <strong>and</strong> COP. B: The red <strong>and</strong> purple curves show the temperature before<br />
<strong>and</strong> after heat supply to the absorption unit. The brown curve shows how much heat the high<br />
temperature desorber receives, <strong>and</strong> the green curve shows how much heat DES1 receives (from<br />
COND2).<br />
Desorber 1<br />
The temperature <strong>of</strong> the low pressure desorber (DES1) is somewhat<br />
restricted by the temperature <strong>of</strong> the high pressure desorber (DES2).<br />
When T DES2 =150 ◦ C, T DES1 must be between 68 ◦ C <strong>and</strong> 88 ◦ C for the system<br />
to operate. From figure 5.13A it can be seen that the optimum <strong>of</strong> the blue<br />
COP curve is rather flat though, so the exact temperature is not so critical<br />
for the performance.<br />
In the st<strong>and</strong>ard configuration, the temperature <strong>of</strong> DES1 is not given<br />
explicitly since the system will not be able to run if e.g. T DES2 is altered<br />
too much while T DES1 remains constant. Instead the ratio <strong>of</strong> the mass<br />
flow rate <strong>of</strong> the refrigerant out <strong>of</strong> the desorber <strong>and</strong> the mass flow rate <strong>of</strong><br />
solution into the desorber is set equal for the two desorbers:<br />
ṁ 50<br />
ṁ 58<br />
= ṁ70<br />
ṁ 78<br />
(5.1)<br />
This is the same as saying that the difference between the strong<br />
<strong>and</strong> weak LiBr-solution is the same for two desorbers. And figure<br />
124
5.3. Partial optimization <strong>of</strong> st<strong>and</strong>ard parameters<br />
Figure 5.13: A+B In the st<strong>and</strong>ard parameter configuration the temperature <strong>of</strong> the low pressure<br />
desorber is set at the temperature where the strong solutions out <strong>of</strong> DES1 <strong>and</strong> DES2 are equal<br />
(intersection <strong>of</strong> red lines on the right figure). But by removing this equation an giving T DES1<br />
explicitly, this can be changed to see how it affects the performance <strong>of</strong> the system.<br />
5.13B shows that the intersection <strong>of</strong> the two red concentration curves<br />
actually gives a desorber temperature quite close to the optimum for<br />
COP ABS,f uel .<br />
5.3.3 SOFC subsystem<br />
Now some <strong>of</strong> the parameters in the SOFC subsystem are investigated. As<br />
mentioned earlier: the anode <strong>and</strong> cathode side <strong>of</strong> the SOFC has the same<br />
inlet temperature <strong>and</strong> the same outlet temperature.<br />
Changing ∆T SOFC<br />
A high temperature increase over the <strong>fuel</strong> cell (∆T SOFC ) is desirable<br />
for several reasons. One <strong>of</strong> the reasons is that it reduces the required<br />
air flow through the <strong>fuel</strong> cell thereby decreasing the blower power<br />
consumption. But ∆T SOFC can in practice not be too high, since a higher<br />
125
5. SIMULATION AND RESULTS<br />
outlet temperature <strong>of</strong> the cell will increase degradation while the inlet<br />
temperature can not be lowered too much if the reactions are to take<br />
place at an acceptable rate. New materials might however change this<br />
in the future so it is now investigated how ∆T SOFC affects the system.<br />
The cell inlet temperature is kept constant at 690 ◦ C, so only the outlet<br />
temperature changes.<br />
Figure 5.14: A The white area is where the SOFCs can run today. The light grey area is what<br />
is likely to become possible in the near future. The dark grey area is probably longer out in the<br />
future. B The green curve is the heat consumption <strong>of</strong> DES2. The Brown curves are the temp.<br />
before <strong>and</strong> after heat supply to DES2.<br />
From figure 5.14A it is seen that the electrical efficiency will benefit<br />
from a higher ∆T SOFC . In the <strong>cells</strong> used today, ∆T SOFC can not be much<br />
higher than 90 ◦ C, but in the near future it is likely to become possible to<br />
increase that number to 120 ◦ C [25], so this should increase the electrical<br />
efficiency from 0,51 to 0,55 (an 8% increase).<br />
The COP <strong>of</strong> the absorption unit remains virtually unaffected. Since<br />
the difference between T 20 <strong>and</strong> T 22 (brown curves) increases, one might<br />
expect the absorption unit to generate more cooling. But the temperature<br />
difference increase is accompanied by a decrease in exhaust gas mass<br />
flow, so the heat supply to DES2 (green line) remains almost constant.<br />
126
5.3. Partial optimization <strong>of</strong> st<strong>and</strong>ard parameters<br />
Figure 5.15: A Blower Power <strong>and</strong> Air Utilization in the SOFC. B Nernst potential, cell voltage<br />
<strong>and</strong> Area Specific Resistance.<br />
Figure 5.15A+B shows why the electrical efficiency changes - three<br />
things occur when the outlet temperature <strong>of</strong> the cell increases:<br />
1. The blower power consumption (black curve) decreases because <strong>of</strong><br />
a smaller air flow (green line: big air utilization = small air flow).<br />
2. The Nernst potential (grey curve) decreases which in itself reduces<br />
the cell voltage.<br />
3. But at the same time the Area Specific Resistance (blue curve)<br />
decreases. From figure 5.15B it can be seen that the ASR decrease<br />
is more dominant than the Nernst potential drop, so as a total, the<br />
cell voltage increases (brown curve).<br />
Changing T SOFC ,in<br />
Now the inlet temperature <strong>of</strong> the SOFC is examined. ∆T SOFC is kept<br />
constant, so when the inlet temperature is increased x degrees, so is the<br />
outlet temperature. Again, it is hard to get the inlet temperature much<br />
lower than 650 ◦ C if the chemical reactions are to take place.<br />
127
5. SIMULATION AND RESULTS<br />
Figure 5.16: A+B It is not possible to run the cell with a voltage (brown curve) <strong>of</strong> less than<br />
0,7kW, since the Nickel will then be oxidized. So at the st<strong>and</strong>ard parameter configuration, the<br />
inlet temperature can not be lower than 650 ◦ C although it becomes possible if the current draw<br />
is reduced).<br />
From figure 5.16A it is seen, that the electrical efficiency is increasing<br />
with the temperature <strong>of</strong> the SOFC inlet. As can be seen in figure 5.16B,<br />
this is due to two <strong>of</strong> the three factors mentioned in the section concerning<br />
∆T SOFC :<br />
1. The Nernst potential (grey curve) decreases which in itself reduces<br />
the cell voltage.<br />
2. At the same time the Area Specific Resistance (blue curve)<br />
decreases. Since the ASR decrease is more dominant than the<br />
Nernst potential drop, so as a total, the cell voltage (brown curve)<br />
increases.<br />
This time the blower power does not change since the air flow is constant.<br />
The COP <strong>of</strong> the absorption cooling unit decreases with T SOFC ,i , since<br />
less energy is available in the exhaust gas when the electrical efficiency<br />
<strong>of</strong> the SOFC is increased.<br />
128
Anode recycling (α SPG1 )<br />
5.3. Partial optimization <strong>of</strong> st<strong>and</strong>ard parameters<br />
There are several reasons for using anode recycling. First <strong>of</strong> all it supplies<br />
water for the pre reformer. But it also means that more the <strong>fuel</strong> is used,<br />
since some <strong>of</strong> the <strong>fuel</strong> that didn’t react the first time through the SOFC<br />
will react next time. This way more <strong>of</strong> the <strong>fuel</strong> will be used even though<br />
the <strong>fuel</strong> utilization factor from the SOFC point <strong>of</strong> view remains constant<br />
at U f =0,7 (it just means that every time the <strong>fuel</strong> is sent through the cell<br />
70% <strong>of</strong> it will be used in the electrochemical reaction).<br />
There is, however, a downside by the anode recycling. The<br />
concentration <strong>of</strong> the species CO, CO 2 , H 2 , <strong>and</strong> H 2 O is affected by the<br />
recycling . Generally the concentration <strong>of</strong> the reaction products are<br />
increased, which makes both the Nernst potential <strong>and</strong> the cell voltage<br />
decreases when the anode cycling fraction is increased (grey <strong>and</strong> brown<br />
curve in figure 5.17B).<br />
Figure 5.17: A+B The OC ratio (green) should be above 2 to avoid carbon depositing, so the<br />
recycling fraction should not be below 0,6.<br />
From figure 5.17A it can be seen that the increased use <strong>of</strong> the <strong>fuel</strong> in<br />
the SOFC more than compensates for the drop in cell voltages, so elec-<br />
129
5. SIMULATION AND RESULTS<br />
tricity wise it is a good idea to increase the anode recycling 5 . It can also<br />
be seen from the green line in figure 5.17B that the recycling fraction can<br />
not be below 0,6, since the OC ratio at the anode inlet will then fall below<br />
2, which would leat to carbon depositing.<br />
The COP <strong>of</strong> the absorption unit decreases with increased anode recycling.<br />
This is mainly due to the SOFC using a bigger fraction <strong>of</strong> the energy<br />
in the <strong>fuel</strong> to produce electricity, thereby leaving less heat for the absorption<br />
cooling unit. So although the electricity generation raises when<br />
the recycling is increased, the decrease in COP ABS,f uel is about twice as<br />
big. So for each kW electricity gained, 2kW cooling is lost.<br />
SOFC load (i d )<br />
In certain situations, such as during a heat wave, it might be desirable to<br />
generate as much cooling as possible even if it would severely lower the<br />
electricity production. In such cases more <strong>of</strong> the energy in the <strong>fuel</strong> could<br />
be used for the absorption unit <strong>and</strong> less for the SOFC system. Given a<br />
fixed number (<strong>and</strong> size) <strong>of</strong> stacks, this can be done in two ways, which<br />
will be compared in the following:<br />
1. Lowering U f : All <strong>fuel</strong> is still sent through the SOFC. But less<br />
current is drawn, <strong>and</strong> hence the utilization factor decreases, leaving<br />
more <strong>fuel</strong> for the burner.<br />
2. Fuel Bypass: Only some <strong>of</strong> the <strong>fuel</strong> is sent through the SOFC, while<br />
the rest is fed directly to the burner (completely bypassing the <strong>fuel</strong><br />
cell). The utilization factor <strong>of</strong> the <strong>fuel</strong> cell remains constant at 0,7.<br />
Figure 5.18 compares the two methods. When Fuel Bypassing (2) is<br />
used, the current density can go all the way from 0 to 3000A/m 2 6 .<br />
But in case (1) where all the <strong>fuel</strong> has to go through the SOFC, the<br />
current density may not fall below 2100A/m 2 . Because when all the <strong>fuel</strong> is<br />
sent through the pre reformer <strong>and</strong> <strong>fuel</strong> cell, most <strong>of</strong> it is reformed, which<br />
5 The model does, however, not include blower power for the recycling blower, but<br />
since the anode side volume flow is quite small, it should not consume especially much<br />
power<br />
6 It has been chosen to monitor the current density, since it is easily comparable to<br />
<strong>fuel</strong> <strong>cells</strong> <strong>of</strong> other sizes due to its independence <strong>of</strong> size<br />
130
5.3. Partial optimization <strong>of</strong> st<strong>and</strong>ard parameters<br />
Figure 5.18: Triangular markers (Case 1) is when all the <strong>fuel</strong> is sent through the cell (<strong>and</strong> U f<br />
varies). Round markers (Case 2) is when some <strong>of</strong> the <strong>fuel</strong> is by passed the SOFC <strong>and</strong> fed directly<br />
to the burner (U f remains constant).<br />
is an endothermic reaction. But the exothermic electrochemical reaction<br />
only occurs at a rate corresponding the current draw, <strong>and</strong> the exothermic<br />
water gas shift is not enough to make up for the heat consumption <strong>of</strong> the<br />
endothermic reforming. Furthermore the heat generation due to ASR<br />
loss decreases when the current draw is minimized. So when i d goes<br />
below 2100A/m 2 , the <strong>fuel</strong> cell will lack heat, <strong>and</strong> its inlet temperature has<br />
to be higher than the outlet temperature now that the chemical reactions<br />
sum up to be endothermic<br />
It can, however be seen from figure 5.18 that for current densities<br />
over 2100A/m 2 , sending all the <strong>fuel</strong> through the Fuel cell gives the best<br />
η sys,el ,net (while COP ABS,f uel is almost identical). But for current densities<br />
below 2100A/m 2 it is necessary to bypass some <strong>of</strong> the <strong>fuel</strong> directly to the<br />
burner.<br />
Method 1 is more efficient, but only method 2 can be used for lower<br />
current densities. Both these ways <strong>of</strong> increasing cooling power at the<br />
expense <strong>of</strong> electrical power will now be examined:<br />
131
5. SIMULATION AND RESULTS<br />
Method 1: Lowering U f<br />
The size <strong>and</strong> number <strong>of</strong> stacks is held constant, <strong>and</strong> the <strong>fuel</strong> input<br />
remains at 100kW into GGHEX1, but the <strong>fuel</strong> utilization factor varies<br />
with the current density.<br />
Figure 5.19: A+B: The x-axis now represents the Utilization factor, the corresponding current<br />
density can be seen as the green line. The results are only valid for U f > 0,35 since below this<br />
value the SOFC will not generate enough heat to maintain its temperature throughout the cell<br />
Figure 5.19B shows what happens when all the <strong>fuel</strong> is sent through<br />
the SOFC <strong>and</strong> the current density is varied:<br />
When more current is drawn, the <strong>fuel</strong> utilization increases. But the<br />
Nernst potential (grey curve) drops because <strong>of</strong> the higher concentration<br />
<strong>of</strong> products <strong>and</strong> lower concentration <strong>of</strong> reactants for the electrochemical<br />
reaction. The cell voltage (brown curve) is further decreased, since<br />
the increased current density will lead to a bigger voltage loss (V cell =<br />
V Ner nst − ASR · i d ). It is seen from η sys,el ,net (black curve) in figure 5.19A<br />
that these two tendencies approximately counterweigh each other in the<br />
region 0,6< U f
5.3. Partial optimization <strong>of</strong> st<strong>and</strong>ard parameters<br />
that it is an advantage to decrease <strong>fuel</strong> utilization to around 0,55 (by<br />
having a current density at around 2600A/m 2 ), since this increases<br />
the cooling power significantly without any considerable decrease in<br />
electrical power production.<br />
Method 2: Fuel Bypass<br />
The size <strong>and</strong> number <strong>of</strong> stacks is held constant 7 , <strong>and</strong> the total <strong>fuel</strong><br />
input remains 100kW, although some <strong>of</strong> it goes directly into the burner.<br />
The Fuel utilization factor remains 0,7 so when no <strong>fuel</strong> is bypassed the<br />
<strong>fuel</strong> cell, the current density is 3000A/m 2 . When the current density is<br />
decreased, the <strong>fuel</strong> bypass will go up in order to keep the <strong>fuel</strong> utilization<br />
factor at 0,7.<br />
Figure 5.20: The green curve shows the <strong>fuel</strong> bypass fraction - how big a part <strong>of</strong> the total <strong>fuel</strong><br />
input which is sent directly into the burner.<br />
The green line in figure 5.20 shows how big a fraction <strong>of</strong> the total <strong>fuel</strong><br />
input which is sent directly into the burner without going through the<br />
<strong>fuel</strong> cell first.<br />
7 The system size is 20,15 stacks since this corresponds to the st<strong>and</strong>ard configuration<br />
- <strong>of</strong> course the number <strong>of</strong> stacks will have to be an integer in reality.<br />
133
5. SIMULATION AND RESULTS<br />
As expected, η sys,el ,net decreases when the current density is reduced,<br />
<strong>and</strong> below 300A/m 2 the electricity generation is not even enough to cover<br />
the blower, fan, <strong>and</strong> pump power consumption.<br />
But as desired, the COP <strong>of</strong> the absorption unit increases, resulting<br />
in COP ABS,f uel approaching COP ABS (which is 1,4) when all the <strong>fuel</strong> is<br />
bypassed the <strong>fuel</strong> cell. COP ABS,f uel will never actually reach COP ABS ,<br />
since some <strong>of</strong> the <strong>fuel</strong> input into the burner will end up going out the<br />
system at point 24.<br />
So during high cooling dem<strong>and</strong>, 100kW <strong>of</strong> <strong>fuel</strong> can give 130kW 8 <strong>of</strong><br />
cooling instead <strong>of</strong> giving the usual 38kW cooling <strong>and</strong> 52kW electricity.<br />
Thus by sacrificing 1kW <strong>of</strong> electricity, 1,8kW <strong>of</strong> cooling can be gained.<br />
There are however two drawbacks:<br />
1. If the absorption cooling unit should be able to generate 130kW <strong>of</strong><br />
cooling, all <strong>of</strong> its components have to be much bigger, than if 38kW<br />
is maximum 9 .<br />
2. From an energy point <strong>of</strong> view it would be more beneficial to<br />
maintain the high electricity production during cooling peak<br />
dem<strong>and</strong>, <strong>and</strong> instead use the generated electricity to drive an<br />
electrical air conditioning unit where COP is typically in the range<br />
<strong>of</strong> 3-4. Of course the savings in <strong>fuel</strong> would have to be held up<br />
against the extra cost <strong>of</strong> the electrical unit minus the extra cost <strong>of</strong><br />
buying a bigger absorption cooling unit.<br />
So to sum up: if only a little more cooling is needed, the current draw<br />
can just be minimized thereby lowering the <strong>fuel</strong> utilization factor thereby<br />
leaving more heat for the absorption unit. If on the other h<strong>and</strong> a lot<br />
more cooling is needed some <strong>fuel</strong> can be sent directly into the burner.<br />
The latter method also makes it possible to maintain a high electricity<br />
generation while generating more cooling by adding <strong>fuel</strong> to the burner<br />
without diminishing the <strong>fuel</strong> flow into GGHEX3.<br />
The best solution does however seem to be using the generated<br />
electricity from the SOFC to run an electrical air conditioner.<br />
8 it is not possible to go below i d = 300A/m 2 since there is not enough electrical<br />
power to drive the blower.<br />
9 in the zero dimensional model it is not possible to see what effect an increased<br />
flow will have on components <strong>of</strong> a given size, so the calculated COP is based on the<br />
components varying in size with the cooling power.<br />
134
5.3. Partial optimization <strong>of</strong> st<strong>and</strong>ard parameters<br />
5.3.4 Closest Approach Temperature Differences (∆T min )<br />
In this section, the effect <strong>of</strong> the closest approach temperature difference<br />
∆T min <strong>of</strong> the various heat exchangers will be investigated. In theory<br />
∆T min can approach 0 but in praxis there will always be undesired<br />
losses, mixing, resistances <strong>and</strong> heat transmission in the direction <strong>of</strong> the<br />
tubes/plates. Hence the real values will be above zero. Since heat<br />
transmission in a liquid is generally better than in a gas, the st<strong>and</strong>ard<br />
closest approach temperature has been set differently for the different<br />
heat exchanger groups (depending on the phase <strong>of</strong> the fluid). Thus each<br />
group <strong>of</strong> heat exchanger will be investigated separately in the following.<br />
Water-Water Heat exchangers<br />
This group includes the evaporator, absorber, desorber2 10 <strong>and</strong> the<br />
internal LiBr solution heat exchangers. These are all liquid-liquid with<br />
a st<strong>and</strong>ard ∆T min <strong>of</strong> 5 ◦ C. All <strong>of</strong> them are now investigated in the range<br />
from 0 to 16 ◦ C: As expected, the system performs better if more efficient<br />
exchangers (lower ∆T min ) are used. The tendency is, however, not as<br />
pronounced as one might have expected. From figure 5.21 it is seen that<br />
the evaporator, absorber <strong>and</strong> SHEX1 are the most important <strong>of</strong> the waterwater<br />
heat exchangers. The cooling power output increases around 3-<br />
4% when ∆T min is reduced from 5 ◦ C to 0 ◦ C. If ∆T min is increased, the<br />
absorber suddenly becomes the most sensitive, <strong>and</strong> above 10 ◦ C it heavily<br />
decreases the COP.<br />
When it comes to value for money, it looks like it would be beneficial<br />
to buy a more efficient SHEX1 <strong>and</strong> a less efficient SHEX2, since COP<br />
is about three times more sensitive to SHEX1 than SHEX2. Of course<br />
SHEX1 is almost twice as big as SHEX2, since it contains the flow <strong>of</strong><br />
both desorbers, so decreasing its ∆T min will probably be about twice as<br />
expensive as for SHEX2 per degree Celsius, but the gain would also be<br />
three times as large.<br />
CATD <strong>of</strong> DES2 is seen to have very limited effect on the COP, so it<br />
doesn’t really matter if the water circuit (point 41 to 43) is used or if<br />
WGHEX1 <strong>and</strong> DES2 were instead integrated.<br />
10 ∆ T,min,DES1 is not examined since WGHEX2 <strong>and</strong> COND2 are assumed always to<br />
be integrated. ∆ T,min,DES2 on the other h<strong>and</strong> could be relevant, if the absorption cooling<br />
unit was originally indirect fired.<br />
135
5. SIMULATION AND RESULTS<br />
Figure 5.21: The influence <strong>of</strong> the Closest Approach Temperature for the liquid-liquid HEXes on<br />
the COP (STD value is 5 ◦ C). The electrical efficiency is not shown since it remains virtually<br />
constant.<br />
Condensers (Heat exchangers)<br />
The two condensers have liquid water inside the tubes, whereas the<br />
refrigerant on the outside is in the 2phase region (changing from higher<br />
gas quality to lower gas quality (saturated water)). So these heat<br />
exchangers must be more efficient than water-gas heat exchangers but<br />
less effective than water-water heat exchangers. Hence their st<strong>and</strong>ard<br />
∆T min is 10 ◦ C. They are also investigated from 0 to 16 ◦ C: As can be seen<br />
from figure 5.22, both condensers are far less sensitive to ∆T min than the<br />
water-water heat exchangers, <strong>and</strong> actually the system does not benefit<br />
from having a more efficient Condenser.<br />
Condenser 1 is a little more sensitive to ∆T min <strong>and</strong> as this increases,<br />
the slope <strong>of</strong> the curve becomes more negative. But when it is compared to<br />
the black line for the absorber in figure 5.21 an interesting fact is revealed.<br />
It turns out that the absorber curve is considerably steeper than the<br />
Condenser1 curve (figure 5.22). This shows than the temperature level<br />
136
5.3. Partial optimization <strong>of</strong> st<strong>and</strong>ard parameters<br />
Figure 5.22: The influence <strong>of</strong> the Closest Approach Temperature for the condensers on the COP<br />
(STD value is 10 ◦ C). The electrical efficiency remains virtually constant.<br />
is more important for the absorber than for Condenser1. In the cooling<br />
tower circuit the condenser has been connected before the absorber<br />
which means that COND1 will be colder than ABSO (since this order<br />
is the normal for absorption cooling machines according to [27]). But as<br />
these curves show, it would be more beneficial to connect them in the<br />
other order so that the absorber becomes colder than the condenser.<br />
To investigate this, simulations were made with the ABSO <strong>and</strong><br />
COND1 in the opposite order, but it turned out that it did not give a<br />
higher COP. 11 . It was hence chosen not to use that configuration anyway.<br />
Water-Gas Heat exchangers<br />
The blue curve in figure 5.23 show how COP ABS,f uel depends on the<br />
CATD <strong>of</strong> WGHEX1 (Water gas heat exchanger supplying the absorption<br />
11 When the temperature <strong>of</strong> the two components were changed at the same time they<br />
affected each others optimum <strong>and</strong> the COP dependency on the exact temperature.<br />
137
5. SIMULATION AND RESULTS<br />
Figure 5.23: The influence <strong>of</strong> the Closest Approach Temperature for the Water-Gas HEXes on<br />
the COP (STD value is 15 ◦ C). The electrical efficiency remains virtually constant. The brown<br />
<strong>and</strong> green line is the temperature <strong>of</strong> the exhaust gas before <strong>and</strong> after heat supply to DES2.<br />
unit with heat). If WGHEX1 becomes less effective (increase <strong>of</strong> ∆T min )<br />
T 21 will increase but so will T 20 due to the air preheating in GGHEX4<br />
(which means less heat transmission in GGHEX3) 12 .<br />
Gas-Gas Heat exchangers<br />
The GGHEX 1,2, <strong>and</strong> 3 have not been investigated, since their ∆T min<br />
is not given explicitly. GGHEX 1 <strong>and</strong> 2 have the same (unspecified)<br />
effectiveness. GGHEX3 is fed with the temperatures at point 13,14, <strong>and</strong><br />
19, so ∆T min can not be specified. So only GGHEX4 will be examined<br />
here. GGHEX4 reuses some <strong>of</strong> the exhaust gas heat after the absorption<br />
unit to preheat the <strong>fuel</strong> cell inlet air, which means that GGHEX3 can leave<br />
more <strong>of</strong> the exhaust gas energy for the absorption unit. So as expected<br />
COP ABS,f uel will increase then GGHEX4 becomes more effective, whereas<br />
12 WGHEX2 is not used in the st<strong>and</strong>ard configuration, end WGHEX3 will be<br />
examined in section 5.3.6 page 140<br />
138
5.3. Partial optimization <strong>of</strong> st<strong>and</strong>ard parameters<br />
Figure 5.24: The influence <strong>of</strong> the Closest Approach Temperature for the Air Pre heater<br />
(GGHEX4) on the COP (STD value is 25 ◦ C). The electrical efficiency remains virtually<br />
constant.<br />
the hot water generation will fall, since there is less energy in the exhaust<br />
gas at point 23.<br />
It appears that GGHEX4 is one <strong>of</strong> the most important heat exchangers<br />
(when it comes to COP variation). When its ∆T min is decreased 50%<br />
(from 25 ◦ C to 12,5 ◦ C), COP ABS,f uel increases from 45,6% to 48,9%. The<br />
second most important heat exchanger (the evaporator) only increases<br />
the COP ABS,f uel from 45,6% to 46,5% when its ∆T min is decreased 50%<br />
(from 5 ◦ C to 2,5 ◦ C).<br />
So cutting ∆T min in halves will give 3,6 percent points for GGHEX4<br />
<strong>and</strong> only 0,9 percent point for the evaporator. And if GGHEX4 is made<br />
more efficient, GGHEX3 can be made less efficient, since T 14 must remain<br />
constant.<br />
139
5. SIMULATION AND RESULTS<br />
5.3.5 ∆T for external circuits<br />
The difference between the highest <strong>and</strong> lowest temperature in each <strong>of</strong><br />
the external cycles, has been set to 5 ◦ C as st<strong>and</strong>ard. They have been<br />
investigated but they only give rise to a slight change in COP, so the<br />
graphs <strong>and</strong> their description has been placed in appendix E.1.2 page 277.<br />
5.3.6 Hot Water<br />
∆ T,min WGHEX3<br />
WGHEX3 uses the last <strong>of</strong> the energy in the exhaust gas to heat up<br />
water, which for instance could be used as domestic hot water in a hotel.<br />
The CATD <strong>of</strong> WGHEX3 is now investigated (it has, <strong>of</strong> course, only an<br />
influence in the hot water production, not on the absorption unit).<br />
Figure 5.25: The red lines shows how much heat is transferred to the how water when the<br />
WGHEX3 becomes more or less efficient. The water flow into the WGHEX 3 is adjusted so the<br />
Closest Approach Temperature Difference is the same in both ends - hence the outlet temperature<br />
<strong>of</strong> the water is influenced as well at the amount <strong>of</strong> energy extracted from the exhaust gas.<br />
140
5.3. Partial optimization <strong>of</strong> st<strong>and</strong>ard parameters<br />
When ∆T min,W GHE X 3 is decreased, a bigger amount <strong>of</strong> the energy left<br />
in the exhaust gas can be used to water heating, <strong>and</strong> furthermore the<br />
temperature to which the water can be heated increases (se figure 5.25).<br />
In the investigation ∆T min has been given the same value in both ends<br />
<strong>of</strong> the HEX, but in a real system their relationship will be controlled by<br />
the amount <strong>of</strong> water sent into the HEX (a big water flow means that the<br />
smallest ∆T min will occur at the gas outlet <strong>and</strong> vice versa). So if ∆T min is<br />
e.g. 15 ◦ C the temperature <strong>of</strong> the water doesn’t necessarily have to be 67 ◦ C<br />
as shown in the figure. By sending more water through, ∆T min would be<br />
smallest at the gas outlet end, yielding a smaller water outlet temperature<br />
(e.g. to avoid the guests on a hotel from being burned on the hot water<br />
from the tap).<br />
It can be seen from the red curve, that ideally 40% more hot water<br />
could be produced if there were no losses in the HEX (∆T min = 0 rather<br />
than 15 ◦ C).<br />
141
5. SIMULATION AND RESULTS<br />
5.4 Sensitivity Analysis<br />
In the previous sections some <strong>of</strong> the most important/interesting parameters<br />
have been examined thoroughly for different <strong>of</strong> values. In the following<br />
section spider diagrams will be shown for a larger range <strong>of</strong> parameters,<br />
subdivided in 4 groups: Closest Approach Temperature Differences,<br />
Pressure Losses, Heat Losses, <strong>and</strong> (other) Key Parameters. For<br />
each group the effect on the electrical efficiency will be shown on the left<br />
graph, <strong>and</strong> COP ABS,f uel on the right graph. All <strong>of</strong> the spider diagrams are<br />
for the st<strong>and</strong>ard system configuration (Double Stage, Wet Tower, with<br />
Air Preheat).<br />
The Y-axis show the percent increase <strong>of</strong> the COP (so a COP increase<br />
from 50% to 51% corresponds to 2% on the y-axis). The x-axis generally<br />
shows the percent increase in the input parameters for the st<strong>and</strong>ard<br />
configuration, although for the pressure losses in the absorption cycle,<br />
the st<strong>and</strong>ard parameter inputs are 0. So for these pressure loses the<br />
percent change is <strong>of</strong> the absolute pressure in that component. The heat<br />
loss is also 0 in the st<strong>and</strong>ard parameter configuration, so here it has been<br />
chosen to let the x-axis go from 0 to 1kW while the <strong>fuel</strong> input is kept at<br />
100kW.<br />
The y-axis has the same range in all (but one) <strong>of</strong> the figures (-5% to<br />
5%). This makes it easier to compare the effect <strong>of</strong> the different groups<br />
<strong>of</strong> parameters, although it does <strong>of</strong> course make it harder to see the exact<br />
value <strong>of</strong> the less important groups - but again: if all parameters in a group<br />
has a very small effect on COP <strong>and</strong> η sys,el,net their exact value doesn’t<br />
matter much. The only exception is the group ”Key Parameters”, which<br />
has an y-axis going from (-10% to 10%) since some <strong>of</strong> those parameters<br />
are particularly sensitive.<br />
5.4.1 Closest Approach Temperature Difference<br />
These temperatures have been estimated only based on the type <strong>of</strong> fluids<br />
in each heat exchanger (water-water, gas-gas etc.), so they are relatively<br />
uncertain, <strong>and</strong> it is not unlikely that they can be two times as big as<br />
estimated or only half as big (x-values going from -50% to +100%).<br />
142
5.4. Sensitivity Analysis<br />
ηsys,el,net increase<br />
∆T min : Electrical efficiency<br />
5%<br />
4%<br />
3%<br />
2%<br />
1%<br />
0%<br />
-100% -50% 0% 50% 100%<br />
-1%<br />
-2%<br />
-3%<br />
-4%<br />
-5%<br />
∆T min increase<br />
ABSO,s,o<br />
COND2,r,o<br />
EVAP,r,i<br />
GGHEX4,c,o<br />
SHEX1,ws,i<br />
SHEX2,ws,i<br />
TOWER,a,o,wet<br />
WGHEX1,w,i<br />
WGHEX3,w,i<br />
COPABS,<strong>fuel</strong> increase<br />
∆T min : COP<br />
5%<br />
4%<br />
3%<br />
2%<br />
1%<br />
0%<br />
ABSO,s,o<br />
COND2,r,o<br />
EVAP,r,i<br />
GGHEX4,c,o<br />
SHEX1,ws,i<br />
SHEX2,ws,i<br />
TOWER,a,o,wet<br />
WGHEX1,w,i<br />
WGHEX3,w,i<br />
-100% -50% 0%<br />
-1%<br />
50% 100%<br />
-2%<br />
-3%<br />
-4%<br />
-5%<br />
∆T min increase<br />
Figure 5.26: The relative influence <strong>of</strong> the Closest Approach Temperatures on η el ,sys,net <strong>and</strong><br />
COP ABS,f uel . The reason that some <strong>of</strong> the influential curves only ranges from -49% to 99% on<br />
the x-axis is to make the lines hidden below them visible.<br />
η sys,el ,net<br />
The most important CATD (see figure 5.26A) is that <strong>of</strong> the cooling tower<br />
(-3,5%) since a higher ∆T min means a lower air outlet temperature, which<br />
requires more air flow (<strong>and</strong> more fan power). GGHEX4 only has a slight<br />
influence (0,5%) because it changes the cooling power <strong>and</strong> hence the<br />
blower power for the cooling tower.<br />
COP ABS,f uel<br />
The CATD is most important for the GGHEX4 (-15%). The second most<br />
important is the evaporator (-5%) then comes the SHEX1 (-4%) (see<br />
figure 5.26B). So if any <strong>of</strong> the ”heat exchanger components” should be<br />
improved, those three are the most important.<br />
5.4.2 Pressure Losses<br />
Generally the components in the SOFC system <strong>and</strong> all the heat exchangers<br />
involving exhaust gas only influence the electrical efficiency (since<br />
a bigger pressure loss leads to a bigger blower power consumption), so<br />
143
5. SIMULATION AND RESULTS<br />
these are only included in the figure with the electrical efficiency (figure<br />
5.27A). The components in the ABS system generally only affect the cooling<br />
power so these are only included in the figure with the COP (figure<br />
5.27B).<br />
ηsys,el,net increase<br />
SOFC system Pressure Losses: El. efficiency<br />
5%<br />
4%<br />
3%<br />
2%<br />
1%<br />
0%<br />
∆pBurn,i,2<br />
∆pGGHEX3,c<br />
∆pGGHEX3,h<br />
∆pGGHEX4,c<br />
∆pGGHEX4,h<br />
∆pMIXG2,i,1<br />
∆pSPG2,o,1<br />
∆pWGHEX1,g<br />
∆pWGHEX2,g<br />
∆pWGHEX3,g<br />
-50% -30% -10% 10% 30% 50%<br />
-1%<br />
-2%<br />
-3%<br />
-4%<br />
-5%<br />
Increase <strong>of</strong> ∆p (relative to std parameter cfg.)<br />
COPABS,<strong>fuel</strong> increase<br />
ABS unit Pressure Losses: COP<br />
5%<br />
4%<br />
3%<br />
2%<br />
1%<br />
0%<br />
-10% -5% 0% 5% 10%<br />
-1%<br />
-2%<br />
-3%<br />
-4%<br />
-5%<br />
Increase <strong>of</strong> ∆p compared to absolute pressure<br />
∆pABSO,r<br />
∆pABSO,s<br />
∆pCOND1,r<br />
∆pCOND2,r<br />
∆pDES1<br />
∆pSHEX1,ss<br />
∆pDES2<br />
∆pSHEX1,ws<br />
∆pEVAP,r<br />
∆pMIXL1,1<br />
∆pMIXL1,2<br />
∆pMIXR1,1<br />
∆pMIXR1,2<br />
∆pSHEX2,ss<br />
∆pSHEX2,ws<br />
Figure 5.27: A Note that the left figure shows the components <strong>of</strong> the SOFC system <strong>and</strong> exhaust<br />
gas. These components have a pressure losses to begin with, so the x-axis shows the percentage<br />
increase <strong>of</strong> this value. B The right figures shows the components <strong>of</strong> the ABS system. They do not<br />
have a pressure loss to begin with (it is zero as st<strong>and</strong>ard). So for these the percentage increase <strong>of</strong><br />
the loss (x-axis) is <strong>of</strong> the absolute pressure in the given component.<br />
η sys,el ,net<br />
The pressure losses in the SOFC system have been approximated to<br />
values from the TOFC models, so they are assumed to be relatively<br />
reliable, <strong>and</strong> hence they are assumed to lay within +/- 50% <strong>of</strong> the<br />
st<strong>and</strong>ard parameter value.<br />
It can be seen that all the pressure losses are relatively insignificant<br />
- the most influential is the Burner <strong>and</strong> GGHEX3, which can change the<br />
electrical efficiency one percent (0,5 percent point), see figure 5.27A. The<br />
reason why these have a bigger influence than the other pressure losses<br />
is, that the st<strong>and</strong>ard loss is 4kPa in both <strong>of</strong> these (while the pressure<br />
loss is smaller for each <strong>of</strong> the other components) which means that if<br />
144
5.4. Sensitivity Analysis<br />
the pressure loss is increased by 50%, it means a larger increase in kPa<br />
than for the other components.<br />
COP ABS,f uel<br />
In the st<strong>and</strong>ard parameter configuration the pressure losses <strong>of</strong> the<br />
absorption unit components have been neglected. Hence it is not possible<br />
to talk about increasing the pressure loss by a certain percentage. So<br />
another way had to be found, <strong>and</strong> since the absolute pressure changes<br />
very much (from 0,65kPa in the evaporator to 120kPa in the high<br />
temperature desorber) it has been chosen to let the pressure loss be a<br />
percentage <strong>of</strong> the total (absolute) pressure in each component. It has<br />
been chosen to use 10% <strong>and</strong> the values are only plotted on the positive<br />
x-axis, since a negative x-axis would suggest a pressure increase for the<br />
components where the st<strong>and</strong>ard pressure loss is zero.<br />
For the absorption cycle the most important components are seen to<br />
be the evaporator <strong>and</strong> absorber (figure 5.27B). COP ABS,f uel is decreased<br />
a little less than 1,5% if the pressure loss <strong>of</strong> EVAP <strong>and</strong> ABSO is 0,066kPa<br />
(10% <strong>of</strong> the total pressure which is 0,66kPa). And these components even<br />
have the disadvantage, that the volume flow <strong>of</strong> fluid in them is quite<br />
large, since the low pressure increases the specific volume <strong>of</strong> the gas.<br />
But again the influence on COP is quite small relative to e.g. CATD<br />
<strong>and</strong> some <strong>of</strong> the parameters to come in the next subsection.<br />
5.4.3 Heat Losses<br />
η sys,el ,net<br />
It is seen that the heat losses generally have a very limited effect on<br />
the electrical efficiency with the exception <strong>of</strong> the SOFC, which actually<br />
increases the net generated electricity by almost 1%, see figure 5.28A.<br />
This is because less cooling <strong>of</strong> the SOFC is needed, so less air is sent<br />
through the blower, which diminishes blower power consumption.<br />
COP ABS,f uel<br />
The absorption unit generally suffers when heat losses occur, since it<br />
means less energy for evaporating the refrigerant in the desorbers. The<br />
difference between the different components (see figure 5.28B) occur<br />
145
5. SIMULATION AND RESULTS<br />
Heat Losses: Electrical efficiency<br />
5%<br />
4%<br />
3%<br />
BURN<br />
DES1<br />
DES2<br />
PR<br />
SHEX1<br />
SHEX2<br />
SOFC<br />
Heat Losses: COP<br />
5%<br />
4%<br />
3%<br />
BURN<br />
DES1<br />
DES2<br />
PR<br />
SHEX1<br />
SHEX2<br />
SOFC<br />
ηsys,el,net increase<br />
2%<br />
1%<br />
0%<br />
-1.0 -0.5 0.0 0.5 1.0<br />
-1%<br />
-2%<br />
-3%<br />
-4%<br />
-5%<br />
Component heat loss [kW]<br />
COPABS,<strong>fuel</strong> increase<br />
2%<br />
1%<br />
0%<br />
-1.0 -0.5 0.0 0.5 1.0<br />
-1%<br />
-2%<br />
-3%<br />
-4%<br />
-5%<br />
Component heat loss [kW]<br />
Figure 5.28: Component heat loss vs A: η sys,el ,net . B: COP ABS,f uel . A+B: None <strong>of</strong> the<br />
components have been given a heat loss in the st<strong>and</strong>ard parameter configuration, so it is not<br />
possible to talk about a percentage increase in heat loss. Hence it has been chosen to see what<br />
happens if 1kW <strong>of</strong> heat is lost to the surroundings in some selected components (the total <strong>fuel</strong><br />
input into the system is still 100kW).<br />
because <strong>of</strong> the following: When heat is lost before DES2 it reduces the heat<br />
input into both desorbers whereas heat lost after DES2 will only reduce<br />
the heat input into the low temperature desorber.<br />
5.4.4 (Other) Key Parameters<br />
The last group concerns a range <strong>of</strong> different parameters mainly concerning<br />
the SOFC system. Many <strong>of</strong> the parameters themselves have been<br />
estimated, so their value is associated with a significant degree <strong>of</strong> uncertainty.<br />
For each <strong>of</strong> them it has been estimated to the best extend <strong>of</strong> the<br />
authors capability how much the true value may be below or above the<br />
chosen parameter value (in appendix D.2 page 272 it is described how<br />
these values have been chosen). Then these two values have been used<br />
to define the interval in which each parameter is plotted in the spider diagram<br />
in figure 5.29. So from these spider diagrams three things can be<br />
read:<br />
146
5.4. Sensitivity Analysis<br />
1. The x-value in each end <strong>of</strong> a curve shows how much the real input<br />
is (at most) likely to deviate from the chosen parameter value.<br />
2. The y-value in each end <strong>of</strong> a curves shows how much the COP<br />
or electrical efficiency will change if the x-value is as far from the<br />
st<strong>and</strong>ard parameter value as the interval allows.<br />
3. The slope <strong>of</strong> each curve shows how much the COP or electrical<br />
efficiency will change if the given input parameter changes 1%.<br />
ηsys,el,net increase<br />
Key Parameters: Electrical efficiency<br />
10%<br />
8%<br />
6%<br />
4%<br />
2%<br />
0%<br />
-100% -50% 0% 50% 100%<br />
-2%<br />
-4%<br />
-6%<br />
-8%<br />
-10%<br />
Paramter increase<br />
ASR<br />
∆pTower,air,wet<br />
∆TSOFC,av<br />
ηWB,Tower<br />
FR<br />
FW<br />
id<br />
ηFAN<br />
ηBLOWER<br />
COPABS,<strong>fuel</strong> increase<br />
Key Parameters: COP<br />
10%<br />
8%<br />
6%<br />
4%<br />
2%<br />
0%<br />
-100% -50% 0% 50% 100%<br />
-2%<br />
-4%<br />
-6%<br />
-8%<br />
-10%<br />
Parameter increase<br />
ASR<br />
∆pTower,air,wet<br />
∆TSOFC,av<br />
ηWB,Tower<br />
FR<br />
FW<br />
id<br />
ηFAN<br />
ηBLOWER<br />
Figure 5.29: A range <strong>of</strong> different parameters are changed <strong>and</strong> the effect on η el,sys,net (A) <strong>and</strong><br />
COP ABS,f uel (B) is plotted. Note that the y-axis scale has been increased to 10% (from 5% in<br />
the previous figures).<br />
η sys,el ,net<br />
The current density (blue curve in figure 5.29A) doesn’t change so much<br />
in itself, but each percent change has a very big influence on the electrical<br />
efficiency, so it becomes the overall most important parameter so it seems<br />
to be a good idea to buy a little more <strong>cells</strong> per kW <strong>of</strong> <strong>fuel</strong> input (this will<br />
decrease current density).<br />
The ASR (black) also has a very big influence on the efficiency despite<br />
a limited uncertainty on the input (x-) value. The pressure loss <strong>of</strong><br />
147
5. SIMULATION AND RESULTS<br />
the cooling tower(orange) is also seen to have a big influence (due to<br />
increased FAN power consumption) mostly because the input value is<br />
associated with a large uncertainty. The temperature at which ASR is<br />
evaluated (T SOFC ,out − ∆T SOFC ,av ) is also significant. And the isentropic<br />
efficiency <strong>of</strong> the blower (turquoise) has a big influence on the blower<br />
power.<br />
COP ABS,f uel<br />
The COP generally shows the opposite tendency, see figure 5.29B. The<br />
things which are good for electrical efficiency are bad for COP <strong>and</strong> vice<br />
versa. The only exceptions are cooling tower pressure loss (which is<br />
neutral for COP) <strong>and</strong> an increased fraction <strong>of</strong> reforming (FR) in the pre<br />
reformer, which seems to be bad for COP as well as η.<br />
148
5.5 Total optimization <strong>of</strong> system<br />
5.5. Total optimization <strong>of</strong> system<br />
Now where all the different parameters <strong>of</strong> the st<strong>and</strong>ard parameter<br />
configuration have been investigated it is time to optimize the system<br />
(Double Stage, Wet Tower + Air Preheat). Four things will be viewed:<br />
1. The values <strong>of</strong> the ABS subsystem (mainly ∆T min <strong>and</strong> T DES ) will be<br />
adjusted/improved.<br />
2. The current (density) draw will be optimized to give the optimum<br />
combination <strong>of</strong> electricity <strong>and</strong> cooling.<br />
3. Future Case: What happens if the SOFC tolerate a higher<br />
temperature at the outlet.<br />
5.5.1 Absorption subsystem<br />
In the st<strong>and</strong>ard parameter configuration all the heat exchangers in the<br />
absorption cooling subsystem were given a ∆T min depending only on<br />
the phase <strong>of</strong> the fluids going through them (liquid-liquid = 5 ◦ C, liquidliquid/gas<br />
= 10 ◦ C, <strong>and</strong> liquid-gas = 15 ◦ C). From the investigations in<br />
the previous sections it was seen that the components in the following<br />
list were the most important for the COP (none <strong>of</strong> them had any<br />
significant influence on electrical efficiency. The list shows how much<br />
the COP ABs,f uel is increased when ∆T min for the component is halved.<br />
(The number in the parenthesis shows the st<strong>and</strong>ard value <strong>of</strong> the ∆T min .<br />
Ċ r atio is the heat capacity flow ratio):<br />
1. GGHEX4: 8,7% (∆T min =25 ◦ C, ɛ=0,77, NTU=2,4) Ċ r atio = 0,78<br />
2. SHEX1: 2,4% (∆T min =5 ◦ C, ɛ=0,87, NTU=5,0) Ċ r atio = 0,88<br />
3. EVAP: 1,6% (∆T min =5 ◦ C, ɛ=0,50, NTU=0,7) Ċ r atio = 0<br />
4. ABSO: 1,6% (∆T min =5 ◦ C, ɛ=0,40, NTU=0,5) Ċ r atio = 0 13<br />
5. SHEX2: 1,5% (∆T min =5 ◦ C, ɛ=0,87, NTU=5,0) Ċ r atio = 0,89<br />
13 The temperature distribution throughout the absorber is not known, so it has<br />
been assumed that it is uniform (equal to the solution outlet temperature) in the entire<br />
absorber. This corresponds to the solution/refrigerant having an infinite heat capacity<br />
flow compared to the external cooling water. Hence Ċ r atio is assumed to be zero.<br />
149
5. SIMULATION AND RESULTS<br />
Efficiency vs NTU for counterflow HEX<br />
ε<br />
1,0<br />
0,9<br />
0,8<br />
0,7<br />
0,6<br />
0,5<br />
0,4<br />
0,3<br />
0,2<br />
0,1<br />
0,0<br />
C_ratio = 0<br />
C_ratio = 0,25<br />
C_ratio = 0,50<br />
C_ratio = 1,00<br />
0 1 2 3 4 5<br />
NTU<br />
Figure 5.30: The figure shows the relation between ɛ (effectiveness) <strong>and</strong> NTU (Number <strong>of</strong><br />
Transfer Units) for a counterflow heat exchanger.<br />
The correlation between NTU <strong>and</strong> ɛ for a counter flow heat exchanger<br />
can be seen in figure 5.30. (GGHEX4 <strong>and</strong> the SHEXes are assumed to be<br />
counterflow, <strong>and</strong> the EVAP <strong>and</strong> ABSO has a heat capacity flow ratio <strong>of</strong> 0<br />
which means that the flow ɛ-NTU relation is unaffected by the flow configuration<br />
<strong>and</strong> only depends on NTU).<br />
It is seen that the SHEXes have the largest relative sizes (a large NTU<br />
means that the HEX is large relative to the (smallest) heat capacity flow).<br />
Hence it is easiest (<strong>and</strong> cheapest) to improve the heat exchangers which<br />
have a low NTU number. So the SHEXes will not be improved further,<br />
whereas the GGHEX, EVAP <strong>and</strong> ABSO can be improved. The list below<br />
show the values used in the optimization.<br />
1. GGHEX4: 8,7% (∆T min =9,4 ◦ C, ɛ=0,9, NTU=5,0) Ċ r atio = 0,78<br />
2. SHEX1: 2,4% (∆T min =5 ◦ C, ɛ=0,87, NTU=5,0 Ċ r atio = 0,88)<br />
3. EVAP: 1,6% (∆T min =2,7 ◦ C, ɛ=0,65, NTU=1,0)Ċ r atio = 0<br />
4. ABSO: 1,6% (∆T min =1,8 ◦ C, ɛ=0,65, NTU=1,0) Ċ r atio = 0<br />
5. SHEX2: 1,5% (∆T min =5 ◦ C, ɛ=0,87, NTU=5,0) Ċ r atio = 0,89<br />
Since GGHEX4 is very important, it has been decided that a very good<br />
HEX should be used (NTU=5). For the evaporator <strong>and</strong> absorber the NTU<br />
150
5.5. Total optimization <strong>of</strong> system<br />
is only set to 1. The reason that it is not set to 5 as for some <strong>of</strong> the other<br />
components is that it would give a ∆T min <strong>of</strong> less than 1 ◦ C <strong>and</strong> that just<br />
doesn’t seem realistic.<br />
It was seen in section 5.3.2 page 123 that the system performed best if<br />
T DES2 as well as T DES1 was lowered a little relative to the st<strong>and</strong>ard parameter<br />
configuration. So this have been done now (with the new ∆T min s applied),<br />
<strong>and</strong> it turns out that the ideal value <strong>of</strong> the desorber temperatures<br />
is T DES1 = 67 ◦ C <strong>and</strong> T DES2 = 133 ◦ C.<br />
Figure 5.31: A: Optimized parameters (∆T min for ABSO, EVAP, GGHEX4 <strong>and</strong> T DES1+2 ). B:<br />
The Trade<strong>of</strong>f factor shows how many kW <strong>of</strong> cooling which can be gained by sacrificing 1kW <strong>of</strong><br />
electricity (regulated by the current draw).<br />
Figure 5.31A shows how much the optimized parameters improved<br />
the system. COP ABS,f uel is increased 5 to 10 percent points depending<br />
on the current density, while the electrical efficiency remains virtually<br />
unaffected. Only the hot water production decrees a little with the<br />
optimized parameters.<br />
151
5. SIMULATION AND RESULTS<br />
5.5.2 Current density<br />
The next point is to decide how much current to draw from the system.<br />
As figure 5.31A shows, there is a very flat optimum for the electrical<br />
efficiency around a current density <strong>of</strong> 3000A/m 2 . The cooling power is,<br />
however, largest for small current draws. And around 3000A/m 2 the<br />
gradient <strong>of</strong> the COP is not at all as flat as the electrical efficiency. So<br />
when the current density is decreased, more cooling is gained while only<br />
a little electricity is lost.<br />
So the question is where the optimal trade<strong>of</strong>f between electricity <strong>and</strong><br />
cooling lays. The optimum is found by the following reasoning: if<br />
more cooling is needed this can be done by using some <strong>of</strong> the generated<br />
electricity in a normal electrical air conditioner to create cooling. These<br />
generally have a COP <strong>of</strong> 3-4 for the conditions <strong>of</strong> the case (ambient<br />
temperature <strong>of</strong> 30 ◦ C <strong>and</strong> a produced cooling water at 6 ◦ C). This implies<br />
that electricity is 3-4 times more valuable than cooling. For simplicity<br />
it is here assumed that a supplementary electrical air conditioning unit<br />
already is present for peak load, backup etc. so the electricity can directly<br />
be used to generate cooling. Figure 5.31B shows the trade<strong>of</strong>f factor<br />
between cooling <strong>and</strong> electricity.<br />
It is seen that when i d = 2700A/m 2 , the trade<strong>of</strong>f factor is 3,4 meaning<br />
that when the electricity generation is decreased 1kW (by lowering i d )<br />
then 3,4kW <strong>of</strong> cooling is gained. So optimum is seen to be at a current<br />
density <strong>of</strong> 2700A/m 2 .<br />
Furthermore it can be seen from figure 5.31B that the total ”efficiency”<br />
<strong>of</strong> the system exceeds 1,0 (i.e. the total output <strong>of</strong> electricity plus heat<br />
plus cooling exceeds the <strong>fuel</strong> input). And the smaller the current density,<br />
the larger this total ”efficiency” becomes. This also makes sense since it<br />
would be equal to COP ABS (=1,45) if all the energy <strong>of</strong> the <strong>fuel</strong> was sent<br />
directly into the desorber <strong>of</strong> the absorption cooling subsystem.<br />
The first two columns <strong>of</strong> figure 5.32 show how much the efficiencies<br />
<strong>and</strong> COP has been improved by going from the st<strong>and</strong>ard parameter<br />
configuration to an optimized situation (with better ABSO, EVAP,<br />
GGHEX4, optimized T DES1+2 <strong>and</strong> current draw). The electrical power<br />
has fallen 2 kW (per 100kW <strong>fuel</strong> input), <strong>and</strong> the hot water generation<br />
has fallen 4kW, but the cooling power has increased 13kW. The fall in<br />
electrical power is mainly due to the current density being decreased<br />
from 3000A/m 2 to 2700A/m 2 in order to reach the optimum trade<strong>of</strong>f<br />
between electricity <strong>and</strong> cooling.<br />
152
5.5. Total optimization <strong>of</strong> system<br />
eta | COP<br />
St<strong>and</strong>ard vs Optimized parameters<br />
1,2<br />
1,1<br />
1,0<br />
0,9<br />
0,8<br />
0,7<br />
0,6<br />
0,5<br />
0,4<br />
0,3<br />
0,2<br />
0,1<br />
0,0<br />
0,07<br />
0,46<br />
0,03<br />
0,52 0,50<br />
0,03<br />
0,59 0,51<br />
eta_HW<br />
COP_ABS,<strong>fuel</strong><br />
eta_sys,el,net<br />
0,55<br />
St<strong>and</strong>ard Optimized Optimized<br />
ΔT_SOFC=120<br />
Figure 5.32: All bars are for the Double stage with Air Preheat. The right <strong>and</strong> middle columns<br />
are both for the optimized system, where i d has been optimized by aiming for a trade<strong>of</strong>f factor<br />
between cooling <strong>and</strong> electricity <strong>of</strong> 3,4.<br />
With the new ∆T min = 11 ◦ C for the additional air preheat (GGHEX4),<br />
the total gain <strong>of</strong> using air preheat is 14kW (59kW with air preheat vs<br />
45 kW for the same parameters without air preheat (not shown in the<br />
figure)).<br />
5.5.3 Future: ∆T SOFC = 120 ◦ C<br />
It is now investigated what will happen if it in the future becomes<br />
possible to use a 120 ◦ C temperature span over the <strong>fuel</strong> cell (i.e. inlet<br />
temperature is kept constant while outlet temperature is increased from<br />
780 ◦ C to 810 ◦ C).<br />
As seen in figure 5.32 the electricity generation increases 5kW while<br />
the cooling power decreases 8kW 14 . From a cooling perspective this<br />
14 the current density has been adjusted to give the same trade<strong>of</strong>f factor between<br />
153
5. SIMULATION AND RESULTS<br />
might sound like bad news, since cooling power does decrease by 8kW.<br />
But the additional 5kW <strong>of</strong> electricity can be used to generate around 5kW<br />
·3,4 = 17kW <strong>of</strong> cooling with a normal electrical air conditioner. So it is<br />
definitely worthwhile to increase the SOFC outlet temperature.<br />
cooling <strong>and</strong> electricity (3,4) as in the ”Optimized” situation. This gives a current density<br />
<strong>of</strong> 3000A/m 2<br />
154
C H A P T E R<br />
6<br />
CASES AND ECONOMICS<br />
6.1 Air conditioning <strong>of</strong> hotels<br />
In chapter 2 three different market segments - APU, CHP <strong>and</strong> DG - were<br />
examined <strong>and</strong> it was concluded that Distributed Generation (DG) was<br />
the best one for integrating a SOFC system with an absorption chilling<br />
unit 1 . A hotel was seen to be an interesting industry for applying DG<br />
technology because the dem<strong>and</strong> <strong>of</strong> electricity, air conditioning <strong>and</strong> hot<br />
water to some extend matches the supply <strong>of</strong> the SOFC-ABS.<br />
In section 2.4 it was concluded that a system combined <strong>of</strong> a SOFC-<br />
ABS is more pr<strong>of</strong>itable in a climate where AC is needed all year (Hot<br />
Climate) compared to a climate where it is only required part <strong>of</strong> the year<br />
(Normal Climate).<br />
In this chapter potential geographical locations for a SOFC-ABS unit<br />
will be discussed, the water consumption <strong>of</strong> the cooling tower will be<br />
evaluated, <strong>and</strong> the assumptions in the economical calculations will be<br />
compared to the results <strong>of</strong> the thermodynamical model.<br />
better<br />
1 APU for ships also looked promising but it was concluded that DG was slightly<br />
155
6. CASES AND ECONOMICS<br />
Three geographical locations are investigated:<br />
1. Hotel in The Seychelles - Climate with high humidity.<br />
2. Hotel in Bangkok - Climate with very high humidity.<br />
3. Hotel in Las Vegas - Climate with low humidity.<br />
The investigations are based on the double stage system configuration<br />
with optimized parameters as described in section 5.5.<br />
6.2 High humidity climate<br />
6.2.1 Seychelles<br />
The Seychelles is a group <strong>of</strong> isl<strong>and</strong>s located northeast <strong>of</strong> Madagascar<br />
(about 1600 km east <strong>of</strong> Kenya). The primary industry is tourism [37]<br />
<strong>and</strong> thus it is expected that a lot <strong>of</strong> hotels exist. Additionally the primary<br />
energy supply is based on oil, <strong>and</strong> the government wants to shift towards<br />
a more sustainable energy source. These two circumstances makes the<br />
Seychelles a potentially attractive market for a SOFC-ABS system.<br />
Figure 6.1: Weather data for Port Victoria, Seychelles. Average condition. Table taken from [6].<br />
The Climate in the Seychelles is quite humid (see the average weather<br />
condition data from Port Victoria in figure 6.1). The data is taken from<br />
156
6.2. High humidity climate<br />
BBC Home Weather web page [6]. The relative humidity is in the range<br />
74-79% <strong>and</strong> the temperature is also quite stable in the range <strong>of</strong> 24-29 ◦ C<br />
with peaks up to 33 ◦ C.<br />
To evaluate the behavior <strong>of</strong> the SOFC-ABS system in different<br />
climates the performance has been plotted as function <strong>of</strong> the ambient<br />
temperature, see figure 6.2. The relative humidity (φ) is kept constant<br />
at 80%. When the humidity is high, it is an advantage to use a higher<br />
temperature for DES2. So a desorber temperature <strong>of</strong> 150 ◦ C has been<br />
used. This is sufficient for ambient temperatures up to 32 ◦ C when the<br />
relative humidity is 80%, so for most <strong>of</strong> the days this will suffice for<br />
the Seychelles. For the few days with a temperature above 32 ◦ C, the<br />
desorber temperature must be increased as discussed in the next section.<br />
Figure 6.2: The relative humidity is φ = 0,8. The desorber temperature is kept at 150 ◦ C. The<br />
water consumption corresponds to a <strong>fuel</strong> input <strong>of</strong> 100kW.<br />
6.2.2 Bangkok<br />
In Thail<strong>and</strong> tourism is important for the economy <strong>of</strong> the country (about<br />
6% <strong>of</strong> GDP) [38]. So it looks like Thail<strong>and</strong> could be a potential market for<br />
SOFC-ABS integrated systems.<br />
157
6. CASES AND ECONOMICS<br />
Data from Bangkok is shown in figure 6.3 to illustrate the climate <strong>of</strong><br />
the middle part the country. The relative humidity varies a lot <strong>and</strong> is<br />
more extreme than in the Seychelles: The relative humidity is up to 94% 2 ,<br />
<strong>and</strong> the temperature is normally in the range <strong>of</strong> 20-35 ◦ C but can be as<br />
high as 41 ◦ C.<br />
Figure 6.3: Weather data for Bangkok, Thail<strong>and</strong>. Average condition. Table taken from [3].<br />
Keeping these climate data in mind, the COP <strong>of</strong> the system (blue<br />
line with round dots in figure 6.4A) shows that it is not sufficient to<br />
use a desorber temperature (DES2) <strong>of</strong> 150 ◦ C since COP ABS,f uel decreases<br />
drastically at about 30 ◦ C. Thus it has been necessary to increase T DES2 3 in<br />
order to extend the range <strong>of</strong> the ambient temperature at which the system<br />
can operate (blue line with triangular markers in figure 6.4A). When the<br />
temperature <strong>of</strong> DES2 is increased, the ambient temperature can be up to<br />
about 40 ◦ C, but the high ambient temperature does significantly decrease<br />
COP ABS .<br />
The biggest problem though is that DES2 is exposed to a temperature<br />
<strong>of</strong> up to 190 ◦ C which is much higher than the recommended maximum<br />
temperature <strong>of</strong> 150 ◦ C according to [27] (see brown curve market with<br />
triangles in figure 6.4B). Thus it should not be expected that a st<strong>and</strong>ard<br />
absorption unit can operate under this high temperature due to corrosion<br />
problems.<br />
2 The most extreme values <strong>of</strong> the humidity is likely to be caused by fluctuating<br />
temperature, so it is assumed that the humidity is not above 0,9 during daytime.<br />
3 The desorber temperature <strong>of</strong> DES1 has been changed as well since its optimum<br />
value depends on the temperature <strong>of</strong> DES2.<br />
158
6.2. High humidity climate<br />
Figure 6.4: A: The relative humidity is φ = 0,9. B: The desorber temperature is either kept<br />
at 150 ◦ C (moderate humidity) or varied (VAR.)(very high humidity). The water consumption<br />
corresponds to a <strong>fuel</strong> input <strong>of</strong> 100kW.<br />
It might be possible to design a desorber which is capable to operate<br />
at this high temperature by means <strong>of</strong> more corrosion resistant materials,<br />
but it is out <strong>of</strong> the scope <strong>of</strong> this report to investigate this further.<br />
The above results show that it is more complicated to implement a<br />
system <strong>of</strong> SOFC integrated with absorption air conditioning in a climate<br />
like the one in Bangkok than the one in the Seychelles. This should be<br />
taken into account when potentially new markets are considered.<br />
159
6. CASES AND ECONOMICS<br />
6.3 Low humidity climate<br />
6.3.1 Las Vegas<br />
Tourism <strong>and</strong> gaming is the major industry <strong>of</strong> Las Vegas which is located<br />
in the Mojave Desert, Nevada, USA. The city has had more than 39<br />
million visitors a year (2007) [36]. So one can imagine that hotels are<br />
in dem<strong>and</strong> in this area.<br />
Figure 6.5: Weather data for Las Vegas, USA. Average condition. Table taken from [5].<br />
The climate reflects the location in the desert - dry <strong>and</strong> very hot<br />
during the summer although colder during winter (see table in figure<br />
6.5). So air conditioning is mostly needed during the late spring, summer<br />
<strong>and</strong> fall.<br />
In this area the relative humidity is around 40% (see figure 6.6) so<br />
the desorber temperature is set equal to that <strong>of</strong> the optimized parameter<br />
configuration (T DES2 = 133 ◦ C). The figure shows that the system is<br />
efficient up to 40 ◦ C in contrast to the humid climates (φ = 0,8−0,9) where<br />
the ambient temperature had to be below 30 ◦ C for a maximum desorber<br />
temperature <strong>of</strong> 150 ◦ C. For the dry climate the maximum allowable<br />
ambient temperature is 42 ◦ C, which is just enough to cope with the<br />
maximum average temperature in Las Vegas 6.5.<br />
A problem might occur when the ambient temperature reaches the<br />
peak temperature in July <strong>and</strong> August (46 ◦ C), but the relative humidity is<br />
160
6.3. Low humidity climate<br />
Figure 6.6: The relative humidity is φ = 0,4. The ambient temperature is varied for the system<br />
with optimized parameter configuration. ṁ is the water consumption <strong>of</strong> the wet cooling tower.<br />
low in this period - around 20% 4 . The system has been simulated under<br />
these conditions which showed that even at 48 ◦ C the COP ABS,f uel is still<br />
above 0,5 (see appendix E.2 page 283).<br />
6.3.2 Water consumption<br />
Another important difference between a dry <strong>and</strong> a humid climate is<br />
the consumption <strong>of</strong> water in the cooling tower. In the case with high<br />
humidity (see figure 6.4B) the water consumption is in the order <strong>of</strong> 0,03 kg<br />
s<br />
(corresponding to approximately 950 m3<br />
year )5 . In the dry climate (φ = 0,4)<br />
the water consumption is 0,06 kg<br />
s<br />
(figure 6.6) - twice that <strong>of</strong> the humid<br />
4 The relative humidity ranges from 14 to 32% in July/Aug, but when the<br />
temperature is at its highest (during the day), the relative humidity is generally at the<br />
lowest. So during peak temperature the humidity in Las Vegas should not be above<br />
20%<br />
5 Assuming the system runs at full load all year around. Fuel input <strong>of</strong> 100kW.<br />
161
6. CASES AND ECONOMICS<br />
climate. So the annually water consumption for the cooling tower is up<br />
to about 1900 m3 if the system is running at full load 24/7.<br />
year<br />
The price <strong>and</strong> the availability <strong>of</strong> water depends very much on local<br />
conditions. It is out <strong>of</strong> the scope <strong>of</strong> this report to investigate the exact<br />
circumstances. Instead a rough estimate <strong>of</strong> the expenses <strong>of</strong> water has<br />
been made <strong>and</strong> compared to the monetary value <strong>of</strong> the electrical power<br />
produced by the SOFC in order to assess the proportions <strong>of</strong> the water<br />
consumption. The calculations are found in appendix D.3 (page 273).<br />
The price <strong>of</strong> water is assumed to be 10 DKK 6 <strong>and</strong> electricity is assumed<br />
m 3<br />
to be 2 DKK 7 kWh<br />
. For the humid climate (φ = 0,9) the expense <strong>of</strong> water is about<br />
1% <strong>of</strong> the value <strong>of</strong> electricity produced 8 . For the dry climate (φ = 0,4) the<br />
expense is about 2%. If the water price doubled <strong>and</strong> the electricity price<br />
was reduced by 50%, the expense <strong>of</strong> water would be about 4% <strong>and</strong> 8% <strong>of</strong><br />
the value <strong>of</strong> electricity produced for the wet <strong>and</strong> dry climate respectively.<br />
So these rough calculations show that the water consumption might<br />
play an important role if the SOFC-ABS system was to be implemented<br />
in an area where fresh water is in short supply. Thus it is important to<br />
address this issue when new markets are considered.<br />
6 The price is inspired by fresh water price for households in Denmark without taxes,<br />
<strong>and</strong> does not include water treatment.<br />
7 Based on Danish prices including all taxes.<br />
8 Generally it is assumed that the electric efficiency <strong>of</strong> the SOFC is 0,5 <strong>and</strong> that the<br />
system is operated at full load all year.<br />
162
6.4. Economics<br />
6.4 Economics<br />
When the pr<strong>of</strong>itability calculations in chapter 2 regarding the hotel were<br />
made, the thermodynamical EES model was not yet created, <strong>and</strong> hence<br />
the efficiencies, COP etc. had to be estimated - partially by looking at<br />
similar commercial products.<br />
It is now examined how the assumptions used in the Hotel case fit<br />
with the results <strong>of</strong> the EES model.<br />
W [kW] | Q [kW]<br />
1000<br />
900<br />
800<br />
700<br />
600<br />
500<br />
400<br />
300<br />
200<br />
100<br />
0<br />
EES model vs Hotel Case assumption<br />
141<br />
141<br />
268 292<br />
399 406<br />
Hotel Calculations<br />
Hot Water Heating<br />
Cooling Power<br />
Electricical Power<br />
Optimized Model<br />
Figure 6.7: The left bar shows the generation <strong>of</strong> electricity, cooling <strong>and</strong> heating in the Hotel<br />
Case calculations for the Hot Climate (based on estimated η el <strong>and</strong> COP). The right bar shows the<br />
output <strong>of</strong> the optimized EES model for the same <strong>fuel</strong> input (800kW). The hot water production<br />
has been set to 141kW as in the hotel calculations 9 .<br />
In the hotel case ”Hot Climate” the natural gas consumption was<br />
800kW in order to generate enough electricity for the hotel. So the <strong>fuel</strong><br />
input into the optimized EES model has been set to 800kW as well. In<br />
the hotel case it was decided that the total dem<strong>and</strong> <strong>of</strong> domestic hot water<br />
(141kW) should come from the waste heat. So in the EES model the ABS<br />
unit has only been allowed to use so big a fraction <strong>of</strong> the waste heat, that<br />
there was enough heat left to generate 141kW <strong>of</strong> hot water 10 .<br />
10 In all the previous EES simulations, the ABS unit has been allowed to extract as<br />
much energy from the exhaust gas as possible go generate a bigger amount <strong>of</strong> cooling<br />
<strong>and</strong> a smaller amount <strong>of</strong> hot water.<br />
163
6. CASES AND ECONOMICS<br />
It can be seen from figure 6.7 that the assumed electricity, cooling,<br />
<strong>and</strong> hot water production (for a <strong>fuel</strong> input <strong>of</strong> 800kW) lays quite close<br />
to the ultimate values generated by the optimized EES model. The net<br />
electricity generation is almost identical while the cooling generation<br />
is about 10% bigger in the EES model. So if anything, the estimations<br />
<strong>of</strong> efficiencies <strong>and</strong> COP in the hotel case economics have been a little<br />
conservative.<br />
It must however be remembered that many <strong>of</strong> the parameters in the<br />
EES model are subjected to a significant uncertainty. So just because<br />
the values <strong>of</strong> the Hotel case economics are close to those <strong>of</strong> the EES<br />
model, it doesn’t prove that they are 100% correct. It just means that the<br />
economical calculations <strong>and</strong> the thermodynamical model are congruent.<br />
164
C H A P T E R<br />
7<br />
DISCUSSION<br />
In this chapter major findings <strong>of</strong> this project will be listed <strong>and</strong> discussed.<br />
7.1 The thermodynamical model<br />
The investigations <strong>of</strong> the SOFC-ABS system showed that the COP <strong>of</strong> the<br />
ABS unit did not depend so strongly on the evaporator temperature<br />
as it would for an electrical air conditioner. Thus, one can conclude<br />
that a water-LiBr ABS unit seem more advantageous relative to an<br />
electrical unit when the required cooling temperature is low. But since<br />
the refrigerant <strong>of</strong> the ABS unit is water, the temperature <strong>of</strong> the chilled<br />
water must be above 0 ◦ C. So it seems that the water-Libr ABS unit has<br />
the biggest advantage when the required cooling temperature is around<br />
5-10 ◦ C.<br />
The optimizations in chapter 5 showed that for a 100kW <strong>fuel</strong> input in<br />
a SOFC-ABS system it should be possible to obtain approximately:<br />
• 50kW <strong>of</strong> electricity.<br />
• 59kW <strong>of</strong> cooling.<br />
• 3kW <strong>of</strong> heat for hot water production.<br />
• 112kW total (Sum <strong>of</strong> all services).<br />
165
7. DISCUSSION<br />
The conditions for this were a forward/return temperature <strong>of</strong> the<br />
chilled water <strong>of</strong> 11 ◦ C/6 ◦ C, an ambient air temperature <strong>of</strong> 30 ◦ C, a relative<br />
humidity <strong>of</strong> 40%, <strong>and</strong> a wet tower for cooling absorber <strong>and</strong> condenser.<br />
The choice <strong>of</strong> a wet cooling tower was made because the investigations<br />
showed that the absorber <strong>and</strong> condenser temperature is quite critical.<br />
If these temperatures become too high relative to the desorber temperature,<br />
the system will not be able to operate. When the temperature<br />
<strong>of</strong> DES2 is 150 ◦ C, the system will only run if the water temperature out<br />
<strong>of</strong> the cooling tower (T 39 is below 28 ◦ C). So when the dry cooling tower<br />
<strong>of</strong> the model 1 is used, the ambient temperature may not be above 20 ◦ C.<br />
The wet tower would tolerate an ambient temperature <strong>of</strong> around 38 ◦ C at<br />
40% air humidity.<br />
The wet tower does however have the disadvantage <strong>of</strong> a water<br />
consumption <strong>of</strong> about 0,06kg/s (1900m 3 /y) for a <strong>fuel</strong> input <strong>of</strong> 100 kW. This<br />
is quite a lot <strong>and</strong> could be a problem for areas with water shortage. The<br />
amount <strong>of</strong> water is a very rough estimate due to following: The model<br />
<strong>of</strong> the cooling tower is quite simple <strong>and</strong> hence not completely accurate<br />
<strong>and</strong> the data for temperature <strong>and</strong> humidity are average values (a varying<br />
pr<strong>of</strong>ile <strong>of</strong> both temperature <strong>and</strong> humidity might give a different result).<br />
Two solutions could help to reduce the water consumption:<br />
1. First <strong>of</strong> all if the desorber temperature could be increased it would<br />
be possible to use a higher temperature for condenser <strong>and</strong> absorber.<br />
If T DES2 is increased from 150 ◦ C to 190 ◦ C, T 35 can be increased by<br />
10 ◦ C so the dry tower can run at an ambient temperature <strong>of</strong> 30 ◦ C.<br />
This does however increase the corrosion rate <strong>of</strong> the desorber, so<br />
new or more expensive materials would have to be used 2 .<br />
2. A semi-wet cooling tower could be used which is basically a dry<br />
tower where water can be sprayed over the tubes when extra<br />
cooling is needed. This way the amount <strong>of</strong> water being evaporated<br />
can be controlled more accurate so the tower only uses enough<br />
water to bring the temperature down to an acceptable level <strong>and</strong><br />
not to a unnecessarily low level. And during colder days the tower<br />
can run purely as a dry tower.<br />
1 ∆T min <strong>of</strong> the dry tower is set to 8 ◦ C in both ends<br />
2 According to [27] it should be avoided to use desorber temperatures above 150 ◦ C<br />
in order to avoid desorber corrosion<br />
166
7.1.1 Accuracy <strong>and</strong> sensitivity<br />
7.1. The thermodynamical model<br />
A lot <strong>of</strong> different parameters have been set in the EES model, <strong>and</strong> all<br />
<strong>of</strong> them are subjected to a certain amount <strong>of</strong> uncertainty. It has been<br />
attempted to estimate these as exact as possible, but in a zero dimensional<br />
model, it is not possible to calculate values such as ∆T min or pressure<br />
losses or heat losses. So a sensitivity analysis has been carried out in<br />
section 5.4 page 142. This showed that no single parameter 3 could change<br />
the value <strong>of</strong> the electrical efficiency or COP by more than 6% 4 . Of course<br />
several parameters could be wrong at the same time (with many <strong>of</strong> them<br />
pulling in the same direction), so the total output <strong>of</strong> the model can <strong>of</strong><br />
course vary more than just the 6%.<br />
But the electrical efficiency is quite close to that <strong>of</strong> the TOFC models.<br />
This is partly because a lot <strong>of</strong> parameters such as ASR, reforming fraction,<br />
<strong>and</strong> pressure losses have been approximated those <strong>of</strong> the TOFC models,<br />
although the ASR in the EES model only depends on the cell temperature<br />
<strong>and</strong> not <strong>of</strong> the partial pressures or current density. So the <strong>fuel</strong> cell part <strong>of</strong><br />
the model should give relatively realistic values.<br />
The ABS unit in the optimized system gives a COP (based on the heat<br />
input into the desorber) <strong>of</strong> 1,4 to 1,5 depending on ambient conditions<br />
etc. During the market research only one commercial dual stage<br />
absorption unit was found. This was the Chinese ”Broad BCT23” which<br />
had a COP <strong>of</strong> 1,1. But this unit was actually the cheapest absorption<br />
cooling unit per kW <strong>of</strong> cooling for systems <strong>of</strong> that size. So it is likely that<br />
the quite low COP is due to cheap materials <strong>and</strong> inefficient design.<br />
Other theoretical models ([20]) have suggested a COP <strong>of</strong> around 1,3.<br />
So the model <strong>of</strong> this project seems to be a little optimistic, which might<br />
be due to the neglecting <strong>of</strong> pressure losses <strong>and</strong> heat losses. The SHEXes<br />
<strong>of</strong> the model have also been set to a quite efficient level (∆T min = 5 ◦ C<br />
corresponding to a NTU <strong>of</strong> 5), since it turned out that they were some <strong>of</strong><br />
the most sensitive heat exchangers.<br />
3 other than the current density, which is a variable controlled by the operator <strong>and</strong><br />
hence not a normal ”fixed” parameter.<br />
4 For the most important parameters it has been individually estimated how much<br />
the value <strong>of</strong> each parameter could be <strong>of</strong>f compared to that <strong>of</strong> a true system. This was<br />
typically between 10% <strong>and</strong> 100%.<br />
167
7. DISCUSSION<br />
7.2 Economical considerations<br />
In chapter 2 (page 19) the economical potential in different applications<br />
were viewed, keeping in mind that some crude assumptions have been<br />
made. First <strong>of</strong> all only average consumption <strong>and</strong> production has been<br />
viewed i.e. assuming that electricity can be bought <strong>and</strong> sold to the<br />
electrical grid for the same price as long as the net export is zero. The<br />
costs <strong>and</strong> losses associated with the storage <strong>of</strong> cooling <strong>and</strong> heating have<br />
also been neglected - assuming that the cooling need remains constant<br />
throughout each day. The degradation <strong>of</strong> the SOFC has not been taken<br />
into account either - it has been assumed, that it keeps its performance<br />
throughout the lifetime.<br />
The reality is likely to be much less favorable than the above assumptions<br />
suggest, so the economical potential found in the calculations is<br />
likely to be too optimistic. But as mentioned before, they are mostly<br />
meant to show the overall tendencies <strong>and</strong> find out which applications<br />
that seem to have most potential.<br />
7.2.1 Auxillary Power Unit (APU)<br />
Truck APU<br />
The combination <strong>of</strong> SOFC <strong>and</strong> heat driven cooling turned out not to be<br />
a good match for trucks. This was partly because the air conditioning<br />
need (3kW) is larger than the electricity need (2kW) <strong>and</strong> because the<br />
commercially available Sorption unit had a nominal heat consumption<br />
<strong>of</strong> 12,5kW <strong>and</strong> a COP <strong>of</strong> only 0,4.<br />
So the only way it could become a decent match is if small (3kW) ABS<br />
units in the future are made as a double cycle with a COP <strong>of</strong> around the<br />
1,4-1,5 <strong>of</strong> the model. With this COP 2kW <strong>of</strong> waste heat could produce<br />
around 3kW <strong>of</strong> cooling, which would be just the required amount.<br />
Of course this means that either an additional electrical AC should be<br />
installed for cooling the truck during the driving time or the APU should<br />
run during daytime as well although the generated electricity would<br />
probably not be needed. A third variant could be to let the ABS unit<br />
receive heat from the exhaust gas <strong>of</strong> the main engine during driving. But<br />
mounting a heat exchanger in the truck exhaust system would probably<br />
be expensive, <strong>and</strong> the soot deposits would be likely to inhibit effective<br />
heat transfer. So this option would not be so straight forward.<br />
168
7.2. Economical considerations<br />
Furthermore one <strong>of</strong> the producers <strong>of</strong> absorption air conditioning units<br />
claim that they are fairly sensitive to the inclination <strong>of</strong> the floor [7]. So<br />
during acceleration, braking, turning <strong>and</strong> hill driving a truck is likely to<br />
impose unfavorable inclinations <strong>and</strong> accelerations to the unit.<br />
So still the conclusion is that the truck APU market doesn’t look too<br />
promising for the SOFC-ABS combination. There might however be a<br />
potential in cooling cold rooms in cargo trucks, but this has not been<br />
investigated here.<br />
Ship APU<br />
Mounting an ABS unit on an existing SOFC unit for air conditioning on a<br />
ship seemed to be an economical advantage with a payback time <strong>of</strong> less<br />
than 2 years if the system were to run at least 40% <strong>of</strong> the time. The results<br />
were fairly sensitive to the diesel price, SOFC efficiency <strong>and</strong> usage time<br />
fraction - changing one <strong>of</strong> these by 10% meant that the yearly savings<br />
would change by around 12%.<br />
The calculations did not take the installation, piping <strong>and</strong> maintenance<br />
costs into account. But since a 10% increase <strong>of</strong> the purchase price <strong>of</strong><br />
the ABS unit only decreases the yearly savings by around 3,5% the<br />
pr<strong>of</strong>itability would only decrease around 35% if the installation, piping,<br />
<strong>and</strong> maintenance costs turned out to be as large as the purchase price <strong>of</strong><br />
the ABS unit itself.<br />
It must also be remembered that the calculations only examined<br />
whether it is pr<strong>of</strong>itable to mount an ABS unit on an existing SOFC unit. It<br />
has not been calculated if the SOFC unit itself is an advantage to use in<br />
the first place 5 .<br />
7.2.2 Micro Combined Heat <strong>and</strong> Power (µCHP)<br />
µCHP - Air conditioning<br />
The idea to use SOFC in conjunction with hot water heating <strong>and</strong> a heat<br />
driven air condition unit in a private house did not look so promising<br />
with the heat driven cooling units on the market today as the smallest one<br />
5 Ship diesel engines are quite efficient, so there might not be so big a gain on<br />
efficiency by swapping the auxiliary diesel engine with a SOFC.<br />
169
7. DISCUSSION<br />
giving 5kW <strong>of</strong> Cooling for 12,5kW <strong>of</strong> driving heat. Even if a small ABS<br />
unit cold be made with a COP <strong>of</strong> 1,5 as in the model, the approximately<br />
1kW <strong>of</strong> waste heat (assuming 1kW SOFC electricity production) would<br />
only generate 1,5kW <strong>of</strong> cooling. And this is only around 1/3 <strong>of</strong> the<br />
estimated cooling need for a normal house in a hot climate.<br />
So for private homes the SOFC-ABS solution doesn’t seem realistic<br />
unless the SOFC is over dimensioned in order to sell the surplus<br />
electricity generation to the electricity grid or used for other purposes<br />
like an electric car.<br />
µCHP - Refrigerators<br />
Using the waste heat <strong>of</strong> the SOFC for driving a refrigerator was<br />
another option. But it turned out that heat driven refrigerators cost<br />
around 11.000DKK while a normal class A++ electrical refrigerator costs<br />
4.000DKK. And since the electricity consumption <strong>of</strong> the latter is only<br />
around 200kWh/year, the electricity savings only amounted to around<br />
400DKK/year, so with a discount factor <strong>of</strong> 5%, the pay back time will be<br />
around 50 years 6 . This even assumes that the electricity for the electrical<br />
refrigerator is bought from the electrical grid (2DKK/kWh), but if a<br />
SOFC unit is purchased anyway, the cost <strong>of</strong> the electricity would be even<br />
cheaper meaning an even longer pay back time for the absorption cooling<br />
refrigerator.<br />
Of course much <strong>of</strong> the price difference between the ABS refrigerator<br />
<strong>and</strong> the electrical refrigerator is due to the ABS unit being produced in<br />
much smaller numbers. So if ABS refrigerators became more common<br />
the price might approach that <strong>of</strong> electrical units. But on the other h<strong>and</strong><br />
installation <strong>and</strong> piping costs for the ABS unit have not been included in<br />
the calculations <strong>and</strong> this will pull in the opposite direction.<br />
All in all there seems to be no potential for combining a SOFC with<br />
ABS refrigerators in private homes.<br />
6 With a discount factor <strong>of</strong> 0% the pay back time will be 18years ((11.000-<br />
4.000)DKK/y/400DKKDKK/y), but with a discount factor <strong>of</strong> 5% the savings in the last<br />
years become very small when discounted.<br />
170
7.2.3 Distributed Generation (DG)<br />
DG - Hotel<br />
7.2. Economical considerations<br />
A favorable DG application is a hotel in a warm or hot climate, where<br />
electricity <strong>and</strong> air conditioning as well as domestic hot water production<br />
is needed. Other applications might fit the supply <strong>of</strong> electricity <strong>and</strong><br />
cooling even better e.g. manufacturing. However, the dem<strong>and</strong> for<br />
electricity <strong>and</strong> cooling for manufacturing applications is much harder to<br />
estimate in general since they are much more diversified.<br />
The economical calculations showed that for a hotel with 230 rooms<br />
in a hot climate, with a SOFC-system price <strong>of</strong> 2.700DKK/kW <strong>and</strong> a<br />
ABS price <strong>of</strong> 3.700DKK/kW, the total expense <strong>of</strong> gas, electricity, air<br />
conditioning units <strong>and</strong> SOFC in the assumed component lifetime <strong>of</strong> 10<br />
years would be approximately:<br />
• 27mio DKK for grid electricity supply + electrical air conditioning<br />
• 15mio DKK for SOFC electricity + electrical air conditioning<br />
• 14mil DKK for SOFC electricity + ABS air conditioning<br />
SOFC<br />
So by far the biggest savings (12mio DKK) would come from the<br />
SOFC itself with pay back time would be around 1 year. This does<br />
however depend very much on the gas price <strong>and</strong> electricity price <strong>of</strong><br />
0,20DKK/kWh <strong>and</strong> 0,75DKK/kWh respectively. If, for instance, the<br />
gas price was increased to 0,38DKK/kWh, the SOFC would never be<br />
pr<strong>of</strong>itable (with an electrical efficiency <strong>of</strong> 0,5), since it would be cheaper<br />
to import the electricity.<br />
The price <strong>of</strong> the SOFC is also important although not as much as<br />
one might expect. If the SOFC price is 12.000 DKK/kW instead <strong>of</strong> the<br />
assumed 2.700DKK/kW, the pay back time will increase from 1 year to<br />
3 years (figure 2.5 page 34). The investment would still look pr<strong>of</strong>itable,<br />
but if the gas or electricity at the same price changed a little, the pay<br />
back time might approach the life time <strong>of</strong> the system. And it should be<br />
remembered that the SOFC price is very uncertain, since the technology<br />
today is at a state where there is no real large scale production, <strong>and</strong> the<br />
reliability/stamination <strong>of</strong> the cell is not satisfactory either.<br />
171
7. DISCUSSION<br />
This leads to the next uncertainty - the lifetime which has been<br />
assumed to be 10 years. This is a lot longer than what is possible today.<br />
But as seen in figure 2.7 (page 36), the pr<strong>of</strong>itability doesn’t depend so<br />
much on lifetime. So even if it is just 5 years, the gains from using the<br />
SOFC is less than 10% smaller than if the lifetime was 10 years.<br />
It must also be remembered that for all the calculations (<strong>of</strong> both SOFC,<br />
ABS, <strong>and</strong> ECH) installation <strong>and</strong> maintenance costs have been neglected.<br />
But even if these costs sum up to be as large as the purchase price <strong>of</strong><br />
SOFC unit during its 10 years lifetime, the pay back time <strong>of</strong> the SOFC<br />
system will increase from around 1 to 1,5 years.<br />
The model has been made as steady state <strong>and</strong> the selling <strong>and</strong> buying<br />
prices <strong>of</strong> electricity have been assumed equal in the calculations in lack<br />
<strong>of</strong> better data. In reality the sale price is likely to be lower than the<br />
purchase price, but since the cost <strong>of</strong> the SOFC was seen not to have so<br />
big an influence on the pr<strong>of</strong>itability, it might be a good idea to buy a unit<br />
50% larger than average load, so it could be regulated up <strong>and</strong> down.<br />
ABS unit<br />
The ABS unit would give an extra gain <strong>of</strong> around 1,5 mil. DKK during<br />
its 10 years expected lifetime which is quite good considering that the<br />
additional purchase price <strong>of</strong> the ABS unit is only around 0,5 mil. DKK. 7 .<br />
This way the pay back time <strong>of</strong> the ABS unit becomes around 1,5 years<br />
for the hot climate, assuming the purchase price is 3700DKK/kW. If the<br />
price were doubled, the pay back time would be 6 years. But the ABS<br />
units are (in contrast to SOFCs) already on the market today, <strong>and</strong> the<br />
estimated price is hence much more accurate than the estimated price <strong>of</strong><br />
the SOFC. There are however not so many suppliers <strong>of</strong> ABS units, <strong>and</strong><br />
very few <strong>of</strong> them make double stage units, so the price is still somewhat<br />
uncertain, <strong>and</strong> one could imagine that it would decrease if the market<br />
grew.<br />
But as mentioned, the installation <strong>and</strong> maintenance costs have been<br />
neglected for all units. If maintenance <strong>and</strong> installation costs for the ABS<br />
sums up to be the same as the purchase price for the unit (during its 10<br />
years lifetime), the pay back time <strong>of</strong> the ABS unit will increase from 1,5<br />
7 The actual price <strong>of</strong> the ABS unit is 1mio DKK, but the supplementary ECH unit<br />
can be smaller than if no ABS were used, so the cost <strong>of</strong> the ECH decreases from 1,4mio<br />
DKK to 0,9mio DKK<br />
172
7.2. Economical considerations<br />
to 6 years 8 . So before it is decided to make such a system, the installation<br />
<strong>and</strong> maintenance costs should be established.<br />
One disadvantage <strong>of</strong> the ABS AC unit is that when the ambient<br />
temperature raises, so does the need for air conditioning, but at the same<br />
time the COP <strong>of</strong> the ABS unit decreases. So during very hot periods,<br />
this can give rise to a lack <strong>of</strong> cooling unless the ABS units is originally<br />
overdimensioned 9 . This is however not so much a problem in the hotel<br />
case where a supplementary electrical air conditioner is already present<br />
since the ABS unit can only generate about 1/3 <strong>of</strong> the required cooling<br />
due to the restricted amount <strong>of</strong> waste heat.<br />
Just as for the SOFC the ABS unit has only been modeled as steady<br />
state assuming that it runs at full load all the time. But since there was<br />
only enough waste heat in the SOFC exhaust gas to generate around 1/3<br />
<strong>of</strong> the entire cooling dem<strong>and</strong> <strong>of</strong> the hotel, the ABS unit should be able to<br />
run as base load all the time, <strong>and</strong> the supplementary ECH should be used<br />
to regulate the total cooling production. So the steady state assumption<br />
should not give so big an error on the ABS unit.<br />
ABS vs Hot water production<br />
In the economical calculations for the hotel, it has been assumed that all<br />
the hot water production should be done by using waste heat from the<br />
exhaust gas. This was done partly to make it easier to compare it to the<br />
”naked” SOFC system, case B (with no ABS, so there was plenty <strong>of</strong> heat<br />
for the hot water production), <strong>and</strong> partly because generating hot water<br />
from the exhaust gas only takes a heat exchanger, whereas generating<br />
cooling takes a much more expensive ABS unit.<br />
But if the hotel is placed in a hot climate, the hot water heating<br />
could quite inexpensively be done by solar heating panels because the<br />
required temperature for the domestic hot water is so low - around 60 ◦ C<br />
compared to the approximately 150 ◦ C needed for the ABS unit. And<br />
when additional air preheating is used in the SOFC-ABS system, the ABS<br />
unit can use almost all <strong>of</strong> the waste heat. If the ABS unit is allowed to<br />
8 This is under the assumption that the installation <strong>and</strong> maintenance cost <strong>of</strong> the ECH<br />
is the same regardless <strong>of</strong> whether an ABS unit is installed - after all there will be an ECH<br />
in either case - the only difference is a 35% reduction in size <strong>of</strong> the ECH if an ABS is also<br />
installed.<br />
9 Or it could just be tolerated that the indoor temperature raises a couple <strong>of</strong> degrees<br />
during heat waves (as long as there is some air conditioning, the consequences <strong>of</strong> a heat<br />
wave should not be life threatening for anyone)<br />
173
7. DISCUSSION<br />
extract as much <strong>of</strong> the waste heat as it can, there will only be enough<br />
waste heat left to make 3kW <strong>of</strong> hot water per 100kW <strong>fuel</strong> input (see figure<br />
5.32 page 153). This means that almost all <strong>of</strong> the waste heat can be used<br />
in the ABS unit. So if domestic hot water heating is to be made from the<br />
SOFC exhaust gas then the cooling production will decrease a lot, <strong>and</strong> for<br />
each kW the hot water production is decreased, approximately 1,5kW <strong>of</strong><br />
cooling can be made (since COP ABS = 1,48).<br />
Hotel locations<br />
One <strong>of</strong> the really good places to use the SOFC-ABS would be at the<br />
Seychelles. First <strong>of</strong> all the primary industry for this group <strong>of</strong> isl<strong>and</strong>s is<br />
tourism so there are a lot <strong>of</strong> hotels. Secondly their primary energy source<br />
is oil which the government wants to replace which is an advantage for<br />
the SOFC. Thirdly the climate is perfect for using the ABS air conditioning:<br />
the average temperature is between 24 <strong>and</strong> 30 degrees all year, creating<br />
a certain need for air conditioning all year round. And since the<br />
average temperature rarely exceeds 33 ◦ C, the absorption unit is capable<br />
<strong>of</strong> running just about all the time with a desorber temperature <strong>of</strong> no more<br />
than 150 ◦ C which is the maximum ambient temperature that can be used<br />
with this desorber temperature is only 33 ◦ C since the relative humidity is<br />
around 80%.<br />
Bangkok could at first glance also be a potential place for the SOFC-ABS.<br />
The temperature is a couple <strong>of</strong> degrees higher than for the Seychelles during<br />
summer (increasing the air conditioning need). But since the maximum<br />
temperature is higher, <strong>and</strong> the climate is very humid (up to 90%<br />
relative humidity), the desorber temperature will have to be increased<br />
up to 190 ◦ C for the system to even run at this ambient temperature. So<br />
fairly expensive materials are likely to be needed in order to minimize<br />
the corrosion rate <strong>of</strong> the Desorber (<strong>and</strong> probably also SHEX), meaning<br />
that Bangkok after all might not be the best place to use the absorption<br />
cooling unit after all.<br />
Las Vegas has even higher maximum temperatures (up to 46 ◦ C), but since<br />
the air humidity is much lower than in Bangkok, the system will run at<br />
temperature up to 48 ◦ C at a desorber temperature <strong>of</strong> 150 ◦ C. So this makes<br />
for a much better place to put the SOFC-ABS unit - especially since there<br />
are a lot <strong>of</strong> hotels <strong>and</strong> casinos which needs air condition <strong>and</strong> electricity.<br />
Although in this climate, the water consumption could be a problem.<br />
174
7.2. Economical considerations<br />
As mentioned earlier: the simple model <strong>of</strong> the cooling tower as<br />
well as the climate data (only average <strong>and</strong> extremes values) makes the<br />
simulation <strong>of</strong> varying the climate uncertain. The exact results should<br />
hence be used with caution, but the tendencies in three cases are still<br />
valid.<br />
Heat waves/peak load<br />
As mentioned the optimization showed that for 100kW <strong>of</strong> <strong>fuel</strong> input,<br />
50kW <strong>of</strong> electricity <strong>and</strong> 59kW <strong>of</strong> cooling (<strong>and</strong> 3kW <strong>of</strong> hot water) could<br />
be generated. If during a heat wave one wishes to make as much cooling<br />
as possible regardless <strong>of</strong> the effect on electricity, approximately 130kW <strong>of</strong><br />
cooling <strong>and</strong> 0kW <strong>of</strong> electricity could be generated by sending most <strong>of</strong> the<br />
<strong>fuel</strong> directly into the burner - only feeding the SOFC with enough <strong>fuel</strong> to<br />
generate electricity needed for the blower.<br />
This might at first glance look like an easy way to increase the cooling,<br />
but there are two drawbacks:<br />
• First <strong>of</strong> all, more cooling could be generated by the same amount<br />
<strong>of</strong> <strong>fuel</strong> by running the SOFC-ABS system at the normal optimized<br />
operating point (Ẇ el = 50kW <strong>and</strong> ˙Q cooling = 59kW ) <strong>and</strong> just use<br />
the 50kW <strong>of</strong> electricity in an electrical air conditioner (with an<br />
estimated COP <strong>of</strong> 3,5). This would give a cooling power <strong>of</strong><br />
59kW+50kW·3,4=230kW which is much more than the 130kW<br />
obtained by the <strong>fuel</strong> by pass.<br />
• Secondly, if the ABS unit should be able to cope with a cooling<br />
power <strong>of</strong> 130kW, it had to be heavily over dimensioned for the<br />
normal load (59kW), which would significantly increase the cost.<br />
And since the waste heat from the SOFC is only enough to supply<br />
the hotel with half its average cooling dem<strong>and</strong> it would most likely<br />
have a supplementary ECH anyway. So it would be cheaper to let<br />
the ECH be a little over dimensioned <strong>and</strong> let this take care <strong>of</strong> the<br />
peak load during heat waves.<br />
175
7. DISCUSSION<br />
7.3 Other considerations<br />
The steady state assumption has made the modeling work more<br />
simple (less time consuming) but as mentioned a lot <strong>of</strong> estimations<br />
<strong>and</strong> assumptions have been made in order to make the model work.<br />
This however has introduced a lot <strong>of</strong> uncertainties in the calculated<br />
performance <strong>and</strong> the economics.<br />
The pr<strong>of</strong>ile <strong>of</strong> the dem<strong>and</strong> <strong>of</strong> electricity, cooling <strong>and</strong> hot water<br />
(throughout the day <strong>and</strong> year 10 ) has been assumed to be constant which<br />
is a very crude assumption. How, <strong>and</strong> how much these dem<strong>and</strong>s will<br />
vary is hard to say, but it might have significant impact on the system.<br />
A way to cope with the varying dem<strong>and</strong> <strong>of</strong> cooling <strong>and</strong> hot water<br />
would be to introduce storages. These would to some extend make<br />
the production <strong>of</strong> cooling <strong>and</strong> hot water constant, but they would also<br />
introduce additional losses, investment <strong>and</strong> maintenance costs which<br />
have not been taken into account. The required capacity <strong>of</strong> the storages<br />
depends very much on the dem<strong>and</strong> pr<strong>of</strong>iles. And the size also has an<br />
impact on the losses to the surroundings, so finding the best storage size<br />
is a matter <strong>of</strong> economical optimization.<br />
Another issue is the interplay with the rest <strong>of</strong> the energy system. It has<br />
been assumed that electricity can be exported to the grid at any time the<br />
local dem<strong>and</strong> for electricity is below the production <strong>of</strong> the SOFC. How<br />
the electricity system copes with this depends very much on the type <strong>of</strong><br />
electricity generation (power stations etc.).<br />
For a system with a lot <strong>of</strong> renewable intermitted electricity generation<br />
(e.g. wind turbines <strong>and</strong> photovoltaic) it would probably not be the best<br />
match to use the SOFC as base load. From a system manager point<br />
<strong>of</strong> view it would be much better to use the SOFC only when there<br />
is not enough electricity production from the renewable sources. I.e.<br />
the electricity production <strong>of</strong> the SOFC should followed the electricity<br />
prices (which <strong>of</strong>ten are correlated to dem<strong>and</strong> minus the production <strong>of</strong><br />
intermitted capacity). But that solution would not be good for the SOFC-<br />
ABS combination, since the ABS unit would only be able to run when<br />
the SOFC was active, so the savings from the ABS unit would be smaller<br />
relative to the purchase price <strong>of</strong> the system.<br />
10 for the ”Normal Climate” is has however been assumed that the cooling need only<br />
arises during summer, <strong>and</strong> that it is zero during the 6 winter months<br />
176
C H A P T E R<br />
8<br />
CONCLUSION<br />
System configuration<br />
It turned out that a double stage configuration for the ABS unit could<br />
give a cooling power <strong>of</strong> around 59kW <strong>of</strong> cooling per 100kW <strong>fuel</strong> input<br />
in contrast to the only 26kW <strong>of</strong> cooling that was obtained with the single<br />
stage.<br />
An additional air preheating (GGHEX4) turned out to give 14kW <strong>of</strong><br />
extra cooling for the double stage with the optimized parameters, so this<br />
must be considered a very worthwhile addition.<br />
The model showed that it was almost essential to use a wet cooling<br />
tower. If a dry cooling tower was used, the ABS unit could only<br />
run at ambient temperatures below 20 ◦ C for a desorber temperature <strong>of</strong><br />
150 ◦ C. If the desorber temperature was increased to 190 ◦ C, the ambient<br />
temperature could be up to 30 ◦ C, but this would increase corrosion <strong>of</strong><br />
the desorber significantly. Since air conditioning is not so necessary<br />
when the ambient temperature is much below 30 ◦ C, the conclusion <strong>of</strong><br />
the absorber/condenser-cooling was that the tower had to be wet or at<br />
least semi-wet, whereby the amount <strong>of</strong> water used for evaporation could<br />
be controlled to fit the need.<br />
Critical components for good performance<br />
The investigations showed that the most critical heat exchangers with<br />
respect to the system COP were: the internal water-LiBr heat exchangers<br />
(SHEX1+2), the evaporator (EVAP) <strong>and</strong> the air pre heater (GGHEX4).<br />
177
8. CONCLUSION<br />
So by looking at how the effectiveness depends on NTU, these heat<br />
exchangers were optimized to what could reasonably be expected to be<br />
possible.<br />
The sensitivity analysis showed that the pressure loss <strong>and</strong> heat loss<br />
<strong>of</strong> the components in the ABS unit were not so influential, so neglecting<br />
these were probably not a significant source to uncertainty.<br />
The temperature <strong>of</strong> the evaporator turned out not to be as important<br />
as one would expect for a cooling device. If the temperature <strong>of</strong> the cooled<br />
fluid out <strong>of</strong> the evaporator is increased from 5 ◦ C to 30 ◦ C the amount <strong>of</strong><br />
generated cooling only increases by 1/5. So compared to an electrical<br />
unit, the ABS is most advantageous for low temperatures (where the<br />
COP <strong>of</strong> an ECH decreases more rapidly). But <strong>of</strong> course the temperature<br />
may not be below 0 ◦ C for water-LiBr ABS unit since the water would<br />
freeze.<br />
Performance<br />
When the model was optimized with respect to the different temperatures<br />
<strong>and</strong> the effectiveness <strong>of</strong> heat exchangers etc. the following performance<br />
was obtained for a 100kW <strong>fuel</strong> (methane) input:<br />
• 50kW <strong>of</strong> electricity.<br />
• 59kW <strong>of</strong> cooling.<br />
• 3kW <strong>of</strong> heat for hot water production.<br />
• 112kW total (Sum <strong>of</strong> total services).<br />
If instead the waste heat had been used for hot water production only,<br />
the system would have given less than 100kW <strong>of</strong> total services (i.e. 50kW<br />
<strong>of</strong> electricity <strong>and</strong> approximately 45kW <strong>of</strong> hot water). So by utilizing<br />
the ABS unit, the amount <strong>of</strong> total services per kW <strong>fuel</strong> input has been<br />
increased, <strong>and</strong> furthermore the value <strong>of</strong> the cooling is <strong>of</strong>ten higher than<br />
that <strong>of</strong> heating.<br />
Market segments, Economics <strong>and</strong> Climate<br />
The market investigations indicated a potential economical advantage by<br />
using a SOFC-ABS system in two <strong>of</strong> the three market segments:<br />
178
For the APU segment a SOFC-ABS system could be placed on a ship<br />
to generate electrical power <strong>and</strong> produce air conditioning. The rough<br />
calculations suggested a pay back time <strong>of</strong> the ABS unit <strong>of</strong> around 2 years.<br />
For the DG segment the calculations indicated a potential for using a<br />
SOFC-ABS system in a hotel with supply <strong>of</strong> electricity, air conditioning<br />
<strong>and</strong> hot water. The location should preferably be a climate which is<br />
hot all year <strong>and</strong> has a low air humidity as well. This way a cooling<br />
dem<strong>and</strong> is present all year so the ABS unit will have a lot <strong>of</strong> operating<br />
hours, <strong>and</strong> it would be possible to run the ABS unit at high temperatures<br />
(up to 48 ◦ C for φ=0,2). In a hot <strong>and</strong> humid climate (φ=0,8), the ABS<br />
unit would only work at ambient temperatures up to 33 ◦ C unless the<br />
desorber temperature was raised above 150 ◦ C, which would require<br />
special desorber materials. So this makes the dry climate a better choice.<br />
In the case study following examples <strong>of</strong> locations were concluded to<br />
be attractive for using a SOFC-ABS in a hotel:<br />
• Las Vegas: Many hotels, a relative humidity <strong>of</strong> around 40% (less<br />
during high temperature) <strong>and</strong> a very high ambient temperature<br />
during summer (op to 46 ◦ C) leads to a large air conditioning need,<br />
although the cooling need in the winter half <strong>of</strong> the year is modest.<br />
• The Seychelles: Many hotels <strong>and</strong> an abient temperature <strong>of</strong> around<br />
30 ◦ C leads to an air conditioning need throughout the year. There<br />
is a high humidity - around 80%, but that is not a problem for the<br />
ABS unit as long as the ambient temperature does not exceed 33 ◦ C.<br />
The economical calculations indicated that the pay back time <strong>of</strong> the<br />
SOFC <strong>and</strong> ABS unit for a hotel in a hot climate would be around 1<br />
year <strong>and</strong> 1,5 year respectively. But this did not include installation <strong>and</strong><br />
maintenance costs, <strong>and</strong> it has been based on average values (assuming<br />
that the purchase/sales price <strong>of</strong> the electricity from/to the electrical grid<br />
would be the same, as long as the net export <strong>of</strong> electricity was zero). In<br />
reality the sales price is likely to be lower than the purchase price.<br />
The neglected installation <strong>and</strong> maintenance costs have significant<br />
influence on the pay back time, so the economical calculations might<br />
be too optimistic. Especially the installation <strong>and</strong> maintenance costs <strong>of</strong><br />
the ABS unit were seen to have a high impact on pr<strong>of</strong>itability. If the<br />
installation <strong>and</strong> maintenance costs during the 10 year lifetime summed<br />
up to be as high as the original purchase price the pay back time would<br />
increase from 1,5 to 6 years.<br />
179
8. CONCLUSION<br />
Furthermore the system has been modeled as steady state which adds<br />
to the uncertainty <strong>of</strong> the economical calculations.<br />
In hot climates it might be a good idea to utilize as much <strong>of</strong> the waste<br />
heat as possible for cooling instead <strong>of</strong> hot water, which can be produced<br />
cheaper by other means, e.g. solar collectors. <strong>Ea</strong>ch kW <strong>of</strong> waste heat can<br />
give around 1,5kW <strong>of</strong> cooling but only about 1kW <strong>of</strong> hot water.<br />
Sum up<br />
The project has shown that integrating a SOFC with an absorption<br />
cooling unit should be a thermodynamically good match, <strong>and</strong> the market<br />
investigations suggest that for certain applications there could be an<br />
economical potential as well. But before a specific market area is chosen,<br />
more detailed economical calculations should be made, <strong>and</strong> the time<br />
variation <strong>of</strong> dem<strong>and</strong> for electricity, cooling <strong>and</strong> hot water should be taken<br />
into account.<br />
180
C H A P T E R<br />
9<br />
FURTHER WORK<br />
Some ideas for further work could be:<br />
1. Conduct an exergy analysis <strong>of</strong> the entire system.<br />
2. Time series for electricity, cooling <strong>and</strong> heating could be made <strong>and</strong><br />
different purchase <strong>and</strong> selling price for electricity could be used.<br />
3. A Storage (cooling/heating) could be made to account for the<br />
variations, <strong>and</strong> the cost <strong>and</strong> losses <strong>of</strong> this could be calculated.<br />
4. Improve the modeling <strong>of</strong> the cooling tower component.<br />
5. It could be investigated which materials are normally used for the<br />
desorbers, which new materials could be used, <strong>and</strong> what maximum<br />
temperature these would be able to tolerate.<br />
6. A triple or quadruple stage water-LiBr ABS unit could be modeled<br />
<strong>and</strong> integrated with a SOFC.<br />
7. The reduction in CO2 mitigation for the system could be examined,<br />
since this provides an insensitive other than the purely economical.<br />
8. The economical calculations could be improved by gathering<br />
information about installation costs, maintenance costs etc.<br />
9. A ammonia-water ABS units could be modeled.<br />
10. The SOFC ABS system could be compared to a Solar heating/cooling<br />
system.<br />
181
9. FURTHER WORK<br />
11. The system could be compared to a gas engine driven generator<br />
with ABS or a micro turbine with ABS.<br />
12. More cases could be investigated, e.g. the ammonia-water<br />
absorption unit applied for industrial freezing.<br />
13. Analysis <strong>of</strong> how the SOFC-ABS system interact with the surrounding<br />
energy system (e.g. national electricity supply system).<br />
182
BIBLIOGRAPHY<br />
[1] Acfshop.dk: http://www.acfshop.dk/Pages/Search.aspx<br />
search=RGE%20400 (feb 19, 2010)<br />
[2] Bath: http://people.bath.ac.uk/ccsshb/12cyl/ (June 18,<br />
2010)<br />
[3] BBC Weater, avereage condition Bangkok: http://www.bbc.<br />
co.uk/weather/world/city_guides/results.shtmltt=<br />
TT002890 (June 14, 2010)<br />
[4] BBC Weater, avereage condition Cairo: http://www.bbc.co.<br />
uk/weather/world/city_guides/results.shtmltt=<br />
TT000180 (June 14, 2010)<br />
[5] BBC Weater, avereage condition Las Vegas: http://www.bbc.<br />
co.uk/weather/world/city_guides/results.shtmltt=<br />
TT001410 (June 14, 2010)<br />
[6] BBC Weater, avereage condition Port Victoria: http://www.bbc.<br />
co.uk/weather/world/city_guides/results.shtmltt=<br />
TT004860 (June 14, 2010)<br />
[7] Climate Well: http://www.thermostat.com.tw/pdf/<br />
cognition_10.pdf, (February 26, 2003).<br />
[8] Elgiganten.dk: http://www.elgiganten.dk/product/<br />
hvidevarer/kol-frys/kol-frys/KGV36X27/<br />
bosch-kole-fryseskab (feb 19, 2010)<br />
[9] Energy Information Administration (EIA): Annual Energy Outlook<br />
2003, Washington, DC, (January, 2003).<br />
[10] Energy Information Administration (EIA): http://www.eia.<br />
doe.gov/cneaf/electricity/epm/table5_6_a.html<br />
(February 18, 2010)<br />
[11] Etaiwannnews (EIA): http://www.etaiwannews.com/etn/<br />
print.php (February 18, 2010)<br />
183
BIBLIOGRAPHY<br />
[12] Energinet.dk: http://www.energinet.dk/NR/rdonlyres/<br />
F53D95F7-36FF-477A-AD71-35C64DEDAFA4/0/<br />
Analyseforuds%C3%A6tninger20072016.pdf, (June 15,<br />
2010).<br />
[13] Energy <strong>and</strong> Environmental Analysis, Inc.: CHP in the Hotel <strong>and</strong><br />
Casino Market Sectors , (December 2005). www.eea-inc.com.<br />
[14] Engineering toolbox: http://www.engineeringtoolbox.<br />
com/cooling-tower-efficiency-d_699.html, (maj 2, 2010).<br />
[15] Flickr: http://farm4.static.flickr.com/3244/<br />
2447599956_201047feeb.jpg (June 18, 2010)<br />
[16] Fontell, E. et al.: Conceptual study <strong>of</strong> a 250kW planar SOFC system for<br />
CHP application www.dgs.de/uploads/media/MICROCHEAP_<br />
literature_CRES.doc (feb 19, 2010)<br />
[17] Gas prices: http://www.eia.doe.gov/dnav/ng/<br />
ng_pri_sum_dcu_SCA_a.htm http://www.ens.dk/<br />
da-DK/Info/TalOgKort/Statistik_og_noegletal/<br />
Maanedsstatistik/Documents/Energistatistik%<br />
202008.pdf (February 18, 2010)<br />
[18] Gr<strong>and</strong>ryd, Eric et al.: Refrigeration Engineering, (2005).<br />
[19] Burer, M.: Multi-criteria optimizaion <strong>of</strong> a dristrict cogeneration plant<br />
integrating a <strong>solid</strong> <strong>oxide</strong> <strong>fuel</strong> cell-gas turbine combined cyle, heat pumps<br />
<strong>and</strong> chillers. Energy 28, page 497-518, (2002).<br />
[20] Grossmann, Gershon: ABSIM - modular simulation <strong>of</strong> advanced<br />
absorption systems. International Journal <strong>of</strong> Refrigeration 24, page<br />
531-543, (2001).<br />
[21] Grossmann, Gershon: Advanced modular simulation <strong>of</strong> absorption<br />
systems. International Journal <strong>of</strong> Refrigeration 17, page 231-244,<br />
(1994).<br />
[22] Jax autohaus.com : http://jaxautohaus.com/apu1.htm (June<br />
15, 2010).<br />
[23] Larminine, James et al.: Fuel Cell Systems Explpained. Wiley, (2003).<br />
184
Bibliography<br />
[24] Nordea invest: http://www.google.dk/imgresimgurl=<br />
http://www.nordeainvest.dk/sitemod/upload/<br />
Root/www_nordeainvest_dk/Grafer/Brentoil.<br />
jpg&imgrefurl=http://www.nordeainvest.dk/<br />
Nyheder/Nyheder%2B2009/Ugens%2BPerspektiv%<br />
2B2009/20082009%2BOptimisme%2Bp%25C3%25A5%2Br%<br />
25C3%25A5varemarkederne/1142802.html&usg=__<br />
1vQEq1C1rbLKso8m2OD8SRX1lms=&h=459&w=699&sz=<br />
82&hl=da&start=7&um=1&itbs=1&tbnid=73TJWdJD-_<br />
0OkM:&tbnh=91&tbnw=139&prev=/images%3Fq%3Dh%25C3%<br />
25B8jeste%2Boliepris%26um%3D1%26hl%3Dda%26sa%3DN%<br />
26tbs%3Disch:1 (June 15, 2010).<br />
[25] Petersen, Thomas Frank: Verbal referance, (2010).<br />
[26] Delano,Andrew Design Analysis <strong>of</strong> the Einstein Refrigeration Cycle.<br />
Georgia Institute <strong>of</strong> Technology. http://www.me.gatech.edu/<br />
energy/<strong>and</strong>y_phd/IMG00020.GIF (June 22, 2010)<br />
[27] Sc<strong>and</strong>inavian Energy Group Aps.: Mulige anvendelser af absorptionskøling,<br />
(2010).<br />
Included in appendix F.1 page 285.<br />
[28] Scribd: http://www.scribd.com/doc/16648848/<br />
Fans-BlowersCalculation-<strong>of</strong>-Power, (may 2, 2010).<br />
[29] Southern California Gas Company: Absorption Chillers - Guideline.<br />
New Buildings Institute. Advanced Design Guideline Series, (1998).<br />
[30] Topsoe Fuel Cell - APU: http://www.topsoe<strong>fuel</strong>cell.com/<br />
business_areas/apu.aspx, (June 16, 2010).<br />
[31] Topsoe Fuel Cell - DG: http://www.topsoe<strong>fuel</strong>cell.com/<br />
business_areas/dg.aspx, (June 16, 2010).<br />
[32] Topsoe Fuel Cell - Mirco CHP: http://www.topsoe<strong>fuel</strong>cell.<br />
com/business_areas/micro_chp.aspx, (June 16, 2010).<br />
[33] U.S. Department <strong>of</strong> Energy: Fuel Cell H<strong>and</strong>book (Seventh Edition),<br />
(November 2004).<br />
[34] Weber, Céline: Optimization <strong>of</strong> an SOFC-based decentralized polygeneration<br />
system for providing energy services in an <strong>of</strong>fice-building in Tokyo.<br />
Applied Thermal Engineering 26, page 1409-1419, (2006).<br />
185
BIBLIOGRAPHY<br />
[35] Wu, D.W. et al.: Combined coolng, heating <strong>and</strong> power: A review.<br />
Progress in Energy <strong>and</strong> Combustion Science 32, page 459-495,<br />
(2006).<br />
[36] Wikipedia - Las Vegas: http://en.wikipedia.org/wiki/<br />
Las_Vegas,_Nevada, (juni 15, 2010).<br />
[37] Wikipedia - Seychelles: http://en.wikipedia.org/wiki/<br />
Seychelles, (juni 15, 2010).<br />
[38] Wikipedia - Thail<strong>and</strong>: http://en.wikipedia.org/wiki/<br />
Thail<strong>and</strong>, (juni 15, 2010).<br />
186
Appendices<br />
187
A P P E N D I X<br />
A<br />
MARKET INVESTIGATION<br />
189
A. MARKET INVESTIGATION<br />
A.1 Market Investigation Appendix -<br />
Introduction<br />
Some <strong>of</strong> the quite important prices in the calculations are those <strong>of</strong> oil,<br />
natural gas <strong>and</strong> electricity. Since fossil <strong>fuel</strong>s are slowly being depleted,<br />
while CO2 emission become more <strong>and</strong> more unpopular, the price <strong>of</strong><br />
electricity as well as gas is likely to increase in the coming years. It is<br />
however very difficult to give an accurate estimate <strong>of</strong> the future price<br />
development (in 2003 it was for instance estimated that the oil price from<br />
2003 to 2025 would lay between $20 <strong>and</strong> $35 per barrel [9], which is quite<br />
far from the $140/barrel[24] which was reached during the financial<br />
crisis 2007/2008). And since the rest <strong>of</strong> the numbers in the calculations<br />
are also quite uncertain, it has been assumed in this report, that the<br />
electricity prices, gas prices, <strong>and</strong> diesel prices will just increase with the<br />
rate <strong>of</strong> the inflation.<br />
190
A.2. APU appendix<br />
A.2 APU appendix<br />
A.2.1<br />
A.2.1.1<br />
Ship APU appendix<br />
Assumptions<br />
• All prices are ex VAT.<br />
• Discount rate 5%<br />
• Diesel oil price 4,50DKK/l<br />
• Heating value 42,7MJ/kg<br />
• Density 840kg/m3<br />
• Full load hours per year 4380<br />
• SOFC efficiency 0,5<br />
• Absorption cooling power = 20kW<br />
• COP elec.ac = 3,6<br />
• Usage time fraction = 0,5<br />
• Electricity for electrical chiller is made by the SOFC (price 0,60DKK<br />
per kWh)<br />
• Electrical AC price: Enviromax 20kW = 61,000DKK<br />
• Absorption AC price: Robour = 10,000DKK/kW * 20kW =<br />
200,000DKK (incl. hexes)<br />
• Absorption AC electrical consumption 1,0kW<br />
• No service needed on either refrigerator<br />
A usage time fraction is set to 50% <strong>of</strong> the time, since it is assumed that<br />
the SOFC will generate electricity for the ship almost all the time (both<br />
sailing <strong>and</strong> docking), <strong>and</strong> that it is big enough to deliver enough heat for<br />
the absorption air condition to run all the time. But there is probably not<br />
always a need for air conditioning - for instance the ships some time sail<br />
in cold climates.<br />
191
A. MARKET INVESTIGATION<br />
No cost for distribution piping or user-side heat exchangers has been<br />
included, since this equipment is assumed to be the same whether an<br />
absorption air conditioner or an electrical air conditioner is used.<br />
192
Aircondition 20kW ship. SOFC+ABS vs SOFC+ECH<br />
(prices are excl. VAT)<br />
Electrical Aircondition COP = 3,6 (4kW heat, 3,5kW cooling)<br />
Ship SOFC runs 50% <strong>of</strong> the time<br />
Elec price ship:<br />
1,13 DKK/kWh<br />
Assuming that the SOFC is big enough to supply enough waste heat for the ABS at all time<br />
Diesel oil price 4,23DKK/l<br />
Heating value 42,7MJ pr kg<br />
Density 840kg/m3<br />
SOFC el eff 0,4<br />
Price pr l Density Heat value Heating value Price pr MJ kWh/MJ Price pr kWh_d<br />
DKK/L kg/L MJ/kg MJ/L DKK/MJ kWh/MJ DKK/kWh<br />
4,50 0,84 42,7 35,9 0,125 0,28 0,452<br />
Usage fraction 0,50 Price pr kWh_EL<br />
Full load hours 4380 DKK/kWh<br />
Electricity price 4945 DKK/y/kW 1,129<br />
Normal Heat pump AC, electricity from SOFC<br />
Enviromax 20 kW 61128 DKK (excl. VAT)<br />
Coooing power 20 kW<br />
Discount rate 5,0%<br />
year Purchase Electricity Net payment NPV_i NPV tot Annuity<br />
0 61'128 61'128 61'128 61'128<br />
1 98'891 98'891 94'182 155'310 163'075<br />
2 98'891 98'891 89'697 245'006 131'766<br />
3 98'891 98'891 85'426 330'432 121'337<br />
4 98'891 98'891 81'358 411'790 116'130<br />
5 98'891 98'891 77'483 489'273 113'010<br />
6 98'891 98'891 73'794 563'067 110'934<br />
7 98'891 98'891 70'280 633'347 109'455<br />
8 98'891 98'891 66'933 700'280 108'349<br />
9 98'891 98'891 63'746 764'025 107'491<br />
10 98'891 98'891 60'710 824'736 106'807<br />
11 98'891 98'891 57'819 882'555 106'250<br />
12 98'891 98'891 55'066 937'621 105'787<br />
13 98'891 98'891 52'444 990'065 105'398<br />
14 98'891 98'891 49'947 1'040'012 105'066<br />
15 98'891 98'891 47'568 1'087'580 104'780<br />
9<br />
193
Absorpton unit (free waste heat)<br />
Price ABS 10'000 DKK/kW Including HEXes, Robur 16,9kW = 170,000DKK<br />
Cooling power 20 KW<br />
electrical consomp 1,03 kW<br />
year Purchase Electricity Net payment NPV_i NPV tot Annuity<br />
0 200'000 200'000 200'000 200'000<br />
1 5'091 5'091 4'848 204'848 215'091<br />
2 5'091 5'091 4'618 209'466 112'652<br />
3 5'091 5'091 4'398 213'864 78'533<br />
4 5'091 5'091 4'188 218'052 61'493<br />
5 5'091 5'091 3'989 222'041 51'286<br />
6 5'091 5'091 3'799 225'839 44'494<br />
7 5'091 5'091 3'618 229'457 39'655<br />
8 5'091 5'091 3'446 232'903 36'035<br />
9 5'091 5'091 3'282 236'185 33'229<br />
10 5'091 5'091 3'125 239'310 30'992<br />
11 5'091 5'091 2'976 242'286 29'169<br />
12 5'091 5'091 2'835 245'121 27'656<br />
13 5'091 5'091 2'700 247'821 26'382<br />
14 5'091 5'091 2'571 250'392 25'296<br />
15 5'091 5'091 2'449 252'841 24'359<br />
Savings by using Absorption<br />
year Purchase Electricity Net payment NPV_i NPV tot Annuity<br />
0 -138'872 0 -138'872 -138'872 -138'872 0<br />
1 0 93'800 93'800 89'333 -49'539 -52'016<br />
2 0 93'800 93'800 85'079 35'540 19'114<br />
3 0 93'800 93'800 81'028 116'568 42'805<br />
4 0 93'800 93'800 77'169 193'738 54'636<br />
5 0 93'800 93'800 73'495 267'232 61'724<br />
6 0 93'800 93'800 69'995 337'227 66'440<br />
7 0 93'800 93'800 66'662 403'889 69'800<br />
8 0 93'800 93'800 63'487 467'377 72'313<br />
9 0 93'800 93'800 60'464 527'841 74'262<br />
10 0 93'800 93'800 57'585 585'426 75'815<br />
11 0 93'800 93'800 54'843 640'269 77'081<br />
12 0 93'800 93'800 52'231 692'500 78'132<br />
13 0 93'800 93'800 49'744 742'244 79'016<br />
14 0 93'800 93'800 47'375 789'619 79'770<br />
15 0 93'800 93'800 45'119 834'739 80'421<br />
Positive NPV means that Absorption chiller is advantageous<br />
9<br />
194
Sensitivity analysis<br />
The effect on the 10 years anuity difference is investigated<br />
-9,75 0 9,75<br />
Increase (%) x: -10 0 10<br />
y- y0 y+ ∆y-/y0 ∆y+/y0<br />
Purchase price ABS 78'170 75'815 73'225 3,1 0,0 -3,4<br />
Purchase price EAC 75'096 75'815 76'607 -0,9 0,0 1,0<br />
Diesel price 67'288 75'815 85'195 -11,2 0,0 12,4<br />
Efficiency SOFC 85'195 75'815 67'288 12,4 0,0 -11,2<br />
Usage time fraction 67'288 75'815 85'195 -11,2 0,0 12,4<br />
Discount rate 76'210 75'815 75'376 0,5 0,0 -0,6<br />
Sensitivity analysis <strong>of</strong> Ship ABS vs ECH<br />
15<br />
Annuity increase [%]<br />
10<br />
5<br />
0<br />
-10 -5 0 5 10<br />
-5<br />
-10<br />
-15<br />
Increase in variables [%]<br />
Purchase price ABS<br />
Purchase price EAC<br />
Diesel price<br />
Efficiency SOFC<br />
Usage time fraction<br />
Discount rate<br />
An incrase in y-value means, that the advantage <strong>of</strong> using the absorption refrigerator becomes even larger.<br />
The electricity price <strong>and</strong> anual electricity consumption are exactly on top <strong>of</strong> each other as could be expected<br />
195
A. MARKET INVESTIGATION<br />
A.3 CHP appendix<br />
A.3.1<br />
Assumptions<br />
• All prices are incl VAT since it is seen from the consumer viewpoint,<br />
<strong>and</strong> electricity etc. is incl VAT.<br />
• Electrical refrigerator (Bosch energy class A++) price = 3.999DKK<br />
Footnote[Bosch KGV 36X27 225l refrigeration <strong>and</strong> 91liter freezer].<br />
• Absorption refrigerator (RGE 400 from Åbybro camping og fritid<br />
224L + 76L) price = 11.000DKK.<br />
• Electrical refrigerator electricity consumption = 208kWh/y.<br />
• Absorption refrigerator electricity consumption = 0kWh/y.<br />
• Electricity price 2 DKK/kWh (Danish prices).<br />
• No service needed on either refrigerator.<br />
• No price for a HEX between the SOFC exhaust gas <strong>and</strong> the<br />
refrigerator has been included, so in reality this might add an extra<br />
cost for the absorption refrigerator.<br />
• Discount factor 5% per year.<br />
196
Refrigerators for private end users (incl VAT)<br />
Discount rate<br />
Annually el. cons.<br />
El. price<br />
5,00%<br />
208,00 kWh<br />
2,00 DKK/kWh (incl. VAT)<br />
Electrical Refrigerator (A++)<br />
Bosch KGV 36X27 225l refritiation <strong>and</strong> 91liter freezer<br />
year Purchase Electricity Net payment NPV_i NPV tot Annuity<br />
0 3'999 3'999 3'999 3'999<br />
1 416 416 396 4'395 4615<br />
2 416 416 377 4'773 2567<br />
3 416 416 359 5'132 1884<br />
4 416 416 342 5'474 1544<br />
5 416 416 326 5'800 1340<br />
6 416 416 310 6'110 1204<br />
7 416 416 296 6'406 1107<br />
8 416 416 282 6'688 1035<br />
9 416 416 268 6'956 979<br />
10 416 416 255 7'211 934<br />
11 416 416 243 7'454 897<br />
12 416 416 232 7'686 867<br />
13 416 416 221 7'907 842<br />
14 416 416 210 8'117 820<br />
15 416 416 200 8'317 801<br />
16 416 416 191 8'508 785<br />
17 416 416 181 8'689 771<br />
18 416 416 173 8'862 758<br />
19 416 416 165 9'026 747<br />
20 416 416 157 9'183 737<br />
21 416 416 149 9'333 728<br />
22 416 416 142 9'475 720<br />
23 416 416 135 9'610 712<br />
24 416 416 129 9'739 706<br />
25 416 416 123 9'862 700<br />
26 416 416 117 9'979 694<br />
27 416 416 111 10'091 689<br />
28 416 416 106 10'197 684<br />
29 416 416 101 10'298 680<br />
30 416 416 96 10'394 676<br />
10'975<br />
197
Absorption Refrigerator<br />
RGE 400 from Åbybro camping og fritid 224L + 76L<br />
The absorption refrigerator doesn't use any electricity<br />
year Purchase Electricity Net payment NPV_i NPV tot Annuity<br />
0 10'975 10'975 10'975 10'975<br />
1 0 0 10'975 11524<br />
2 0 0 10'975 5902<br />
3 0 0 10'975 4030<br />
4 0 0 10'975 3095<br />
5 0 0 10'975 2535<br />
6 0 0 10'975 2162<br />
7 0 0 10'975 1897<br />
8 0 0 10'975 1698<br />
9 0 0 10'975 1544<br />
10 0 0 10'975 1421<br />
11 0 0 10'975 1321<br />
12 0 0 10'975 1238<br />
13 0 0 10'975 1168<br />
14 0 0 10'975 1109<br />
15 0 0 10'975 1057<br />
16 0 0 10'975 1013<br />
17 0 0 10'975 973<br />
18 0 0 10'975 939<br />
19 0 0 10'975 908<br />
20 0 0 10'975 881<br />
21 0 0 10'975 856<br />
22 0 0 10'975 834<br />
23 0 0 10'975 814<br />
24 0 0 10'975 795<br />
25 0 0 10'975 779<br />
26 0 0 10'975 763<br />
27 0 0 10'975 750<br />
28 0 0 10'975 737<br />
29 0 0 10'975 725<br />
30 0 0 10'975 714<br />
198
Absorption - electrical A++ refrigerator<br />
year Purchase Electricity Net payment NPV_i NPV tot Annuity<br />
0 -6'976 0 -6'976 -6'976 -6'976 0<br />
1 0 416 416 396 -6'580 -6909<br />
2 0 416 416 377 -6'202 -3336<br />
3 0 416 416 359 -5'843 -2146<br />
4 0 416 416 342 -5'501 -1551<br />
5 0 416 416 326 -5'175 -1195<br />
6 0 416 416 310 -4'865 -958<br />
7 0 416 416 296 -4'569 -790<br />
8 0 416 416 282 -4'287 -663<br />
9 0 416 416 268 -4'019 -565<br />
10 0 416 416 255 -3'764 -487<br />
11 0 416 416 243 -3'521 -424<br />
12 0 416 416 232 -3'289 -371<br />
13 0 416 416 221 -3'068 -327<br />
14 0 416 416 210 -2'858 -289<br />
15 0 416 416 200 -2'658 -256<br />
16 0 416 416 191 -2'467 -228<br />
17 0 416 416 181 -2'286 -203<br />
18 0 416 416 173 -2'113 -181<br />
19 0 416 416 165 -1'949 -161<br />
20 0 416 416 157 -1'792 -144<br />
21 0 416 416 149 -1'642 -128<br />
22 0 416 416 142 -1'500 -114<br />
23 0 416 416 135 -1'365 -101<br />
24 0 416 416 129 -1'236 -90<br />
25 0 416 416 123 -1'113 -79<br />
26 0 416 416 117 -996 -69<br />
27 0 416 416 111 -884 -60<br />
28 0 416 416 106 -778 -52<br />
29 0 416 416 101 -677 -45<br />
30 0 416 416 96 -581 -38<br />
Positive NPV means that Absorption refrigerator is advantageous 0<br />
Approximation <strong>of</strong> wast heat needed for the absorption refrigerator<br />
Electrical refrigerator:<br />
Electricity consumption 208 kWh/y A++ refrigerators use 208kWh/y<br />
COP_ECH 2 The COP <strong>of</strong> a normal refrigerator is assumed to be 2<br />
Cooling energy<br />
416 kWh/y<br />
Absorption refrigerator:<br />
COP_ABS 0,25 The COP <strong>of</strong> a small platen cycle unit is around 0,25<br />
Heat energy<br />
1664 kWh/y<br />
Heat power (avg)<br />
0,190 kW<br />
Estimation <strong>of</strong> electrical refrigerator COP<br />
T_H T_C COP_carnot<br />
AC 318 288 9,6<br />
Refrigiator 303 263 6,6 199
Sensitivity analysis<br />
The effect on the 10 years anuity difference is investigated<br />
-9,8 0 9,8<br />
Increase (%) x: -10 0 10<br />
y- y0 y+ ∆y-/y0 ∆y+/y0<br />
Purchase price ABS -358 -487 -630 -26 0 29<br />
Purchase price El-unit -535 -487 -436 10 0 -10<br />
Electricity price -525 -487 -446 8 0 -8<br />
Anual electricity consump -525 -487 -446 8 0 -8<br />
Discount rate -468 -487 -509 -4 0 5<br />
Sensitivity analysis <strong>of</strong> refrigiator ABS vs ECH<br />
30<br />
20<br />
Annuity increase [%]<br />
10<br />
0<br />
-10 -5 0 5 10<br />
-10<br />
-20<br />
-30<br />
Increase in variables [%]<br />
Purchase price ABS<br />
Purchase price El-unit<br />
Electricity price<br />
Anual electricity consump<br />
Discount rate<br />
An incrase in y-value means, that the disadvantage <strong>of</strong> using the ABS refrigerator becomes even larger.<br />
The electricity price <strong>and</strong> anual electricity consumption are exactly on top <strong>of</strong> each other<br />
200
Pay back time<br />
ABS refregiator price PB Time<br />
4000 0<br />
4500 1,4<br />
5000 2,7<br />
6000 5,7<br />
7000 9,2<br />
8000 13,5<br />
9000 19<br />
10000 26<br />
11000<br />
12000<br />
15000<br />
12000<br />
Pay Back Time for absorption refrigerator<br />
ABS refrigerator Purchase<br />
Price [DKK]<br />
10000<br />
8000<br />
6000<br />
4000<br />
2000<br />
0<br />
0 5 10 15 20 25<br />
Pay Back Time [years]<br />
The price <strong>of</strong> the normal refrigerator is 4000Dkk, so if the absorption refrigerator matches that price<br />
the pay back time will be zero<br />
201
A. MARKET INVESTIGATION<br />
A.4 DG appendix<br />
In order to see whether there was a match between SOFC waste heat,<br />
absorption cooling heat dem<strong>and</strong> <strong>and</strong> hot water heat dem<strong>and</strong>, the Gas<br />
consumption <strong>and</strong> the electricity consumption was obtained for a typical<br />
18.000m 2 Hotel with 230 rooms in three different American states [13].<br />
This data did however not specify how much <strong>of</strong> the gas was used<br />
for space heating <strong>and</strong> how much for hot water heating. And neither<br />
did it specify how much <strong>of</strong> the electricity was used for electrical air<br />
conditioning <strong>and</strong> how much for lighting etc. So the fraction for these<br />
things was approximated by using data for the energy consumption <strong>of</strong><br />
the total hotel <strong>and</strong> lodging industry in the US [13].<br />
This meant that 65% <strong>of</strong> the gas use is assumed to be for space heating,<br />
<strong>and</strong> 35% for hot water, while 27% <strong>of</strong> the electricity is for Air conditioning<br />
<strong>and</strong> 73% is for other equipment (including refrigeration). The cooling<br />
dem<strong>and</strong> is then estimated by assuming a COP <strong>of</strong> 4 for the electrical air<br />
conditioning <strong>and</strong> multiplying this with the electricity use for air conditioning.<br />
These numbers now represent what in this report is called ”normal climate”.<br />
A hot climate has then been approximated by assuming that the<br />
cooling dem<strong>and</strong> (kWh/y) is twice that <strong>of</strong> the normal climate (since air<br />
condition will run all year), <strong>and</strong> that no energy is needed for space heating<br />
anymore, whereas the hot water heating consumes the same power<br />
as in the normal climate.<br />
Somewhere in the report the annuity has been used, elsewhere NPV is<br />
used. This is because <strong>of</strong> the following:<br />
The annuity is preferable for the so called chain investments which is<br />
when a new identical unit is bought as soon as the old one is worn down.<br />
Imagine you have the following two options: A) will give a total NPV <strong>of</strong><br />
1mio DKK during a lifespan on 1 year, whereas B) will give a total NPV<br />
<strong>of</strong> 3 mil. DKK during a life span <strong>of</strong> 6 years. Option B will have the highest<br />
NPV, but if a new unit is purchased each time the old one is worn up,<br />
option A will give 1 mil. DKK per year, whereas option B will only give<br />
0,5mio DKK per year (both continuing year after year). So option A is to<br />
prefer although option B has the highest NPV per investment cycle.<br />
202<br />
The problem with the annuity is that it can not be calculated for 0
A.4. DG appendix<br />
years, so if the pay back time is less than 1 year, it becomes impossible to<br />
calculate the Pay Back Time by interpolating between 0 <strong>and</strong> 1 year.<br />
The NPV is excellent to compare two investments with the SAME lifespan<br />
or two mutually exclusive investments which can only be made<br />
once. The benefit <strong>of</strong> the NPV is that it shows directly how much the<br />
investment will return in present time money. But it is not good for chain<br />
investments. But in contrast to annuity, it has a value (equal to the purchase<br />
price) for t=0years.<br />
203
From the "CHP in the Hotel <strong>and</strong> Casino market Sectors" report<br />
In this entire case the energy consumption is reported as kW, which is meant to be "average kW during a yearly cycle". It could just as well have reported in "kWh/year"<br />
but the "average kW" has been chosen in order to give the reader a better feeling <strong>of</strong> how big the power consumptions are relative to a SOFC or ABS unit <strong>of</strong> a given kW size.<br />
Hotel example<br />
1kWh equals 3412 Btu<br />
(Indfyrede effekter)<br />
Unit/Place Average Anaheim Las Vegas Minneapolis<br />
Climate Mild Hot Cold<br />
Rooms 230 230 230<br />
Square meters m2 18.115 18.115 18.115<br />
Anual El. use MWh 3.131 3.548 2.960<br />
Anual gas use Milion Btu 7.836 8.780 19.660<br />
Anual gas use MWh 2.297 2.573 5.762<br />
El Peak kW 745 840 832<br />
El avg kW 367 357 405 338<br />
El min kW 250 260 240<br />
Gas av kW 405 262 294 658<br />
Gas + El total, avg 771 619 699 996<br />
Total Lodging industry<br />
AC, el ind 10^9 Btu/y 55<br />
Space Heating 10^9 Btu/y 118<br />
Water Heating 10^9 Btu/y 63<br />
Lignting 10^9 Btu/y 45<br />
Other 10^9 Btu/y 40<br />
Cooking 10^9 Btu/y 19<br />
Office Eqipment 10^9 Btu/y 15<br />
Ventilation 10^9 Btu/y 15<br />
Refrigiation 10^9 Btu/y 14<br />
Electricity total 10^9 Btu/y 203<br />
AC fraction - 0,27<br />
Other el fraction - 0,73<br />
Gas total 10^9 Btu/y 181<br />
Space heat frac - 0,65<br />
Water heat frac - 0,35
Total lodging pr Hotel (calculated)<br />
Space heating (1=yes, 0=no) 0 1 0 1 0 1<br />
Aircondition (1=normal, 2=all year) 2 1 2 1 2 1<br />
AC running time (fraction <strong>of</strong> year) 1 0,5 1 0,5 1 0,5<br />
ECH ECH FC+HotW FC+HotW FC+AC+HotW FC+AC+HotW<br />
Hot climate Normal clim. Hot climate Normal clim. Hot climate Normal clim.<br />
Waste heat driven: average - - HotW HotW AC+HotW AC+HotW<br />
AC, electricity kW 199 99 199 99 199 99<br />
Other electricity kW 267 267 267 267 267 267<br />
Space Heating kW 0 264 0 264 0 264<br />
Water Heating kW 141 141 141 141 141 141<br />
Total kW 607 771 607 771 607 771<br />
EL use (excl cool) kWe 267 267 267 267 267 267<br />
COP (prev) Electrial Chiller 4 4 4 4 4 4<br />
Cooling use (Q_c) kWt 795 397 795 397 795 397<br />
Heat use (Q_h) kWt - - 141 141 141 141<br />
Fractions EL = 1 1 1 1 1<br />
Cooling 2,97 1,49 2,97 1,49<br />
Heating 0,5 0,5 0,5 0,5<br />
Heat exchanger eff 0,8 0,8 0,8 0,8<br />
SOFC eff (LHV) 0,5 0,5 0,5 0,5<br />
COP_ABS 1,3 1,3<br />
Cooling from ABS(yearly average) 268 104<br />
ABS size summer production 268 208<br />
Cooling from ECH (yearly average) 795 397 795 397 526 293<br />
ECH size summer production 795 795 795 795 526 587<br />
Power consumption ECH 199 99 199 99 132 73<br />
Total electricity need 466 367 466 367 399 341<br />
El import from net 466 367 0 0 0 0<br />
SOFC size = av el power 466 367 399 341<br />
Gas for SOFC <strong>and</strong> space heating 141 405 932 997 798 945<br />
Gas for SOFC only 798 681
Hotel with 230 rooms <strong>and</strong> 18000 m^2 Arbsorption Chiller<br />
Assumptions<br />
Default values<br />
COP_ECH 4,0 4 USD/Dkr 5,3<br />
COP_ABS 1,3 1,3 GBP/Dkk 8,5<br />
eta_SOFC 0,5 0,5<br />
Gas price kr/kWh 0,20 0,2 California, commercial<br />
Electricity pr kr/kWh 0,75 0,75 California, commercial<br />
SOFC Price kr/kW 2650 2650 $500/kW<br />
ABS Price kr/kW 3670 3'670 Broard price pr kW corected which is the size correlation seen for WEGRACAL ABS units<br />
ECH Price kr/kW 1798 1798 P_(Enviromax 20 kW) * 0,5 (half kW price for a 250kW unit compared to the 20kW)<br />
Storage price/Cooling price 0,00 Storage size factor 0,50<br />
Discount 0,050 Hot climate Normal clim. Hot climate Normal clim. Hot climate Normal clim.<br />
- - HotW HotW ABS+HotW ABS+HotW<br />
SOFC eff (LHV) 0,0 0,0 0,5 0,5 0,5 0,5<br />
COP_ABS 0,0 0,0 0,0 0,0 1,3 1,3<br />
Cooling from ABS(yearly average) 268 104<br />
ABS size 268 208<br />
Cooling from ECH (yearly average) 795 397 795 397 526 293<br />
ECH size 795 795 795 795 526 587<br />
Power consumption ECH 199 99 199 99 132 73<br />
Total electricity need 466 367 466 367 399 341<br />
El import from net 466 367 0 0 0 0<br />
SOFC size = av el power 466 367 399 341<br />
Gas for SOFC <strong>and</strong> space heating 141 405 932 997 798 945
Electricity + Electrical Chiller, HOT<br />
kW kWh/y<br />
P_gas 141 1'233'534<br />
P_el 466 4'082'246<br />
P_el, SOFC<br />
P_ECH 795<br />
P_ABS<br />
Year Electricity Gas ECH Net payment NPV_i NPV_akk Anuity<br />
0 1'428'754 1'428'754 1'428'754 1'428'754<br />
1 3'061'685 246'707 3'308'392 3'150'849 4'579'603 4'808'583<br />
2 3'061'685 246'707 3'308'392 3'000'809 7'580'411 4'076'782<br />
3 3'061'685 246'707 3'308'392 2'857'913 10'438'324 3'833'042<br />
4 3'061'685 246'707 3'308'392 2'721'822 13'160'146 3'711'317<br />
5 3'061'685 246'707 3'308'392 2'592'211 15'752'358 3'638'398<br />
6 3'061'685 246'707 3'308'392 2'468'773 18'221'130 3'589'881<br />
7 3'061'685 246'707 3'308'392 2'351'212 20'572'342 3'555'308<br />
8 3'061'685 246'707 3'308'392 2'239'250 22'811'592 3'529'451<br />
9 3'061'685 246'707 3'308'392 2'132'619 24'944'211 3'509'403<br />
10 3'061'685 246'707 3'308'392 2'031'065 26'975'276 3'493'422<br />
11 3'061'685 246'707 3'308'392 1'934'348 28'909'624 3'480'398<br />
12 3'061'685 246'707 3'308'392 1'842'236 30'751'860 3'469'591<br />
13 3'061'685 246'707 3'308'392 1'754'511 32'506'371 3'460'491<br />
14 3'061'685 246'707 3'308'392 1'670'963 34'177'333 3'452'730<br />
15 3'061'685 246'707 3'308'392 1'591'393 35'768'726 3'446'041
SOFC + Water Heating (no ABS), Cooling ALL YEAR<br />
The ABS only runs all year. The cooling power is all year equal to the sommer power <strong>of</strong> the "sommer Case"<br />
SOFC runs all the time 24/7<br />
kW kWh/y<br />
P_gas 932 8'164'493<br />
P_el, SOFC 466<br />
P_el, import 0 0 Electricity is imported from the grid to cover the extra need for the ECH<br />
P_ECH 795<br />
P_ABS<br />
Year Electricity GAS for FC ECH SOFC ABS Storage Net payment NPV_i NPV_akk Anuity<br />
0 1'428'754 1'234'926 2'663'680 2'663'680 2'663'680<br />
1 0 1'632'899 1'632'899 1'555'141 4'218'821 4'429'762<br />
2 0 1'632'899 1'632'899 1'481'087 5'699'908 3'065'439<br />
3 0 1'632'899 1'632'899 1'410'559 7'110'467 2'611'025<br />
4 0 1'632'899 1'632'899 1'343'390 8'453'857 2'384'088<br />
5 0 1'632'899 1'632'899 1'279'419 9'733'276 2'248'141<br />
6 0 1'632'899 1'632'899 1'218'494 10'951'770 2'157'690<br />
7 0 1'632'899 1'632'899 1'160'470 12'112'240 2'093'235<br />
8 0 1'632'899 1'632'899 1'105'210 13'217'450 2'045'028<br />
9 0 1'632'899 1'632'899 1'052'581 14'270'031 2'007'652<br />
10 0 1'632'899 1'632'899 1'002'458 15'272'489 1'977'857<br />
11 0 1'632'899 1'632'899 954'722 16'227'211 1'953'576<br />
12 0 1'632'899 1'632'899 909'259 17'136'470 1'933'429<br />
13 0 1'632'899 1'632'899 865'961 18'002'431 1'916'463<br />
14 0 1'632'899 1'632'899 824'725 18'827'156 1'901'994<br />
15 0 1'632'899 1'632'899 785'452 19'612'608 1'889'524
SOFC + Water heating + ABS, Cooling ALL YEAR<br />
S<strong>of</strong>c running full year, netimport electricity = 0<br />
A storage will take care <strong>of</strong> the daily variation <strong>of</strong> cooling dem<strong>and</strong><br />
No room heating. Hot water is made by the SOFC waste heat<br />
Part <strong>of</strong> the cooling is made by the ABS, <strong>and</strong> the rest by the ECH<br />
Cooling need ALL YEAR (30 Celcius all year)<br />
The ABS runs all year (thereby nu waste heat is wasted)<br />
The SOFC delivers to the ABS all the time, <strong>and</strong> no real seasonal variation in el-in/export<br />
It is assumed that the heat exchangers for the aircondition devise is the same no matter what CH is used, so that price is not included<br />
SOFC runs all the time 24/7<br />
kW kWh/y<br />
P_gas 798 6'988'834<br />
P_el, SOFC 399<br />
P_el, import 0 0<br />
P_ECH 526<br />
P_ABS 268<br />
Year Electricity GAS for FC ECH SOFC ABS Storage Net payment NPV_i NPV_akk Anuity<br />
0 946'210 1'057'101 984'971 0 2'988'282 2'988'282 2'988'282<br />
1 0 1'397'767 1'397'767 1'331'206 4'319'488 4'535'462<br />
2 0 1'397'767 1'397'767 1'267'816 5'587'304 3'004'879<br />
3 0 1'397'767 1'397'767 1'207'443 6'794'747 2'495'089<br />
4 0 1'397'767 1'397'767 1'149'946 7'944'693 2'240'497<br />
5 0 1'397'767 1'397'767 1'095'187 9'039'880 2'087'984<br />
6 0 1'397'767 1'397'767 1'043'035 10'082'915 1'986'510<br />
7 0 1'397'767 1'397'767 993'367 11'076'282 1'914'201<br />
8 0 1'397'767 1'397'767 946'064 12'022'345 1'860'119<br />
9 0 1'397'767 1'397'767 901'013 12'923'358 1'818'188<br />
10 0 1'397'767 1'397'767 858'108 13'781'466 1'784'763<br />
11 0 1'397'767 1'397'767 817'245 14'598'711 1'757'523<br />
12 0 1'397'767 1'397'767 778'329 15'377'040 1'734'921<br />
13 0 1'397'767 1'397'767 741'266 16'118'305 1'715'887<br />
14 0 1'397'767 1'397'767 705'967 16'824'272 1'699'655<br />
15 0 1'397'767 1'397'767 672'350 17'496'622 1'685'665
16000<br />
Pay Back Time: Entire System (SOFC+ABS)<br />
14000<br />
SOFC Price [DKK/kW]<br />
12000<br />
10000<br />
8000<br />
6000<br />
4000<br />
2000<br />
0<br />
Normal Climate<br />
Hot Climate<br />
0 1 2 3 4 5<br />
Time [years]<br />
10000<br />
ABS Price [DKK/kW]<br />
9000<br />
8000<br />
7000<br />
6000<br />
5000<br />
4000<br />
3000<br />
2000<br />
1000<br />
0<br />
Pay Back Time: Absorption Cooling Unit (ABS)<br />
Normal Climate<br />
Hot Climate<br />
0 2 4 6 8 10 12<br />
Time [years]
Electricity + Electrical Chiller, Cooling Normal climate<br />
kW kWh/y<br />
P_gas 405 3'543'962<br />
P_el, SOFC<br />
P_el 367 3'212'000<br />
P_ECH 795<br />
P_ABS<br />
Year Electricity Gas ECH Net payment NPV_i NPV_akk Anuity<br />
0 1'428'754 1'428'754 1'428'754 1'428'754<br />
1 2'409'000 708'792 3'117'792 2'969'326 4'398'080 4'617'984<br />
2 2'409'000 708'792 3'117'792 2'827'930 7'226'010 3'886'183<br />
3 2'409'000 708'792 3'117'792 2'693'266 9'919'276 3'642'443<br />
4 2'409'000 708'792 3'117'792 2'565'016 12'484'292 3'520'718<br />
5 2'409'000 708'792 3'117'792 2'442'872 14'927'164 3'447'799<br />
6 2'409'000 708'792 3'117'792 2'326'545 17'253'708 3'399'282<br />
7 2'409'000 708'792 3'117'792 2'215'757 19'469'465 3'364'709<br />
8 2'409'000 708'792 3'117'792 2'110'245 21'579'710 3'338'852<br />
9 2'409'000 708'792 3'117'792 2'009'757 23'589'467 3'318'804<br />
10 2'409'000 708'792 3'117'792 1'914'054 25'503'521 3'302'823<br />
11 2'409'000 708'792 3'117'792 1'822'909 27'326'430 3'289'799<br />
12 2'409'000 708'792 3'117'792 1'736'104 29'062'533 3'278'992<br />
13 2'409'000 708'792 3'117'792 1'653'432 30'715'965 3'269'892<br />
14 2'409'000 708'792 3'117'792 1'574'697 32'290'662 3'262'131<br />
15 2'409'000 708'792 3'117'792 1'499'711 33'790'374 3'255'442
SOFC + Water Heating (no ABS), Cooling SUMMER ONLY<br />
The ABS only runs in the summer. No cooling needed at winter time<br />
SOFC runs all the time 24/7<br />
During summer there will be a net import <strong>of</strong> electricity (for the ECH), <strong>and</strong> during winter a net exp<br />
kW kWh/y<br />
P_gas 997 8'734'429<br />
P_el, SOFC 367<br />
P_el, import 0 0 Electricity is imported from the grid to cover the extra need for the ECH<br />
P_ECH 795<br />
P_ABS<br />
Year Electricity GAS for FC ECH SOFC ABS Storage Net payment NPV_i NPV_akk Anuity<br />
0 1'428'754 971'667 2'400'420 2'400'420 2'400'420<br />
1 0 1'746'886 1'746'886 1'663'701 4'064'121 4'267'327<br />
2 0 1'746'886 1'746'886 1'584'477 5'648'598 3'037'843<br />
3 0 1'746'886 1'746'886 1'509'026 7'157'623 2'628'341<br />
4 0 1'746'886 1'746'886 1'437'167 8'594'791 2'423'833<br />
5 0 1'746'886 1'746'886 1'368'731 9'963'521 2'301'322<br />
6 0 1'746'886 1'746'886 1'303'553 11'267'074 2'219'810<br />
7 0 1'746'886 1'746'886 1'241'479 12'508'553 2'161'726<br />
8 0 1'746'886 1'746'886 1'182'361 13'690'914 2'118'283<br />
9 0 1'746'886 1'746'886 1'126'058 14'816'973 2'084'601<br />
10 0 1'746'886 1'746'886 1'072'436 15'889'409 2'057'751<br />
11 0 1'746'886 1'746'886 1'021'368 16'910'777 2'035'870<br />
12 0 1'746'886 1'746'886 972'731 17'883'508 2'017'714<br />
13 0 1'746'886 1'746'886 926'411 18'809'919 2'002'424<br />
14 0 1'746'886 1'746'886 882'296 19'692'215 1'989'386<br />
15 0 1'746'886 1'746'886 840'282 20'532'497 1'978'148
SOFC + Water heating + ABS, Cooling SUMMER ONLY<br />
S<strong>of</strong>c running full year, netimport electricity = 0<br />
A storage will take care <strong>of</strong> the daily variation <strong>of</strong> cooling dem<strong>and</strong><br />
Room heating will always be made by gas - only hot water is made by the SOFC waste heat<br />
Part <strong>of</strong> the cooling is made by the ABS, <strong>and</strong> the rest by the ECH<br />
Cooling SUMMER ONLY<br />
The ABS only runs in the summer. No cooling needed at winter time<br />
The SOFC delivers to the ABS at summer, <strong>and</strong> wastes heat in the winter.<br />
During summer there will be a net import <strong>of</strong> electricity (for the ECH), <strong>and</strong> during winter a net exp<br />
SOFC runs all the time 24/7<br />
It is assumed that the heat exchangers for the aircondition devise is the same no matter what CH is used, so that price is not included<br />
kW kWh/y<br />
P_gas 945 8'279'206<br />
P_el, SOFC 341<br />
P_el, import 0 0<br />
P_ECH 587<br />
P_ABS 208<br />
Year Electricity GAS for FC ECH SOFC ABS Storage Net payment NPV_i NPV_akk Anuity<br />
0 1'055'066 902'812 762'773 0 2'720'651 2'720'651 2'720'651<br />
1 0 1'655'841 1'655'841 1'576'992 4'297'643 4'512'525<br />
2 0 1'655'841 1'655'841 1'501'897 5'799'539 3'119'021<br />
3 0 1'655'841 1'655'841 1'430'378 7'229'917 2'654'888<br />
4 0 1'655'841 1'655'841 1'362'265 8'592'182 2'423'097<br />
5 0 1'655'841 1'655'841 1'297'395 9'889'577 2'284'243<br />
6 0 1'655'841 1'655'841 1'235'614 11'125'191 2'191'857<br />
7 0 1'655'841 1'655'841 1'176'775 12'301'967 2'126'024<br />
8 0 1'655'841 1'655'841 1'120'739 13'422'705 2'076'785<br />
9 0 1'655'841 1'655'841 1'067'370 14'490'075 2'038'610<br />
10 0 1'655'841 1'655'841 1'016'543 15'506'618 2'008'178<br />
11 0 1'655'841 1'655'841 968'136 16'474'754 1'983'377<br />
12 0 1'655'841 1'655'841 922'034 17'396'789 1'962'800<br />
13 0 1'655'841 1'655'841 878'128 18'274'917 1'945'470<br />
14 0 1'655'841 1'655'841 836'312 19'111'229 1'930'692<br />
15 0 1'655'841 1'655'841 796'488 19'907'717 1'917'955
Hot climate SOFC + ABS + HW vs pure El<br />
Must be updated manually!<br />
NO SOFC SOFC + ABS + HW ------------------------------------------------------------------------------------------------<br />
SOFC pris DKK/kW<br />
Year 1'000 2'000 2'650 4'000 6'000 8'000 10'000 15'000<br />
0 1'428'754 2'330'087 2'728'993 2'988'282 3'526'805 4'324'617 5'122'429 5'920'241 7'914'771<br />
1 4'579'603 3'661'293 4'060'199 4'319'488 4'858'011 5'655'823 6'453'635 7'251'447 9'245'977<br />
2 7'580'411 4'929'109 5'328'015 5'587'304 6'125'827 6'923'639 7'721'451 8'519'263 10'513'793<br />
3 10'438'324 6'136'552 6'535'458 6'794'747 7'333'270 8'131'082 8'928'894 9'726'706 11'721'236<br />
4 13'160'146 7'286'498 7'685'404 7'944'693 8'483'216 9'281'028 10'078'840 10'876'652 12'871'183<br />
5 15'752'358 8'381'685 8'780'591 9'039'880 9'578'403 10'376'215 11'174'027 11'971'839 13'966'369<br />
6 18'221'130 9'424'720 9'823'626 10'082'915 10'621'438 11'419'250 12'217'062 13'014'874 15'009'404<br />
7 20'572'342 10'418'087 10'816'993 11'076'282 11'614'805 12'412'617 13'210'429 14'008'241 16'002'771<br />
8 22'811'592 11'364'150 11'763'056 12'022'345 12'560'868 13'358'680 14'156'492 14'954'304 16'948'835<br />
9 24'944'211 12'265'163 12'664'069 12'923'358 13'461'881 14'259'693 15'057'505 15'855'317 17'849'847<br />
10 26'975'276 13'123'271 13'522'177 13'781'466 14'319'989 15'117'801 15'915'613 16'713'425 18'707'955<br />
11 28'909'624 13'940'516 14'339'422 14'598'711 15'137'234 15'935'046 16'732'858 17'530'670 19'525'200<br />
12 30'751'860 14'718'845 15'117'751 15'377'040 15'915'563 16'713'375 17'511'187 18'308'999 20'303'529<br />
13 32'506'371 15'460'110 15'859'016 16'118'305 16'656'828 17'454'640 18'252'452 19'050'264 21'044'795<br />
14 34'177'333 16'166'077 16'564'983 16'824'272 17'362'795 18'160'608 18'958'420 19'756'232 21'750'762<br />
15 35'768'726 16'838'427 17'237'333 17'496'622 18'035'145 18'832'957 19'630'769 20'428'581 22'423'111<br />
1 1 1 2 2 3 3 5<br />
PB time 0,5 0,7 0,9 1,2 1,6 2,1 2,6 3,6
Hot climate SOFC + ABS + HW vs SFOC + HW<br />
Must be updated manually!<br />
Delta NPV_10 SOFC + ABS + HW - (SOFC + HW) ------------------------------------------------------------------------------------------------<br />
ABS pris DKK/kW<br />
Year 2'000 2'450 3'000 3'670 5'000 6'000 7'000 8'000 10'000<br />
0 123'538 2'751 -144'877 -324'715 -681'708 -950'123 -1'218'538 -1'486'954 -2'023'784<br />
1 347'473 226'686 79'058 -100'780 -457'773 -726'188 -994'603 -1'263'019 -1'799'849<br />
2 560'745 439'958 292'329 112'491 -244'501 -512'917 -781'332 -1'049'747 -1'586'578<br />
3 763'860 643'074 495'445 315'607 -41'386 -309'801 -578'216 -846'631 -1'383'462<br />
4 957'304 836'517 688'889 509'050 152'058 -116'357 -384'773 -653'188 -1'190'019<br />
5 1'141'536 1'020'749 873'121 693'282 336'290 67'875 -200'541 -468'956 -1'005'787<br />
6 1'316'995 1'196'208 1'048'580 868'741 511'749 243'334 -25'082 -293'497 -830'328<br />
7 1'484'099 1'363'312 1'215'683 1'035'845 678'853 410'437 142'022 -126'393 -663'224<br />
8 1'643'245 1'522'458 1'374'830 1'194'992 837'999 569'584 301'169 32'753 -504'077<br />
9 1'794'813 1'674'026 1'526'398 1'346'560 989'567 721'152 452'737 184'321 -352'509<br />
10 1'939'164 1'818'377 1'670'748 1'490'910 1'133'918 865'502 597'087 328'672 -208'159<br />
11 2'076'640 1'955'854 1'808'225 1'628'387 1'271'394 1'002'979 734'564 466'149 -70'682<br />
12 2'207'571 2'086'784 1'939'155 1'759'317 1'402'325 1'133'909 865'494 597'079 60'248<br />
13 2'332'266 2'211'479 2'063'851 1'884'012 1'527'020 1'258'605 990'189 721'774 184'944<br />
14 2'451'024 2'330'237 2'182'608 2'002'770 1'645'778 1'377'362 1'108'947 840'532 303'701<br />
15 2'564'126 2'443'339 2'295'711 2'115'872 1'758'880 1'490'465 1'222'049 953'634 416'803<br />
PB time<br />
0,0 0,7 1,5 3,2 4,7 6,2 7,8 11,5
Assumptions<br />
SOFC price = 2650kr/kW<br />
10 years lifetime<br />
Electricity can be im/exported at same price as long at netexport < 0<br />
no gas for room heating<br />
Cooling ALL YEAR<br />
Cooling in Sommer only<br />
Annuity_5 Annuity_10 Annuity_15 Annuity_5 Annuity_10 Annuity_15<br />
EL 3'638'398 3'493'422 3'446'041 3'447'799 3'302'823 3'255'442<br />
SOFC+WH 2'248'141 1'977'857 1'889'524 2'301'322 2'057'751 1'978'148<br />
SOFC+WH+ABS 2'087'984 1'784'763 1'685'665 2'284'243 2'008'178 1'917'955<br />
HOT climate.<br />
Annual price for all energy equipment + gas <strong>and</strong> electricity use<br />
Normal climate.<br />
Annual price for all energy equipment + gas <strong>and</strong> electricity use<br />
Annuity price [DKK/y]<br />
4'000'000<br />
3'500'000<br />
3'000'000<br />
2'500'000<br />
2'000'000<br />
1'500'000<br />
1'000'000<br />
Annuity_5<br />
Annuity_10<br />
Annuity_15<br />
Annuity price [DKK/y]<br />
4'000'000<br />
3'500'000<br />
3'000'000<br />
2'500'000<br />
2'000'000<br />
1'500'000<br />
1'000'000<br />
Annuity_5<br />
Annuity_10<br />
Annuity_15<br />
500'000<br />
500'000<br />
0<br />
EL SOFC+WH SOFC+WH+ABS<br />
0<br />
EL SOFC+WH SOFC+WH+ABS
It is seen, that it is by far more advantageous to use the ABS in HOT climates with cooling needs all year<br />
Sensitivity analysis<br />
The effect on the 10 years anuity difference is investigated<br />
HOT climate<br />
Summer only (not shown in report)<br />
(SOFC + WH + ABS) - (SOFC + WH)<br />
(SOFC + WH + ABS) - (SOFC + WH)<br />
Positive values => ABS is advantageous<br />
Positive values => ABS is advantageous<br />
Delta NPV Delta Anuity Delta NPV Delta Anuity<br />
0 -324'602 0 -320'231 0<br />
1 -100'667 -105'700 -233'522 -245'198<br />
2 112'605 60'559 -150'942 -81'177<br />
3 315'720 115'935 -72'294 -26'547<br />
4 509'164 143'590 2'609 736<br />
5 693'396 160'157 73'944 17'079<br />
6 868'855 171'180 141'883 27'953<br />
7 1'035'959 179'034 206'587 35'702<br />
8 1'195'105 184'909 268'209 41'498<br />
9 1'346'673 189'464 326'897 45'991<br />
10 1'491'024 193'094 382'791 49'573<br />
11 1'628'500 196'053 436'022 52'492<br />
12 1'759'431 198'508 486'719 54'914<br />
13 1'884'126 200'576 535'002 56'954<br />
14 2'002'884 202'339 580'986 58'693<br />
15 2'115'986 203'859 624'780 60'193
Hot climate<br />
Increase (Delta NPV_10) -10 0 10<br />
Electricity price 1'491'024 1'491'024 1'491'024<br />
Gas price 1'325'967 1'491'024 1'672'586<br />
Discount rate 1'531'779 1'491'024 1'447'734<br />
COP_ECH 1'656'193 1'491'024 1'334'841<br />
COP_ABS 1'381'390 1'491'024 1'606'966<br />
eta_SOFC 2'066'664 1'491'024 1'018'709<br />
SOFC price 1'474'858 1'491'024 1'508'806<br />
ECH price 1'447'156 1'491'024 1'539'278<br />
ABS price 1'580'567 1'491'024 1'392'527<br />
-10 0 10<br />
Net Present Value increase [%]<br />
Sensitivity analysis: SOFC+HW+ABS vs SOFC+WH<br />
Electricity price 0 0 0<br />
Gas price -11 0 12<br />
-20<br />
Discount rate 3 0 -3<br />
COP_ECH 11 0 -10<br />
-30<br />
COP_ABS -7 0 8<br />
eta_SOFC 39 0 -32<br />
Increase in variables [%]<br />
SOFC price -1 0 1<br />
ECH price -3 0 3 A positive value <strong>of</strong> e.g. 5% means, that after 10 years, the difference in NPV will<br />
ABS price 6 0 -7 be 5% higher (in favour <strong>of</strong> the ABS solution)<br />
30<br />
20<br />
10<br />
0<br />
-10 -5 0 5 10<br />
-10<br />
ECH price<br />
COP_ABS<br />
Electricity price<br />
COP_ECH<br />
Discount rate<br />
Gas price<br />
eta_SOFC<br />
SOFC price<br />
ABS price
A.5 Absorption cooling unit prices<br />
A.5. Absorption cooling unit prices<br />
219
Prices <strong>of</strong> absorption cooling units<br />
Name Rotarica Rotarica CHEM SorTech AG SorTech AG EAW Cooling Tech<br />
Model Splar 045 Splar 045v AAdC ACS 08 ASC 15 WEGRACAL 15 Cooltech 5<br />
Refrigerant water water water ammonia<br />
Ab/adsorbent silica gel silica gel LiBr water<br />
Providing heat yes yes no<br />
Cooling power, nom Q_C kW 4,5 4,5 5,0 8 15 15 17,6<br />
Cooling power interval [Q_C] kW 2->8 2->8 5->11 10->23<br />
Electrical power P kW 0,4 1,11 0,5 0,007 0,014 0,3 1,3<br />
Heat Consumption Q_D kW 12,5 13 25 21,1 25,9<br />
COP COP 0,7 0,7 0,4 0,6 0,6 0,71 0,68<br />
T_hotw (i/o) T_Hw C 90 90 72->65 72->65 Gas<br />
T_cool,fwd TC_o C 12 12 15 15 11 7,2<br />
T_cool,return TC_I C 12 12 18 18 17 12,8<br />
T_condenser T_Cond C 32->27 32->28 30-->36<br />
HEX Warm included no no no yes<br />
HEX Cold included no no no no<br />
HEX Hot, (hot water) included yes yes yes no<br />
HEX Hot, (gas burner) included no no no yes<br />
HEX Hot, (exhaust gas) included no no no no<br />
Lager<br />
kWh<br />
(kg) m kg 240 280 295 590 650 475<br />
Price @ 1unit (excl VAT) kr 114'800 169'900 111'154 139'920<br />
Price @ 1000units (excl VAT) kr 93'280<br />
Price pr kW @ 1unit (excl VAT) DKK/kW 0 0 14'350 11'327 7'410 7'950<br />
Price pr kW @ 1000units (excl VAT) DKK/kW 0 0 0 0 0 5'300<br />
HEX Warm included DKK 45'000 65'000 65'000 0<br />
HEX Cold included DKK 3'796 7'118 7'118 8'352<br />
HEX Hot, (exhaust gas) included DKK 3'164 5'932 5'013 6'141<br />
Total ext eq. (excl VAT) DKK 0 0 0 51'960 78'050 77'131 14'494<br />
Total price for AC (air/air) system (incl VAT) DKK 0 0 0 166'760 247'950 188'285 154'414
Yazaki ClimateWell Robur Broad EAW EAW EAW EAW Name<br />
SC 5 TM 10 GAHP-AR BCT23 WEGRACAL 50 WEGRACAL 80 WEGRACAL 140 WEGRACAL200 Model<br />
water water ammonia water water water water water Refrigerant<br />
LiBr LiCl water LiBr LiBr LiBr LiBr LiBr Ab/adsorbent<br />
yes yes yes Providing heat<br />
17,6 20 16,9 23 54 83 140 200 Cooling power, nom<br />
Cooling power interval<br />
0,043 0,11 0,87 1,80 3,4 3,4 3,4 3,4 Electrical power<br />
25,1 29,4 25,3 20,8 72,0 111 187 267 Heat Consumption<br />
0,7 0,68 0,67 1,11 0,75 0,75 0,75 0,75 COP<br />
88 Gas Gas 86-->71 86-->71 86-->71 86-->71 T_hotw (i/o)<br />
7 17 [7] 7,2 7 9 9 9 9 T_cool,fwd<br />
12,5 12,7 14 15 15 15 15 T_cool,return<br />
30 [20] 27-->32 27-->32 27-->32 27-->32 T_condenser<br />
no no no yes no no no no HEX Warm included<br />
no no no no no no no no HEX Cold included<br />
yes yes (no) yes (84%) yes yes yes yes HEX Hot, (hot water) included<br />
no no yes yes (100%) no no no no HEX Hot, (gas burner) included<br />
no no no yes (98%) no no no no HEX Hot, (exhaust gas) included<br />
60 Lager<br />
420 740 380 700 2250 2900 3400 4300 (kg)<br />
143'600 111'900 92'504 119'360 379'453 436'485 598'777 684'306 Price @ 1unit (excl VAT)<br />
93'250 0 0 0 0 0 0 Price @ 1000units (excl VAT)<br />
8'159 5'595 5'474 5'190 7'027 5'259 4'277 3'422 Price pr kW @ 1unit (excl VAT)<br />
0 4'663 0 0 0 0 0 0 Price pr kW @ 1000units (excl VAT)<br />
65'000 75'217 65'000 0 191'803 294'809 497'268 710'383 HEX Warm included<br />
8'352 9'491 8'020 10'915 25'626 39'388 66'438 94'912 HEX Cold included<br />
5'956 6'979 6'006 0 17'084 26'259 44'292 63'275 HEX Hot, (exhaust gas) included<br />
79'308 91'687 79'026 10'915 234'514 360'456 607'998 868'569 Total ext eq. (excl VAT)<br />
222'908 203'587 171'530 130'275 613'967 796'941 1'206'775 1'552'875 Total price for AC (air/air) system (incl VAT)
1'000'000<br />
900'000<br />
800'000<br />
143'600<br />
700'000<br />
Price [DKK]<br />
600'000<br />
500'000<br />
400'000<br />
300'000<br />
200'000<br />
100'000<br />
0<br />
ECH vs ABS vs ADS<br />
9'000<br />
15'000 12'400 16'000 50'865 58'510 8'000 80'265 91'730<br />
12'500<br />
7'000<br />
ECH<br />
ABS<br />
Adsorption<br />
0 50 100 150 200<br />
Cooling capacity [kW]<br />
Price [DKK/kW]<br />
6'000<br />
5'000<br />
4'000<br />
3'000<br />
2'000<br />
1'000<br />
0<br />
Prices pr kW for different ABS br<strong>and</strong>s<br />
ABSorption<br />
0 50 100 150 200 250<br />
Cooling capacity [kW]<br />
The marked investigation showed the following prices for different cooling capacities for electrical chillers (ECH), absorption units (ABS) <strong>and</strong> Adsorption units.<br />
The reason for the large spread for kW price (right figure) <strong>of</strong> the low sizes is that it is different br<strong>and</strong>s og different performance <strong>and</strong> quality, hence the development <strong>of</strong> the<br />
kW price can not be attributed solely to the size <strong>of</strong> the unit, <strong>and</strong> for establishing the size-kW-price correlation, the price dependency <strong>of</strong> the WEGSECAL ABS units is<br />
used (see next page)
Prices <strong>of</strong> WEGRACAL absorption cooling units <strong>of</strong> different size<br />
Model WEGRACAL 15 50 80 140 200<br />
Capacity kW 15 54 83 140 200<br />
Mass kg 650 2250 2900 3400 4300<br />
Catalog price Euro 14'900 50'865 58'510 80'265 91'730<br />
Price ex VAT Dkr 111'154 379'453 436'485 598'777 684'306<br />
Euro exchange rate 7,46<br />
Data comes from:<br />
http://www.easy-server.org/ebg_neu/Klimaanlage/preislistekwkk.pdf<br />
The WEGRACAL data has been used to get a correlation between size <strong>and</strong> price for absorption cooling units<br />
since they are all the same manufacturer, the price difference must be due to size only (<strong>and</strong> not<br />
Quality, performance, stamination etc).<br />
WEGRACAL Absorption coolnig unit<br />
800'000<br />
Price<br />
700'000<br />
600'000<br />
Price [DKK]<br />
500'000<br />
400'000<br />
300'000<br />
200'000<br />
100'000<br />
0<br />
0 50 100 150 200 250<br />
Cooling power [kW]<br />
WEGRACAL Absorption coolnig unit<br />
Price [DKK]<br />
5'000<br />
4'500<br />
4'000<br />
3'500<br />
3'000<br />
2'500<br />
2'000<br />
1'500<br />
1'000<br />
500<br />
0<br />
Mass<br />
0 50 100 150 200 250<br />
Cooling power [kW]
A. MARKET INVESTIGATION<br />
A.6 Gas <strong>and</strong> electricity prices<br />
224
Retail gas prices<br />
2008<br />
prices<br />
2008<br />
prices<br />
39,48 GJ/1000 m^3 (LHV)<br />
5,41 DKK/USD<br />
0,02831685 m^3/cubic foot<br />
DKK/kWh<br />
Residential Industry Commercial<br />
Residential Industry Commercial<br />
Taiwan USD/1000 Cubic Feet 0,00 0,00 0,00<br />
Singapore USD/1000 Cubic Feet 0,00 0,00 0,00<br />
Malaysia USD/1000 Cubic Feet 0,00 0,00 0,00<br />
California 12,74 10,71 11,72 USD/1000 Cubic Feet 0,22 0,19 0,20<br />
Hawaii 44,75 26,74 39,01 USD/1000 Cubic Feet 0,78 0,47 0,68<br />
US avg. 13,68 9,58 11,99 USD/1000 Cubic Feet 0,24 0,17 0,21<br />
2008<br />
prices<br />
2008<br />
prices<br />
USD/m^3 DKK/m^3DKK/GJ DKK/MWH DKK/kWh<br />
Taiwan 0,00 0,00 0,00 0,00 0,00<br />
Singapore 0,00 0,00 0,00 0,00 0,00<br />
Malaysia 0,00 0,00 0,00 0,00 0,00<br />
California 0,45 2,43 61,65 221,95 0,22<br />
Hawaii 1,58 8,55 216,56 779,60 0,78<br />
US avg. 0,48 2,61 66,20 238,32 0,24<br />
Retail natural gas price<br />
0,90<br />
0,80<br />
0,70<br />
0,60<br />
Residential<br />
Industry<br />
Commercial<br />
DKK/kWh<br />
0,50<br />
0,40<br />
0,30<br />
0,20<br />
0,10<br />
0,00<br />
Taiwan Singapore Malaysia California Hawaii US avg.<br />
http://tonto.eia.doe.gov/dnav/ng/ng_pri_sum_dcu_nus_a.htm<br />
http://www.ens.dk/da-DK/Info/TalOgKort/Statistik_og_noegletal/Maanedsstatistik/Documents/Energistatistik%202008.pdf<br />
http://www.xe.com/ucc/convert.cgiAmount=1&From=USD&To=DKK&image.x=41&image.y=13&image=Submit<br />
http://www.onlineconversion.com/volume.htm<br />
http://www.eia.doe.gov/emeu/cabs/taiwan.html#gas<br />
http://www.eia.doe.gov/dnav/ng/ng_pri_sum_dcu_SCA_a.htm<br />
225
Retail electricity prices<br />
Exchange rate in DKK<br />
TWD USD<br />
0,1687 5,41<br />
2007<br />
prices<br />
2009<br />
prices<br />
In DKK/kWh<br />
Residential Industry Commercial Currency Residential Industry Commercial<br />
Taiwan 2,5855 1,8331 n/a TWD/kWh 0,44 0,31 n/a<br />
Singapore 4,4842 3,5121 n/a TWD/kWh 0,76 0,59 n/a<br />
Malaysia 2,301 2,2201 n/a TWD/kWh 0,39 0,37 n/a<br />
California 14,08 11,43 13,93 Uscent/kWh 0,76 0,62 0,75<br />
Hawaii 26,45 20,49 24,35 Uscent/kWh 1,43 1,11 1,32<br />
US avg. 11,76 6,68 10,22 Uscent/kWh 0,64 0,36 0,55<br />
Retail electricity price<br />
1,60<br />
1,40<br />
1,20<br />
Residential<br />
Industry<br />
Commercial<br />
DKK/kWh<br />
1,00<br />
0,80<br />
0,60<br />
0,40<br />
0,20<br />
0,00<br />
Taiwan Singapore Malaysia California Hawaii US avg.<br />
sources:<br />
US<br />
Taiwan<br />
http://www.eia.doe.gov/cneaf/electricity/epm/table5_6_a.html<br />
http://www.etaiwannews.com/etn/print.php<br />
226
A P P E N D I X<br />
B<br />
DIAGRAMS AND PLOTS<br />
227
B. DIAGRAMS AND PLOTS<br />
B.1 GAX diagram<br />
Figure B.1: Diagram <strong>of</strong> GAX cycle. Taken from [20].<br />
228
B.2. Double stage diagram<br />
B.2 Double stage diagram<br />
COND2<br />
21<br />
HEAT<br />
DES2<br />
29<br />
27<br />
22<br />
SHEX<br />
2<br />
23<br />
VA2<br />
31<br />
32<br />
VB2<br />
PUMP<br />
2<br />
26<br />
25<br />
2<br />
COND1<br />
COOLING<br />
1<br />
MIXR<br />
0<br />
10<br />
MIXL<br />
9<br />
DES1<br />
SHEX<br />
1<br />
α<br />
8<br />
SPL<br />
1-α<br />
7<br />
3<br />
VA1<br />
EVAP<br />
4<br />
11<br />
12<br />
VB1<br />
ABSO<br />
PUMP<br />
1<br />
6<br />
5<br />
CHILLED WATER<br />
COOLING<br />
Figure B.2: Diagram <strong>of</strong> double stage absorption cycle.<br />
229
B. DIAGRAMS AND PLOTS<br />
B.3 Closed adsorption cycle<br />
Figure B.3: Diagram <strong>of</strong> closed adsorption cycle - two-bed system. Taken from [35].<br />
230
B.4. Property plots<br />
B.4 Property plots<br />
B.4.1<br />
Phase diagram <strong>of</strong> water-LiBr-solution<br />
Figure B.4: Only states <strong>of</strong> solution <strong>of</strong> water <strong>and</strong> LiBr applies for the absorption cycle.<br />
Precipitation must be avoided to avoid blocks in tubes <strong>and</strong> damage <strong>of</strong> the machine.<br />
231
B. DIAGRAMS AND PLOTS<br />
B.4.2<br />
p-T diagram <strong>of</strong> water-LiBr-solution<br />
Figure B.5: p-T diagram <strong>of</strong> water-LiBr. w is the concentration <strong>of</strong> the LiBr-solution (on mass<br />
basis).<br />
232
A P P E N D I X<br />
C<br />
EES<br />
C.1 Parameter configuration<br />
This is the optimized parameter configuration. The st<strong>and</strong>ard parameter<br />
configuration is very similar <strong>and</strong> only parameters which are different<br />
from the optimized one are shown with blue numbers.<br />
FUEL CELL related<br />
α SPG1 = 0,62 [·]<br />
λ Bur n;i = 1,5 [·]<br />
A cell = 0,0228 [ m 2]<br />
ASR = 280 · exp ( −0,0083 · T SOFC ;av<br />
)<br />
· 10<br />
−4 [ Ω · m 2]<br />
F R = 0,14 [·]<br />
FW = 0,6 [·]<br />
∆ Ḣ f uel = 100 [kW ]<br />
i d = 2700 [ A/m 2] 3000<br />
n cell = 60 [·]<br />
U f = 0,565 [·] 0,70<br />
Effectiveness<br />
ɛ GGHE X 1;c = ɛ GGHE X 2;c [·]<br />
233
C. EES<br />
Efficiencies<br />
SOFC<br />
η inver t = 0,95 [·]<br />
η i s;BLOW 1 = 0,60 [·]<br />
General<br />
η blower ;TOW ER1 = 0,4 [·]<br />
η wb;TOW ER1 = 0,75 [·]<br />
ABS<br />
η PU MP1 = 0,5 [·]<br />
η PU MP2 = 0,5 [·]<br />
Mass flows at inlet - [CH 4 ; CO ; CO 2 ; H 2 ; H 2 O ; N 2 ; O 2 ]<br />
SOFC<br />
ṁ 1; 1..7 = [ṁ i ; 0; 0; 0; 0; 0; 0] kg<br />
s<br />
ṁ 11; 1..5<br />
= [0; 0; 0; 0; 0]<br />
kg<br />
s<br />
Burner additional <strong>fuel</strong> input<br />
ṁ Bur ni ;3 ; 1..7 = [ ṁ bur n;add ; 0; 0; 0; 0; 0; 0 ] kg<br />
s<br />
FuelBP Ratio = 0,0 [·]<br />
234
C.1. Parameter configuration<br />
Humidity<br />
φ TOW ERair ;i<br />
= 0,4 [·]<br />
Pressure - Absolute<br />
p re f = 100 [kPa]<br />
SOFC<br />
p BLOW 1i = p re f<br />
[kPa]<br />
General<br />
p W GHE X 3g ;o<br />
= p re f<br />
[kPa]<br />
p W GHE X 3w;i = 1000 [kPa]<br />
ABS<br />
p DES1h;i = 2000 [kPa]<br />
p COND1c;i = 2000 [kPa]<br />
p EV APc;i = 2000 [kPa]<br />
p DES2h;i = 2000 [kPa]<br />
Pressure loss <strong>of</strong> components<br />
SOFC<br />
∆ p;BURN ;i ;1 = −8 [kPa]<br />
∆ p;BURN ;i ;2 = −1 [kPa]<br />
∆ p;GGHE X 1;h = −1 [kPa]<br />
235
C. EES<br />
∆ p;GGHE X 1;c = −1 [kPa]<br />
∆ p;GGHE X 2;h = −1 [kPa]<br />
∆ p;GGHE X 2;c = −1 [kPa]<br />
∆ p;GGHE X 3;h = −4 [kPa]<br />
∆ p;GGHE X 3;c = −4 [kPa]<br />
∆ p;GGHE X 4;c = −2 [kPa]<br />
∆ p;GGHE X 4;h = −2 [kPa]<br />
∆ p;M I XG1;i ;1 = −0,1 [kPa]<br />
∆ p;M I XG2;i ;1 = −0,1 [kPa]<br />
∆ p;PR = −5 [kPa]<br />
∆ p;SOFC ;ano = −1 [kPa]<br />
∆ p;SOFC ;cat = −3 [kPa]<br />
∆ p;SPG1;o;1 = −0,1 [kPa]<br />
∆ p;SPG1;o;2 = −0,1 [kPa]<br />
∆ p;SPG2;o;1 = −0,1 [kPa]<br />
∆ p;SPG2;o;2 = −0,1 [kPa]<br />
General<br />
∆ p;TOW ER1;w = 0 [kPa]<br />
∆ p;W GHE X 1;g = −2 [kPa]<br />
∆ p;W GHE X 1;w = 0 [kPa]<br />
∆ p;W GHE X 2;g = −2 [kPa]<br />
∆ p;W GHE X 2;w = 0 [kPa]<br />
∆ p;W GHE X 3;g = −2 [kPa]<br />
∆ p;W GHE X 3;w = 0 [kPa]<br />
∆ p;TOW ER1;air ;dr y = 0,15 [kPa]<br />
∆ p;TOW ER1;air ;wet = 0,15 [kPa]<br />
236
C.1. Parameter configuration<br />
ABS<br />
∆ p;ABSO;1 = 0 [kPa]<br />
∆ p;ABSO;2 = 0 [kPa]<br />
∆ p;ABSO;c = 0 [kPa]<br />
∆ p;COND1;r = 0 [kPa]<br />
∆ p;COND1;c = 0 [kPa]<br />
∆ p;COND2;r = 0 [kPa]<br />
∆ p;COND2;c = 0 [kPa]<br />
∆ p;DES1;r = 0 [kPa]<br />
∆ p;DES1;s = 0 [kPa]<br />
∆ p;DES1;h = 0 [kPa]<br />
∆ p;DES2;r = 0 [kPa]<br />
∆ p;DES2;s = 0 [kPa]<br />
∆ p;EV AP;r = 0 [kPa]<br />
∆ p;EV AP;c = 0 [kPa]<br />
∆ p;M I X R1;1 = 0 [kPa]<br />
∆ p;M I X R1;2 = 0 [kPa]<br />
∆ p;M I X L1;1 = 0 [kPa]<br />
∆ p;M I X L1;2 = 0 [kPa]<br />
∆ p;SHE X 1;ws = 0 [kPa]<br />
∆ p;SHE X 1;ss = 0 [kPa]<br />
∆ p;SHE X 2;ws = 0 [kPa]<br />
∆ p;SHE X 2;ss = 0 [kPa]<br />
Heat loss <strong>of</strong> components<br />
SOFC<br />
˙Q loss;BLOW 1 = 0 [kW ]<br />
237
C. EES<br />
˙Q loss;Bur n = 0 [kW ]<br />
˙Q loss;PR = 0 [kW ]<br />
˙Q loss;SOFC = 0 [kW ]<br />
General<br />
˙Q loss;W GHE X 1 = 0 [kW ]<br />
˙Q loss;W GHE X 2 = 0 [kW ]<br />
˙Q loss;W GHE X 3 = 0 [kW ]<br />
˙Q loss;W W HE X 1 = 0 [kW ]<br />
ABS<br />
˙Q loss;ABSO = 0 [kW ]<br />
˙Q loss;COND1 = 0 [kW ]<br />
˙Q loss;COND2 = 0 [kW ]<br />
˙Q loss;DES1 = 0 [kW ]<br />
˙Q loss;DES2 = 0 [kW ]<br />
˙Q loss;EV AP = 0 [kW ]<br />
˙Q loss;PU MP1 = 0 [kW ]<br />
˙Q loss;PU MP2 = 0 [kW ]<br />
˙Q loss;SHE X 1 = 0 [kW ]<br />
˙Q loss;SHE X 2 = 0 [kW ]<br />
˙Q loss;V A1 = 0 [kW ]<br />
˙Q loss;V A2 = 0 [kW ]<br />
˙Q loss;V B1 = 0 [kW ]<br />
˙Q loss;V B2 = 0 [kW ]<br />
238
C.1. Parameter configuration<br />
Qualities<br />
qu COND1r ;o<br />
= 0 [·]<br />
qu COND2r ;o<br />
= 0 [·]<br />
qu EV APr ;o<br />
= 1 [·]<br />
Temperatures<br />
T re f = 25 [C ]<br />
T Bur ni ;3<br />
= T re f [C ]<br />
T amb;dr y = 18 [C ]<br />
T amb;wet = 30 [C ]<br />
SOFC<br />
T GGHE X 1c;i = T re f [C ]<br />
T BLOW 1i = T re f [C ]<br />
T SOFCano;i = 690 [C ]<br />
T SOFCcat;i = T SOFCano;i [C ]<br />
T W GHE X 3w;i = T amb [C ]<br />
T W GHE X 3w;o = 65 [C ]<br />
T DES2s;o = 133 [C ] 150<br />
ABS<br />
T DES1;h;i = 67 [C ] 78<br />
T EV APc;o = 6,0 [C ]<br />
T amb;evap = T amb − T EV APc;o [C ]<br />
Temperature changes<br />
239
C. EES<br />
SOFC<br />
∆ T ;SOFC ;av = 30 [C ]<br />
∆ T ;SOFC = 90 [C ]<br />
General<br />
∆ T ;c;TOW ER1 = 5 [C ]<br />
ABS<br />
∆ T ;chill;EV AP = 5 [C ]<br />
∆ T ;h;DES1 = 5 [C ]<br />
∆ T ;h;DES2 = 5 [C ]<br />
∆ T ;min<br />
∆ T ;min;DES1;r ;o = 0 [C ]<br />
∆ T ;min;DES2;r ;o = 0 [C ]<br />
Liquid-Liquid HEXES<br />
∆ T ;min;ABSO;s;o = 1,8 [C ] 5<br />
∆ T ;min;SHE X 1;ws;i = 5 [C ]<br />
∆ T ;min;SHE X 2;ws;i = 5 [C ]<br />
∆ T ;min;EV AP;r ;i = 2,7 [C ] 5<br />
240<br />
Liquid-Gas/liquid HEXES<br />
∆ T ;min;COND1;r ;o;S = 12,5 [C ]
C.1. Parameter configuration<br />
∆ T ;min;COND1;r ;o;D = 10 [C ]<br />
∆ T ;min;COND2;r ;o = 15 [C ] 12,5<br />
(∆ T ;min;COND2;r ;o is set so ∆ T ;min;COND2;mp = 10[C ] in both STD <strong>and</strong> OPTI)<br />
Gas/liquid HEXES<br />
∆ T ;min;W GHE X 1;w;i = 15 [C ]<br />
∆ T ;min;W GHE X 2;w;i = 15 [C ]<br />
∆ T ;min;W GHE X 3;w;i = 15 [C ]<br />
Gas-Gas HEXES<br />
∆ T ;min;GGHE X 4;c;o = 9,4 [C ] 25<br />
TOWERs<br />
∆ T ;min;TOW ER1;a;o;wet = 3 [C ]<br />
∆ T ;min;TOW ER1;a;o;dr y = 8 [C ]<br />
∆ T ;min;TOW ER1;a;i ;dr y = ∆ T ;min;TOW ER1;a;o [C ]<br />
241
C. EES<br />
C.2 Results - St<strong>and</strong>ard parameter configuration<br />
ABSO c;i = 36 ABSO c;o = 37<br />
ABSO r ;i = 54 ABSO s;i = 62<br />
ABSO s;o = 55<br />
AddPreHeat$ = ‘On’<br />
Air Fuel Ratio;m = 92,78 [-] Air Fuel Ratio;n = 8,355 [-]<br />
Air i = 11 [-] α SPG1 = 0,62 [-]<br />
α SPG2 = 0,0461 [-]<br />
ASR = 0,00005542 [ Ω·m 2] α SPL1 = 0,4351 [-]<br />
A cell = 0,0228 [ m 2]<br />
BLOW 1 i = 11 BLOW 1 o = 12<br />
Bur n i ;1 = 10 [-] Bur n i ;2 = 16 [-]<br />
Bur n i ;3 = 0 Bur n o = 18 [-]<br />
COND1 c;i = 35 COND1 c;o = 36<br />
COND1 r ;i = 51 COND1 r ;o = 52<br />
COND2 c;i = 33 COND2 c;o = 34<br />
COND2 r ;i = 71 COND2 r ;o = 72<br />
COP ABS = 1,412 [-] COP ABS;f uel = 0,4556 [-]<br />
COP ABS;heat = 0,7657 [-] C p M I X L1;o = 1,912 [ k J/kg-K ]<br />
C p pump1;i = 1,978 [ k J/kg-K ] C p pump1;o = 1,978 [ k J/kg-K ]<br />
C p pump2;i = 2,037 [ k J/kg-K ] C p pump2;o = 2,037 [ k J/kg-K ]<br />
C p SHE X 1;hi = 1,912 [ k J/kg-K ] C p SHE X 2;hi = 1,987 [ k J/kg-K ]<br />
∆ h;C HK ;min = 13,63 [ k J/kg ] ∆ Ḣ f uel = 100<br />
∆ Ḣ i = 100 [kW ] ∆ h;M I X L1;chk = 13,63 [ k J/kg ]<br />
∆ h;V B1;chk = 11,61 [ k J/kg ] ∆ h;V B2;chk = 24,12 [ k J/kg ]<br />
∆ p;ABSO;1 = 0 [kPa]<br />
∆ p;ABSO;2 = 0 [kPa]<br />
∆ p;ABSO;c = 0 [kPa]<br />
∆ p;BURN ;i ;1 = −8 [kPa]<br />
∆ p;BURN ;i ;2 = −1 [kPa]<br />
∆ p;COND1;c = 0 [kPa]<br />
∆ p;COND1;r = 0 [kPa]<br />
∆ p;COND2;c = 0 [kPa]<br />
∆ p;COND2;r = 0 [kPa]<br />
∆ p;DES1;h = 0 [kPa]<br />
∆ p;DES1;r = 0 [kPa]<br />
∆ p;DES1;s = 0 [kPa]<br />
∆ p;DES2;h = 2,776 × 10 −17 [kPa] ∆ p;DES2;r = 0 [kPa]<br />
∆ p;DES2;s = 0 [kPa]<br />
∆ p;EV AP;c = 0 [kPa]<br />
∆ p;EV AP;r = 0 [kPa]<br />
∆ p;GGHE X 1;c = −1 [kPa]<br />
∆ p;GGHE X 1;h = −1 [kPa] ∆ p;GGHE X 2;c = −1 [kPa]<br />
∆ p;GGHE X 2;h = −1 [kPa] ∆ p;GGHE X 3;c = −4 [kPa]<br />
∆ p;GGHE X 3;h = −4 [kPa] ∆ p;GGHE X 4;c = −2 [kPa]<br />
∆ p;GGHE X 4;h = −2 [kPa] ∆ p;M I XG1;i ;1 = −0,1 [kPa]<br />
∆ p;M I XG1;i ;2 = 9,1 [kPa] ∆ p;M I XG2;i ;1 = −0,1 [kPa]<br />
∆ p;M I XG2;i ;2 = −1,1 [kPa] ∆ p;M I X L1;1 = 0 [kPa]<br />
∆ p;M I X L1;2 = 0 [kPa]<br />
∆ p;M I X R1;1 = 0 [kPa]<br />
242
C.2. Results - St<strong>and</strong>ard parameter configuration<br />
∆ p;M I X R1;2 = 0 [kPa]<br />
∆ p;PR = −5 [kPa]<br />
∆ p;PU MP1 = 4,05 [kPa]<br />
∆ p;PU MP2 = 74,44 [kPa]<br />
∆ p;SHE X 1;ss = 0 [kPa]<br />
∆ p;SHE X 1;ws = 0 [kPa]<br />
∆ p;SHE X 2;ss = 0 [kPa]<br />
∆ p;SHE X 2;ws = 0 [kPa]<br />
∆ p;SOFC ;ano = −1 [kPa]<br />
∆ p;SOFC ;cat = −3 [kPa]<br />
∆ p;SPG1;o;1 = −0,1 [kPa] ∆ p;SPG1;o;2 = −0,1 [kPa]<br />
∆ p;SPG2;o;1 = −0,1 [kPa] ∆ p;SPG2;o;2 = −0,1 [kPa]<br />
∆ p;TOW ER1;air = 0,15 [kPa] ∆ p;TOW ER1;air ;dr y = 0,15 [kPa]<br />
∆ p;TOW ER1;air ;wet = 0,15 [kPa] ∆ p;TOW ER1;w = 0 [kPa]<br />
∆ p;W GHE X 1;g = −2 [kPa] ∆ p;W GHE X 1;w = 0 [kPa]<br />
∆ p;W GHE X 2;g = −2 [kPa] ∆ p;W GHE X 2;w = 0 [kPa]<br />
∆ p;W GHE X 3;g = −2 [kPa] ∆ p;W GHE X 3;w = 0 [kPa]<br />
∆ T ;CFG;C HK = 34,17 [C ] ∆ T ;chill;EV AP = 5 [C ]<br />
∆ T ;COND;DES = 54,88 [C ] ∆ T ;c;ABSO = 3,397 [C ]<br />
∆ T ;c;COND1 = 1,498 [C ] ∆ T ;c;COND2 = 5 [C ]<br />
∆ T ;c;TOW ER1 = 5 [C ] ∆ T ;EV AP;ABSO = 20,71 [C ]<br />
∆ T ;h;DES1 = 5 [C ] ∆ T ;h;DES2 = 5 [C ]<br />
∆ T ;min;ABSO;s;o = 5 [C ] ∆ T ;min;COND1;mp = 7,067 [C ]<br />
∆ T ;min;COND1;r ;i = 8,502 [C ] ∆ T ;min;COND1;r ;o = 10 [C ]<br />
∆ T ;min;COND1;r ;o;D = 10 [C ] ∆ T ;min;COND1;r ;o;S = 12,5 [C ]<br />
∆ T ;min;COND2;mp = 10,24 [C ] ∆ T ;min;COND2;r ;i = 66,8 [C ]<br />
∆ T ;min;COND2;r ;o = 15 [C ] ∆ T ;min;DES1;r ;o = 0 [C ]<br />
∆ T ;min;DES2;r ;o = 0 [C ] ∆ T ;min;EV AP;r ;i = 5 [C ]<br />
∆ T ;min;EV AP;r ;o = 10 [C ] ∆ T ;min;GGHE X 1;c;i = 443,1 [C ]<br />
∆ T ;min;GGHE X 1;c;o = 96,12 [C ] ∆ T ;min;GGHE X 2;c;i = 151,6 [C ]<br />
∆ T ;min;GGHE X 2;c;o = 90 [C ] ∆ T ;min;GGHE X 3;c;i = 186,6 [C ]<br />
∆ T ;min;GGHE X 3;c;o = 148,7 [C ] ∆ T ;min;GGHE X 4;c;i = 27,89 [C ]<br />
∆ T ;min;GGHE X 4;c;i ; = 27,89 [C ] ∆ T ;min;GGHE X 4;c;o = 25 [C ]<br />
∆ T ;min;GGHE X 4;c;o; = 25 [C ] ∆ T ;min;SHE X 1;ws;i = 5 [C ]<br />
∆ T ;min;SHE X 1;ws;o = 8,98 [C ] ∆ T ;min;SHE X 2;ws;i = 5 [C ]<br />
∆ T ;min;SHE X 2;ws;o = 13,91 [C ] ∆ T ;min;TOW ER1;a;i ;dr y = 3 [C ]<br />
∆ T ;min;TOW ER1;a;o = 3 [C ] ∆ T ;min;TOW ER1;a;o;dr y = 8 [C ]<br />
∆ T ;min;TOW ER1;a;o;wet = 3 [C ] ∆ T ;min;W GHE X 1;w;i = 15 [C ]<br />
∆ T ;min;W GHE X 1;w;i ; = 15 [C ] ∆ T ;min;W GHE X 1;w;o = 171,6 [C ]<br />
∆ T ;min;W GHE X 1;w;o; = 171,6 [C ] ∆ T ;min;W GHE X 2;w;i = 81,8 [C ]<br />
∆ T ;min;W GHE X 2;w;i ; = 15 [C ] ∆ T ;min;W GHE X 2;w;o = 81,8 [C ]<br />
∆ T ;min;W GHE X 3;w;i = 15 [C ] ∆ T ;min;W GHE X 3;w;o = 17,02 [C ]<br />
∆ T ;SOFC = 90 [C ] ∆ T ;SOFC ;av = 30 [C ]<br />
DES1 h;i = 31 DES1 h;o = 32<br />
DES1 i = 58 DES1 r ;o = 50<br />
DES1 s;o = 59 DES2 h;i = 41<br />
243
C. EES<br />
244<br />
DES2 h;o = 42 DES2 i = 78<br />
DES2 r ;o = 70 DES2 s;o = 79<br />
EB SOFC ;sys = −16,18 [kW ] EB tot = −0,00000 [kW ]<br />
ɛ ABSO = 0,4045 [-] ɛ COND1;2P = 0,2933 [-]<br />
ɛ COND1;SH = −1,891 × 10 −13 [-] ɛ COND2;2P = 0,3176 [-]<br />
ɛ COND2;SH = 0,8473 [-] ɛ DES1 = 1 [-]<br />
ɛ DES2 = 1 [-] ɛ EV AP = 0,5 [-]<br />
ɛ GGHE X 1 = 0,765 [-] ɛ GGHE X 1;c = 0,765 [-]<br />
ɛ GGHE X 1;h = 0,1278 [-] ɛ GGHE X 2 = 0,765 [-]<br />
ɛ GGHE X 2;c = 0,765 [-] ɛ GGHE X 2;h = 0,6386 [-]<br />
ɛ GGHE X 3 = 0,7757 [-] ɛ GGHE X 3;c = 0,7757 [-]<br />
ɛ GGHE X 3;h = 0,7481 [-] ɛ GGHE X 4 = 0,7736 [-]<br />
ɛ GGHE X 4;c = 0,7736 [-] ɛ GGHE X 4;c; = 0,7736 [-]<br />
ɛ GGHE X 4;h = 0,7494 [-] ɛ GGHE X 4;h; = 0,7494 [-]<br />
ɛ M AX = 0,9431 [-] ɛ SHE X 1 = 0,873 [-]<br />
ɛ SHE X 1;ss = 0,873 [-] ɛ SHE X 1;ws = 0,7718 [-]<br />
ɛ SHE X 2 = 0,9431 [-] ɛ SHE X 2;s = 0,9431 [-]<br />
ɛ SHE X 2;ws = 0,8417 [-] ɛ W GHE X 1 = 0,9151 [-]<br />
ɛ W GHE X 1;g = 0,9151 [-] ɛ W GHE X 1;g ; = 0,9151 [-]<br />
ɛ W GHE X 1;w = 0,02831 [-] ɛ W GHE X 1;w; = 0,02831 [-]<br />
ɛ W GHE X 2 = 2,513 × 10 −10 [-] ɛ W GHE X 2;g = 2,513 × 10 −10 [-]<br />
ɛ W GHE X 2;w = 0 [-] ɛ W GHE X 3 = 0,7117 [-]<br />
ɛ W GHE X 3;g = 0,7117 [-] ɛ W GHE X 3;w = 0,6728 [-]<br />
η blower ;TOW ER1 = 0,4 [-] η HW = 0,07184 [-]<br />
η inver t = 0,95 [-] η i s;BLOW 1 = 0,6 [-]<br />
η PU MP1 = 0,5 [-] η PU MP2 = 0,5 [-]<br />
η SOFC ;el ;SOLO = 0,5357 [-] η sys;el ;net = 0,516 [-]<br />
η sys;tot = 1,044 [-] η wb;TOW ER1 = 0,75 [-]<br />
EV AP c;i = 48 EV AP c;o = 49<br />
EV AP r ;i = 53 EV AP r ;o = 54<br />
F R = 0,14 [-] FuelBP Ratio = 0<br />
Fuel i = 1 FW = 0,6 [-]<br />
GGHE X 1 c;i = 1 GGHE X 1 c;o = 2<br />
GGHE X 1 h;i = 7 GGHE X 1 h;o = 8<br />
GGHE X 2 c;i = 4 GGHE X 2 c;o = 5<br />
GGHE X 2 h;i = 6 GGHE X 2 h;o = 7<br />
GGHE X 3 c;i = 13 GGHE X 3 c;o = 14<br />
GGHE X 3 h;i = 19 GGHE X 3 h;o = 20<br />
GGHE X 4 c;i = 12 GGHE X 4 c;o = 13<br />
GGHE X 4 h;i = 22 GGHE X 4 h;o = 23<br />
I = 68,4 [A] input1 = 70
C.2. Results - St<strong>and</strong>ard parameter configuration<br />
input2 = 77 input3 = 79<br />
i d = 3000 [ A/m 2] K W GS = 1,139 [-]<br />
λ Bur n;i = 1,5 [-] λ SOFC ;i = 4,409 [-]<br />
λ SOFC ;o = 12,36 [-] LG r atio;TOW ER1 = 0,6473 [-]<br />
M I XG1 i ;1 = 2 M I XG1 i ;2 = 9<br />
M I XG1 o = 3 M I XG2 i ;1 = 18<br />
M I XG2 i ;2 = 17 M I XG2 o = 19<br />
M I X L1 i ;1 = 59 M I X L1 i ;2 = 82<br />
M I X L1 o = 60 M I X R1 i ;1 = 50<br />
M I X R1 i ;2 = 73 M I X R1 o = 51<br />
ṁ bur n;add = 0 ṁ i = 0,001999 [ kg /s ]<br />
ṁ tr ans;TOW ER1 = 0,04812 [ kg /s ] n cell = 60 [-]<br />
n st ack = 20,15 [-] OC r atio = 2,133 [-]<br />
out put1 = 71 out put2 = 78<br />
out put3 = 80 PR i = 3<br />
PR o = 4 PU MP1 i = 55<br />
PU MP1 o = 56 PU MP2 i = 75<br />
PU MP2 o = 76<br />
p re f = 100 [kPa]<br />
˙Q air ; = 85,93 [kW ] ˙Q Chill;EV AP = 45,56 [kW ]<br />
˙Q c;ABSO = 54,02 [kW ] ˙Q c;COND1 = 23,82 [kW ]<br />
˙Q c;COND2 = 25,93 [kW ] ˙Q c;TOW ER1 = 77,84 [kW ]<br />
˙Q Heat;DES1 = 25,93 [kW ] ˙Q Heat;DES2 = 32,26 [kW ]<br />
˙Q HW = 7,184 [kW ] ˙Q hw; = 7,184 [kW ]<br />
˙Q loss;ABSO = 0 [kW ] ˙Q loss;BLOW 1 = 0 [kW ]<br />
˙Q loss;Bur n = 0 [kW ] ˙Q loss;COND1 = 0 [kW ]<br />
˙Q loss;COND2 = 0 [kW ] ˙Q loss;DES1 = 0 [kW ]<br />
˙Q loss;DES2 = 0 [kW ] ˙Q loss;EV AP = 0 [kW ]<br />
˙Q loss;PR = 0 [kW ] ˙Q loss;PU MP1 = 0 [kW ]<br />
˙Q loss;PU MP2 = 0 [kW ] ˙Q loss;SHE X 1 = 0 [kW ]<br />
˙Q loss;SHE X 2 = 0 [kW ] ˙Q loss;SOFC = 0 [kW ]<br />
˙Q loss;V A1 = 0 [kW ] ˙Q loss;V A2 = 0 [kW ]<br />
˙Q loss;V B1 = 0 [kW ] ˙Q loss;V B2 = 0 [kW ]<br />
˙Q loss;W GHE X 1 = 0 [kW ] ˙Q loss;W GHE X 2 = 0 [kW ]<br />
˙Q loss;W GHE X 3 = 0 [kW ] ˙Q loss;W W HE X 1 = 0 [kW ]<br />
˙Q tr ans;SHE X 1 = 13,58 [kW ] ˙Q tr ans;SHE X 2 = 19,24 [kW ]<br />
˙Q tr ans;W GHE X 1 = 32,26 [kW ] ˙Q tr ans;W GHE X 2 = 0 [kW ]<br />
˙Q tr ans;W GHE X 3 = 7,184 [kW ] ˙Q w;add; = 6,135<br />
SHE X 1 ss;i = 60 SHE X 1 ss;o = 61<br />
SHE X 1 ws;i = 56 SHE X 1 ws;o = 57<br />
SHE X 2 ss;i = 80 SHE X 2 ss;o = 81<br />
SHE X 2 ws;i = 76 SHE X 2 ws;o = 77<br />
245
C. EES<br />
SOFC ano;i = 5 SOFC ano;o = 6<br />
SOFC cat;i = 14 SOFC cat;o = 15<br />
SPG1 i = 8 SPG1 o;1 = 9<br />
SPG1 o;2 = 10 SPG2 i = 15<br />
SPG2 o;1 = 16 SPG2 o;2 = 17<br />
SPL1 i = 57 SPL1 o;1 = 58<br />
SPL1 o;2 = 75<br />
SysC f g $ = ‘Double’<br />
TOW ER$ = ‘WET’ TOW ER1 w;add = 38 [ kg /s ]<br />
TOW ER1 w;i = 37 TOW ER1 w;o = 39<br />
TOW ER air ;i = 45 TOW ER air ;mp = 46<br />
TOW ER air ;o = 47 T 47;aim = 23,77<br />
T 60SHE X = 78,2 [C ] T amb = 30 [C ]<br />
T amb;dr y = 18 [C ] T amb;evap = 24<br />
T amb;wet = 30 [C ] T DES1;h;i = 85 [C ]<br />
T M I X L1;sat60 = 78,2 T re f = 25 [C ]<br />
T SHE X 2;sat81 = 150 [C ] T SOFC ;av = 750 [C ]<br />
T V B1;sat62 = 42,17 [C ] T V B2;sat82 = 78,2 [C ]<br />
T wb;TOW ER1 = 20,04 [C ] T W GHE X 1;g ;o = 165 [C ]<br />
U air = 0,1588 [-] U f = 0,7 [-]<br />
V A1 i = 52 V A1 o = 53<br />
V A2 i = 72 V A2 o = 73<br />
V B1 i = 61 V B1 o = 62<br />
V B2 i = 81<br />
V cell = 0,7514 [V ]<br />
V B2 o = 82<br />
˙V air ;TOW ER1 = 5,205 [ m 3 /s ]<br />
V Ner nst = 0,9177 [V ] V st ack = 45,09 [V ]<br />
W GHE X 1 g ;i = 20 W GHE X 1 g ;o = 21<br />
W GHE X 1 w;i = 42 W GHE X 1 w;o = 43<br />
W GHE X 2 g ;i = 21 W GHE X 2 g ;o = 22<br />
W GHE X 2 w;i = 34 W GHE X 2 w;o = 31<br />
W GHE X 3 g ;i = 23 W GHE X 3 g ;o = 24<br />
W GHE X 3 w;i = 27 W GHE X 3 w;o = 28<br />
W Q R AT IO;TOW ER1 = 0,02507 [-] Ẇ AC = 59,05 [kW ]<br />
Ẇ BLOW 1 = 5,48 [kW ] Ẇ F AN = 1,952 [kW ]<br />
Ẇ PU MP1 = 0,001122 [kW ] Ẇ PU MP2 = 0,01175 [kW ]<br />
Ẇ SOFC = 62,16 [kW ] Ẇ SOFC ;SOLO = 53,57 [kW ]<br />
Ẇ st ack = 3,084 [kW ] Ẇ sys;net = 51,6 [kW ]<br />
246
C.2. Results - St<strong>and</strong>ard parameter configuration<br />
Point T i p i ṁ i qu i h i w i ∆˙<br />
[ ] [ ]<br />
H i<br />
[C ] [kPa] kg /s [-] k J/kg [-] [kW ]<br />
0 25 0 0<br />
1 25 130,3 0,001999 100<br />
2 431,4 129,3 0,001999 102,4<br />
3 459,6 129,2 0,01645 141,3<br />
4 376 124,2 0,01645 141,3<br />
5 690 123,2 0,01645 151,8<br />
6 780 122,2 0,02331 75,69<br />
7 527,6 121,2 0,02331 65,22<br />
8 468,1 120,2 0,02331 62,86<br />
9 468,1 120,1 0,01445 38,97<br />
10 468,1 120,1 0,008857 23,89<br />
11 25 100 0,1855 0<br />
12 54,14 122,2 0,1855 5,48<br />
13 140 120,2 0,1855 21,66<br />
14 690 116,2 0,1855 132<br />
15 780 113,2 0,1786 146<br />
16 780 113,1 0,008234 6,728<br />
17 780 113,1 0,1704 139,2<br />
18 1271 112,1 0,01709 30,61<br />
19 838,7 112 0,1875 169,8<br />
20 326,6 108 0,1875 59,5<br />
21 165 106 0,1875 27,24<br />
22 165 104 0,1875 27,24<br />
23 82,02 102 0,1875 11,06<br />
24 45 100 0,1875 3,876<br />
25<br />
26<br />
27 30 1000 0,0491 126,6<br />
28 65 1000 0,0491 272,9<br />
29<br />
30<br />
31 83,2 2000 1,238 349,9<br />
32 78,2 2000 1,238<br />
33 78,2 2000 1,238<br />
34 83,2 2000 1,238 349,9<br />
247
C. EES<br />
Point T i p i ṁ i qu i h i w i ∆˙<br />
[ ]<br />
[ ]<br />
H i<br />
[C ] [kPa] kg /s [-] k J/kg [-] [kW ]<br />
35 21,81 2000 3,806<br />
36 23,31 2000 3,806<br />
37 26,71 2000 3,806 113,7<br />
38 30 2000 0,04812 127,5<br />
39 21,81 2000 3,806 93,29<br />
40<br />
41 155 2000 1,496<br />
42 150 2000 1,496 633,3<br />
43 155 2000 1,496 654,8<br />
45 30 100 5,88 57,67<br />
46 30,32 100,2 5,88<br />
47 23,71 100 5,928 71,7<br />
48 11 2000 2,179<br />
49 6 2000 2,179<br />
50 78,2 4,708 0,008368 100 2646 0<br />
51 31,81 4,708 0,01923 0,5107 1372 0<br />
52 31,81 4,708 0,01923 0 133,3 0<br />
53 1 0,6571 0,01923 0,05167 133,3 0<br />
54 1 0,6571 0,01923 1 2502 0<br />
55 31,71 0,6571 0,226 0 81,37 0,5595<br />
56 31,71 4,708 0,226 -100 81,37 0,5595<br />
57 62,09 4,708 0,226 -100 141,5 0,5595<br />
58 62,09 4,708 0,09835 -100 141,5 0,5595<br />
59 78,2 4,708 0,08998 0 196,7 0,6115<br />
60 71,07 4,708 0,2068 -100 183,1 0,6115<br />
61 36,71 4,708 0,2068 -100 117,4 0,6115<br />
62 35,91 0,6571 0,2068 -100 117,4 0,6115<br />
70 150 79,15 0,01086 100 2778 0<br />
71 150 79,15 0,01086 100 2778 0<br />
72 93,2 79,15 0,01086 0 390,4 0<br />
73 31,81 4,708 0,01086 0,106 390,4 0<br />
75 62,09 4,708 0,1277 -100 141,5 0,5595<br />
76 62,13 79,15 0,1277 -100 141,6 0,5595<br />
77 136,1 79,15 0,1277 -100 292,2 0,5595<br />
78 136,1 79,15 0,1277 -100 292,2 0,5595<br />
79 150 79,15 0,1168 0 337,3 0,6115<br />
80 150 79,15 0,1168 0 337,3 0,6115<br />
81 67,13 79,15 0,1168 -100 172,6 0,6115<br />
82 65,58 4,708 0,1168 -100 172,6 0,6115<br />
248
C.2. Results - St<strong>and</strong>ard parameter configuration<br />
Point y i ;1 y i ;2 y i ;3 y i ;4 y i ;5 y i ;6 y i ;7<br />
[-] [-] [-] [-] [-] [-] [-]<br />
0<br />
1 1,000 -0,000 -0,000 -0,000 0,000 0,000 -0,000<br />
2 1,000 -0,000 -0,000 -0,000 0,000 0,000 -0,000<br />
3 0,170 0,048 0,229 0,107 0,447 0,000 -0,000<br />
4 0,139 0,027 0,259 0,211 0,363 0,000 -0,000<br />
5 0,139 0,027 0,259 0,211 0,363 0,000 -0,000<br />
6 -0,000 0,058 0,275 0,129 0,538 -0,000 0,000<br />
7 -0,000 0,058 0,275 0,129 0,538 -0,000 0,000<br />
8 -0,000 0,058 0,275 0,129 0,538 -0,000 0,000<br />
9 0,000 0,058 0,275 0,129 0,538 0,000 -0,000<br />
10 0,000 0,058 0,275 0,129 0,538 -0,000 -0,000<br />
11 -0,000 0,000 -0,000 0,000 0,000 0,790 0,210<br />
12 -0,000 0,000 -0,000 0,000 0,000 0,790 0,210<br />
13 -0,000 0,000 -0,000 0,000 0,000 0,790 0,210<br />
14 -0,000 0,000 -0,000 0,000 0,000 0,790 0,210<br />
15 -0,000 0,000 0,000 0,000 -0,000 0,817 0,183<br />
16 -0,000 -0,000 0,000 -0,000 0,000 0,817 0,183<br />
17 0,000 0,000 -0,000 0,000 -0,000 0,817 0,183<br />
18 0,000 -0,000 0,199 0,000 0,398 0,374 0,028<br />
19 0,000 0,000 0,019 0,000 0,038 0,775 0,168<br />
20 0,000 0,000 0,019 0,000 0,038 0,775 0,168<br />
21 0,000 0,000 0,019 0,000 0,038 0,775 0,168<br />
22 0,000 0,000 0,019 0,000 0,038 0,775 0,168<br />
23 0,000 0,000 0,019 0,000 0,038 0,775 0,168<br />
24 0,000 0,000 0,019 0,000 0,038 0,775 0,168<br />
249
C. EES<br />
C.3 Results - Optimized parameter<br />
configuration<br />
ABSO c;i = 36 ABSO c;o = 37<br />
ABSO r ;i = 54 ABSO s;i = 62<br />
ABSO s;o = 55<br />
AddPreHeat$ = ‘On’<br />
Air Fuel Ratio;m = 54,44 [-] Air Fuel Ratio;n = 4,902 [-]<br />
Air i = 11 [-] α SPG1 = 0,62 [-]<br />
α SPG2 = 0,1412 [-]<br />
ASR = 5,54 × 10 −5 [ Ω·m 2] α SPL1 = 0,6199 [-]<br />
A cell = 0,0228 [ m 2]<br />
BLOW 1 i = 11 BLOW 1 o = 12<br />
Bur n i ;1 = 10 [-] Bur n i ;2 = 16 [-]<br />
Bur n i ;3 = 0 Bur n o = 18 [-]<br />
COND1 c;i = 35 COND1 c;o = 36<br />
COND1 r ;i = 51 COND1 r ;o = 52<br />
COND2 c;i = 33 COND2 c;o = 34<br />
COND2 r ;i = 71 COND2 r ;o = 72<br />
COP ABS = 1,484 [-] COP ABS;f uel = 0,5872 [-]<br />
COP ABS;heat = 1,089 [-] C p M I X L1;o = 2,011 [ k J/kg-K ]<br />
C p pump1;i = 2,055 [ k J/kg-K ] C p pump1;o = 2,055 [ k J/kg-K ]<br />
C p pump2;i = 2,115 [ k J/kg-K ] C p pump2;o = 2,115 [ k J/kg-K ]<br />
C p SHE X 1;hi = 2,011 [ k J/kg-K ] C p SHE X 2;hi = 2,013 [ k J/kg-K ]<br />
Ċ SHE X 1;r atio = 0,9005 Ċ SHE X 1;ss = 0,5932<br />
Ċ SHE X 1;ws = 0,6587 Ċ SHE X 2;r atio = 0,8445<br />
Ċ SHE X 2;ss = 0,2176 Ċ SHE X 2;ws = 0,2577<br />
∆ h;C HK ;min = 8,779 [ k J/kg ] ∆ Ḣ f uel = 100<br />
∆ Ḣ i = 100 [kW ] ∆ h;M I X L1;chk = 8,779 [ k J/kg ]<br />
∆ h;V B1;chk = 7,608 [ k J/kg ] ∆ h;V B2;chk = 25,83 [ k J/kg ]<br />
∆ p;ABSO;1 = 0 [kPa]<br />
∆ p;ABSO;2 = 0 [kPa]<br />
∆ p;ABSO;c = 0 [kPa]<br />
∆ p;BURN ;i ;1 = −8 [kPa]<br />
∆ p;BURN ;i ;2 = −1 [kPa]<br />
∆ p;COND1;c = 0 [kPa]<br />
∆ p;COND1;r = 0 [kPa]<br />
∆ p;COND2;c = 0 [kPa]<br />
∆ p;COND2;r = 0 [kPa]<br />
∆ p;DES1;h = 0 [kPa]<br />
∆ p;DES1;r = 0 [kPa]<br />
∆ p;DES1;s = 0 [kPa]<br />
∆ p;DES2;h = 2,776 × 10 −17 [kPa] ∆ p;DES2;r = 0 [kPa]<br />
∆ p;DES2;s = 0 [kPa]<br />
∆ p;EV AP;c = 0 [kPa]<br />
∆ p;EV AP;r = 0 [kPa]<br />
∆ p;GGHE X 1;c = −1 [kPa]<br />
∆ p;GGHE X 1;h = −1 [kPa] ∆ p;GGHE X 2;c = −1 [kPa]<br />
∆ p;GGHE X 2;h = −1 [kPa] ∆ p;GGHE X 3;c = −4 [kPa]<br />
250
C.3. Results - Optimized parameter configuration<br />
∆ p;GGHE X 3;h = −4 [kPa] ∆ p;GGHE X 4;c = −2 [kPa]<br />
∆ p;GGHE X 4;h = −2 [kPa] ∆ p;M I XG1;i ;1 = −0,1 [kPa]<br />
∆ p;M I XG1;i ;2 = 9,1 [kPa] ∆ p;M I XG2;i ;1 = −0,1 [kPa]<br />
∆ p;M I XG2;i ;2 = −1,1 [kPa] ∆ p;M I X L1;1 = 0 [kPa]<br />
∆ p;M I X L1;2 = 0 [kPa]<br />
∆ p;M I X R1;1 = 0 [kPa]<br />
∆ p;M I X R1;2 = 0 [kPa]<br />
∆ p;PR = −5 [kPa]<br />
∆ p;PU MP1 = 3,933 [kPa] ∆ p;PU MP2 = 46,69 [kPa]<br />
∆ p;SHE X 1;ss = 0 [kPa]<br />
∆ p;SHE X 1;ws = 0 [kPa]<br />
∆ p;SHE X 2;ss = 0 [kPa]<br />
∆ p;SHE X 2;ws = 0 [kPa]<br />
∆ p;SOFC ;ano = −1 [kPa]<br />
∆ p;SOFC ;cat = −3 [kPa]<br />
∆ p;SPG1;o;1 = −0,1 [kPa] ∆ p;SPG1;o;2 = −0,1 [kPa]<br />
∆ p;SPG2;o;1 = −0,1 [kPa] ∆ p;SPG2;o;2 = −0,1 [kPa]<br />
∆ p;TOW ER1;air = 0,15 [kPa] ∆ p;TOW ER1;air ;dr y = 0,15 [kPa]<br />
∆ p;TOW ER1;air ;wet = 0,15 [kPa] ∆ p;TOW ER1;w = 0 [kPa]<br />
∆ p;W GHE X 1;g = −2 [kPa] ∆ p;W GHE X 1;w = 0 [kPa]<br />
∆ p;W GHE X 2;g = −2 [kPa] ∆ p;W GHE X 2;w = 0 [kPa]<br />
∆ p;W GHE X 3;g = −2 [kPa] ∆ p;W GHE X 3;w = 0 [kPa]<br />
∆ T ;CFG;C HK = 22,97 [C ] ∆ T ;chill;EV AP = 5 [C ]<br />
∆ T ;COND;DES = 43,68 [C ] ∆ T ;c;ABSO = 3,386 [C ]<br />
∆ T ;c;COND1 = 1,509 [C ] ∆ T ;c;COND2 = 5 [C ]<br />
∆ T ;c;TOW ER1 = 5 [C ] ∆ T ;EV AP;ABSO = 20,71 [C ]<br />
∆ T ;h;DES1 = 5 [C ] ∆ T ;h;DES2 = 5 [C ]<br />
∆ T ;min;ABSO;s;o = 1,81 [C ] ∆ T ;min;COND1;mp = 7,012 [C ]<br />
∆ T ;min;COND1;r ;i = 8,491 [C ] ∆ T ;min;COND1;r ;o = 10 [C ]<br />
∆ T ;min;COND1;r ;o;D = 10 [C ] ∆ T ;min;COND1;r ;o;S = 12,5 [C ]<br />
∆ T ;min;COND2;mp = 10,21 [C ] ∆ T ;min;COND2;r ;i = 61 [C ]<br />
∆ T ;min;COND2;r ;o = 15 [C ] ∆ T ;min;DES1;r ;o = 0 [C ]<br />
∆ T ;min;DES2;r ;o = 0 [C ] ∆ T ;min;EV AP;r ;i = 2,69 [C ]<br />
∆ T ;min;EV AP;r ;o = 7,69 [C ] ∆ T ;min;GGHE X 1;c;i = 457,2 [C ]<br />
∆ T ;min;GGHE X 1;c;o = 105,8 [C ] ∆ T ;min;GGHE X 2;c;i = 142,1 [C ]<br />
∆ T ;min;GGHE X 2;c;o = 90 [C ] ∆ T ;min;GGHE X 3;c;i = 334,8 [C ]<br />
∆ T ;min;GGHE X 3;c;o = 271 [C ] ∆ T ;min;GGHE X 4;c;i = 14,54 [C ]<br />
∆ T ;min;GGHE X 4;c;i ; = 14,54 [C ] ∆ T ;min;GGHE X 4;c;o = 10,1 [C ]<br />
∆ T ;min;GGHE X 4;c;o; = 10,1 [C ] ∆ T ;min;SHE X 1;ws;i = 5 [C ]<br />
∆ T ;min;SHE X 1;ws;o = 8,099 [C ] ∆ T ;min;SHE X 2;ws;i = 5 [C ]<br />
∆ T ;min;SHE X 2;ws;o = 15,99 [C ] ∆ T ;min;TOW ER1;a;i ;dr y = 3 [C ]<br />
∆ T ;min;TOW ER1;a;o = 3 [C ] ∆ T ;min;TOW ER1;a;o;dr y = 8 [C ]<br />
∆ T ;min;TOW ER1;a;o;wet = 3 [C ] ∆ T ;min;W GHE X 1;w;i = 15 [C ]<br />
∆ T ;min;W GHE X 1;w;i ; = 15 [C ] ∆ T ;min;W GHE X 1;w;o = 334,7 [C ]<br />
∆ T ;min;W GHE X 1;w;o; = 334,7 [C ] ∆ T ;min;W GHE X 2;w;i = 76 [C ]<br />
∆ T ;min;W GHE X 2;w;i ; = 15 [C ] ∆ T ;min;W GHE X 2;w;o = 76 [C ]<br />
251
C. EES<br />
∆ T ;min;W GHE X 3;w;i = 15 [C ] ∆ T ;min;W GHE X 3;w;o = 3,673 [C ]<br />
∆ T ;SOFC = 90 [C ] ∆ T ;SOFC ;av = 30 [C ]<br />
DES1 h;i = 31 DES1 h;o = 32<br />
DES1 i = 58 DES1 r ;o = 50<br />
DES1 s;o = 59 DES2 h;i = 41<br />
DES2 h;o = 42 DES2 i = 78<br />
DES2 r ;o = 70 DES2 s;o = 79<br />
EB SOFC ;sys = −9,261 [kW ] EB tot = −0,00000 [kW ]<br />
ɛ ABSO = 0,6516 [-] ɛ COND1;2P = 0,2988 [-]<br />
ɛ COND1;SH = −1,906 × 10 −13 [-] ɛ COND2;2P = 0,3195 [-]<br />
ɛ COND2;SH = 0,8332 [-] ɛ DES1 = 1 [-]<br />
ɛ DES2 = 1 [-] ɛ EV AP = 0,6502 [-]<br />
ɛ GGHE X 1 = 0,7499 [-] ɛ GGHE X 1;c = 0,7499 [-]<br />
ɛ GGHE X 1;h = 0,1299 [-] ɛ GGHE X 2 = 0,7499 [-]<br />
ɛ GGHE X 2;c = 0,7499 [-] ɛ GGHE X 2;h = 0,6352 [-]<br />
ɛ GGHE X 3 = 0,6539 [-] ɛ GGHE X 3;c = 0,6539 [-]<br />
ɛ GGHE X 3;h = 0,6145 [-] ɛ GGHE X 4 = 0,892 [-]<br />
ɛ GGHE X 4;c = 0,892 [-] ɛ GGHE X 4;c; = 0,892 [-]<br />
ɛ GGHE X 4;h = 0,8457 [-] ɛ GGHE X 4;h; = 0,8457 [-]<br />
ɛ M AX = 0,9558 [-] ɛ SHE X 1 = 0,8644 [-]<br />
ɛ SHE X 1;ss = 0,8644 [-] ɛ SHE X 1;ws = 0,7803 [-]<br />
ɛ SHE X 2 = 0,9339 [-] ɛ SHE X 2;s = 0,9339 [-]<br />
ɛ SHE X 2;ws = 0,7887 [-] ɛ W GHE X 1 = 0,9558 [-]<br />
ɛ W GHE X 1;g = 0,9558 [-] ɛ W GHE X 1;g ; = 0,9558 [-]<br />
ɛ W GHE X 1;w = 0,01472 [-] ɛ W GHE X 1;w; = 0,01472 [-]<br />
ɛ W GHE X 2 = 4,542 × 10 −10 [-] ɛ W GHE X 2;g = 4,542 × 10 −10 [-]<br />
ɛ W GHE X 2;w = 1,849 × 10 −15 [-] ɛ W GHE X 3 = 0,905 [-]<br />
ɛ W GHE X 3;g = 0,6121 [-] ɛ W GHE X 3;w = 0,905 [-]<br />
η blower ;TOW ER1 = 0,4 [-] η HW = 0,02752 [-]<br />
η inver t = 0,95 [-] η i s;BLOW 1 = 0,6 [-]<br />
η PU MP1 = 0,5 [-] η PU MP2 = 0,5 [-]<br />
η SOFC ;el ;SOLO = 0,5243 [-] η sys;el ;net = 0,4996 [-]<br />
η sys;tot = 1,114 [-] η wb;TOW ER1 = 0,75 [-]<br />
EV AP c;i = 48 EV AP c;o = 49<br />
EV AP r ;i = 53 EV AP r ;o = 54<br />
F R = 0,14 [-] FuelBP Ratio = 0<br />
Fuel i = 1 FW = 0,6 [-]<br />
GGHE X 1 c;i = 1 GGHE X 1 c;o = 2<br />
GGHE X 1 h;i = 7 GGHE X 1 h;o = 8<br />
GGHE X 2 c;i = 4 GGHE X 2 c;o = 5<br />
GGHE X 2 h;i = 6 GGHE X 2 h;o = 7<br />
252
C.3. Results - Optimized parameter configuration<br />
GGHE X 3 c;i = 13 GGHE X 3 c;o = 14<br />
GGHE X 3 h;i = 19 GGHE X 3 h;o = 20<br />
GGHE X 4 c;i = 12 GGHE X 4 c;o = 13<br />
GGHE X 4 h;i = 22 GGHE X 4 h;o = 23<br />
I = 61,56 [A] input1 = 70<br />
input2 = 77 input3 = 79<br />
i d = 2700 [ A/m 2] K W GS = 1,139 [-]<br />
λ Bur n;i = 1,5 [-] λ SOFC ;i = 2,321 [-]<br />
λ SOFC ;o = 4,037 [-] LG r atio;TOW ER1 = 0,6473 [-]<br />
M I XG1 i ;1 = 2 M I XG1 i ;2 = 9<br />
M I XG1 o = 3 M I XG2 i ;1 = 18<br />
M I XG2 i ;2 = 17 M I XG2 o = 19<br />
M I X L1 i ;1 = 59 M I X L1 i ;2 = 82<br />
M I X L1 o = 60 M I X R1 i ;1 = 50<br />
M I X R1 i ;2 = 73 M I X R1 o = 51<br />
ṁ bur n;add = 0 ṁ i = 0,001999 [ kg /s ]<br />
ṁ tr ans;TOW ER1 = 0,06077 [ kg /s ] n cell = 60 [-]<br />
n st ack = 20,15 [-] OC r atio = 1,919 [-]<br />
out put1 = 71 out put2 = 78<br />
out put3 = 80 PR i = 3<br />
PR o = 4 PU MP1 i = 55<br />
PU MP1 o = 56 PU MP2 i = 75<br />
PU MP2 o = 76<br />
p re f = 100 [kPa]<br />
˙Q air ; = 108,5 [kW ] ˙Q Chill;EV AP = 58,72 [kW ]<br />
˙Q c;ABSO = 67,99 [kW ] ˙Q c;COND1 = 30,31 [kW ]<br />
˙Q c;COND2 = 33,01 [kW ] ˙Q c;TOW ER1 = 98,3 [kW ]<br />
˙Q Heat;DES1 = 33,01 [kW ] ˙Q Heat;DES2 = 39,57 [kW ]<br />
˙Q HW = 2,752 [kW ] ˙Q hw; = 2,752 [kW ]<br />
˙Q loss;ABSO = 0 [kW ] ˙Q loss;BLOW 1 = 0 [kW ]<br />
˙Q loss;Bur n = 0 [kW ] ˙Q loss;COND1 = 0 [kW ]<br />
˙Q loss;COND2 = 0 [kW ] ˙Q loss;DES1 = 0 [kW ]<br />
˙Q loss;DES2 = 0 [kW ] ˙Q loss;EV AP = 0 [kW ]<br />
˙Q loss;PR = 0 [kW ] ˙Q loss;PU MP1 = 0 [kW ]<br />
˙Q loss;PU MP2 = 0 [kW ] ˙Q loss;SHE X 1 = 0 [kW ]<br />
˙Q loss;SHE X 2 = 0 [kW ] ˙Q loss;SOFC = 0 [kW ]<br />
˙Q loss;V A1 = 0 [kW ] ˙Q loss;V A2 = 0 [kW ]<br />
˙Q loss;V B1 = 0 [kW ] ˙Q loss;V B2 = 0 [kW ]<br />
˙Q loss;W GHE X 1 = 0 [kW ] ˙Q loss;W GHE X 2 = 0 [kW ]<br />
˙Q loss;W GHE X 3 = 0 [kW ] ˙Q loss;W W HE X 1 = 0 [kW ]<br />
˙Q tr ans;SHE X 1 = 18,95 [kW ] ˙Q tr ans;SHE X 2 = 15,38 [kW ]<br />
˙Q tr ans;W GHE X 1 = 39,57 [kW ] ˙Q tr ans;W GHE X 2 = 0 [kW ]<br />
253
C. EES<br />
˙Q tr ans;W GHE X 3 = 2,752 [kW ] ˙Q w;add; = 7,748<br />
SHE X 1 ss;i = 60 SHE X 1 ss;o = 61<br />
SHE X 1 ws;i = 56 SHE X 1 ws;o = 57<br />
SHE X 2 ss;i = 80 SHE X 2 ss;o = 81<br />
SHE X 2 ws;i = 76 SHE X 2 ws;o = 77<br />
SOFC ano;i = 5 SOFC ano;o = 6<br />
SOFC cat;i = 14 SOFC cat;o = 15<br />
SPG1 i = 8 SPG1 o;1 = 9<br />
SPG1 o;2 = 10 SPG2 i = 15<br />
SPG2 o;1 = 16 SPG2 o;2 = 17<br />
SPL1 i = 57 SPL1 o;1 = 58<br />
SPL1 o;2 = 75<br />
SysC f g $ = ‘Double’<br />
TOW ER$ = ‘WET’ TOW ER1 w;add = 38 [ kg /s ]<br />
TOW ER1 w;i = 37 TOW ER1 w;o = 39<br />
TOW ER air ;i = 45 TOW ER air ;mp = 46<br />
TOW ER air ;o = 47 T 47;aim = 23,77<br />
T 60SHE X = 69,75 [C ] T amb = 30 [C ]<br />
T amb;dr y = 18 [C ] T amb;evap = 24<br />
T amb;wet = 30 [C ] T DES1;h;i = 85 [C ]<br />
T M I X L1;sat60 = 69,75 T re f = 25 [C ]<br />
T SHE X 2;sat81 = 133 [C ] T SOFC ;av = 750 [C ]<br />
T V B1;sat62 = 36,91 [C ] T V B2;sat82 = 74,67 [C ]<br />
T wb;TOW ER1 = 20,04 [C ] T W GHE X 1;g ;o = 148 [C ]<br />
U air = 0,2434 [-] U f = 0,565 [-]<br />
V A1 i = 52 V A1 o = 53<br />
V A2 i = 72 V A2 o = 73<br />
V B1 i = 61 V B1 o = 62<br />
V B2 i = 81<br />
V cell = 0,7871 [V ]<br />
V B2 o = 82<br />
˙V air ;TOW ER1 = 6,573 [ m 3 /s ]<br />
V Ner nst = 0,9368 [V ] V st ack = 47,23 [V ]<br />
W GHE X 1 g ;i = 20 W GHE X 1 g ;o = 21<br />
W GHE X 1 w;i = 42 W GHE X 1 w;o = 43<br />
W GHE X 2 g ;i = 21 W GHE X 2 g ;o = 22<br />
W GHE X 2 w;i = 34 W GHE X 2 w;o = 31<br />
W GHE X 3 g ;i = 23 W GHE X 3 g ;o = 24<br />
W GHE X 3 w;i = 27 W GHE X 3 w;o = 28<br />
W Q R AT IO;TOW ER1 = 0,02507 [-] Ẇ AC = 55,64 [kW ]<br />
Ẇ BLOW 1 = 3,215 [kW ] Ẇ F AN = 2,465 [kW ]<br />
Ẇ PU MP1 = 0,001598 [kW ] Ẇ PU MP2 = 0,007267 [kW ]<br />
Ẇ SOFC = 58,57 [kW ] Ẇ SOFC ;SOLO = 52,43 [kW ]<br />
Ẇ st ack = 2,907 [kW ] Ẇ sys;net = 49,96 [kW ]<br />
254
C.3. Results - Optimized parameter configuration<br />
Point T i p i ṁ i qu i h i w i ∆˙<br />
[ ] [ ]<br />
H i<br />
[C ] [kPa] kg /s [-] k J/kg [-] [kW ]<br />
0 25 0 0<br />
1 25 130,3 0,001999 100<br />
2 439,2 129,3 0,001999 102,4<br />
3 472 129,2 0,01533 159,3<br />
4 402,9 124,2 0,01533 159,3<br />
5 690 123,2 0,01533 168,7<br />
6 780 122,2 0,0215 103,6<br />
7 545 121,2 0,0215 94,21<br />
8 482,2 120,2 0,0215 91,8<br />
9 482,2 120,1 0,01333 56,92<br />
10 482,2 120,1 0,008169 34,88<br />
11 25 100 0,1088 0<br />
12 54,14 122,2 0,1088 3,215<br />
13 137,9 120,2 0,1088 12,48<br />
14 690 116,2 0,1088 77,45<br />
15 780 113,2 0,1027 83,99<br />
16 780 113,1 0,01449 11,86<br />
17 780 113,1 0,08817 72,13<br />
18 1504 112,1 0,02266 46,74<br />
19 961 112 0,1108 118,9<br />
20 472,7 108 0,1108 53,9<br />
21 148 106 0,1108 14,33<br />
22 148 104 0,1108 14,33<br />
23 68,67 102 0,1108 5,073<br />
24 45 100 0,1108 2,321<br />
25<br />
26<br />
27 30 1000 0,01881 126,6<br />
28 65 1000 0,01881 272,9<br />
29<br />
30<br />
31 72 2000 1,579 303<br />
32 67 2000 1,579<br />
33 67 2000 1,579<br />
34 72 2000 1,579 303<br />
255
C. EES<br />
Point T i p i ṁ i qu i h i w i ∆˙<br />
[ ]<br />
[ ]<br />
H i<br />
[C ] [kPa] kg /s [-] k J/kg [-] [kW ]<br />
35 21,81 2000 4,807<br />
36 23,32 2000 4,807<br />
37 26,71 2000 4,807 113,7<br />
38 30 2000 0,06077 127,5<br />
39 21,81 2000 4,807 93,29<br />
40<br />
41 138 2000 1,852<br />
42 133 2000 1,852 560,4<br />
43 138 2000 1,852 581,7<br />
45 30 100 7,426 57,67<br />
46 30,32 100,2 7,426<br />
47 23,71 100 7,486 71,7<br />
48 11 2000 2,808<br />
49 6 2000 2,808<br />
50 67 4,708 0,01101 100 2625 0<br />
51 31,81 4,708 0,02474 0,5051 1358 0<br />
52 31,81 4,708 0,02474 0 133,3 0<br />
53 3,31 0,7749 0,02474 0,04788 133,3 0<br />
54 3,31 0,7749 0,02474 1 2507 0<br />
55 28,52 0,7749 0,3205 0 64,18 0,5282<br />
56 28,52 4,708 0,3205 -100 64,19 0,5282<br />
57 57,29 4,708 0,3205 -100 123,3 0,5282<br />
58 57,29 4,708 0,1987 -100 123,3 0,5282<br />
59 67 4,708 0,1876 0 152,5 0,5592<br />
60 65,39 4,708 0,2957 -100 153,8 0,5724<br />
61 33,52 4,708 0,2957 -100 89,74 0,5724<br />
62 33,03 0,7749 0,2957 -100 89,74 0,5724<br />
70 133 51,4 0,01374 100 2746 0<br />
71 133 51,4 0,01374 100 2746 0<br />
72 82 51,4 0,01374 0 343,3 0<br />
73 31,81 4,708 0,01374 0,08661 343,3 0<br />
75 57,29 4,708 0,1218 -100 123,3 0,5282<br />
76 57,32 51,4 0,1218 -100 123,4 0,5282<br />
77 117 51,4 0,1218 -100 249,6 0,5282<br />
78 117 51,4 0,1218 -100 249,6 0,5282<br />
79 133 51,4 0,1081 0 298,4 0,5954<br />
80 133 51,4 0,1081 0 298,4 0,5954<br />
81 62,32 51,4 0,1081 -100 156,1 0,5954<br />
82 61,44 4,708 0,1081 -100 156,1 0,5954<br />
256
C.3. Results - Optimized parameter configuration<br />
Point y i ;1 y i ;2 y i ;3 y i ;4 y i ;5 y i ;6 y i ;7<br />
[-] [-] [-] [-] [-] [-] [-]<br />
0<br />
1 1,000 0,000 0,000 0,000 -0,000 0,000 -0,000<br />
2 1,000 0,000 0,000 0,000 -0,000 0,000 -0,000<br />
3 0,170 0,079 0,198 0,172 0,381 0,000 -0,000<br />
4 0,139 0,039 0,248 0,291 0,283 0,000 0,000<br />
5 0,139 0,039 0,248 0,291 0,283 0,000 0,000<br />
6 0,000 0,095 0,239 0,207 0,459 0,000 -0,000<br />
7 0,000 0,095 0,239 0,207 0,459 0,000 -0,000<br />
8 0,000 0,095 0,239 0,207 0,459 0,000 -0,000<br />
9 0,000 0,095 0,239 0,207 0,459 0,000 0,000<br />
10 0,000 0,095 0,239 0,207 0,459 0,000 -0,000<br />
11 -0,000 0,000 0,000 -0,000 -0,000 0,790 0,210<br />
12 -0,000 0,000 0,000 -0,000 -0,000 0,790 0,210<br />
13 -0,000 0,000 0,000 -0,000 -0,000 0,790 0,210<br />
14 -0,000 0,000 0,000 -0,000 -0,000 0,790 0,210<br />
15 0,000 0,000 -0,000 0,000 -0,000 0,833 0,167<br />
16 -0,000 -0,000 0,000 0,000 0,000 0,833 0,167<br />
17 0,000 -0,000 -0,000 0,000 0,000 0,833 0,167<br />
18 0,000 0,000 0,151 0,000 0,303 0,511 0,034<br />
19 0,000 0,000 0,032 0,000 0,064 0,765 0,139<br />
20 0,000 0,000 0,032 0,000 0,064 0,765 0,139<br />
21 0,000 0,000 0,032 0,000 0,064 0,765 0,139<br />
22 0,000 0,000 0,032 0,000 0,064 0,765 0,139<br />
23 0,000 0,000 0,032 0,000 0,064 0,765 0,139<br />
24 0,000 0,000 0,032 0,000 0,064 0,765 0,139<br />
257
C. EES<br />
C.4 Results - Uncertainty propagation (STD)<br />
C.4.1 ∆Tmin<br />
Variable+Uncertainty Partial Derivative % <strong>of</strong> Uncertainty<br />
COP ABS;f uel = 0,4556 ± 0,03738[-]<br />
∆T ;min;ABSO;s;o = 5 ± 2,5[C ] ∂COP ABS;f uel /∂∆T ;min;ABSO;s;o = −0,002944 3,88 %<br />
∆T ;min;COND1;r ;o;D = 10 ± 5[C ] ∂COP ABS;f uel /∂∆T ;min;COND1;r ;o;D = −0,0008637 1,33 %<br />
∆T ;min;COND1;r ;o;S = 12,5 ± 6,25[C ] ∂COP ABS;f uel /∂∆T ;min;COND1;r ;o;S = 0,00001849 0,00 %<br />
∆T ;min;COND2;r ;o = 15 ± 7,5[C ] ∂COP ABS;f uel /∂∆T ;min;COND2;r ;o = −0,0004227 0,72 %<br />
∆T ;min;DES1;r ;o = 0 ± 0[C ] ∂COP ABS;f uel /∂∆T ;min;DES1;r ;o = −0,0002961 0,00 %<br />
∆T ;min;DES2;r ;o = 0 ± 0[C ] ∂COP ABS;f uel /∂∆T ;min;DES2;r ;o = 0,00000817 0,00 %<br />
∆T ;min;EV AP;r ;i = 5 ± 2,5[C ] ∂COP ABS;f uel /∂∆T ;min;EV AP;r ;i = −0,004363 8,51 %<br />
∆T ;min;GGHE X 4;c;o; = 25 ± 12,5[C ] ∂COP ABS;f uel /∂∆T ;min;GGHE X 4;c;o; = −0,002668 79,62 %<br />
∆T ;min;SHE X 1;ws;i = 5 ± 2,5[C ] ∂COP ABS;f uel /∂∆T ;min;SHE X 1;ws;i = −0,003402 5,18 %<br />
∆T ;min;SHE X 2;ws;i = 5 ± 2,5[C ] ∂COP ABS;f uel /∂∆T ;min;SHE X 2;ws;i = −0,001267 0,72 %<br />
∆T ;min;TOW ER1;a;o;dr y = 8 ± 4[C ] ∂COP ABS;f uel /∂∆T ;min;TOW ER1;a;o;dr y = 0,000003731 0,00 %<br />
∆T ;min;TOW ER1;a;o;wet = 3 ± 1,5[C ] ∂COP ABS;f uel /∂∆T ;min;TOW ER1;a;o;wet = 0,00001602 0,00 %<br />
∆T ;min;W GHE X 1;w;i = 15 ± 7,5[C ] ∂COP ABS;f uel /∂∆T ;min;W GHE X 1;w;i = −0,00009774 0,04 %<br />
∆T ;min;W GHE X 2;w;i ; = 15 ± 7,5[C ] ∂COP ABS;f uel /∂∆T ;min;W GHE X 2;w;i ; = 0,000001012 0,00 %<br />
∆T ;min;W GHE X 3;w;i = 15 ± 7,5[C ] ∂COP ABS;f uel /∂∆T ;min;W GHE X 3;w;i = 7,875E − 07 0,00 %<br />
ηHW = 0,07184 ± 0,02776[-]<br />
∆T ;min;ABSO;s;o = 5 ± 2,5[C ] ∂ηHW /∂∆T ;min;ABSO;s;o = −8,809E − 16 0,00 %<br />
∆T ;min;COND1;r ;o;D = 10 ± 5[C ] ∂ηHW /∂∆T ;min;COND1;r ;o;D = −3,795E − 15 0,00 %<br />
∆T ;min;COND1;r ;o;S = 12,5 ± 6,25[C ] ∂ηHW /∂∆T ;min;COND1;r ;o;S = −8,674E − 16 0,00 %<br />
∆T ;min;COND2;r ;o = 15 ± 7,5[C ] ∂ηHW /∂∆T ;min;COND2;r ;o = −2,259E − 17 0,00 %<br />
258
C.4. Results - Uncertainty propagation (STD)<br />
∆T ;min;DES1;r ;o = 0 ± 0[C ] ∂ηHW /∂∆T ;min;DES1;r ;o = 7,115E − 15 0,00 %<br />
∆T ;min;DES2;r ;o = 0 ± 0[C ] ∂ηHW /∂∆T ;min;DES2;r ;o = 0,00007009 0,00 %<br />
∆T ;min;EV AP;r ;i = 5 ± 2,5[C ] ∂ηHW /∂∆T ;min;EV AP;r ;i = −1,172E − 12 0,00 %<br />
∆T ;min;GGHE X 4;c;o; = 25 ± 12,5[C ] ∂ηHW /∂∆T ;min;GGHE X 4;c;o; = 0,001891 72,53 %<br />
∆T ;min;SHE X 1;ws;i = 5 ± 2,5[C ] ∂ηHW /∂∆T ;min;SHE X 1;ws;i = −8,095E − 11 0,00 %<br />
∆T ;min;SHE X 2;ws;i = 5 ± 2,5[C ] ∂ηHW /∂∆T ;min;SHE X 2;ws;i = 9,758E − 15 0,00 %<br />
∆T ;min;TOW ER1;a;o;dr y = 8 ± 4[C ] ∂ηHW /∂∆T ;min;TOW ER1;a;o;dr y = 3,939E − 15 0,00 %<br />
∆T ;min;TOW ER1;a;o;wet = 3 ± 1,5[C ] ∂ηHW /∂∆T ;min;TOW ER1;a;o;wet = 5,647E − 15 0,00 %<br />
∆T ;min;W GHE X 1;w;i = 15 ± 7,5[C ] ∂ηHW /∂∆T ;min;W GHE X 1;w;i = 0,00007009 0,04 %<br />
∆T ;min;W GHE X 2;w;i ; = 15 ± 7,5[C ] ∂ηHW /∂∆T ;min;W GHE X 2;w;i ; = −5,474E − 12 0,00 %<br />
∆T ;min;W GHE X 3;w;i = 15 ± 7,5[C ] ∂ηHW /∂∆T ;min;W GHE X 3;w;i = −0,001939 27,44 %<br />
ηsys;el ;net = 0,516 ± 0,008916[-]<br />
∆T ;min;ABSO;s;o = 5 ± 2,5[C ] ∂ηsys;el;net /∂∆T ;min;ABSO;s;o = 0,00006305 0,03 %<br />
∆T ;min;COND1;r ;o;D = 10 ± 5[C ] ∂ηsys;el;net /∂∆T ;min;COND1;r ;o;D = 0,00001514 0,01 %<br />
∆T ;min;COND1;r ;o;S = 12,5 ± 6,25[C ] ∂ηsys;el;net /∂∆T ;min;COND1;r ;o;S = −3,248E − 07 0,00 %<br />
∆T ;min;COND2;r ;o = 15 ± 7,5[C ] ∂ηsys;el;net /∂∆T ;min;COND2;r ;o = 0,000003054 0,00 %<br />
∆T ;min;DES1;r ;o = 0 ± 0[C ] ∂ηsys;el ;net /∂∆T ;min;DES1;r ;o = 7,689E − 07 0,00 %<br />
∆T ;min;DES2;r ;o = 0 ± 0[C ] ∂ηsys;el ;net /∂∆T ;min;DES2;r ;o = 0,000002356 0,00 %<br />
∆T ;min;EV AP;r ;i = 5 ± 2,5[C ] ∂ηsys;el ;net /∂∆T ;min;EV AP;r ;i = 0,00009601 0,07 %<br />
∆T ;min;GGHE X 4;c;o; = 25 ± 12,5[C ] ∂ηsys;el ;net /∂∆T ;min;GGHE X 4;c;o; = 0,0001151 2,61 %<br />
∆T ;min;SHE X 1;ws;i = 5 ± 2,5[C ] ∂ηsys;el ;net /∂∆T ;min;SHE X 1;ws;i = 0,0000857 0,06 %<br />
∆T ;min;SHE X 2;ws;i = 5 ± 2,5[C ] ∂ηsys;el ;net /∂∆T ;min;SHE X 2;ws;i = 0,0000326 0,01 %<br />
∆T ;min;TOW ER1;a;o;dr y = 8 ± 4[C ] ∂ηsys;el ;net /∂∆T ;min;TOW ER1;a;o;dr y = −6,960E − 08 0,00 %<br />
∆T ;min;TOW ER1;a;o;wet = 3 ± 1,5[C ] ∂ηsys;el;net /∂∆T ;min;TOW ER1;a;o;wet = −0,00586 97,22 %<br />
∆T ;min;W GHE X 1;w;i = 15 ± 7,5[C ] ∂ηsys;el;net /∂∆T ;min;W GHE X 1;w;i = 0,000004248 0,00 %<br />
∆T ;min;W GHE X 2;w;i ; = 15 ± 7,5[C ] ∂ηsys;el;net /∂∆T ;min;W GHE X 2;w;i ; = −1,505E − 08 0,00 %<br />
259
C. EES<br />
∆T ;min;W GHE X 3;w;i = 15 ± 7,5[C ] ∂ηsys;el ;net /∂∆T ;min;W GHE X 3;w;i = −1,594E − 08 0,00 %<br />
260
C.4.2 Miscellaneous parameters<br />
Variable+Uncertainty Partial Derivative % <strong>of</strong> Uncertainty<br />
COP ABS;f uel = 0,4556 ± 0,1035[-]<br />
C.4. Results - Uncertainty propagation (STD)<br />
ASR = 0,00005542 ± 0,00002771 [ Ω·m 2] ∂COP ABS;f uel /∂ASR = 2616 49,08 %<br />
∆p;TOW ER1;air ;dr y = 0,15 ± 0,075[kPa] ∂COP ABS;f uel /∂∆p;TOW ER1;air ;dr y = 0,001043 0,00 %<br />
∆p;TOW ER1;air ;wet = 0,15 ± 0,075[kPa] ∂COP ABS;f uel /∂∆p;TOW ER1;air ;wet = 0,0005637 0,00 %<br />
∆T ;SOFC ;av = 30 ± 15[C ] ∂COP ABS;f uel /∂∆T ;SOFC ;av = −0,0003557 0,27 %<br />
ηblower ;TOW ER1 = 0,4 ± 0,2[-] ∂COP ABS;f uel /∂ηblower ;TOW ER1 = 0,000187 0,00 %<br />
ηi s;BLOW 1 = 0,6 ± 0,3[-] ∂COP ABS;f uel /∂ηi s;BLOW 1 = 0,00009776 0,00 %<br />
ηwb;TOW ER1 = 0,75 ± 0,375[-] ∂COP ABS;f uel /∂ηwb;TOW ER1 = 0,03229 1,37 %<br />
F R = 0,14 ± 0,07[-] ∂COP ABS;f uel /∂F R = −0,0928 0,39 %<br />
FW = 0,6 ± 0,3[-] ∂COP ABS;f uel /∂FW = 0,0064 0,03 %<br />
id = 3000 ± 1500 [ A/m 2] ∂COP ABS;f uel /∂id = 0,00004822 48,86 %<br />
ηHW = 0,07184 ± 0,04285[-]<br />
ASR = 0,00005542 ± 0,00002771 [ Ω·m 2] ∂ηHW /∂ASR = 824,6 28,44 %<br />
∆p;TOW ER1;air ;dr y = 0,15 ± 0,075[kPa] ∂ηHW /∂∆p;TOW ER1;air ;dr y = 1,279E − 08 0,00 %<br />
∆p;TOW ER1;air ;wet = 0,15 ± 0,075[kPa] ∂ηHW /∂∆p;TOW ER1;air ;wet = 2,982E − 13 0,00 %<br />
∆T ;SOFC ;av = 30 ± 15[C ] ∂ηHW /∂∆T ;SOFC ;av = −0,000106 0,14 %<br />
ηblower ;TOW ER1 = 0,4 ± 0,2[-] ∂ηHW /∂ηblower ;TOW ER1 = −6,964E − 10 0,00 %<br />
ηi s;BLOW 1 = 0,6 ± 0,3[-] ∂ηHW /∂ηi s;BLOW 1 = −0,09133 40,89 %<br />
ηwb;TOW ER1 = 0,75 ± 0,375[-] ∂ηHW /∂ηwb;TOW ER1 = 1,374E − 09 0,00 %<br />
F R = 0,14 ± 0,07[-] ∂ηHW /∂F R = 0,08439 1,90 %<br />
FW = 0,6 ± 0,3[-] ∂ηHW /∂FW = −0,006182 0,19 %<br />
id = 3000 ± 1500 [ A/m 2] ∂ηHW /∂id = 0,00001523 28,44 %<br />
ηsys;el ;net = 0,516 ± 0,1288[-]<br />
ASR = 0,00005542 ± 0,00002771 [ Ω·m 2] ∂ηsys;el ;net /∂ASR = −3145 45,77 %<br />
261
C. EES<br />
∆p;TOW ER1;air ;dr y = 0,15 ± 0,075[kPa] ∂ηsys;el ;net /∂∆p;TOW ER1;air ;dr y = 0,000009298 0,00 %<br />
∆p;TOW ER1;air ;wet = 0,15 ± 0,075[kPa] ∂ηsys;el ;net /∂∆p;TOW ER1;air ;wet = −0,1327 0,60 %<br />
∆T ;SOFC ;av = 30 ± 15[C ] ∂ηsys;el;net /∂∆T ;SOFC ;av = 0,0004208 0,24 %<br />
ηblower ;TOW ER1 = 0,4 ± 0,2[-] ∂ηsys;el;net /∂ηblower ;TOW ER1 = 0,05002 0,60 %<br />
ηi s;BLOW 1 = 0,6 ± 0,3[-] ∂ηsys;el;net /∂ηi s;BLOW 1 = 0,09133 4,52 %<br />
ηwb;TOW ER1 = 0,75 ± 0,375[-] ∂ηsys;el;net /∂ηwb;TOW ER1 = −0,05275 2,36 %<br />
F R = 0,14 ± 0,07[-] ∂ηsys;el;net /∂F R = −0,06511 0,13 %<br />
FW = 0,6 ± 0,3[-] ∂ηsys;el;net /∂FW = 0,004777 0,01 %<br />
id = 3000 ± 1500 [ A/m 2] ∂ηsys;el;net /∂id = −0,0000581 45,77 %<br />
262
C.4. Results - Uncertainty propagation (STD)<br />
C.4.3 ∆p for SOFC subsystem<br />
Variable+Uncertainty Partial Derivative % <strong>of</strong> Uncertainty<br />
COP ABS;f uel = 0,4556 ± 0,000321[-]<br />
∆p;BURN ;i ;1 = −8 ± −8[kPa] ∂COP ABS;f uel /∂∆p;BURN ;i ;1 = −0,0000252 39,45 %<br />
∆p;BURN ;i ;2 = −1 ± −1[kPa] ∂COP ABS;f uel /∂∆p;BURN ;i ;2 = −0,0001575 24,06 %<br />
∆p;GGHE X 1;c = −1 ± −1[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 1;c = −0,0001223 14,52 %<br />
∆p;GGHE X 1;h = −1 ± −1[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 1;h = −0,00009441 8,65 %<br />
∆p;GGHE X 2;c = −1 ± −1[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 2;c = −0,0000729 5,16 %<br />
∆p;GGHE X 2;h = −1 ± −1[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 2;h = −0,00005776 3,24 %<br />
∆p;GGHE X 3;c = −4 ± −4[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 3;c = −0,00001097 1,87 %<br />
∆p;GGHE X 3;h = −4 ± −4[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 3;h = −0,000008776 1,20 %<br />
∆p;GGHE X 4;c = −2 ± −2[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 4;c = −0,000014 0,76 %<br />
∆p;GGHE X 4;h = −2 ± −2[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 4;h = −0,00001118 0,48 %<br />
∆p;M I XG1;i ;1 = −0,1 ± −0,1[kPa] ∂COP ABS;f uel /∂∆p;M I XG1;i ;1 = −0,0001554 0,23 %<br />
∆p;M I XG2;i ;1 = −0,1 ± −0,1[kPa] ∂COP ABS;f uel /∂∆p;M I XG2;i ;1 = −0,0001227 0,15 %<br />
∆p;PR = −5 ± −5[kPa] ∂COP ABS;f uel /∂∆p;PR = −0,000002214 0,12 %<br />
∆p;SPG1;o;1 = −0,1 ± −0,1[kPa] ∂COP ABS;f uel /∂∆p;SPG1;o;1 = −0,00007397 0,05 %<br />
∆p;SPG1;o;2 = −0,1 ± −0,1[kPa] ∂COP ABS;f uel /∂∆p;SPG1;o;2 = −0,0000502 0,02 %<br />
∆p;SPG2;o;1 = −0,1 ± −0,1[kPa] ∂COP ABS;f uel /∂∆p;SPG2;o;1 = −0,00003108 0,01 %<br />
∆p;SPG2;o;2 = −0,1 ± −0,1[kPa] ∂COP ABS;f uel /∂∆p;SPG2;o;2 = −0,00004615 0,02 %<br />
∆p;W GHE X 1;g = −2 ± −2[kPa] ∂COP ABS;f uel /∂∆p;W GHE X 1;g = −0,000001465 0,01 %<br />
∆p;W GHE X 2;g = −2 ± −2[kPa] ∂COP ABS;f uel /∂∆p;W GHE X 2;g = −3,646E − 07 0,00 %<br />
∆p;W GHE X 3;g = −2 ± −2[kPa] ∂COP ABS;f uel /∂∆p;W GHE X 3;g = −7,671E − 07 0,00 %<br />
ηHW = 0,07184 ± 0,01676[-]<br />
∆p;BURN ;i ;1 = −8 ± −8[kPa] ∂ηHW /∂∆p;BURN ;i ;1 = −1,782E − 10 0,00 %<br />
∆p;BURN ;i ;2 = −1 ± −1[kPa] ∂ηHW /∂∆p;BURN ;i ;2 = −0,002301 1,89 %<br />
263
C. EES<br />
∆p;GGHE X 1;c = −1 ± −1[kPa] ∂ηHW /∂∆p;GGHE X 1;c = −7,258E − 10 0,00 %<br />
∆p;GGHE X 1;h = −1 ± −1[kPa] ∂ηHW /∂∆p;GGHE X 1;h = −4,811E − 14 0,00 %<br />
∆p;GGHE X 2;c = −1 ± −1[kPa] ∂ηHW /∂∆p;GGHE X 2;c = −4,845E − 14 0,00 %<br />
∆p;GGHE X 2;h = −1 ± −1[kPa] ∂ηHW /∂∆p;GGHE X 2;h = 3,862E − 14 0,00 %<br />
∆p;GGHE X 3;c = −4 ± −4[kPa] ∂ηHW /∂∆p;GGHE X 3;c = −0,002301 30,18 %<br />
∆p;GGHE X 3;h = −4 ± −4[kPa] ∂ηHW /∂∆p;GGHE X 3;h = −0,002301 30,18 %<br />
∆p;GGHE X 4;c = −2 ± −2[kPa] ∂ηHW /∂∆p;GGHE X 4;c = −0,002301 7,54 %<br />
∆p;GGHE X 4;h = −2 ± −2[kPa] ∂ηHW /∂∆p;GGHE X 4;h = −0,002301 7,54 %<br />
∆p;M I XG1;i ;1 = −0,1 ± −0,1[kPa] ∂ηHW /∂∆p;M I XG1;i ;1 = −1,426E − 08 0,00 %<br />
∆p;M I XG2;i ;1 = −0,1 ± −0,1[kPa] ∂ηHW /∂∆p;M I XG2;i ;1 = −0,002301 0,02 %<br />
∆p;PR = −5 ± −5[kPa] ∂ηHW /∂∆p;PR = −1,475E − 11 0,00 %<br />
∆p;SPG1;o;1 = −0,1 ± −0,1[kPa] ∂ηHW /∂∆p;SPG1;o;1 = 3,388E − 14 0,00 %<br />
∆p;SPG1;o;2 = −0,1 ± −0,1[kPa] ∂ηHW /∂∆p;SPG1;o;2 = 8,640E − 13 0,00 %<br />
∆p;SPG2;o;1 = −0,1 ± −0,1[kPa] ∂ηHW /∂∆p;SPG2;o;1 = −0,002301 0,02 %<br />
∆p;SPG2;o;2 = −0,1 ± −0,1[kPa] ∂ηHW /∂∆p;SPG2;o;2 = −7,361E − 10 0,00 %<br />
∆p;W GHE X 1;g = −2 ± −2[kPa] ∂ηHW /∂∆p;W GHE X 1;g = −0,002301 7,54 %<br />
∆p;W GHE X 2;g = −2 ± −2[kPa] ∂ηHW /∂∆p;W GHE X 2;g = −0,002301 7,54 %<br />
∆p;W GHE X 3;g = −2 ± −2[kPa] ∂ηHW /∂∆p;W GHE X 3;g = −0,002301 7,54 %<br />
ηsys;el ;net = 0,516 ± 0,01676[-]<br />
∆p;BURN ;i ;1 = −8 ± −8[kPa] ∂ηsys;el;net /∂∆p;BURN ;i ;1 = −4,987E − 09 0,00 %<br />
∆p;BURN ;i ;2 = −1 ± −1[kPa] ∂ηsys;el;net /∂∆p;BURN ;i ;2 = 0,002301 1,89 %<br />
∆p;GGHE X 1;c = −1 ± −1[kPa] ∂ηsys;el;net /∂∆p;GGHE X 1;c = −6,200E − 08 0,00 %<br />
∆p;GGHE X 1;h = −1 ± −1[kPa] ∂ηsys;el;net /∂∆p;GGHE X 1;h = −7,212E − 08 0,00 %<br />
∆p;GGHE X 2;c = −1 ± −1[kPa] ∂ηsys;el;net /∂∆p;GGHE X 2;c = −2,729E − 08 0,00 %<br />
∆p;GGHE X 2;h = −1 ± −1[kPa] ∂ηsys;el;net /∂∆p;GGHE X 2;h = −4,800E − 09 0,00 %<br />
∆p;GGHE X 3;c = −4 ± −4[kPa] ∂ηsys;el;net /∂∆p;GGHE X 3;c = 0,002301 30,18 %<br />
264
C.4. Results - Uncertainty propagation (STD)<br />
∆p;GGHE X 3;h = −4 ± −4[kPa] ∂ηsys;el;net /∂∆p;GGHE X 3;h = 0,002301 30,18 %<br />
∆p;GGHE X 4;c = −2 ± −2[kPa] ∂ηsys;el;net /∂∆p;GGHE X 4;c = 0,002301 7,54 %<br />
∆p;GGHE X 4;h = −2 ± −2[kPa] ∂ηsys;el;net /∂∆p;GGHE X 4;h = 0,002301 7,54 %<br />
∆p;M I XG1;i ;1 = −0,1 ± −0,1[kPa] ∂ηsys;el;net /∂∆p;M I XG1;i ;1 = −1,652E − 07 0,00 %<br />
∆p;M I XG2;i ;1 = −0,1 ± −0,1[kPa] ∂ηsys;el;net /∂∆p;M I XG2;i ;1 = 0,002301 0,02 %<br />
∆p;PR = −5 ± −5[kPa] ∂ηsys;el;net /∂∆p;PR = −8,231E − 09 0,00 %<br />
∆p;SPG1;o;1 = −0,1 ± −0,1[kPa] ∂ηsys;el;net /∂∆p;SPG1;o;1 = −9,460E − 08 0,00 %<br />
∆p;SPG1;o;2 = −0,1 ± −0,1[kPa] ∂ηsys;el;net /∂∆p;SPG1;o;2 = −4,558E − 07 0,00 %<br />
∆p;SPG2;o;1 = −0,1 ± −0,1[kPa] ∂ηsys;el;net /∂∆p;SPG2;o;1 = 0,002301 0,02 %<br />
∆p;SPG2;o;2 = −0,1 ± −0,1[kPa] ∂ηsys;el;net /∂∆p;SPG2;o;2 = 5,435E − 07 0,00 %<br />
∆p;W GHE X 1;g = −2 ± −2[kPa] ∂ηsys;el;net /∂∆p;W GHE X 1;g = 0,002301 7,54 %<br />
∆p;W GHE X 2;g = −2 ± −2[kPa] ∂ηsys;el;net /∂∆p;W GHE X 2;g = 0,002301 7,54 %<br />
∆p;W GHE X 3;g = −2 ± −2[kPa] ∂ηsys;el;net /∂∆p;W GHE X 3;g = 0,002301 7,54 %<br />
265
C. EES<br />
C.4.4 ∆p for absorption subsystem<br />
Variable+Uncertainty Partial Derivative % <strong>of</strong> Uncertainty<br />
COP ABS;f uel = −9999 ± 0,004593[-]<br />
∆p;ABSO;1 = −0,01 ± 0,03286[kPa] ∂COP ABS;f uel /∂∆p;ABSO;1 = 0,09195 43,27 %<br />
∆p;ABSO;2 = −0,01 ± 0,03286[kPa] ∂COP ABS;f uel /∂∆p;ABSO;2 = −0,00008428 0,00 %<br />
∆p;COND1;r = −0,01 ± 0,2354[kPa] ∂COP ABS;f uel /∂∆p;COND1;r = 0,002045 1,10 %<br />
∆p;COND2;r = −0,01 ± 3,958[kPa] ∂COP ABS;f uel /∂∆p;COND2;r = 0,0001977 2,90 %<br />
∆p;DES1;r = −0,01 ± 0,2354[kPa] ∂COP ABS;f uel /∂∆p;DES1;r = −0,0001494 0,01 %<br />
∆p;DES2;r = −0,01 ± 3,958[kPa] ∂COP ABS;f uel /∂∆p;DES2;r = 0,00001242 0,01 %<br />
∆p;EV AP;r = −0,01 ± 0,03286[kPa] ∂COP ABS;f uel /∂∆p;EV AP;r = 0,09961 50,79 %<br />
∆p;M I X L1;1 = −0,01 ± 0,2354[kPa] ∂COP ABS;f uel /∂∆p;M I X L1;1 = 0,0004834 0,06 %<br />
∆p;M I X L1;2 = −0,01 ± 0,2354[kPa] ∂COP ABS;f uel /∂∆p;M I X L1;2 = −0,00004397 0,00 %<br />
∆p;M I X R1;1 = −0,01 ± 0,2354[kPa] ∂COP ABS;f uel /∂∆p;M I X R1;1 = 0,001951 1,00 %<br />
∆p;M I X R1;2 = −0,01 ± 0,2354[kPa] ∂COP ABS;f uel /∂∆p;M I X R1;2 = 0,00003391 0,00 %<br />
∆p;SHE X 1;ss = −0,01 ± 0,2354[kPa] ∂COP ABS;f uel /∂∆p;SHE X 1;ss = 0,0001362 0,00 %<br />
∆p;SHE X 1;ws = −0,01 ± 0,2354[kPa] ∂COP ABS;f uel /∂∆p;SHE X 1;ws = 0,0002474 0,02 %<br />
∆p;SHE X 2;ss = −0,01 ± 3,958[kPa] ∂COP ABS;f uel /∂∆p;SHE X 2;ss = 0,00005226 0,20 %<br />
∆p;SHE X 2;ws = −0,01 ± 3,958[kPa] ∂COP ABS;f uel /∂∆p;SHE X 2;ws = 0,00009274 0,64 %<br />
ηHW = −9999 ± 4,050 × 10 −11 [-]<br />
∆p;ABSO;1 = −0,01 ± 0,03286[kPa] ∂ηHW /∂∆p;ABSO;1 = 3,388E − 13 0,00 %<br />
∆p;ABSO;2 = −0,01 ± 0,03286[kPa] ∂ηHW /∂∆p;ABSO;2 = −3,524E − 12 0,00 %<br />
∆p;COND1;r = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;COND1;r = 4,506E − 12 0,07 %<br />
∆p;COND2;r = −0,01 ± 3,958[kPa] ∂ηHW /∂∆p;COND2;r = 6,607E − 12 41,69 %<br />
∆p;DES1;r = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;DES1;r = 4,167E − 12 0,06 %<br />
∆p;DES2;r = −0,01 ± 3,958[kPa] ∂ηHW /∂∆p;DES2;r = −5,557E − 12 29,49 %<br />
∆p;EV AP;r = −0,01 ± 0,03286[kPa] ∂ηHW /∂∆p;EV AP;r = −3,795E − 12 0,00 %<br />
266
C.4. Results - Uncertainty propagation (STD)<br />
∆p;M I X L1;1 = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;M I X L1;1 = −4,506E − 12 0,07 %<br />
∆p;M I X L1;2 = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;M I X L1;2 = 6,776E − 14 0,00 %<br />
∆p;M I X R1;1 = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;M I X R1;1 = −4,811E − 12 0,08 %<br />
∆p;M I X R1;2 = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;M I X R1;2 = 9,012E − 12 0,27 %<br />
∆p;SHE X 1;ss = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;SHE X 1;ss = 1,389E − 12 0,01 %<br />
∆p;SHE X 1;ws = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;SHE X 1;ws = −3,388E − 13 0,00 %<br />
∆p;SHE X 2;ss = −0,01 ± 3,958[kPa] ∂ηHW /∂∆p;SHE X 2;ss = −4,845E − 12 22,42 %<br />
∆p;SHE X 2;ws = −0,01 ± 3,958[kPa] ∂ηHW /∂∆p;SHE X 2;ws = 2,473E − 12 5,84 %<br />
ηsys;el ;net = −9999 ± 0,000101[-]<br />
∆p;ABSO;1 = −0,01 ± 0,03286[kPa] ∂ηsys;el ;net /∂∆p;ABSO;1 = −0,001982 41,53 %<br />
∆p;ABSO;2 = −0,01 ± 0,03286[kPa] ∂ηsys;el ;net /∂∆p;ABSO;2 = 0,000002275 0,00 %<br />
∆p;COND1;r = −0,01 ± 0,2354[kPa] ∂ηsys;el ;net /∂∆p;COND1;r = −0,00001229 0,08 %<br />
∆p;COND2;r = −0,01 ± 3,958[kPa] ∂ηsys;el ;net /∂∆p;COND2;r = 0,000006445 6,38 %<br />
∆p;DES1;r = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;DES1;r = −0,000006068 0,02 %<br />
∆p;DES2;r = −0,01 ± 3,958[kPa] ∂ηsys;el;net /∂∆p;DES2;r = 0,000001443 0,32 %<br />
∆p;EV AP;r = −0,01 ± 0,03286[kPa] ∂ηsys;el;net /∂∆p;EV AP;r = −0,00217 49,79 %<br />
∆p;M I X L1;1 = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;M I X L1;1 = −0,0000109 0,06 %<br />
∆p;M I X L1;2 = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;M I X L1;2 = −6,505E − 07 0,00 %<br />
∆p;M I X R1;1 = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;M I X R1;1 = −0,00001644 0,15 %<br />
∆p;M I X R1;2 = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;M I X R1;2 = 0,000002001 0,00 %<br />
∆p;SHE X 1;ss = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;SHE X 1;ss = −0,000004218 0,01 %<br />
∆p;SHE X 1;ws = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;SHE X 1;ws = −0,000003342 0,01 %<br />
∆p;SHE X 2;ss = −0,01 ± 3,958[kPa] ∂ηsys;el ;net /∂∆p;SHE X 2;ss = 0,000002051 0,65 %<br />
∆p;SHE X 2;ws = −0,01 ± 3,958[kPa] ∂ηsys;el ;net /∂∆p;SHE X 2;ws = 0,000002563 1,01 %<br />
267
C. EES<br />
C.4.5 ˙Qloss for absorption subsystem<br />
Variable+Uncertainty Partial Derivative % <strong>of</strong> Uncertainty<br />
COP ABS;f uel = 0,4556 ± 0,03209[-]<br />
˙Qloss;Bur n = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;Bur n = −0,01392 18,82 %<br />
˙Qloss;DES1 = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;DES1 = −0,007894 6,05 %<br />
˙Qloss;DES2 = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;DES2 = −0,014 19,03 %<br />
˙Qloss;PR = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;PR = −0,01403 19,11 %<br />
˙Qloss;SHE X 1 = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;SHE X 1 = −0,008557 7,11 %<br />
˙Qloss;SHE X 2 = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;SHE X 2 = −0,01406 19,21 %<br />
˙Qloss;SOFC = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;SOFC = −0,01049 10,68 %<br />
ηHW = 0,07184 ± 0,003323[-]<br />
˙Qloss;Bur n = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;Bur n = −2,882E − 10 0,00 %<br />
˙Qloss;DES1 = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;DES1 = −1,016E − 14 0,00 %<br />
˙Qloss;DES2 = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;DES2 = 4,574E − 14 0,00 %<br />
˙Qloss;PR = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;PR = −1,321E − 14 0,00 %<br />
˙Qloss;SHE X 1 = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;SHE X 1 = 3,795E − 14 0,00 %<br />
˙Qloss;SHE X 2 = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;SHE X 2 = −2,473E − 14 0,00 %<br />
˙Qloss;SOFC = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;SOFC = −0,003323 100,00 %<br />
ηsys;el;net = 0,516 ± 0,003461[-]<br />
˙Qloss;Bur n = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;Bur n = 0,0006088 3,09 %<br />
˙Qloss;DES1 = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;DES1 = 0,0004529 1,71 %<br />
˙Qloss;DES2 = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;DES2 = 0,0006089 3,09 %<br />
˙Qloss;PR = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;PR = 0,0006089 3,09 %<br />
˙Qloss;SHE X 1 = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;SHE X 1 = 0,0004679 1,83 %<br />
˙Qloss;SHE X 2 = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;SHE X 2 = 0,0006089 3,09 %<br />
˙Qloss;SOFC = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;SOFC = 0,003174 84,08 %<br />
268
C.5. Guide to EES files<br />
C.5 Guide to EES files<br />
Four versions <strong>of</strong> the main file have been appended. All <strong>of</strong> them use the<br />
same sub-files (LIB files) which have also been appended. All 4 versions<br />
are capable <strong>of</strong> running as single stage, double stage, dual reheat, with<br />
wet tower, dry tower etc.<br />
The reason they are all supplied is that they each contain the<br />
parametric tables with the numeric results <strong>of</strong> the investigations <strong>of</strong> the<br />
different sections in the report:<br />
• Single Stage.EES contains all the results for investigating the single<br />
cycle (section 5.1).<br />
• 12Config.EES contains the results for comparing the 12 different<br />
system configurations (section 5.2).<br />
• STD.EES shows the results from the investigations with the<br />
st<strong>and</strong>ard parameter configurations (section 5.2 through 5.4).<br />
• OPTI.EES shows the results from the investigations with the<br />
optimized parameter configurations (from section 5.4 through 6.1).<br />
269
A P P E N D I X<br />
D<br />
OTHER<br />
D.1 Explanation <strong>of</strong> chosen Parameters<br />
In this section the choice <strong>of</strong> some <strong>of</strong> the parameters will be explained.<br />
∆T min<br />
The heat exchangers have been described by the Closest Approach<br />
Temperature Difference (∆T min ) which has been estimated since it is not<br />
possible to calculate the UA values in a zero dimensional model. It was<br />
decided to let the ∆T min be 5 ◦ C for all the water-water heat exchangers,<br />
15 ◦ C for all the water-gas heat exchangers, <strong>and</strong> 25 ◦ C for all the gas-gas<br />
heat exchangers.<br />
Then later in the project investigations could be carried out to see<br />
which <strong>of</strong> the heat exchangers were important <strong>and</strong> which ones were not,<br />
<strong>and</strong> it could then be decided which <strong>of</strong> the heat exchangers that should be<br />
improved in order to optimize the system.<br />
Pressure losses<br />
The pressure losses <strong>of</strong> the components in the SOFC part <strong>of</strong> the system<br />
have been approximated to values used in the models used by Topsoe<br />
Fuel Cell, although the values have been altered a little to prevent<br />
publishing classified data.<br />
271
D. OTHER<br />
The pressure loss <strong>of</strong> GGHEX4 have been set to half the pressure loss <strong>of</strong><br />
GGHEX3. Because those two heat exchangers experience the same mass<br />
flows, but GGHEX4 transfers much less heat, so it is assumed to be much<br />
shorter (reducing pressure loss in tubes / between plates)<br />
Inlet conditions<br />
The water added in the cooling tower is assumed to be at ambient<br />
temperature.<br />
The air <strong>and</strong> <strong>fuel</strong> at the inlet <strong>of</strong> the SOFC were assumed to be 25 ◦ C<br />
(instead <strong>of</strong> being equal to the ambient temperature). This way the<br />
ambient temperature could be changed to examine its influence on the<br />
cooling tower without having the results ”polluted” by changes from the<br />
SOFC.<br />
D.2 Spider diagram parameter interval choice<br />
272<br />
• ASR: In reality ASR depends on a number <strong>of</strong> factors such as<br />
temperature, current density, <strong>and</strong> oxygen partial pressure. In this<br />
model it only depends on temperature. And in different models<br />
from TOFC the value differs somewhat. So it has been estimated<br />
that it is in reality likely to be within +/-20% <strong>of</strong> the value in the<br />
model.<br />
• ∆p tower,wet : The pressure loss <strong>of</strong> the cooling tower has been<br />
estimated by looking at how much fan power small commercially<br />
available cooling towers consume relative to the cooling power <strong>and</strong><br />
then calculate the pressure loss from this. But in reality the pressure<br />
loss depends on how big the system is physically build relative to<br />
the amount <strong>of</strong> cooling to be removed. Also the temperature <strong>of</strong> the<br />
fluids matters. So this way it can vary a lot, <strong>and</strong> it is hence estimated<br />
that it can be somewhere between double as large <strong>and</strong> half as large<br />
as the estimated value.<br />
• T SOFC ,in = 690 ◦ C, T SOFC ,out = 780 ◦ C, <strong>and</strong> T SOFC ,max is probably a<br />
little over 800 ◦ C. So the average temperature must for sure be over<br />
690 <strong>and</strong> below 800 ◦ C. At the st<strong>and</strong>ard parameter configuration it<br />
is 750 ◦ C (∆T SOFC ,av = 30 ◦ C). And with T SOFC ,max > T SOFC ,out , the<br />
average temperature must be closer to T SOFC ,out than to T SOFC ,in .
D.3. Water consumption<br />
Hence it is likely to be between 735 ◦ C <strong>and</strong> 780 ◦ C (15 ◦ C < ∆T SOFC ,av<br />
< 60 ◦ C))<br />
• η W B,Tower is typically around 0,75 according to [14]. Since 0 equals<br />
no evaporation at all <strong>and</strong> 1 equals the best possible theoretical<br />
situation, it must be reasonable to assume that the value would not<br />
be outside the interval 0,6 to 0,9.<br />
• FR <strong>and</strong> FW: These values have been set so the change <strong>of</strong> the<br />
flow (partial pressure) for the different species in the pre reformer<br />
reassembles the TOFC data. Hence the st<strong>and</strong>ard configuration<br />
values must be quite close to reality. FR (0,14) is assumed to be<br />
within [0,1 to 0,2] whereas FW (0,6) is assumed to be within [0,45 to<br />
0,75]<br />
• i d The current density is controlled by the operator, so this can be<br />
set exactly as desired - it is just a matter <strong>of</strong> buying the right amount<br />
<strong>of</strong> <strong>cells</strong> for the desired current draw. As was shown in figure 5.19B<br />
page 132 the current density can not go below 2100Ωm 2 if the <strong>fuel</strong><br />
input remains at the 100kW for the given number <strong>of</strong> <strong>cells</strong> since<br />
the heat generated in the electrochemical reaction is not enough to<br />
make up for the energy used in the endothermic reforming process.<br />
The current density can not go above 3300Ωm 2 either, since the<br />
voltage falls below 0,7V (0=>Nickel Oxidation).<br />
• The efficiency <strong>of</strong> the FAN (for the cooling tower) can vary quite<br />
a lot depending on the size <strong>of</strong> the system (<strong>and</strong> hence FAN), so<br />
depending on the system size, it is assumed that it can range from<br />
0,3 to 0,6.<br />
• The isentropic efficiency <strong>of</strong> the blower in the SOFC system should<br />
be relatively exact for the given size (100kW <strong>of</strong> <strong>fuel</strong>), since the<br />
blower power consumption fits very well with being 10% <strong>of</strong> the<br />
net electricity [25]. But it does depend a lot on the size, so it can<br />
be suspected to range from 0,4 to 0,8 if the system is scaled up or<br />
down.<br />
D.3 Water consumption<br />
273
High humidity - low water price, high electricity price<br />
Unit Water Electricity<br />
Consumption kg/s 0,03<br />
Density kg/m^3 1000<br />
Consumption m^3/year 946<br />
Unit price DKK/m^3 10<br />
Fuel input kW 100<br />
Eta_sys,el,net - 0,5<br />
Production kWh/year 438.000<br />
Unit price DKK/kWh 2<br />
Total price DKK 9.461 876.000<br />
Fraction <strong>of</strong> water expenses <strong>and</strong> electricity value: 1,1%<br />
High humidity - high water price, low electricity price<br />
Unit Water Electricity<br />
Consumption kg/s 0,03<br />
Density kg/m^3 1000<br />
Consumption m^3/year 946<br />
Unit price DKK/m^3 20<br />
Fuel input kW 100<br />
Eta_sys,el,net - 0,5<br />
Production kWh/year 438.000<br />
Unit price DKK/kWh 1<br />
Total price DKK 18.922 438.000<br />
Fraction <strong>of</strong> water expenses <strong>and</strong> electricity value: 4,3%<br />
Low humidity - low water price, high electricity price<br />
Unit Water Electricity<br />
Consumption kg/s 0,06<br />
Density kg/m^3 1000<br />
Consumption m^3/year 1892<br />
Unit price DKK/m^3 10<br />
Fuel input kW 100<br />
Eta_sys,el,net - 0,5<br />
Production kWh/year 438.000<br />
Unit price DKK/kWh 2<br />
Total price DKK 18.922 876.000<br />
Fraction <strong>of</strong> water expenses <strong>and</strong> electricity value: 2,2%<br />
Low humidity - high water price, low electricity price<br />
Unit Water Electricity<br />
Consumption kg/s 0,06<br />
Density kg/m^3 1000<br />
Consumption m^3/year 1892<br />
Unit price DKK/m^3 20<br />
Fuel input kW 100<br />
Eta_sys,el,net - 0,5<br />
Production kWh/year 438.000<br />
Unit price DKK/kWh 1<br />
Total price DKK 37.843 438.000<br />
Fraction <strong>of</strong> water expenses <strong>and</strong> electricity value: 8,6%<br />
274
A P P E N D I X<br />
E<br />
OPTIMIZATION GRAPHS<br />
275
E. OPTIMIZATION GRAPHS<br />
E.1 Simulations <strong>and</strong> Results<br />
E.1.1<br />
All 12 Configurations<br />
eta | COP<br />
1.1<br />
1.0<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0.0<br />
System Configurations<br />
eta_HW<br />
COP_ABS,<strong>fuel</strong><br />
eta_sys,el,net<br />
0.07<br />
0.10<br />
0.07<br />
0.26<br />
0.23<br />
0.13<br />
0.09 0.10<br />
0.10 0.06<br />
0.12 0.09<br />
0.46<br />
0.42<br />
0.23 0.26<br />
0.23<br />
0.31<br />
0.35<br />
0.34<br />
0.38<br />
0.15 0.17<br />
0.21<br />
0.51 0.51 0.53 0.53 0.51 0.49<br />
0.53 0.52 0.50 0.49 0.52 0.52<br />
SSd- SSdA SSw- SSwA DSd- DSdA DSw- DSwA DHd- DHdA DHw- DHwA<br />
Figure E.1: Comparison <strong>of</strong> system configurations<br />
Figure E.1 shows the COP <strong>and</strong> efficiencies <strong>of</strong> the 12 different<br />
configurations described by the 4 letters below each column:<br />
1. SS = Single stage, DS = Double Stage, DH = Double Stage Dual<br />
Heat<br />
2. d = Dry Tower, w = Wet Tower<br />
3. A = Air preheat, - = no Air Preheat<br />
276
E.1. Simulations <strong>and</strong> Results<br />
E.1.2<br />
E.1.2.1<br />
∆T for external circuits<br />
∆T EV AP<br />
The temperature <strong>of</strong> the chilling water into the evaporator (T 48 ) is set to<br />
11 ◦ C (this value is not changed in this simulation). ∆T min,EV AP is 5 ◦ C so<br />
to prevent the refrigerant (water) from freezing, ∆T EV AP can not be larger<br />
than 6 ◦ C.<br />
Figure E.2<br />
When the temperature increase in the chilling water circuit (∆T EV AP )<br />
is decreased from 5 ◦ C to 1 ◦ C, the COP ABS,f uel is increased a little over 3%<br />
(1,5 percent points), see figure E.2. So there is a little to gain, but since<br />
both the evaporator <strong>and</strong> the hex at the other end at the external circuit<br />
has to be larger (<strong>and</strong> hence more expensive) it is probably not one <strong>of</strong> the<br />
best places to optimize the process.<br />
277
E. OPTIMIZATION GRAPHS<br />
E.1.2.2<br />
∆T DES1<br />
The temperature increase in the external water cycle between DES1, COND2<br />
<strong>and</strong> WGHEX2 is most relevant when using the reheat configuration. When<br />
the pure double cycle is used, COND2 <strong>and</strong> DES1 would in reality be integrated<br />
in the same component (hence ∆T DES1 should be zero). It is<br />
however investigated how big an effect it would have on the system if<br />
the heat transmission between DES1, COND2 <strong>and</strong> WGHEX2 was in fact<br />
made by an external water cycle with a ∆T DES1 .<br />
Figure E.3<br />
It is seen from figure E.3 that as long as ∆T DES1 is below 10 ◦ C, there<br />
is only a very little effect on COP, while η sys,el ,net <strong>and</strong> η HW t are constant.<br />
E.1.2.3<br />
∆T DES2<br />
WGHEX1 is assumed to be integrated in DES2, but it could also be made<br />
by an external water circuit. In that case the temperature change in<br />
the external circuit (∆T DES2 ) could be varied, <strong>and</strong> this is done in the<br />
following: It appears from figure E.4 that ∆T DES2 has no influence on<br />
278
E.1. Simulations <strong>and</strong> Results<br />
Figure E.4<br />
the efficiencies or COP. This is because the closest approach temperature<br />
difference takes place in the water inlet side <strong>of</strong> the WGHEX1 (15 ◦ C)<br />
whereas the closest approach temperature difference at the water outlet<br />
side is above 100 ◦ C. So when ∆T DES2 is increased, ∆T min,DES2,w,o is just<br />
decreased by the same amount.<br />
279
E. OPTIMIZATION GRAPHS<br />
E.1.3<br />
Towers<br />
The influence <strong>of</strong> the Closest Approach Temperature Difference on the<br />
two different types <strong>of</strong> towers is now investigated.<br />
E.1.3.1 ∆ T,min,Tower<br />
Figure E.5<br />
The COP ABS,f uel (blue curve in figure E.5) is heavily dependent on<br />
the ∆ T,min when the DRY Tower is used because a large ∆ T,min,Tower<br />
will give a large absorber <strong>and</strong> condenser temperature. The electrical<br />
efficiency <strong>of</strong> the system (black curve) raises a little when ∆ T,min,Tower is<br />
increased, but that is merely due to lower FAN power consumption when<br />
the absorption cooling unit becomes less efficient <strong>and</strong> this way needs less<br />
low quality heat removed.<br />
For the WET Tower the COP ABS,f uel (figure E.6A) is unaffected by<br />
the ∆ T,min . This is because the (somewhat simple) model <strong>of</strong> the wet<br />
tower only uses the air inlet conditions <strong>and</strong> tower (wet bulb) efficiency to<br />
determine the water outlet temperature. So the water outlet temperature<br />
is not affected by the ∆ T,min (hence COP is unaffected).<br />
280
E.1. Simulations <strong>and</strong> Results<br />
Figure E.6: A: Efficiencies, COP, <strong>and</strong> water consumption. B: Air temperatures <strong>and</strong> fan power.<br />
The air outlet temperature, however, is directly dependent on ∆ T,min .<br />
So when the ∆ T,min,Tower is increased the air outlet temperature falls<br />
(orange curve in figure E.6B). This means that more water will be<br />
consumed (lost through evaporation) since each kg <strong>of</strong> the outlet air<br />
carries less energy out <strong>of</strong> the system (T air,out < T air,in , so some <strong>of</strong> the<br />
evaporation energy will be used to cool down the air). Furthermore<br />
since the airflow increases, the FAN power consumption will rise (brown<br />
curve). So the electrical efficiency will decrease significantly.<br />
281
E. OPTIMIZATION GRAPHS<br />
E.1.3.2<br />
∆ T,Tower<br />
∆ T,Tower is the difference between point 37 <strong>and</strong> 39. And since T 39 is given<br />
by the cooling tower <strong>and</strong> ambient conditions, ∆ T,Tower will effectively<br />
control T 37 . In a physical system this is done by regulating the water flow<br />
in the circuit point 35 to 39. In lack <strong>of</strong> exact numbers, it has been assumed<br />
that the outlet temperature <strong>of</strong> the air remains at the same relative position<br />
between the water in- <strong>and</strong> outlet <strong>of</strong> the tower (green curve relative to the<br />
two blue lines in figure E.7B). This seemed more realistic than keeping<br />
∆T min constant at the 3 ◦ C, which would have made the air outlet become<br />
colder than the water outlet for ∆ T,Tower < 3.<br />
Figure E.7: A: Efficiencies, COP, <strong>and</strong> water consumption. B: Air <strong>and</strong> water temperatures.<br />
T air,in = T 45 ,T air,out = T 47 ,T water,in = T 37 <strong>and</strong> T water,out = T 39 .<br />
As can be seen in figure E.7, the COP <strong>of</strong> the absorption unit increases<br />
when ∆ T,Tower is reduced because T 39 is decreased. But the fan power<br />
rises considerably mainly because <strong>of</strong> the increased air flow, which comes<br />
from the increased amount <strong>of</strong> water evaporated. Hence the electrical<br />
efficiency decreases.<br />
282
E.2. Cases<br />
E.2 Cases<br />
E.2.1<br />
Extreme low relative humidity<br />
Figure E.8: The relative humidity is only φ = 0,2. The ambient temperature is varied for the<br />
system with optimized parameter configuration. ṁ is the water consumption <strong>of</strong> the wet cooling<br />
tower.<br />
283
A P P E N D I X<br />
F<br />
LITERATURE<br />
F.1 Sc<strong>and</strong>inavian Energy Group Aps.<br />
285
SEG<br />
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Mulige anvendelser af absorptionskøling<br />
Absorptionskøling evner i grundprincippet at tage varme fra to temperaturniveauer (en lavtemperatur energikilde<br />
og en højtemperatur energikilde) og aflevere hele varmemængden ved en mellemtemperatur. For at processen<br />
skal være mulig skal denne mellemtemperatur ligge tættest på lavtemperatur energikilden<br />
Grafisk fremstillet kan det se ud som følger :<br />
Temperatur akse<br />
Varmetilførsel ved høj temperatur<br />
Varmetilførsel ved lav temperatur<br />
Varmeafgivelse ved mellemtemperatur<br />
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En mere uddybende beskrivelse er angivet i følgende hvor de reelle begrænsninger er beskrevet mere detaljeret.<br />
1. Da kølemidlet er v<strong>and</strong> kan der ikke opereres med temperaturer under 0 °C. I praksis er det uden specielle<br />
foranstaltninger dog ikke realistisk at køre med udgangstemperaturer på det kølede v<strong>and</strong> fra<br />
fordamperen på under 6 °C da der skal være en rimelig margin mellem driftstemperatur og<br />
frysevagtstemperaturen der generer sikkerhedsstop.<br />
2. Af hensyn til begrænsning af indre korrosion laver man normalt ikke driftstemperaturer på generatoren<br />
på over 150 °C.<br />
3. Højere temperaturforskel mellem fordamper og absorber kræver højere LiBr koncentration. Den<br />
maksimale koncentration der kan tolereres svarer til ca. 40 °C i temperaturforskel. For at opnå den<br />
nødvendige LiBr koncentration uden for store hedeflader kræves der en temperaturforskel mellem<br />
kondensatorudgang og generator som typisk er 20 °C hørere end temperaturforskellen mellem fordamper<br />
og absorber (udgangstemperaturer).<br />
4. Varmeafgivelsen kommer desuden ikke fra ét sted, men i stedet fra to steder i processen som ikke<br />
nødvendigvis har samme temperaturniveau. Varmen genereres nemlig både i absorberen der absorbere<br />
dampene fra fordamperen (ca. 56 % af varmeafgivelsen) og kondensatoren der kondenserer dampene fra<br />
generatoren (ca. 44 % af varmeafgivelsen). Kølev<strong>and</strong>et til de to varmeafgivere er normalt koblet i serie så<br />
de fremstår som én kilde, men <strong>and</strong>re koblinger er også muligt. På varmepumper (højtemperatur maskiner<br />
som laver fjernvarme) er absorberen altid koblet før kondensatoren. På kølemaskiner (lavtemperatur<br />
maskiner som laver v<strong>and</strong> til køleformål) er koblingen normalt modsat.<br />
5. Energimæssigt udgør lavtemperatur energikilden 70-75 % af højtemperatur energikilden. Da v<strong>and</strong>s<br />
fordampningsvarme er dominerende i forhold varmekapaciteten (henført til nogle graders<br />
temperaturvariation) er dette forhold næsten uafhængigt af driftstemperaturer og belastning for en given<br />
maskine.<br />
6. Absorptions varmepumpers interne el-forbrug består i det væsentlige i forsyning af to små pumper. For<br />
større maskiner (i MW størrelse og op efter) ligger el-forbruget på ca. 2 promille af køleeffekten. For helt<br />
små maskiner (100 kW) ligger forbruget dog på ca. 1 % af køleydelsen. Under alle omstændigheder et ret<br />
ubetydeligt forbrug som langt overgås af de effekter der kræves til pumper for at cirkulere v<strong>and</strong> fra de<br />
eksternt koblede kredse gennem maskinerne. Dette forbrug kan dog for varmepumper sidestilles med<br />
forbruget ved alternative måder at fremstille varme på.<br />
Der kan nu på næste side opstilles følgende mere fyldestgørende principskitse.<br />
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Temperatur akse<br />
Ind og udgangstemperatur for<br />
højtemperatur energikilde til gene-<br />
rator<br />
generatortemperatur (udgangstemperatur fra generatoren)<br />
For at processen skal være termodynamisk<br />
mulig skal denne temperaturforskel være større end<br />
forskellen mellem absorber og fordamper (ca. 20 °C over<br />
for at holde hedeflade arealet på et rimeligt niveau)<br />
Ind og udgangstemperaturer for<br />
kondensator<br />
Ind og udgangstemperaturer for<br />
Absorber<br />
Ind og udgangstemperatur for<br />
lavtemperatur energikilde til fordamper<br />
Mindst 6 °C over nul<br />
0 °C<br />
Maksimalt 40 °C i temperaturforskel for varmepumper<br />
(for kølemaskiner en anelse lavere)<br />
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Absorptionskøling med v<strong>and</strong> som kølemiddel og Lithiumbromid som<br />
absorbant<br />
Hvordan virker det<br />
Hovedprincippet for teknikken er at Lithiumbromid er stærkt v<strong>and</strong>sugende. Damptrykket over en v<strong>and</strong>ig opløsning<br />
af LiBr er altså meget lavere end for rent v<strong>and</strong> ved samme temperatur. Nedenstående diagram beskriver<br />
fænomenet.<br />
Ligevægtsdiagram for v<strong>and</strong>ig LiBr opløsning<br />
kurverne repræsenterer 0, 46, 50, 54, 58, 62, 66 og 70 vægt % LiBr<br />
Dugpunkts temperatur og tryk for v<strong>and</strong> i trykligevægt med<br />
opløsningen (°C)<br />
120<br />
100<br />
80<br />
60<br />
40<br />
20<br />
LiBr cyklus<br />
V<strong>and</strong> / damp cyklus<br />
I generator<br />
I absorber<br />
I intern veksler<br />
Kondensering<br />
Tryksænkning<br />
Fordampning<br />
0,01<br />
0<br />
0,007<br />
0 20 40 60 80 100 120 140 160<br />
Opløsnings tem peratur (°C)<br />
Rent v<strong>and</strong><br />
Krystallisations<br />
grænse for LiBr . H 2 O<br />
46 %<br />
50 %<br />
54 %<br />
58 %<br />
62 %<br />
66 %<br />
70 %<br />
2,00<br />
1,50<br />
1,00<br />
0,70<br />
0,50<br />
0,30<br />
0,20<br />
0,15<br />
0,10<br />
0,07<br />
0,05<br />
0,03<br />
0,02<br />
0,015<br />
Damptryk<br />
i<br />
bar(a)<br />
Som eksempel har rent v<strong>and</strong> ved 20 °C et damptryk på 0,0234 bar absolut. Det ses af diagrammet at man har ca.<br />
samme damptryk over en 58 % Lithiumbromid ved 57 °C eller en 62 % Lithiumbromid ved 66 °C. Det skal hertil<br />
bemærkes at damptrykket alene udgøres af v<strong>and</strong>et. Saltet (Lithiumbromiden) fordamper overhovedet ikke.<br />
Ved de nævnte temperaturer er de 3 væsker altså i trykmæssig ligevægt. Er det rene v<strong>and</strong> derimod blot en anelse<br />
varmere (f.eks. 21 °C) vil der altså være uligevægt med følgende resultat.<br />
V<strong>and</strong>et vil fordampe ved 21 °C og blive absorberet til lithiumbromiden ved de højere temperaturer. Herved vil<br />
v<strong>and</strong>et optage fordampningsvarme ved de 21 °C og afgive kondenseringsvarmen plus lidt bl<strong>and</strong>ingsvarme ved de<br />
57/66 °C. Samtidig optager lithiumbromiden så meget v<strong>and</strong>damp at koncentrationen falder og de 62 % LiBr bliver<br />
til 58 % LiBr. Det er præcis hvad der sker i underdelen af kølemaskinen.<br />
Efter af Lithiumbromiden har optaget v<strong>and</strong>et falder evnen til at opsuge mere v<strong>and</strong> og det må regeneres. Det sker<br />
ved at pumpe den fortyndede LiBr-opløsning (med 289 f.eks. 58 % LiBr) gennem modstrømsvarmeveksleren og til<br />
overdelen hvor processen går baglæns.<br />
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I generatoren tilføres så meget varme at opløsningen koger og v<strong>and</strong>et drives ud. Den koncentrerede LiBr-opløsning<br />
(med f.eks. 62 % LiBr) løber tilbage til absorberen via modstrømsvarmeveksleren og ringen er sluttet. V<strong>and</strong>dampen<br />
fra generatoren kondenseres i kondensatoren og løber via v<strong>and</strong>udlader tilbage til fordamperen. På dets vej<br />
forkøles det ca. 80 °C kondensat dog med fjernvarmev<strong>and</strong> inden det når underdelens lave tryk.<br />
Øvrige kemikalier<br />
Ud over LiBr og v<strong>and</strong> tilsættes Oktylalkohol og Lithiummolybdat.<br />
Alkoholen (kun ca. én promille af v<strong>and</strong> + LiBr) nedsætter overfladespændingen og giver dermed lidt bedre<br />
varmeovergangstal da det giver en bedre spredning af væskerne over røroverfladerne. Eller som englænderne<br />
mere beskrivende kalder det ”Wetting agent”.<br />
Lithiummolybdat eller inhibitor reducerer korrosionshastigheden.<br />
Tre ting der skal undgås<br />
Faren der traditionelt er betragtet som værst er frostsprængning af fordamperen. Det er dog primært et problem<br />
for kølemaskiner der kører med fordampertemperaturerer på få grader celsius. Maskiner er dog af samme grund<br />
udstyret med 2 flowvagter ud over temperaturføleren. Kommer maskinen i frysefare går den i nødstop og stopper<br />
begge interne pumper.<br />
Hvis temperaturen mellem generator og kondensator bliver for stor kan koncentrationen blive meget høj. Bliver<br />
væsken herefter afkølet kan det størkne (krystallisere). Se nedenstående diagram krystallisationsgrænser for LiBr.<br />
Krystallisationsgrænse for v<strong>and</strong>ig opløsning af LiBr<br />
140<br />
120<br />
100<br />
Opløsning<br />
°C<br />
80<br />
60<br />
40<br />
LiBr . H 2 O<br />
+<br />
opløsning<br />
20<br />
0<br />
LiBr . 2H 2 O + opløsning<br />
LiBr . H 2 O + LiBr .<br />
2H 2 O<br />
-20<br />
-40<br />
LiBr . 3H 2 O + opløsning<br />
LiBr . 2H 2<br />
O +<br />
LiBr . 3H 2 O<br />
-60<br />
45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75<br />
Opløsningskoncentration (w /w % LiBr)<br />
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Problemet opstår dog sjældent og medfører normalt ikke skader på maskinerne.<br />
Slutteligt skal man undgå luftindtrængning i maskinen da luft som selv i små mængder virker meget hæmmende<br />
på processen. Ved de lave damptryk der forekommer vil selv små mængder luft give stor effekt da det hindrer<br />
v<strong>and</strong>dampen i at komme til primært absorberen hvor luften vil ophobes efter som v<strong>and</strong>et absorberes i væsken.<br />
Luft i maskinen vil desuden også få den til at korrodere. Derfor fyldes maskinerne normalt med kvælst<strong>of</strong> i<br />
forbindelse med eventuelle reparationer.<br />
Løbende vedligeholdelse af processen<br />
Der er to ting som kan hæmme eller stoppe den beskrevne proces.<br />
Det ene er som nævnt luft. Der er 2 kilder til luft (ikke kondenserbare gasser). Der ene er luft fra omgivelserne<br />
p.g.a. utætheder og det <strong>and</strong>et er brint som dannes ved reaktion mellem v<strong>and</strong> og jern som danner brint og rust. De<br />
ikke kondenserbare gasser fjernes en gang i mellem med vakuumpumpen som startes og stoppes manuelt.<br />
Det <strong>and</strong>et som kan hæmme den beskrevne proces er LiBr i kølemidler (v<strong>and</strong>et). Ganske vist fordamper LiBr ikke og<br />
der er dråbefang mellem generator og kondensator, men efter lang tids drift vil mikroskopiske dråber som rives<br />
med v<strong>and</strong>dampen bringe LiBr til fordamperen og dermed udligne koncentrationsforskellen mellem fordamper og<br />
absorber. Dette problem løses normalt ved med passende mellemrum at dræne v<strong>and</strong> fra fordamperen til<br />
absorberen ved at åbne en manuel ventil. Behovet for denne ”nedblæsning” kan være svingende. Fra ugentlig til<br />
månedligt.<br />
Desuden efterfyldning og kontrol af olien i vakuumpumpen<br />
Egentlig service<br />
Den egentlige service består typisk én gang om året at udtage en LiBr prøve (den fortyndede LiBr-opløsning) og<br />
analysere den for : Inhibitor, alkalinitet , jern og kobber. Er der for lidt inhibitor tilsættes lidt (op til 300 ppm) og er<br />
prøven for sur eller basisk tilsættes lidt LiOH eller HBr. Alkohol tilsættes efter lugt.<br />
Desuden måles de 2 pumpers TRG værdi. Slid og dermed spillerum mellem aksel og glideleje giver vibrationer som<br />
generer en lille vekselspænding.<br />
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Maskinens principopbygning<br />
CT4 Gen.’ tryk CT 12<br />
Gen. niveau ’<br />
’<br />
’ CT 10<br />
CT 7 ‘<br />
CT 9 CT 6 ’ CT 13<br />
ow switch<br />
‘<br />
’<br />
Vakuum pumpe<br />
CT 2 CT 8 ’<br />
P<br />
‘<br />
’<br />
Vakuum transmitter<br />
CT 1<br />
Ford. niveau ’<br />
Abs. niveau<br />
CT 11 ’<br />
Nedblæsningsventil CT 5 ‘<br />
‘<br />
Kølemiddel<br />
pumpe<br />
LiBr pumpe<br />
CT 3<br />
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A P P E N D I X<br />
G<br />
SYSTEM DIAGRAM<br />
The following pages are full size (A3) system diagrams <strong>of</strong> the three<br />
system configurations:<br />
• Single Stage<br />
• Double Stage<br />
• Double Stage - Dual Heat<br />
293
8<br />
SPG<br />
1<br />
10<br />
1-α<br />
GGHEX1<br />
9<br />
α<br />
7<br />
GGHEX2<br />
6<br />
CH4, add, in<br />
0<br />
1<br />
CH4, in<br />
Air, in<br />
21<br />
2<br />
11<br />
28<br />
MIXG<br />
1<br />
BLOW<br />
1<br />
WGHEX<br />
3<br />
4<br />
ANODE<br />
SOFC<br />
SPG α<br />
CATHODE 2<br />
12 13<br />
14 15 16<br />
1-α<br />
GGHEX4<br />
GGHEX3<br />
23<br />
3<br />
PR<br />
22<br />
20<br />
5<br />
19<br />
10<br />
BURN<br />
17<br />
18<br />
MIXG<br />
2<br />
19<br />
50<br />
22<br />
34<br />
32<br />
WGHEX<br />
2<br />
DES1<br />
21<br />
31<br />
31<br />
58<br />
59<br />
27<br />
Domestic Hot Water<br />
24<br />
Flue gas, out<br />
Saturated air<br />
47<br />
52<br />
35<br />
COND1<br />
36<br />
51<br />
60<br />
61<br />
SHEX<br />
1<br />
57<br />
56<br />
VA1<br />
VB1<br />
PUMP<br />
1<br />
Water add<br />
38<br />
TOWER<br />
46<br />
53<br />
49<br />
EVAP<br />
48<br />
54<br />
62<br />
36<br />
ABSO<br />
37<br />
55<br />
39<br />
37<br />
FAN<br />
45<br />
Atmospheric air<br />
Chilled Water<br />
System Configuration:<br />
●<br />
Single Stage<br />
●<br />
Additional Air Preheating<br />
●<br />
Wet Cooling Tower
1<br />
8<br />
GGHEX1<br />
CH4, in<br />
Air, in<br />
21<br />
2<br />
11<br />
28<br />
27<br />
9<br />
SPG<br />
1<br />
MIXG<br />
1<br />
BLOW<br />
1<br />
WGHEX<br />
3<br />
Domestic Hot Water<br />
α<br />
10<br />
7<br />
4<br />
GGHEX2<br />
ANODE<br />
SOFC<br />
SPG α<br />
CATHODE 2<br />
12 13<br />
14 15 16<br />
1-α<br />
GGHEX4<br />
GGHEX3<br />
23<br />
24<br />
1-α<br />
3<br />
PR<br />
22<br />
Flue gas, out<br />
20<br />
5<br />
19<br />
Saturated air<br />
47<br />
6<br />
10<br />
CH4, add, in<br />
0<br />
BURN<br />
17<br />
52<br />
18<br />
35<br />
MIXG<br />
2<br />
19<br />
COND1<br />
36<br />
51<br />
72<br />
VA2<br />
COND2<br />
71<br />
33 34<br />
MIXL<br />
1<br />
59<br />
60<br />
61<br />
DES1<br />
SHEX<br />
1<br />
57<br />
56<br />
70<br />
79<br />
43<br />
42<br />
80<br />
81<br />
VB2<br />
DES2<br />
SHEX<br />
2<br />
73<br />
82<br />
75<br />
MIXR<br />
32 31<br />
α<br />
1<br />
50<br />
82<br />
20<br />
21<br />
WGHEX<br />
1<br />
58<br />
41<br />
77<br />
76<br />
78<br />
57<br />
PUMP<br />
2<br />
1-α<br />
SPL<br />
1<br />
VA1<br />
VB1<br />
PUMP<br />
1<br />
Water add<br />
38<br />
TOWER<br />
46<br />
53<br />
49<br />
EVAP<br />
48<br />
54<br />
62<br />
36<br />
ABSO<br />
37<br />
55<br />
39<br />
37<br />
FAN<br />
45<br />
Atmospheric air<br />
Chilled Water<br />
System Configuration:<br />
●<br />
Double Stage<br />
●<br />
Additional Air Preheating<br />
●<br />
Wet Cooling Tower
1<br />
8<br />
GGHEX1<br />
CH4, in<br />
Air, in<br />
21<br />
2<br />
11<br />
28<br />
27<br />
9<br />
SPG<br />
1<br />
MIXG<br />
1<br />
BLOW<br />
1<br />
WGHEX<br />
3<br />
Domestic Hot Water<br />
α<br />
10<br />
7<br />
4<br />
GGHEX2<br />
ANODE<br />
SOFC<br />
SPG α<br />
CATHODE 2<br />
12 13<br />
14 15 16<br />
1-α<br />
GGHEX4<br />
GGHEX3<br />
23<br />
24<br />
1-α<br />
3<br />
PR<br />
22<br />
Flue gas, out<br />
20<br />
5<br />
19<br />
Saturated air<br />
47<br />
6<br />
10<br />
CH4, add, in<br />
0<br />
BURN<br />
17<br />
52<br />
18<br />
35<br />
MIXG<br />
2<br />
19<br />
COND1<br />
36<br />
51<br />
72<br />
COND2<br />
71<br />
33 34<br />
MIXL<br />
1<br />
59<br />
60<br />
61<br />
DES1<br />
SHEX<br />
1<br />
57<br />
56<br />
70<br />
79<br />
43<br />
42<br />
80<br />
81<br />
DES2<br />
SHEX<br />
2<br />
VA2<br />
31<br />
VB2<br />
73<br />
82<br />
75<br />
MIXR<br />
32<br />
α<br />
1<br />
50<br />
82<br />
22<br />
34<br />
WGHEX<br />
2<br />
20<br />
21<br />
WGHEX<br />
1<br />
58<br />
41<br />
77<br />
76<br />
78<br />
57<br />
PUMP<br />
2<br />
1-α<br />
SPL<br />
1<br />
VA1<br />
VB1<br />
PUMP<br />
1<br />
Water add<br />
38<br />
TOWER<br />
46<br />
53<br />
49<br />
EVAP<br />
48<br />
54<br />
62<br />
36<br />
ABSO<br />
37<br />
55<br />
39<br />
37<br />
FAN<br />
45<br />
Atmospheric air<br />
Chilled Water<br />
System Configuration:<br />
●<br />
Double Stage, Dual Heat<br />
●<br />
Additional Air Preheating<br />
●<br />
Wet Cooling Tower