integration of solid oxide fuel cells and ... - Ea Energianalyse

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integration of solid oxide fuel cells and ... - Ea Energianalyse

INTEGRATION OF

SOLID OXIDE FUEL CELLS AND

ABSORPTION COOLING UNITS

MASTER THESIS

Casper Frimodt

Kim Frithjof Mygind

JULY 5, 2010

DTU - MECHANICAL ENGINEERING

IN COOPERATION WITH TOPSOE FUEL CELL

SUPERVISORS:

BRIAN ELMEGAARD, MASOUD ROKNI & THOMAS PETERSEN


Empty line

Lyngby July 5, 2010

Casper Frimodt (s042506)

Casper Frimodt (s042506)

Kim Mygind (s030689)

Kim Mygind (s030689)


Abstract

It is investigated whether it is feasible to integrate a solid oxide

fuel cell (SOFC) and an absorption (ABS) air conditioner (AC).

First a market investigation based on rough economical calculations

shows that the SOFC-ABS system fits two market segments -

Auxiliary Power Unit (APU) for ships and Distributed Generation

(DG) for hotels. The latter is the best suited example of an application

and will constitute the basis in this project.

A thermodynamical zero-dimensional steady state model of

the SOFC-ABS system is developed in order to demonstrate the

performance of the integrated system. The thermodynamical model

is mainly based on theory but also partly on empirical knowledge

from the industry.

More system configurations are modeled showing that the

double stage absorption cycle is the best choice if the inlet air for

the SOFC is additionally preheated by the heat from the exhaust

gas remaining after the ABS. A wet cooling tower is necessary for

the double stage ABS unit if the surrounding temperature is above

20 ◦ C - otherwise the desorber temperature will have to exceed the

normal limit of 150 ◦ C.

The system is simulated with a standard parameter configuration,

changing one parameter at a time in order to determine its influence

on the system performance. Additionally a sensitivity analysis

is made in order to determine how crucial the exact values of

the estimated parameters are. From these results an optimized parameter

configuration is found.

In a climate with a temperature of 30 ◦ C and relative humidity of

40% a fuel input (methane gas) of 100kW gives 50kW of electricity,

59kW of cooling and 3kW of hot water.

Three case studies of hotels in different locations show that the

SOFC-ABS system can cope with very hot climates if they are dry.

For humid climates the ABS unit can not run at too high ambient

temperatures.

The thermodynamical model shows that it is feasible to integrate

a SOFC and an ABS unit, and the economical calculations indicate

that it could be an economical advantage as well.


Dansk resumé

Det vil blive undersøgt, om det er muligt at integrere en Solid

Oxide BrændselsCelle (SOFC) med et absorptionsairconditionanlæg

(ABS).

Først laves en markedsundersøgelse på baggrund af økonomiske

overslagsberegninger. Denne viser, at SOFC-ABS-systemet passer

godt til to markedssegmenter - Auxiliary Power Unit (APU) til

skibe og Distributed Generation (DG) til et hotel. Hotellet konkluderes

at være det mest egnede til SOFC-ABS-kombinationen, og

denne case danner derfor grundlag for resten af projektet.

En termodynamisk nul-dimensional steady state model af SOFC-

ABS-systemet udvikles for at beregne ydelsen af det integrerede

system. Den termodynamiske model er hovedsageligt baseret på

teori men også delvist på empirisk viden fra industrien.

Flere forskellige systemkonfigurationer modelleres. Det viser

sig, at dobbelteffekt absorptionskredsløbet giver den bedste ydelse.

I hvert fald hvis luften til brændselscellen forvarmes af den

spildvarme, der er tilbage i udstødningsgassen efter ABS-anlægget.

Et vådkøletårn er nødvendigt, hvis dobbelteffekt-ABS-anlægget

skal bruges i omgivelser med en temperatur på over 20 ◦ C - ellers

kommer desorbertemperaturen over de 150 ◦ C, der normalt anses

for at være den øvre grænse.

Systemet er simuleret med en standardparameterkonfiguration,

hvorefter en parameter ændres ad gangen for at fastlægge, hvordan

den influerer på systemets ydelse. Derudover laves en følsomhedsanalyse

for at vise, hvor følsomt systemet er over for den præcise

værdi af de skønnede parametre. Ud fra disse undersøgelser findes

en optimal parameterkonfiguration.

I et klima med en temperatur på 30 ◦ C og en relativ fugtighed

på 40%, vil det optimerede system, ved et brændselsinput (af

metan) på 100kW, give ca. 50kW elektricitet, 59kW køling og 3kW

vandopvarmning.

Tre cases med hoteller i forskellige egne viser, at SOFC-ABSsystemet

er passende til meget varme klimaer, der samtidigt har

lav luftfugtighed. Hvis der derimod er høj luftfugtighed, kan

absorptionsanlægget ikke køre ved høje omgivelsestemperaturerer.

Simuleringerne og beregningerne viser, at det er muligt at

integrere en SOFC-brændselscelle med et absorptionskøleanlæg og

tyder desuden på, at det også kunne være en økonomisk fordel.


Preface

This report is documentation of our master thesis of 2 times 30 ECTS

points carried out in the period from February to June in 2010. The projet

is conducted under DTU Mechanical Engineering in corporation with

Topsoe Fuel Cell.

ix


Acknowledgment

Thanks to:

Brian Elmegaard

Thomas F. Petersen

Masoud Rokni

Topsoe Fuel Cell for hospitality

Arne Hansen for printing this report

xi


CONTENTS

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

xi

Nomenclature

xxi

Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi

Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii

Greek (and other) Symbols . . . . . . . . . . . . . . . . . . . . . . . . xxiii

Latin Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiv

Subscripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv

1 Introduction 1

1.1 Project outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 General formalities . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 General introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3.1 Distributed generation . . . . . . . . . . . . . . . . . . . 3

1.3.2 Fuel cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3.3 Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3.4 Demand for cooling . . . . . . . . . . . . . . . . . . . . . 5

1.4 SOFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4.1 SOFC Waste heat . . . . . . . . . . . . . . . . . . . . . . . 6

1.4.2 Topsoe Fuel Cell . . . . . . . . . . . . . . . . . . . . . . . 7

1.4.3 APU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4.4 Micro CHP . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4.5 DG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Heat driven cooling . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5.1 Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.5.2 Carré cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.5.3 Platen Munters cycle . . . . . . . . . . . . . . . . . . . . 14

1.5.4 Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.6 Problem delimitation . . . . . . . . . . . . . . . . . . . . . . . . 17

1.7 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2 Market investigation 19

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 Auxiliary Power Unit (APU) . . . . . . . . . . . . . . . . . . . . 21

xii


Contents

2.2.1 Truck APU . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.2 Ship APU . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3 Micro Combined Heat and Power (µCHP) . . . . . . . . . . . 25

2.3.1 Micro CHP - Air condition . . . . . . . . . . . . . . . . . 25

2.3.2 Micro CHP - Refrigerators . . . . . . . . . . . . . . . . . 26

2.4 Distributed Generation (DG) . . . . . . . . . . . . . . . . . . . . 29

2.4.1 Three solutions . . . . . . . . . . . . . . . . . . . . . . . . 30

2.4.2 Hot vs Normal climate . . . . . . . . . . . . . . . . . . . 31

2.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.5 Conclusion of the whole market investigation . . . . . . . . . 39

3 Component description 41

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.1.1 EES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.1.2 Components . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2 Absorber - ABSO . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.3 Blower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.4 Burner - BURN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.5 Condenser - COND . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.6 Desorber - DES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.7 Evaporator - EVAP . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.8 Heat Exchanger - HEX . . . . . . . . . . . . . . . . . . . . . . . . 57

3.9 Mixer - MIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.10 Pre Reformer - PR . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.11 Pump - PUMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.12 Solid Oxide Fuel Cell - SOFC . . . . . . . . . . . . . . . . . . . . 64

3.12.1 Chemical reactions . . . . . . . . . . . . . . . . . . . . . 65

3.13 Splitter - SP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.14 Cooling Tower - TOWER . . . . . . . . . . . . . . . . . . . . . . 71

3.14.1 Dry Cooling Tower - TOWERd . . . . . . . . . . . . . . 72

3.14.2 Wet Cooling Tower - TOWERw . . . . . . . . . . . . . . 73

3.15 Expansion valve - VA/VB . . . . . . . . . . . . . . . . . . . . . 76

3.15.1 Expansion valve for refrigerant - VA . . . . . . . . . . 76

3.15.2 Expansion valve for LiBr solution - VB . . . . . . . . . 76

4 System description 79

4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.2 SOFC subsystem . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.2.1 Fuel pretreatment and recirculation . . . . . . . . . . . 81

4.2.2 Air inlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

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CONTENTS

4.2.3 SOFC stack . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.2.4 Exhaust gas . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.3 Absorption Single Stage . . . . . . . . . . . . . . . . . . . . . . . 86

4.3.1 Refrigerant cycle . . . . . . . . . . . . . . . . . . . . . . . 87

4.3.2 Solution cycle . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.3.3 Pumping factor . . . . . . . . . . . . . . . . . . . . . . . . 88

4.4 Absorption Double Stage . . . . . . . . . . . . . . . . . . . . . . 89

4.5 Absorption Double Stage, Dual Heat . . . . . . . . . . . . . . . 92

4.6 Cooling Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.6.1 Wet Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.6.2 Dry Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.6.3 Hot Water . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.7 System calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.7.1 Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.8 Verification of Model . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.8.1 Energy balance . . . . . . . . . . . . . . . . . . . . . . . . 100

4.8.2 Check of heat exchangers . . . . . . . . . . . . . . . . . 100

4.9 Validation of Model . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.9.1 SOFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.9.2 Absorption cycle . . . . . . . . . . . . . . . . . . . . . . . 102

5 Simulation and Results 105

5.1 Basic absorption cooling . . . . . . . . . . . . . . . . . . . . . . 105

5.1.1 Changing the desorber temperature . . . . . . . . . . . 106

5.1.2 Changing condenser temperature . . . . . . . . . . . . 109

5.1.3 Changing evaporator temperature . . . . . . . . . . . . 111

5.1.4 Changing absorber temperature . . . . . . . . . . . . . 112

5.1.5 Summing up the general behavior of the absorption

cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5.2 System configurations . . . . . . . . . . . . . . . . . . . . . . . . 114

5.2.1 Single, Double, Dual Heat (+/- Air Preheat) . . . . . . 115

5.2.2 Wet vs Dry cooling and ambient temperature . . . . . 117

5.2.3 ∆T min,Tower . . . . . . . . . . . . . . . . . . . . . . . . . . 119

5.3 Partial optimization of standard parameters . . . . . . . . . . 120

5.3.1 Outer conditions . . . . . . . . . . . . . . . . . . . . . . . 120

5.3.2 Desorber temperatures . . . . . . . . . . . . . . . . . . . 123

5.3.3 SOFC subsystem . . . . . . . . . . . . . . . . . . . . . . . 125

5.3.4 Closest Approach Temperature Differences (∆T min ) . 135

5.3.5 ∆T for external circuits . . . . . . . . . . . . . . . . . . . 140

5.3.6 Hot Water . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

5.4 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 142

xiv


Contents

5.4.1 Closest Approach Temperature Difference . . . . . . . 142

5.4.2 Pressure Losses . . . . . . . . . . . . . . . . . . . . . . . . 143

5.4.3 Heat Losses . . . . . . . . . . . . . . . . . . . . . . . . . . 145

5.4.4 (Other) Key Parameters . . . . . . . . . . . . . . . . . . 146

5.5 Total optimization of system . . . . . . . . . . . . . . . . . . . . 149

5.5.1 Absorption subsystem . . . . . . . . . . . . . . . . . . . 149

5.5.2 Current density . . . . . . . . . . . . . . . . . . . . . . . 152

5.5.3 Future: ∆T SOFC = 120 ◦ C . . . . . . . . . . . . . . . . . . 153

6 Cases and Economics 155

6.1 Air conditioning of hotels . . . . . . . . . . . . . . . . . . . . . . 155

6.2 High humidity climate . . . . . . . . . . . . . . . . . . . . . . . 156

6.2.1 Seychelles . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

6.2.2 Bangkok . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

6.3 Low humidity climate . . . . . . . . . . . . . . . . . . . . . . . . 160

6.3.1 Las Vegas . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

6.3.2 Water consumption . . . . . . . . . . . . . . . . . . . . . 161

6.4 Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

7 Discussion 165

7.1 The thermodynamical model . . . . . . . . . . . . . . . . . . . 165

7.1.1 Accuracy and sensitivity . . . . . . . . . . . . . . . . . . 167

7.2 Economical considerations . . . . . . . . . . . . . . . . . . . . . 168

7.2.1 Auxillary Power Unit (APU) . . . . . . . . . . . . . . . 168

7.2.2 Micro Combined Heat and Power (µCHP) . . . . . . . 169

7.2.3 Distributed Generation (DG) . . . . . . . . . . . . . . . 171

7.3 Other considerations . . . . . . . . . . . . . . . . . . . . . . . . . 176

8 Conclusion 177

9 Further work 181

Bibliography 183

Appendices 187

A Market investigation 189

A.1 Market Investigation Appendix - Introduction . . . . . . . . . 190

A.2 APU appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

A.2.1 Ship APU appendix . . . . . . . . . . . . . . . . . . . . . 191

A.3 CHP appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

A.3.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 196

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CONTENTS

A.4 DG appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

A.5 Absorption cooling unit prices . . . . . . . . . . . . . . . . . . . 219

A.6 Gas and electricity prices . . . . . . . . . . . . . . . . . . . . . . 224

B Diagrams and plots 227

B.1 GAX diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

B.2 Double stage diagram . . . . . . . . . . . . . . . . . . . . . . . . 229

B.3 Closed adsorption cycle . . . . . . . . . . . . . . . . . . . . . . . 230

B.4 Property plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

B.4.1 Phase diagram of water-LiBr-solution . . . . . . . . . 231

B.4.2 p-T diagram of water-LiBr-solution . . . . . . . . . . . 232

C EES 233

C.1 Parameter configuration . . . . . . . . . . . . . . . . . . . . . . 233

C.2 Results - Standard parameter configuration . . . . . . . . . . 242

C.3 Results - Optimized parameter configuration . . . . . . . . . 250

C.4 Results - Uncertainty propagation (STD) . . . . . . . . . . . . 258

C.4.1 ∆T min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258

C.4.2 Miscellaneous parameters . . . . . . . . . . . . . . . . . 261

C.4.3 ∆p for SOFC subsystem . . . . . . . . . . . . . . . . . . 263

C.4.4 ∆p for absorption subsystem . . . . . . . . . . . . . . . 266

C.4.5 ˙Q loss for absorption subsystem . . . . . . . . . . . . . . 268

C.5 Guide to EES files . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

D Other 271

D.1 Explanation of chosen Parameters . . . . . . . . . . . . . . . . 271

D.2 Spider diagram parameter interval choice . . . . . . . . . . . 272

D.3 Water consumption . . . . . . . . . . . . . . . . . . . . . . . . . . 273

E Optimization graphs 275

E.1 Simulations and Results . . . . . . . . . . . . . . . . . . . . . . . 276

E.1.1 All 12 Configurations . . . . . . . . . . . . . . . . . . . . 276

E.1.2 ∆T for external circuits . . . . . . . . . . . . . . . . . . . 277

E.1.3 Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

E.2 Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

E.2.1 Extreme low relative humidity . . . . . . . . . . . . . . 283

F Literature 285

F.1 Scandinavian Energy Group Aps. . . . . . . . . . . . . . . . . . 285

G System diagram 293

xvi


LIST OF FIGURES

1.1 Individual air conditioning . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Diagram of single stage absorption cycle . . . . . . . . . . . . . . 10

1.3 Diagram of Platen Munters cycle . . . . . . . . . . . . . . . . . . . 14

2.1 Ship: Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2 Ship: Pay Back Time . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3 Refrigerator: Pay Back Time . . . . . . . . . . . . . . . . . . . . . . 27

2.4 Refrigerator: Sensitivity analysis . . . . . . . . . . . . . . . . . . . 28

2.5 Hotel: Pay Back Time AC . . . . . . . . . . . . . . . . . . . . . . . . 34

2.6 Hotel: Pay Back Time BC . . . . . . . . . . . . . . . . . . . . . . . . 35

2.7 Hotel: Annuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.8 Hotel: Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1 Absorber component . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 QT-diagram for absorber . . . . . . . . . . . . . . . . . . . . . . . . 46

3.3 Blower component . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.4 Burner component . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.5 Condenser component . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.6 QT-diagram for Condenser . . . . . . . . . . . . . . . . . . . . . . . 51

3.7 Desorber component . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.8 QT-diagram for Desorber . . . . . . . . . . . . . . . . . . . . . . . . 54

3.9 Evaporator component . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.10 QT-diagram for evaporator . . . . . . . . . . . . . . . . . . . . . . . 55

3.11 HEX component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.12 QT-diagram for HEXes . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.13 Pre Reformer component . . . . . . . . . . . . . . . . . . . . . . . . 61

3.14 Solution pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.15 SOFC component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.16 Cooling Tower component . . . . . . . . . . . . . . . . . . . . . . . 71

3.17 QT-diagram for TOWERd . . . . . . . . . . . . . . . . . . . . . . . . 72

3.18 Ix-diagram for TOWERw . . . . . . . . . . . . . . . . . . . . . . . . 74

3.19 Expansion valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.1 System diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.2 Diagram of SOFC subsystem . . . . . . . . . . . . . . . . . . . . . . 81

xvii


LIST OF FIGURES

4.3 Diagram of single stage absorption subsystem . . . . . . . . . . . 86

4.4 Diagram of double stage absorption subsystem . . . . . . . . . . 89

4.5 Diagram of double stage, dual heat absorption subsystem . . . 92

4.6 Diagram of cooling system and hot water production . . . . . . 94

5.1 Diagram of single stage absorption cycle . . . . . . . . . . . . . . 105

5.2 ∆T DES vs COP ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

5.3 ∆T DES vs COP ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.4 ∆T COND vs COP ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.5 ∆T EV AP vs COP ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.6 ∆T ABSO vs COP ABS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.7 Comparison of system configurations . . . . . . . . . . . . . . . . 116

5.8 T amb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.9 T EV AP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

5.10 φ air at T DES2 = 150 ◦ C . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.11 φ air at T DES2 = 160 ◦ C . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

5.12 T DES2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.13 T DES1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5.14 ∆T SOFC 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

5.15 ∆T SOFC 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5.16 T SOFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.17 α 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

5.18 i d without bypass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

5.19 U f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

5.20 i d when bypassing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

5.21 ∆T minW W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5.22 ∆T minCOND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

5.23 ∆T minW G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

5.24 ∆T minGG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

5.25 ∆T minW G Hot water . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

5.26 Spider diagram ∆T min . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5.27 Spider diagram pressures . . . . . . . . . . . . . . . . . . . . . . . . 144

5.28 Spider diagram ˙Q loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

5.29 Spider diagram other parameters . . . . . . . . . . . . . . . . . . . 147

5.30 NTU vs ɛ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

5.31 Optimized parameters, i d . . . . . . . . . . . . . . . . . . . . . . . . 151

5.32 Bar diagram Optimized parameters . . . . . . . . . . . . . . . . . 153

6.1 Weather data for Port Victoria, Seychelles . . . . . . . . . . . . . . 156

6.2 Hotel in high humidity climate (φ = 0,8). . . . . . . . . . . . . . . 157

6.3 Weather data for Bangkok, Thailand . . . . . . . . . . . . . . . . . 158

xviii


List of Figures

6.4 Hotel in high humidity climate (φ = 0,9). . . . . . . . . . . . . . . 159

6.5 Weather data for Las Vegas, USA . . . . . . . . . . . . . . . . . . . 160

6.6 Hotel in low humidity climate (φ = 0,4). . . . . . . . . . . . . . . . 161

6.7 Hotel vs OPTI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

B.1 Diagram of GAX cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 228

B.2 Diagram of double stage absorption cycle . . . . . . . . . . . . . . 229

B.3 Diagram of closed adsorption cycle . . . . . . . . . . . . . . . . . . 230

B.4 Phase diagram of water-LiBr . . . . . . . . . . . . . . . . . . . . . . 231

B.5 p-T diagram of water-LiBr . . . . . . . . . . . . . . . . . . . . . . . 232

E.1 Comparison of system configurations . . . . . . . . . . . . . . . . 276

E.2 T EV AP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

E.3 T DES1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

E.4 T DES2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

E.5 T TOW ERd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

E.6 T TOW ERw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

E.7 T TOW ERw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

E.8 Hotel in extreme low humidity climate. . . . . . . . . . . . . . . . 283

xix


NOMENCLATURE

Acronyms

Acronym

ABS

AC

APU

CATD

CCHP

CHP

DG

ECH

EES

HEX

LiBr

LPG

NP

NPV

NTU

OPTI

STD

VAT

WGS

Description

Absorption chiller

Air Conditioning

Auxiliary Power Unit

Closest Approach Temperature Difference

Combined Cooling, Heating, and Power

Combined Heating and Power

Distributed Generation

Electrical driven Chiller

Engineering Equation Solver

Heat EXchanger

Lithium Bromide

Liquified Petroleum Gas

Net Payment

Net Present Value

Number of Transfer Units

Optimized

Standard

Value Added Tax

Water Gas Shift reaction


NOMENCLATURE

Components

Component

ABSO

BLOW

BURN

COND

DES

EVAP

FAN

GGHEX

MIXL

MIXG

MIXR

PR

PUMP

SOFC

SPL

SPG

SPR

TOFC

TOWER

VA

VB

WGHEX

Description

Absorber

Blower, air

Burner

Condenser

Desorber

Evaporator

Fan, air

Gas-Gas Heat Exchanger

Mixer, LiBr solution

Mixer, gas

Mixer, refrigerant

Pre Reformer

Pump, water

Solid Oxide Fuel Cell

Splitter, LiBr solution

Splitter, gas

Splitter, refrigerant

Topsoe Fuel Cell

Cooling tower

Expansion valve for refrigerant

Expansion valve LiBr solution

Water-gas heat exchanger

xxii


Greek (and other) Symbols

Greek (and other) Symbols

Symbol Unit Description

α [−] mass fraction in splitters

∆ [−] change (increase)

∆ T,min [K] minimum temp. difference between streams in HEX

ɛ [−] effectiveness of HEX

η [−] efficiency

λ [−] air excess number

ρ

o

[ ] kg

m 3

[−]

density

standard pressure (100 kPa)

xxiii


NOMENCLATURE

Latin Symbols

Symbol Unit Description

A

[

m

2 ] Area

ASR [Ωm] Area Specific Resistance

[

Ċ

kW

]

Heat capacity flow rate

K

COP

[

[−]

] Coefficient Of Performance

C kJ

p

heat Capacity, constant pressure

kgK

F R [−] Fraction of gas Reformed in prereformer

FW [−] Fraction of gas in Water gas shift reaction

PF [−] Mass flow ratio of the weak solution and the refrigerant

h

[

kJ

kg

]

mass specific enthalpy

Ḣ [kW] enthalpy flow rate

I [A] current

i d

[

A

m 2 ]

current density

K W GS [−] reaction constant for Water Gas Shift

LG r atio [

[−]

] Liquid-Gas ratio

kg


s

mass flow rate

n [−] number

[


kmol

]

mole flow rate

s

OC r atio [−] Oxygen-Carbon ratio

p [kPa] pressure

˙Q [kW] heat flow rate

qu

[

[−]

] quality of steam in the two phase region

s

kJ

kgK

mass specific entropy

T [ ◦ C] Temperature

U f [

[−]

] fuel Utilization factor

v

m 3

mass specific volume

kg

V

[

[V]

] electric potential (voltage)

˙V

m 3

s

volume flow rate

w [−] concentration of LiBr in water solution

Ẇ [kW] power

W Q r atio [−] power-heat flow rate ratio

x [−] mass fraction

y [−] mole fraction

xxiv


Subscripts

Subscripts

Subscript

2P

air

ABS

amb

ano

av

c

cat

cell

chill

chk

el

g

h

HW

i

inver t

i s

mp

o

over all

r

re f

s

sat

SC

SH

ss

st ack

tr ans

w

ws

Description

two Phase

atmospheric air

Absorption cycle

ambient

anode

average

cold side of heat exchanger

cathode

cell, SOFC

chilling fluid

checking state: sub cooled OR two phase

electric

gas

hot side of heat exchanger

Hot Water

in

inverter (DC to AC)

isentropic process

mid point (in heat exchangers)

out

the entire system

refrigerant

reference

solution of LiBr

saturated

Sub Cooled

Super Heated

strong solution of LiBr

SOFC stack of n cells

transfer

water

weak solution of LiBr

xxv


C H A P T E R

1

INTRODUCTION

1.1 Project outline

In this report the integration of a Solid Oxide Fuel Cell (SOFC) and a heat

driven chiller will be investigated.

Chapter 1, Introduction

The SOFC technology and some of its applications are briefly described

and the principles of heat driven chilling and different technologies are

introduced. In the end of the chapter the problem statement of this

project will be shown.

Chapter 2, Market investigation

In order to see if there is any potential in combining a SOFC with a heat

driven chiller a short market investigation is carried out. Economical

calculations are made to check if the SOFC-absorption system (SOFC-

ABS) can provide an economical advantage over the more traditional

cooling technologies. At this point no thermodynamical model has been

made yet, so the efficiencies will merely be estimated.

Chapter 3, Component description

The individual components of the thermodynamical model of the SOFC-

ABS system are described in details.

1


1. INTRODUCTION

Chapter 4, System description

This chapter is divided into two parts:

a. The system configuration is described i.e. the way in which the

components are arranged relative to each other.

b. The chosen values of the parameters for the components are described.

Chapter 5, Simulation and Results

The model is used to simulate the general behavior of an absorption

chiller and the behavior of the system as a whole under different

conditions. The most important parameters are examined and their

impact on the system performance is illustrated.

Chapter 6, Cases and Economics

Three different case studies of hotels in different climates are described.

Economics and other issues are considered.

Chapter 7, Discussion

The results are discussed and evaluated. The model is compared to

commercial products, and the uncertainty and assumptions of the model

are assessed.

Chapter 8, Conclusion

The results of the entire project and the discussion is summed up, and

the questions of the problem statement are answered.

Chapter 9, Further work

Ideas for further work include new areas which could be investigated

and things that could be done to improve the accuracy of the model and

calculations.

2


1.2. General formalities

1.2 General formalities

Decimal separator

The European decimal separator, decimal comma, is used throughout the

report. Dot is used as thousand separator.

Dot notation

In this report the dot notation is applied, i.e. ẋ is the time derivative of

the variable x.

1.3 General introduction

Climate changes, security of energy supply, and high oil prices are all

arguments for finding alternatives to the worlds energy sources which

today primarily are based on fossil fuels like oil, coal and natural gas. The

increasing demand for energy has a major impact on the environment

especially due to emission of CO 2 which contributes to the green house

effect and thereby increases the average temperature of the Earth 1 . This

is one of the most extensive challenges for mankind in our time and

probably in the future as well. Energy efficiency also play an important

role in reducing the primary energy consumption - in all parts of the

supply chain starting from primary energy to end-use services.

The consumption of primary energy can be split up in sectors

like ”electricity and heat production” (energy conversion), ”industry”,

”business and service”, ”residential” and ”transport”. Some examples of

how energy could be saved within these sectors are briefly described in

the following sections.

1.3.1 Distributed generation

Distributed generation (DG) of electricity and heat is an opportunity

for reducing the energy losses in the ”electricity and heat” sector.

Traditionally most power is produced by large scale power stations and

1 According to IPCC - Intergovernmental Panel on Climate Change

3


1. INTRODUCTION

the electricity and heat 2 is distributed via grids to the end-user which

introduces transmission and distribution losses. These can to some

extend be eliminate by moving the generation of electricity close to the

end-user (covers three of the sectors mentioned above).

Combined Heat and Power (CHP) generation is advantageous, since

the waste heat can be utilized locally for process heating (industrial

sector), space heating, and hot water. This means that the losses are

reduced significantly.

Distributed generation could be applied in several places e.g. in the

manufacturing industry (large scale), hospitals and malls, but also for

private homes (very small scale).

1.3.2 Fuel cells

Fuel cells are one of several DG technologies. One of the strengths of fuel

cell systems is that the efficiency is relatively high and depends very little

on system size which is an important property for this purpose.

The fuel cells are still in the developing phase and only market niches

exist. It is though expected that the market share will grow in the future

as the price of fuel cells decrease (the current price of fuel cells is still far

to high to compete with other technologies on the market).

1.3.3 Transport

The transports sector today is very dependent on fossil fuel especially oil.

The primary energy consumption within this sector is enormous due to

high demand and due to relatively poor energy efficiency of combustion

engines (especially during part load) 3 . In addition the growth rate of

transport demand is large.

The fuel cells can be used to generate electricity for propulsion, but

another option is to use it as an auxiliary power unit (APU) which

supplies electricity when the grid is not accessible or e.g. the main engine

of a truck is turned off.

2 Some countries utilize the waste heat from the electricity generation via district

heating networks, but it is most common to reject the heat to the surroundings.

3 Large engines e.g. in ships have a much better efficiency than combustion engines

in general though - up to more than 50% [2]

4


1.3. General introduction

1.3.4 Demand for cooling

The demand for cooling (air conditioning) is one of the large end-use

energy services. The growing wealth in the world leads to an increased

demand for this service in many countries (especially those with a hot

climate). The most common way to meet this demand is by means

of individual electrically driven air conditioning units (see figure 1.1),

which in many cases is not the most energy efficient way to deliver this

service.

Figure 1.1: Individual air conditioning units on facade. Edited picture taken from [15].

5


1. INTRODUCTION

1.4 SOFC

The fuel cell technology is a candidate for the future energy system.

Basically it is a converter of chemical to electrical energy and it has an

efficiency which is higher than the most of competing technologies of

today 4 . Additionally the efficiency is almost not affected by the size

of the system. Solid Oxide Fuel Cells (SOFC) are operated at high

temperature (700-800 ◦ C) which enable them to accept a lot of different

fuels e.g. diesel, natural gas or biogas. This is an advantage because it

makes the technology more flexible.

1.4.1 SOFC Waste heat

The high temperature at which the Solid Oxide Fuel Cells (SOFCs) are

operated gives them an important advantage compared to other (low

temperature) fuel cells: The waste heat is rejected at a much higher

temperature and that is an advantage if the waste heat is to be utilized

for certain purposes.

The waste heat can be turned into useful energy when it is used for

e.g. space heating or water heating. These are normally low temperature

applications. But in some cases this heating service is not needed.

So another options is to utilize the waste heat in a heat driven heat

pump/chiller which will reduce the consumption of primary energy 5 .

Especially heat driven chilling is interesting since the demand for

cooling (air conditioning) often increases when the outside temperature

is high while the demand for (space) heating decreases. It is also possible

to produce both cooling and heating simultaneously in a Combined

Cooling, Heating and Power (CCHP) unit.

Thus it would be interesting to investigate how a fuel cell could be

integrated with a heat driven chiller.

4 The electrical efficiency of a fuel cell system fueled with methane is about 55%

today [31].

5 Assuming that the produced heating/cooling replaces an energy services which

require primary energy.

6


1.4. SOFC

1.4.2 Topsoe Fuel Cell

Topsoe Fuel Cell (TOFC) (subsidiary company of Haldor Topsøe A/S)

has developed SOFC cells and stacks in corporation with Risø DTU since

1989. TOFC has a small scale production facility of SOFC cells and stacks

which are primarily use for development and demonstration purposes.

The business plan of TOFC is to be a subcontractor to fuel cell system

manufacturers (e.g. Wärtsilä in Finland and Dantherm in Denmark). The

product is a Topsoe PowerCore TM consisting of the fuel cell stack and

other high temperature components in a integrated unit. The focus will

be on three markets which are described in the following.

1.4.3 APU

The Auxiliary Power Unit (APU) is an alternative to small diesel

generators which supply electricity when the electricity grid is not

accessible. The present APU delivers 2,3kW e (electricity) with an

efficiency of 40%. Applications for APU’s include heavy duty trucks,

recreational vehicles and yachts. The most important advantages of a

fuel cell for this purpose are silent operation and high efficiency 6 [30].

1.4.4 Micro CHP

The micro Combined Heat and Power (µCHP) unit is an alternative to

traditional oil and gas burners for residential use. It presently has a

power output of 1kW e and an electrical efficiency of 45%. The overall

efficiency (electricity and heat) is 85%. Acceptable fuels are natural gas,

diesel, biogas, bio diesel and synthetic fuel [32].

1.4.5 DG

Distributed Generation (DG) means that power and heat is produced

close to the consumer. TOFC plans to offer a product in the range of 10-

250kW e (and higher) with an efficiency of 55%. The fuel can be natural

gas, bio gas and in the future bio fuels. Another benefit is the elimination

of NO x and SO x [31].

6 Compared to a large idling truck diesel engine.

7


1. INTRODUCTION

1.5 Heat driven cooling

The most common principle of producing cooling is the vapor compression

cycle (reverse Rankine cycle) which is driven by mechanical work

(normally an electric motor).

An alternative is to produce the cooling by a sorption cycle. ”Sorption”

covers absorption and adsorption cycles which are mainly operated by heat

as energy source [18].

The sorption cycle is in principle like the vapor compression cycle

with a condenser, an expansion valve and an evaporator. The main

difference is how the refrigerant is pressurized after the evaporator:

for the vapor compression cycle it is a mechanical compression, e.g.

a reciprocation or a screw compressor, which compresses evaporated

refrigerant. In the sorption cycle it is a ”heat driven compressor” 7 . How

this work will be explained in the next section.

The heat ratio, COP ABS , of a sorption cycle is the ratio between cooling

load and driving heat 8 .

COP ABS =

˙Q cooling load

˙Q dr i ving heat

(1.1)

This COP is not comparable to the COP of the vapor compression

cycle because the inputs have different value (heat at the relatively low

temperature has a lower exergy than mechanical or electric work) [18].

The medium in sorption cycles is a pair consisting of a refrigerant and

a ”sorbent”. For the absorption cycle the refrigerant is absorbed by the

absorbent (which is either a liquid or a dissolved salt), i.e. a solution,

whereas for the adsorption cycle the refrigerant is adsorbed on the surface

of the adsorbent. The two cycles can be divided into subcategories which

are described in following sections.

7 Actually the physical pressurization is done by a mechanical pump.

8 The small amount of electric or mechanical energy used for driving pumps in some

variants is not included. For systems larger than 1 MW of cooling the consumption of

electrical energy of the pump is about one per thousand of cooling power

8


1.5. Heat driven cooling

1.5.1 Absorption

There are two major types of absorption cycles:

• Carré cycle which is used for cooling and air conditioning (as well

as heat pumps) in the range of 15 kw to megawatts.

• Platen Munters cycle which is used for small (household size)

refrigerators/freezers.

The two cycles are in principle almost identical, but in practice they

differ a lot - hence the very different applications. In the following

sections, the two types will be described.

1.5.2 Carré cycle

The basic principle of the absorption cycle is developed by the French

scientist Ferdinand Carré about 1860.

Working media.

The fluid in the absorption cycle consists of a pair of a refrigerant and

an absorption medium which is capable to absorb the refrigerant. More

than 40 refrigerants and 200 absorption media exist [35].

The most common pairs are ammonia-water (N H 3 − H 2 O) and waterlithium

bromide (H 2 O − LiBr ). Ammonia is the refrigerant in the N H 3 −

H 2 O solution (ammonia has a lower boiling point than water), whereas

water is the refrigerant in the H 2 O − LiBr solution.

Ammonia-water is usable for small as well as large scale units

working at various temperatures, e.g. air conditioning or industrial

cooling/freezing (evaporator temperatures down to -60 ◦ C).

Water-lithium bromide has a limited temperature range due to the

freezing point of water, and in practical applications the chilled water

should never be lower than 6 ◦ C [27]. Thus this pair is feasible for

applications such as production of chilled water or air conditioning.

9


1. INTRODUCTION

Cycle description.

As mentioned, the absorption cycle is very similar to the vapor

compression cycle - the mechanical compressor is just replaced by a

”thermal compressor”. This consists of a desorber 9 (DES), an absorber

(ABSO), a solution heat exchanger (SHEX), an expansion valve (VB), and

a pump as seen in figure 1.2.

COND

1

HEAT

DES

COOLING

9

7

2

SHEX

3

VA

EVAP

4

11

12

VB

ABSO

PUMP

6

5

CHILLED WATER

COOLING

Figure 1.2: Diagram of single stage absorption cycle

The principle of the absorption cycle will now be described.

numbering refers to the state points appearing in figure 1.2.

The

1 → 2: Superheated refrigerant at high pressure is condensed to

saturated liquid in the condenser (COND). The heat is removed by

an external cooling circuit.

2 → 3: The pressure of the liquid refrigerant is reduced from the

high to the low working pressure by the expansion valve (VA).

9 This is some time called a generator, but the phrase desorber will be used throughout

this report.

10


1.5. Heat driven cooling

3 → 4: The refrigerant is evaporated in the evaporator (EVAP).

Heat is transferred at a low temperature from an external circuit of

water or a brine which is thereby being chilled.

4 → 5: The refrigerant is absorbed by the strong absorption

solution (rich in absorption medium) entering at point 12. This

process is exothermic due to both condensing of refrigerant and

mixing of refrigerant and solution. The heat is removed by an

external cooling circuit.

5 → 6: The liquid weak solution (poor in absorption media) is

pressurized by a pump in order to reach the high pressure.

6 → 7: The solution is preheated in the solution heat exchanger.

7 → 9: The weak solution is heated by an external high temperature

heat source which makes the refrigerant boil of.

9 → 11: The strong solution is sent through the solution heat

exchanger and heat is recovered by the weak solution.

11 → 12: The high pressure of the strong solution is reduced to the

low pressure by an expansion valve before it enters the absorber.

In cycles using the ammonia-water solution (or similar solution) it

is necessary to install a rectifier (”water separator”) after the desorber

(DES in figure 1.2) to ensure that only refrigerant (ammonia) is sent to

the condenser ([18]). If the refrigerant is not free of absorption medium,

it will decrease the performance of the system.

Cycle configurations

The performance of the single stage cycle 10 described previously is quite

limited (COP is in the range of 0,6 to 0,8). To increase the performance,

various configurations have been developed. In the following some of

these alternative cycles of ammonia-water and water-lithium bromide

are listed and their respective COP’s are indicated to compare the

performance of the different configurations:

10 In the literature the phrase single effect cycle is often for describing the same thing.

11


1. INTRODUCTION

Ammonia-water

The COP values come from figure 6 in [20] at a heat rejection temperature

of 35 ◦ C. The details about how the cycles work will not be explained here

but a complete diagram is shown in appendix B.1 page 228.

Basic single stage cycle, COP = 0,6

Same cycle as described in previous section and in figure 1.2 (plus

a rectifier between desorber and condenser).

Single stage cycle with pre cooler, COP = 0,65

The same as the above. A pre cooler (the same as a suction line heat

exchanger) is added (transferring heat from point 2 to point 4 in

figure 1.2).

Absorber heat exchanger, COP = 0,9

The same as the above. Two extra solution heat exchangers - one in

the desorber and one in the absorber, are added.

Desorber absorber heat exchange, COP = 1,3

The same as the above. Another extra heat exchange (done by an

external circuit) between absorber and desorber is added. This

configuration is normally called GAX - Generator-Absorber-heat

eXchanger.

These configurations show that it is possible to double up the performance

of the system by adding extra heat exchangers etc.

Water-lithium bromide

For the double, triple and quadruple stage, the mentioned COP’s are

taken from figure 4 in [20] and the temperature in parenthesis is

the heat supply temperature. For the three mentioned configurations

the temperature of heat rejection and chilled water is 29 ◦ C and 7 ◦ C

respectively.

12

Basic single stage cycle, COP = 0,7

Same cycle as described in previously section and shown in figure

1.2 (COP is taken from table 4 in [35]).

Double stage cycle, parallel flow, COP = 1,3 (150 ◦ C)

An extra cycle consisting of a pump, solution heat exchanger,


1.5. Heat driven cooling

desorber, expansion valve and condenser is added to the single

stage cycle (PUMP2, SHEX2, DES2, VB2 and COND2, see diagram

in appendix B.2 page 229).

The desorber (DES1) is now supplied with waste heat from the

upper cycle condenser (COND2). The upper cycle desorber (DES2)

is the only one receiving heat from an external source.

The two cycles are coupled in parallel, which requires further three

components - one splitter and two mixers (SPL, MIXL and MIXR).

Triple stage cycle, parallel flow, COP = 1,7 (200 ◦ C)

This is the same as above, but with yet another cycle on top of the

two. This configuration is also called double condenser coupled.

Quadruple stage cycle, parallel flow, COP = 2,0 (275 ◦ C)

This is the same as above, but with yet another cycle on top of the

three.

Alternatively the water lithium bromide can be configured with series

flow. According to [21] the parallel configuration has a higher COP than

the series configuration at the same operation conditions.

The above mentioned configurations are just a few examples, but

it will be out of the scope of this report to mention all possible

configurations.

The examples show that it is possible to enhance the performance

of an absorption cycle substantially, but it does make the system more

and more complex and expensive. It also appears that cycles with water

lithium bromide has a slightly higher COP than cycles with ammonia

water.

Heat source

Another way to categorize absorptions units is by looking at how the heat

is supplied. Direct fired units use gas-fired combustors whereas indirect

fired units have the heat supplied by hot water or steam. The double (and

triple/quadruple) stage system use either gas-fired combustors or steam

since the input temperature has to be higher than for single stage[29].

13


1. INTRODUCTION

1.5.3 Platen Munters cycle

To some extend the Platen Munters cycle is similar to the Carré cycle with

the ammonia/water working media pair. One important difference is

that the total pressure in the Platen Munters cycle is the same throughout

the whole system. This is possible because a third working medium, an

inert gas (hydrogen), is used together with the refrigerant (ammonia) and

the absorbing medium (water).

Figure 1.3: Diagram of Platen Munters cycle. The generator is the same as a desorber. Diagram

downloaded from [26].

The following description refers to the diagram in figure 1.3. The

temperature in the condenser where pure ammonia vapor condenses

determines the pressure of the system, e.g. 12 bars at approximately

30 ◦ C. The condensed ammonia is sent to the evaporator (point 2). In

the evaporator the liquid ammonia is mixed with hydrogen (point 4) and

the partial pressure of ammonia drops which makes it evaporate.

The gas mixture of ammonia and hydrogen is sent to the absorber

(point 3). The ammonia is absorbed by a poor ammonia water solution

(poor in ammonia, entering at point 6) and the hydrogen is sent back to

the evaporator (point 4).

14


1.5. Heat driven cooling

The rich solution (rich in ammonia) from the absorber (point 5) is sent

to the desorber (generator). Heat from an external source (Q G ) evaporates

some of the ammonia which is then sent to the condenser (point 1) and

the cycle starts over.

In theory the Platen Munters cycle could reach the same COP as the

Carré single stage cycle. But since it is difficult to build a large plant, a

COP of only 0,2 to 0,3 is what is achieved in practise [18].

1.5.4 Adsorption

An adsorbent is a material which attracts water vapor. Zeolite is an

adsorbent which has a surface area of 1000 m2 . Another example of a

g

adsorbent is silica-gel/water.

Closed loop

The closed loop is similar to the Carré cycle described previously, but a

significant difference is the intermitted operation.

The adsorber, which contains refrigerant (water vapor), is heated

by an external source while it is isolated from (not connected to) the

evaporator and condenser. This makes both temperature and pressure

increase. When the pressure reaches the condensation pressure of the

refrigerant the adsorber is connected to the condenser while heating of

the adsorber continues.

The condenser and adsorber are disconnected. The condensed

refrigerant is expanded through a valve and sent to the evaporator.

The adsorber is cooled down to the initial temperature. When this

temperature is reached the adsorber is connected to the evaporator.

The evaporating refrigerant is adsorbed by the adsorber. Finally the

adsorber and evaporator are disconnected and the adsorber is heated.

The cycle start over.

The cycle can be upgraded to a quasi-continuous cycle by applying an

extra adsorber bed. The two-bed adsorption cycle is shown in appendix

B.3 page 230. In practise the COP can reach 0,7 if the adsorber is supplied

with heat at 90 ◦ C [35].

15


1. INTRODUCTION

Open loop

In an open loop the air which should be cooled (or dehumidified) is in

direct contact with the adsorption material. The ”Lizzy” system is an

example of a desiccant cooling system which is often used in connection

with sorption chillers or traditional AC’s [35]. It has one drying process,

one heat exchange process and one humidifying process [18]. The cycle

seems to have a potential COP which is below one [35] and will not be

examined further in this report.

16


1.6. Problem delimitation

1.6 Problem delimitation

Topsoe Fuel Cell (TOFC) manufactures solid oxide fuel cell (SOFC) stacks

integrated with other high temperature components in a PowerCore TM .

TOFC develops three different products with focus on three market

segments: Auxiliary Power Unit (APU), Distributed Generation (DG)

and micro Combined Heat and Power (µCHP). The latter two generates

heat (hot water) besides electricity.

The waste heat from a SOFC has a relative high temperature which

might be an opportunity for producing heat driven cooling instead of (or

in combination with) hot water.

TOFC wants to know whether it is technically feasible to integrate

SOFC and heat driven cooling and which market segments that are

suited for such a product - is there a match between generation and

demand for electricity, cooling and heat

The absorption cycle (ABS) with water-lithium bromide solution is

chosen as the heat driven cooling technology, because it seems to have

most advantages for this purpose. As described in previous section it

has one of the best performances and many possibilities to enhance it,

and it is more simple than the ABS cycle with ammonia-water. Although

there is the drawback that the application can only operate above zero

degree Celsius to avoid water freezing.

To determine whether integration of SOFC and ABS is feasible and

whether there is a match between electric power, cooling and heating

demands, it is necessary to make a thermodynamic model, which can

simulate the interplay of such components. Practical experiments could

be an alternative approach but it is both a very expensive and time

consuming task, which is less feasible for a master thesis like this.

17


1. INTRODUCTION

1.7 Problem statement

In order to determine if the SOFC-ABS combination is at all economically

feasible, some rough economical calculations will be made for each of the

three of TOFCs intended market segments, APU, DG and µCHP.

The next step will be to develop a thermodynamic model to simulate

the interaction of the essential components of a SOFC-ABS system such

as SOFC stack, absorption chiller unit, heat exchangers etc. The behavior

of these components must be simulated and then efficiencies (electrical,

cooling, heating and overall) will be determined and compared for

different system configurations.

The model should be so general that it is capable of simulating a

range of different applications with different temperatures and powers,

flows, ambient conditions etc. The purpose of the model should be to

make an estimation of whether the combination of SOFC-ABS is a good

thermodynamical match, and to investigate if and how the electrical and

thermal output of the system can be increased.

An example of an application will be simulated in order to demonstrate

the capabilities of the model.

The following questions will be answered in this report.

• For which market segments is there a good match between SOFC

and absorption cooling

• Which of the system components are especially critical for obtaining

a good performance

• Which system configuration gives the best CCHP performance

• How does climate influence the performance of the CCHP system

• How does the relation between generated electricity, cooling, and

heating match the demand, and can this be improved

18


C H A P T E R

2

MARKET INVESTIGATION

2.1 Introduction

Introduction to the cases

Before looking into the thermodynamical aspects of combining a SOFC

with an absorption cooling unit, a short economical analysis is made in

order to see if there is a market / economical potential for this. Three

different market segments are examined: APU (Auxiliary Power Unit),

CHP (Combined Heat and Power), and DG (Distributed Generation).

Many of the input parameters in the economical model (COPs, prices

etc) have been obtained by contacting several distributers of absorption

and adsorption cooling units asking for preliminary offers. The prices resulting

from this can be seen in appendix A.5 page 219. Other parameters

have been estimated by searching for prices on the internet and reading

reports from agencies such as the ”Energy Information Administration”.

Some data which was not available (e.g. usage time/full load hours for

a given application) has been estimated by the authors. So the results of

the calculations in this section are merely guidelines meant to show if the

synergetic effects of a given application can add up to an amount equal

to or bigger than the extra cost of buying the extra equipment. Sensitivity

analyses have however been made to see how the different input parameters

affect the outcome.

Some general assumptions about the input parameters are described in

19


2. MARKET INVESTIGATION

appendix A.1 page 190.

All the prices in the calculations are made up in real prices (as in

opposition to nominal prices). So the approximation that the electricity

prices and gas prices will only increase with the rate of the inflation

means that the price of a kWh will be the same each year (in real prices).

In all the cases a discount factor of 5% (in real prices) has been used,

corresponding to 7-8% in nominal prices, since inflation is generally 2-

3%. This means that an investment will be regarded favorable if it yields

an average return of 5% (plus inflation) per year or more. This value is

intentionally set a little low, since it is assumed that economical gains

will only be part of the reason for choosing this option. The reduction

of energy consumption will also be good for the image of the company,

since a green image is becoming more and more important, and it is also

likely that the price of CO 2 quotas will increase in the coming years [12].

The economical calculations have been made by calculating the NPV

(Net Present Value) for the net payment (NP) each year:

NPV i = NP · (1 + R D ) −t

Then the accumulated NPV has been found for each year by:

NPV akk,i = Σ i 1 NPV i

Finally the annuity has been found as:

Annui t y i = NPV akk,i · R D /(1 − (1 − R D ) −t )

Since only the expenses have been viewed 1 , it has been chosen to let the

values be positive for expenses. So the smaller the NPV akk and annuities,

the cheaper the solution is.

The full calculations in Excel can be seen in appendix A.2, A.3, and A.4

page 191 to 202.

In the next section the three different market segments will be examined

one by one.

1 The application has a certain need of cooling (and electricity), and as long as it

is provided at the correct temperature and rate it has the same value regardless of the

process used to create it.

20


2.2 Auxiliary Power Unit (APU)

2.2.1 Truck APU

2.2. Auxiliary Power Unit (APU)

Large trucks normally idle their main engine when they are parked in

order to generate air conditioning for cooling the cabin and electricity

for equipment such as microwave ovens, TV, DVD player etc. Idling

the engine for this is, however, quite inefficient, since a diesel engine

efficiency is quite small at low loads. One solution for this problem could

be to mount a SOFC on the truck to generate electricity when parked, and

then use the waste heat to drive an absorption air condition. But there

are two problems:

1. The air conditioning need is in the order of 3kW reference [22], and

the electricity need (excluding electric air condition) seems to be

no higher than 2kW. So if a SOFC should generate the electricity, it

would probably suffice with a unit of 2kWe combined with some

batteries to take care of peak load. And the approximately 2kW

of waste heat would not be nearly enough to generate sufficient

cooling, since the COP of the smallest (4kW cooling) absorption

unit is only 0,4.

2. Even the smallest (4kW cooling) heat driven AC sorption units

weighs 216kg excl HEXes, and takes up a lot of space. This is

disadvantageous on a truck since it is desired to have as much space

as possible cleared for the cargo. Furthermore the extra weight

slightly reduces the maximum cargo load.

Hence the SOFC/ABS AC is not a good match for a truck.

21


2. MARKET INVESTIGATION

2.2.2 Ship APU

Large ships are usually equipped with a separate diesel engine to

generate electricity for light, air conditioning and other auxiliary

equipment. A possibility could be to replace this secondary engine with

a fuel cell which would increase the electrical efficiency, reduce the NO x

and particle emission and lower the noise. If that is done it might be

possible to use the waste heat from the SOFC to drive an absorption air

condition.

An economical estimation of the feasibility has been made by

comparing a ship with a SOFC and a conventional 20kW air conditioning

(electrically driven chiller), relative to a SOFC with a 20kW absorption air

conditioning. The assumptions are as follows:

Assumptions

• Full load usage time fraction = 0,5 (4380 hours per year)

• SOFC electrical efficiency = 0,5

• Absorption cooling power = 20kW

• COP elec.ac = 3,6

• Electrical AC price: 20 kW = 61,000DKK

• Absorption AC price: 20 kW = 200,000DKK (incl HEX’es)

The pay back time is approximately 1,7 years when the absorption air

conditioning runs half the time (approximately 4400 full load hours per

year). During a 10 year lifetime, a total NPV of 520.000DKK can be

saved by using the ABS including the higher purchase price, which is

200.000DKK vs 60.000DKK. The full economical calculations can be seen

in appendixA.2 page 191.

Sensitivity analysis

The biggest impact on the profitability comes from the usage time

fraction, the diesel price, and the SOFC efficiency. A 10% increase of these

variables gives 12% change in the annuity after 10 years. The purchase

22


2.2. Auxiliary Power Unit (APU)

Sensitivity analysis of Ship ABS vs ECH

15

10

Annuity increase [%]

5

0

-10 -5 0 5 10

-5

-10

Purchase price ABS

Purchase price EAC

Diesel price

Efficiency SOFC

Usage time fraction

Discount rate

-15

Increase in variables [%]

Figure 2.1: The percentage increase in annuity gain is shown for a 10% increase of the input

parameters. The annuity is for a lifespan of 10 years. The purchase price of the ABS unit is

200.000DKK. With the chosen parameters the gained annuity is 75.000DKK/y (incl purchase).

price of the ABS unit, however, gives only a 3,5% decrease of the annuity

for a 10% increased price, and the ECH price and discount rate gives even

smaller changes. So the lack of exact knowledge about the price turns out

not to be so critical after all.

The reason for the huge influence from SOFC efficiency and diesel

price is that these factors are determining the price of the electricity

generated for the electrical chiller.

Pay Back Time vs. usage time fraction

As long as the usage time fraction is above 30%, the investment seems to

be quite beneficial (pay back time less than 3 years), but if the usage time

fraction comes below 20%, the pay back time starts to increase quickly.

So for a usage time fraction of 10%, the pay back time is just under 10

years, which is far too long for many companies.

23


2. MARKET INVESTIGATION

Pay Back Time for ABS unit on ship

Usage time fraction [-]

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0,0

0 2 4 6 8 10 12

Pay Back Time [years]

Figure 2.2: The x-axis shows the pay back time for a given usage time fraction (how big a

fraction of the time the Absorption unit runs). The Pay Back Time is for an ABS unit mounted

on an existing SOFC without the cost/gain of the SOFC itself.

Conclusion

If the ABS unit is in use more than about 30% of the time there seems

to be a relatively good economical potential in adding an absorption air

conditioning unit on ships where an SOFC is installed. It has, however,

not been investigated whether the SOFC in itself is profitable to begin

with. Furthermore one of the producers of absorption air conditioning

units claim that they are fairly sensitive to the inclination of the floor [7],

so the rocking motion of ships might pose a problem. This has not been

investigated further though.

24


2.3. Micro Combined Heat and Power (µCHP)

2.3 Micro Combined Heat and Power (µCHP)

2.3.1 Micro CHP - Air condition

If a SOFC is installed in private homes to generate electrical power,

the waste heat can be utilized for domestic hot water as well as space

heating. The space heating, however, is not so relevant during summer

in hot climates, although hot water is still necessary for showering etc.

Many places (e.g. the US or in most asian countries) air conditioners are

employed during most of the summer. So it would be beneficial if the

excessive heat from the SOFC could be used in an absorption cooling

unit to create air conditioning.

By contacting the majority of the producers of ABS units it was

discovered that the smallest available heat driven air conditioning unit

had a cooling power of 4kW, which is in the right range for cooling a

one family house 2 . But the heat demand of the absorption unit was

12.5kW 3 which was far more than the maximum approximately 1kW

heat which would in average be supplied by the SOFC for a 1kW of

electricity production 4 .

Of course the absorption cooling unit could be run at part load, but

the low COP combined with fact that some of the waste heat was to

be used to heat up the hot water, and that some part of the waste heat

can not be extracted due to heat exchanger efficiency below 1, made the

absorption unit a very bad match for the SOFC. Furthermore the small

absorption chillers are fairly expensive per kW, so they have to have a lot

of full load hours in order to make for a reasonable pay back time.

Conclusion

This all meant that there seems not to be a potential for using an

absorption air conditioning unit together with SOFCs in private homes.

2 Assuming a well insulated house or that the climate is not too hot.

3 the small 4kW absorption unit had a COP of only 0,4 whereas most of the larger

single cycle units experienced COPs of around 0,7

4 assuming an electrical efficiency of the SOFC of approximately 0,5 and an expected

electrical power consumption of a single family house of 1kW [32]

25


2. MARKET INVESTIGATION

2.3.2 Micro CHP - Refrigerators

The refrigerators used in hotel rooms are of the absorption type, but

they use the Platen cycle, which means that the COP is only around 0,25

In addition the heat must be supplied at relatively high temperatures

- in the range of 120-180 ◦ C [18]. In hotels the driving heat is typically

provided by an electric heating element which gives quite a high energy

consumption, but this is tolerated since the refrigerator is very quiet. For

other applications like mobil homes LPG is used as energy source.

In theory there might be a potential in combining a SOFC with an

absorption refrigerator for private homes. There is enough waste heat,

since the average waste heat consumption would be in the order of 200W

for the absorption refrigerator (see calculations in Appendix A.3 on page

196).

Assumptions

The following assumptions have been used to calculate the cost (Net

Present Value and annuity) of an electrical and an absorption refrigerator

(all seen from the consumer view point - including taxes and VAT):

• Compressor refrigerator price = 4,000DKK 5 [8]

• Absorption refrigerator price = 11,000DKK 6 [1]

• Compressor refrigerator electricity consumption = 208kWh/y

• Electricity price 2 DKK/kWh (Danish prices)

After 10 years, the annuity cost is 1420 DKK for the absorption and

930DKK for the electrical unit including investment and electricity but

no extra piping or heat exchanger for transferring the SOFC waste heat.

So with a lifespan of 10 years, the absorption unit is estimated to be

about 50% more expensive than the conventional refrigerator including

electricity consumption and purchase price but no piping. The pay back

time will be around 50 years strongly dependent on the discount factor,

which is assumed to be 5%. The full calculations can be seen in appendix

A.3 page 196.

5 Bosch KGV 36X27 225 liter refrigerator and 91 liter freezer.

6 RGE 400 from Åbybro camping og fritid 224 liter refrigerator + 76 liter freezer.

26


Pay Back Time vs. refrigerator price

2.3. Micro Combined Heat and Power (µCHP)

12000

Pay Back Time for absorption refrigerator

ABS refrigerator Purchase

Price [DKK]

10000

8000

6000

4000

2000

0

0 5 10 15 20 25

Pay Back Time [years]

Figure 2.3: The x-axis shows the pay back time for a given purchase price of the absorption

refrigerator (i.e. how long time does it take before the ABS refrigerator becomes cheaper than a

regular electrical refrigerator.

The price of the normal refrigerator used for comparing is 4,000DKK,

so if the absorption refrigerator could be made for the same price 7 , the

pay back time would be zero years. If the lifetime of both types of

refrigerators is 10 years, the price of the absorption unit should be no

more than 7,000DKK if the investment is to become favorable within the

expected 10 year lifespan. Already with a price of 10,000DKK, the pay

back time exceeds 25 years.

Sensitivity analysis

It appears that the most important factor influencing the profitability of

the ABS refrigerator is the purchase price of the unit itself. If this is

increased by 10%, the deficit of the absorption solution is increased by

30%.

The electricity price, annual electricity consumption and the purchase

price of the electrical refrigerators, are all approximately equally

7 with no significant costs to installation and piping from the SOFC exhaust gas

27


2. MARKET INVESTIGATION

Sensitivity analysis of refrigiator ABS vs ECH

30

20

Annuity increase [%]

10

0

-10 -5 0 5 10

-10

Purchase price ABS

Purchase price El-unit

-20

Electricity price

Anual electricity consump

-30

Discount rate

Increase in variables [%]

Figure 2.4: The annuity is already negative to begin with (suggesting that the ABS unit is more

expensive than the electrical counterpart), so an increase in y-value means that using the ABS

unit becomes an even bigger disadvantage.

influential. A 10% increase in their value reduces the deficit of the

absorption refrigerator around 10%.

The discount rate does at first glance not appear so influential, but

since its value can easily differ 50% from the estimated/chosen value, it

is a significant source of uncertainty.

Conclusion

From an economical view point, using SOFC waste heat for refrigerators

doesn’t seem so advantageous. But it does depend very much on

the purchase price of the absorption unit, so if this can be reduced

by 1/3 from the current levels, it starts to make sense economically,

although piping and installation might change the picture somewhat in a

disadvantageous direction. Furthermore the CO 2 savings have not been

assigned any value in these calculations.

Another factor to consider is if it is inconvenient to place the

refrigerator right next to the fuel cell, since you normally prefer to have

the refrigerator in the kitchen and the SOFC in the basement near the hot

water storage.

28


2.4 Distributed Generation (DG)

2.4. Distributed Generation (DG)

As described in chapter 1 distributed generation has many applications.

Hotels are appropriate for a case study since they are often placed in

areas with a hot climate and since the guests expect comfort, hotels are

normally equipped with air conditioning. There is also a substantial

demand for electricity (for misc appliances) and hot water (primarily for

showering). It could be expected that the demand for the three end-use

products (electricity, cooling and hot water) have a good match.

Since traveling still increases both for business and pleasure, more

hotels are being build and these require air conditioning, meaning an

increasing demand for cooling and thus a potential increase of the market

for DG.

So it is examined if a Hotel could use a combination of a SOFC and

an ABS (Absorption cooling) unit to provide electricity, cooling, and heat

for domestic hot water in an economical way. The input parameters and

assumptions are as follows:

Input/assumptions

• 230 room hotel (18.000m 2 )

• 2 different climates - normal (hot summer, cold winter) vs hot all

year

• COP E AC = 4,0

• COP ABS = 1,3

• η SOFC = 0,5

• Gas price 0,20DKK/kWh (see appendix A.6 page 224) [17]

• Electricity price = 0,75DKK/kWh (see appendix A.6 page 224) [10]

+ [11]

• SOFC price 2.650 DKK/kW (=$500/kW) [16]

• ABS price 3.700DKK/kW 8

8 Derived from the market investigation in appendix A.5 page 221

29


2. MARKET INVESTIGATION

• ECH price 1.800DKK/kW 9

• ABS electricity consumption neglected

• Discount factor 5%

2.4.1 Three solutions

In order to examine which part of a profitability that arrives from the

SOFC in itself and which part that arrives from adding the absorption

chiller, three configurations are now considered and compared:

(A) Grid + ECH. All electricity is bought from the grid, and the air

conditioning is purely electrical (ECH). Hot water and space heating

is done with natural gas (efficiency 1,0). So this is the normal

configuration of a hotel.

(B) SOFC + HotWater + ECH. A SOFC is installed and the waste

heat is used to heat up all the hot water for the hotel, but the air

conditioning is still made by an electrical unit. The size of the SOFC

is made so the net production of electricity equals the total electricity

demand of the hotel including the electrical air condition when the

SOFC runs at full load 24/7. This means importing electricity from

the grid during peak load hours, while electricity will be sold to the

grid during hours with less electricity consumption in the hotel. It

is assumed that the buying and selling price for the electricity is the

same 10 . Space heating is done by natural gas.

(C) SOFC + HotWater + ABS + ECH. A SOFC is installed and the waste

heat is used to heat up all the hot water as well as running an

absorption air conditioner. Due to heat exchanger efficiency it is

assumed that only 80% of the waste heat can be extracted from the

exhaust gas. The water heating is done entirely with waste heat, and

the rest of the waste heat energy is used int the absorption cooling 11 .

9 Derived from the market investigation in appendix A.5 page 221

10 This is a somewhat crude assumption, even though the net export of electricity is

zero but again these calculations are only approximations, meant to show the overall

trends.

11 in praxis the absorption cooling unit will of course be the physically first unit to use

some of the waste heat, since it needs higher temperatures than the hot water heating.

But the ABS is allowed no more waste energy than what will leave enough waste heat

for the water heating.

30


2.4. Distributed Generation (DG)

In the hot climate, the absorption unit is set to run all year, whereas

it only runs during the summer in the normal climate (50% of the

time). Since there is not enough waste heat to cover all of the air

conditioning demand, an electrical air conditioner must be used to

supply the rest of the cooling service. Space heating is in all cases

done by natural gas.

2.4.2 Hot vs Normal climate

The climate must be expected to have a big effect on the advantage of

absorption chillers, since a hot climate will facilitate a bigger cooling

demand. Hence the following two climate-cases are considered:

Normal climate

Electricity consumption and hot water need is assumed evenly distributed

throughout the year (the consumption of electricity, air conditioning, domestic

water heating and space heating taken from [13] 12 ). The entire

cooling energy demand is assumed to be evenly distributed throughout

the 6 month of the summer. The air conditioning units (ABS and electrical)

are designed and sized for summer use, and in winter time they

just shut down completely. The space heating will also correspond to the

average demand of the USA and is provided by natural gas.

Hot climate

In the hot climate, a cooling demand is assumed to be present all year,

and hence the needed cooling energy per year is assumed to be double

that of the normal climate cooling need. But the space heating is assumed

to fall to zero since it is hot all year.

The electricity and hot water consumption will be exactly the same as

in the normal climate (showering etc. is still needed in hot climates).

12 The normal climate is assumed to be close the average of the three climates

investigated in [13], which is: Anaheim (Mild climate), Las Vegas (Hot climate), and

Minneapolis (Cold climate)

31


2. MARKET INVESTIGATION

2.4.3 Results

The full results and input can be seen in appendix A.4 page 202. First

of all it turns out, that the waste heat from the SOFC is not at all

enough to cover the entire cooling demand even though a double stage

absorption chiller is used (with a COP of 1,3). In the normal climate

the ABS chiller supplies ¼ of the yearly cooling demand and in the

hot climate, it supplies 1/3 because the SOFC system must be larger in

order to generate additional electricity for the supplementary electrical

air conditioner. This does, however, mean that the small ABS chiller can

run as base load, and hence have a lot of full load hours per year since

the daily variation of cooling demand is probably not so big that it falls

below 1/3 of the average daily cooling demand. But of course both ECH

and ABS will have to be shut off during wintertime in the normal climate.

If the lifetime of all the components in the system is 10 years, the total

cost (Net Present Value) for system components, natural gas or electricity

imported from the net is calculated to be the following:

Hot Climate

Case A: 27mil. DKK (-SOFC, -Absorption unit)

Case B: 15mil. DKK (+SOFC, -Absorption unit)

Case C: 14mil. DKK (+SOFC, +Absorption unit)

With an estimated SOFC price of around 2500DKK/kW, the investment

cost of the SOFC will be just above 1mil. DKK. And hereby a yearly electricity

consumption of 3,0mil. DKK can be exchanged with a gas consumption

of 1,4mil. DKK. So if the lifetime is 10 years, 13mil. DKK can

be saved in fuel (with a discount rate of 5%), and the total surplus will

then become 12mil. DKK.

If an ABS unit is used, the additional investment (compared to a purely

electrical air conditioner) will be 0,4 mil. DKK 13 , and the savings in

fuel/electricity will be around 1,9 mil. DKK. So adding an absorption

13 If no ABS unit is used, the electrical chiller will cost 1,5mil. DKK. If the ABS is

used, the unit in itself will costs around 1,0mil. DKK and the supplementary electrical

air conditioner will cost 0,9mil. DKK.

32


2.4. Distributed Generation (DG)

air conditioner will give a total saving of around 1,5 mil. DKK 14 . So the

investment seems to be quite profitable.

Normal Climate

For this climate the numbers are a little closer:

Case A: 26mil. DKK (-SOFC, -Absorption unit)

Case B: 16mil. DKK (+SOFC, -Absorption unit)

Case C: 16mil. DKK (+SOFC, +Absorption unit)

For this climate the savings of using an SOFC is slightly decreased from

12 to 10mil. DKK. But the gain of using the ABS unit is significantly

reduced from around 1,5mil. DKK to 0,4mil. DKK. So it still looks

profitable although not as good as for the hot climate.

Pay Back Time for the entire system (case A vs case C)

Figure 2.5 shows how long time it takes before case C becomes cheaper

than case A when running a hotel i.e. how long does the entire

SOFC+ABS system has to live in order to be cheaper than just purchasing

the electricity from the electrical grid and use an electrical air conditioner

for cooling. It is seen that if the purchase price of the SOFC is around

the expected 2500DKK/kW, the pay back time for the entire system will

be around 1 year for both climate cases. And even if the SOFC price

is as high as 10.000DKK/kW the payback time is less than 3 years, but

at this price it is seen that the SOFC+ABS investment is slightly more

advantageous for the hot climate.

So if the SOFC price can just be lowered to around 10.000DKK/kW it

could become profitable for at hotel to purchase the SOFC + ABS system.

But the comparison of case A and C says nothing about whether it is

the addition of the absorption chiller or the SOFC in itself which makes

the investment profitable. Hence in the following case B and C will be

compared to see what effect the addition of the absorption chiller has on

the economics (assuming that the SOFC is used either way).

14 The NPV values of case B and C for the hot climate stated above have been rounded

off from 15,27mil. DKK and 13,78mil. DKK respectively

33


2. MARKET INVESTIGATION

16000

14000

Pay Back Time: Entire System (SOFC+ABS)

SOFC Price [DKK/kW]

12000

10000

8000

6000

4000

2000

0

Normal Climate

Hot Climate

0 1 2 3 4 5

Time [years]

Figure 2.5: The x-axis shows the pay back time for a system consisting of a SOFC + ABS +

Hot water heating compared to pure electricity import from the electrical grid + electrical air

conditioner. The varied parameter (y-axis) is the purchase price of the SOFC.

Pay Back time for the ABS unit (case B vs case C)

From figure 2.6 it can be seen how long it takes for the ABS unit to repay

itself. As expected the pay back time is much shorter for the hot climate

than for the normal climate. This is mainly because the number of full

load hours for the ABS is much bigger for the hot climate, where it runs

all year, so more electricity is saved. With the current prices for the ABS

of just below 4000Dkk/kW the pay back time is 1,5 years and 4 years for

the hot and normal climate respectively. It is seen, however, that the pay

back time is fairly sensitive to the purchase price of the ABS. And if the

purchase price goes below approximately 2000DKK/kW the ABS unit

becomes profitable from day one since this is the same as an electrical air

conditioner would cost.

34


2.4. Distributed Generation (DG)

ABS Price [DKK/kW]

10000

9000

8000

7000

6000

5000

4000

3000

2000

1000

0

Pay Back Time: Absorption Cooling Unit (ABS)

Normal Climate

Hot Climate

0 2 4 6 8 10 12

Time [years]

Figure 2.6: The x-axis shows the pay back time if an ABS is added to a system already featuring

a SOFC system. The varied parameter (y-axis) is the purchase price of the ABS unit.

Annuity for all three cases (A vs B vs C)

The pay back time only says how long it takes for the system to become

profitable, not how much money will be spend or saved. So now the

annuity (average annual cost) is viewed.

The three different solutions (A,B,C) are now compared by looking

at their annuity 15 , assuming a life time for all of the components of 5

years, 10 years and 15 years respectively. In the hot climate (figure 2.7A)

it appears that by far the biggest amount of the savings are achieved by

purchasing the SOFC unit - this reduces the annual price by a little more

than 40% of the present costs. Adding the ABS reduces the price further

about 10% compared to when the SOFC is used alone.

For the normal climate (figure2.7B) the SOFC still reduces the price

by a little less than 40%. The effect of the ABS is however a lot smaller

than for the hot climate so only 2-3% of the yearly costs can be saved by

using an ABS unit.

It should be noted that the profitability of the SOFC as well as

15 the annuity includes gas, electricity, and purchase of SOFC, ABS and ECH

35


2. MARKET INVESTIGATION

Annuity price [DKK/y]

4'000'000

3'500'000

3'000'000

2'500'000

2'000'000

1'500'000

1'000'000

500'000

HOT climate.

Annual price for all energy equipment + gas and electricity use

Annuity_5

Annuity_10

Annuity_15

Annuity price [DKK/y]

4'000'000

3'500'000

3'000'000

2'500'000

2'000'000

1'500'000

1'000'000

500'000

Normal climate.

Annual price for all energy equipment + gas and electricity use

Annuity_5

Annuity_10

Annuity_15

0

EL SOFC+WH SOFC+WH+ABS

0

EL SOFC+WH SOFC+WH+ABS

Figure 2.7: The annuity (yearly cost) is examined for an expected lifespan of the SOFC, ABS,

and ECH unit of 5, 10, and 15 years respectively. A: Hot climate. B:Normal climate.

SOFC+ABS does not depend so much on their lifetime because the

purchase price of the SOFC and ABS unit is quite small relative to the

yearly cost of natural gas and electricity. The SOFC cost is approximately

equal to the yearly savings in fuel (1,0 to 1,2 mil. DKK). The cost of the

ABS unit is around 1mil. DKK, but at the same time the price of the

supplementary air conditioning unit decreases from 1,4mil. DKK to 0,9

mil. DKK. 16

Sensitivity analysis

Since there are three setups (A, B and C), all in both hot and normal

climate, a sensitivity analysis could be made for a lot of different setups.

Here it has however been chosen to look only at case B vs C for the

hot climate. I.e. the investigated parameter is the Net Present Value

of the difference in cost between using a SOFC system with an ABS air

conditioner vs a SOFC system with a normal electrical air conditioner.

16 The reason that the annuity of the case with pure electricity import from the grid

(left bars) changes with the component lifetime is that it has been assumed that the ECH

has the same lifetime as the ABS and SOFC unit (either 5, 10 or 15 years). Their lifetime

could have been changed individually, but this would generate even more graphs.

36


2.4. Distributed Generation (DG)

Net Present Value increase [%]

Sensitivity analysis: SOFC+HW+ABS vs SOFC+WH

30

20

10

0

-10 -5 0 5 10

-10

-20

ECH price

COP_ABS

Electricity price

COP_ECH

Discount rate

Gas price

eta_SOFC

SOFC price

ABS price

-30

Increase in variables [%]

Figure 2.8: The y-axis shows the increase in total savings (Net Present value) by using a

SOFC system with ABS instead of importing electricity from the grid and using an electrical air

conditioner in the hot climate. The lifetime of the system has been set to 10 years.

If all prices are as assumed, and the life time of all components is 10

years, then the NPV of the savings by using the ABS with the SOFC (case

C) rather than only using the SOFC, is 1,5 mil. DKK as mentioned earlier.

A positive value of e.g. 10% on the y-axis on figure 2.8 means that the

savings by using the ABS is 10% bigger (i.e. 1,65 mil. DKK)

The efficiency of the fuel cell is seen to have by far the biggest

influence on the result. A bigger SOFC efficiency makes the ABS less

profitable because of a higher efficiency leaving less waste heat for the

ABS, and because the electricity for the ECH (produced by the SOFC)

becomes cheaper.

The gas price and the COP of the two types of chillers are also quite

influential. And the influence of the gas price is even more important

than the figure might indicate, since it changes significantly over time

(price can easily change +/-50% from the estimated value), whereas the

COP of the ABS and ECH is a lot more stable and predictable (the real

COP is likely to be within +/- 10% of the estimated value).

37


2. MARKET INVESTIGATION

2.4.4 Conclusion

In general both the SOFC and the ABS seem to have an economical

potential. The SOFC profitability depends a lot on the purchase

price, and ABS profitability depends a lot on the gas price and SOFC

efficiency. Furthermore it seems that hot climates make the ABS far more

advantageous because of the increased usage fraction.

The general tendency is that the addition of the SOFC (Case B vs

A) is very profitable, since the electricity generated by the SOFC is

only 0,4DKK/kWh - about half the price of the electricity form the grid

(0,75DKK/kWh). So the total cost is almost cut in halves, and 12mil.

DKK is saved over a 10 year period with an original investment of

around 1,0mil. DKK for the SOFC system. This does however require the

fuel cell system to last 10 years, so stack degradation has to be minimized

from today’s level.

But since the yearly savings of electricity is 3,0mil. DKK and the extra

cost of natural gas is 1,5mil. DKK, the purchase price of the SOFC (1,0-

1,2mil. DKK) will be earned back within the first year!

If an ABS unit is used, the additional investment (compared to a purely

electrical air conditioner) will be 0,4 mil. DKK, and the electricity savings

in 10 years are around 1,9mil. DKK for the hot climate, so this looks very

profitable with a pay back time or around 1,5 years).

It must, however, be noted that there are a lot of assumptions and simplifications

in the calculations, such as neglected installation costs, piping,

maintenance, equal selling and buying prices of electricity and nonfluctuation

cooling and electricity consumption during the day (the latter

might be solved by a storage of cold water and electricity).

38


2.5. Conclusion of the whole market investigation

2.5 Conclusion of the whole market

investigation

From the economical investigations it has been concluded that the two

areas appearing to have the biggest advantage of using an absorption

cooling unit in conjunction with a SOFC is the ship APU and the hotel

DG. In both these cases it looks like there is a definite market potential

with the pay back time being just below 2 years (although various

assumptions and neglecting of maintenance, installation costs etc. can

have made the outcome a little too optimistic).

But it seems that the idea of combining the two technologies has a

potential, so it has been decided to carry on with the project and create a

thermodynamical model of the combined system.

39


C H A P T E R

3

COMPONENT DESCRIPTION

3.1 Introduction

3.1.1 EES

The model of the SOFC system and the absorption cycle is carried

out in Engineering Equation Solver (EES) which is a program that

solves algebraic as well as differential equations. One advantages of

this program is that the equations can be stated randomly. Another

advantage is that EES provides fluid property functions for a lot of

different species.

Structure

It is attempted to build up the model by a structure of subroutines in

order to have an overview of the entire system and to reuse components

and functions as much as possible. Each component in the model

corresponds to a physical unit or a part of it. E.g. the evaporator and

the absorber are modeled as to separate components, but physically they

are integrated as one unit.

Most components are modeled as modules which are placed in

separate files. The equations in a module are called from the main system

file and solved simultaneously with equations in other modules, just like

the equation were put all together.

41


3. COMPONENT DESCRIPTION

The helping procedures, on the other hand, are solve in a chronological

sequence like normal programming languages. This reduces the time for

solving these equations.

3.1.2 Components

In section 3.2 to 3.14 each component will be described in detail, but first

common properties of the components will be described in the following

All of the components are modeled as zero dimensional components i.e. the

system can be scaled to any size keeping all extensive variable at the

same ratio. Thus it is necessary to change a lot of parameters if the size

of the system should have any affect on the system performance. For

instance, the blower efficiency would in reality change a little if the size

of the system is changed, but this does not happen automatically in the

model - it can only be done manually by changing the blower efficiency

parameter.

Each component has one or more inlets and outlets (points) each with

a unique name, e.g. ”DES2 ss,i ” which can be interpreted as ”desorber

number two: strong solution, inlet”. All of these points are associated

with a state number. If two different points (normally from two different

components) are associated with the same state number, it means that

those two components are connected through the respective in- and

outlets. This feature also make it relative easy to build up the system

or reconfigure components in the system. This is described further in

chapter 4.

Fluid properties

It is assumed that the fluid properties does not change in between

components, i.e. that losses in the piping system are neglected.

The entire system consists of seven different fluid streams (each

composed of one or more species) which are indicated by a specific color

to make it easy to distinguish those from each other, see figure 4.1 page

80 or in appendix G page 293. Some streams might be variants of the

same fluid.

42


3.1. Introduction

The seven stream are indicated by their corresponding color in the

following list:

1. Flue gas (including atmospheric air and fuel input).

2. External heat transfer loops.

3. Domestic hot water.

4. Atmospheric air.

5. Absorption cycle: Refrigerant.

6. Absorption cycle: Weak solution of LiBr water.

7. Absorption cycle: Strong solution of water-LiBr.

The flue gas stream is used in the components around the SOFC

component (SOFC sub-system) and in the heat exchangers connecting it

to the ABS cycles and Hot Water heating. These components have been

modeled to accept seven different chemical species: C H 4 , CO, CO 2 , H 2 ,

H 2 O, N 2 and O 2 . All seven species are assumed to behave like ideal

gases, i.e. the enthalpy is independent of pressure (and there are no

phase changes). This can be assumed since the pressure change in the

components is relatively small.

The reference pressure and temperature for enthalpy of these gasses

are 100 kPa and 25 ◦ C respectively. The enthalpy of formation is included

in the chemical compounds.

A mixture of the species is assumed to be ideal, which means that the

physical property of a mixture is the sum of properties of each species in

the mixture.

The enthalpy flow rate Ḣ at state point ”j” is calculated as the sum of

mass flow rate times enthalpy of species ”k”:

Ḣ j =

7∑

ṁ j,k h j,k (3.1)

k=1

The fluid in the external heat transferring loops and domestic hot water is

sub cooled water. A real water fluid property function is applied in these

streams. To keep the water sub cooled, an sufficiently high pressure is

applied.

43


3. COMPONENT DESCRIPTION

The components in the Absorption cycle operate with LiBr and/or water.

The Absorption cycle can be split up into two sub cycles: a refrigeration

cycle and a solution cycle. The water used in the refrigeration cycle is a

real fluid since the fluid undergo phase transition.

The water-LiBr solution in the solution cycle is also calculated by a

real fluid function ”LiBrH2O”. The function is valid for saturated liquid

only, e.g. the quality qu = 0. Several properties, e.g. pressure and heat

capacity are calculated from input of temperature and the mass fraction

of LiBr, w, which must be in the range of 0 to about 0,75 1 (can be seen in

phase diagram in appendix B.4.1 page 231).

Since the function only work for saturated liquid, just two state

variables are necessary to define the state. The properties for both

refrigerant and the cooling water are determined by the internal EES real

fluid function ”Water”.

General assumptions

All heat flow rates ˙Q and power Ẇ are calculated as positive quantities.

It is assumed that the components don’t leak any fluid to the surroundings:

ṁ o = ṁ i (3.2)

Potential and kinetic energy is neglected for all components. The

energy required to circulate water in the external heat transferring loops

(including domestic hot water) has been neglected as well. The heat

loss from the components to the surroundings is assumed to be zero if

nothing else is stated, but can be given by a heat loss parameter for each

single component.

Wherever it is feasible, the heat exchangers are assumed to be

configured in counterflow.

1 Very dependent on temperature and pressure. The range is valid for the normal

operation of an absorption cycle.

44


3.2. Absorber - ABSO

3.2 Absorber - ABSO

In the absorber the strong water-LiBr solution absorbs the refrigerant

which is water. The absorption process is exothermic. The heat from

this process is removed by an external cooling circuit, which is water, see

figure 3.1.

When the weak solution (ws,o) leaves the absorber it is assumed to be

saturated liquid. The strong solution is either a liquid (can be sub cooled)

or in the two phase region. The refrigerant can be either in the two phase

region, saturated vapor, or super heated.

Figure 3.1: Absorber component. Strong solution (ss,i) (rich in LiBr), is absorbed by the

refrigerant (r,i) and sent out as weak solution (ws,o). The absorption process is cooled by a

fluid (c,i) and (c,o).

At the inlet of the absorber, water vapor (at low temperature) and

strong LiBr solution (at a higher temperature) is mixed. It is quite

difficult to determine whether the water vapor and strong LiBr solution

are perfectly mixed just after the inlets, before they become cooled, or

if the mixing happens during the cooling - and this is very difficult

to calculate in a Zero dimensional model. In reality there must be

some temperature distribution throughout the absorber, but finding this

temperature distribution is not an easy task, and it is not required for

the energy balance, mass balance, state variables (at inlets/outlet) etc.

to work. It is only relevant for designing the heat exchanger part of

the absorber and setting the parameters associated with it. So finding

the temperature distribution has been accomplished by the following

reasoning:

Since the cooling circuit removes energy from the solution, the

temperature around the inlet of the solution and refrigerant (T st ar t ) must

be larger than (or at least equal to) the outlet temperature (T ws,o ). (This is

confirmed by [20], page 537).

∆T minws,o = T ws,o − T c,o (3.3)

45


3. COMPONENT DESCRIPTION

T [° C ]

T ss , i

T c ,o

T start

ΔT min ,ws , o

T ws ,o

T c ,i

˙Q[kW ]

Figure 3.2: ABSO: The temperature of the hot fluid into the absorber is not known fore sure, so

the heat exchanger part is made as co-flow to make sure that no approach temperature difference

is smaller that the one given by ∆T min .

So by modeling the heat transfer in the absorber as a co-flow heat exchanger

(figure 3.2) there should be no doubt that the smallest approach

temperature difference (∆T min ) occurs between the solution outlet and

the cooling circuit outlet: Due to lack of knowledge about the temperature

distribution the effectiveness of the heat transfer is not determined

(it is not known which flow has the smaller heat capacity flow, since the

temperature distribution of the solution is not known), so for this component,

only ∆T min is calculated.

The amount of heat to be removed by the cooling circuit is calculated

by the energy balance, which includes a loss to the surroundings ( ˙Q loss ),

which should be zero (adiabatic component) or positive (heat loss to the

surroundings).

Ḣ ss,i + Ḣ r,i + Ḣ c,i = Ḣ ws,o + Ḣ c,o + ˙Q loss (3.4)

A mass balance of H 2 O as well as LiBr is needed, but since the absorber

is connected in a closed loop, they are not given explicitly (in one of

the components in a closed loop, the mass balance must be omitted to

avoid over specification). So the following two mass balances are given

46


3.2. Absorber - ABSO

implicitly through the desorber:

ṁ ws,o = ṁ ss,i + ṁ r,i (3.5)

ṁ ws,o · w ws,o = ṁ ss,i · w ss,i (3.6)

The pressure losses (given as a negative pressure increases) are defined

as three different ∆P parameters:

p ws,o = p r,i + ∆p r (3.7)

p ws,o = p ss,i + ∆p ss (3.8)

p c,o = p c,i + ∆p c (3.9)

47


3. COMPONENT DESCRIPTION

3.3 Blower

Figure 3.3: Blower component. ”i” is the inlet and ”o” is the outlet. Ẇ is the blower power.

It is assumed that no chemical reaction takes place in the blower, so

the mass flow of each species out of the blower is equal to its mass flow

into the blower. All species have been modeled as ideal gasses. They are

hence in gas phase all the time, and the enthalpy only depends on the

temperature, while the entropy also depends on the pressure. The blower

uses an isentropic efficiency to determine the enthalpy and temperature

(i=inlet, 2=state just after the compression).

η i s = Ḣ2,i s − Ḣ i

Ḣ 2 − Ḣ i

(3.10)

The blower work is then determined as the enthalpy flow difference

during the compression.

Ẇ = (Ḣ 2 − Ḣ 1 ) (3.11)

The energy balance then includes the parameter ˙Q loss which is the

amount of heat lost to the surroundings (assumed to happen after the

compression). So the outlet temperature is determined from the enthalpy

flow in the outlet (o) which will be:

Ḣ o = Ḣ i +Ẇ − ˙Q loss (3.12)

48


3.4. Burner - BURN

3.4 Burner - BURN

Figure 3.4: Catalytic burner component. The fuel and air inlets are ”i,1” and ”i,2” respectively.

Additional fuel (C H 4 ) can be added directly at ”CH4,add,i”. ”o” is the exhaust gas outlet.

The burner makes all the combustibles at the inlets react 100% with

oxygen to produce water and carbon dioxide by the following three

reactions:

C H 4 + 2O 2 → CO 2 + 2H 2 O

CO + 1 2 O 2 → CO 2

H 2 + 1 2 O 2 → H 2 O

∆H o c

∆H o f

∆H o f

= +890,00

kJ

mol

= −282,62

kJ

mol

= −241,82

kJ

mol

(3.13)

(3.14)

(3.15)

The release of chemical energy is then translated into temperature of the

gasses and a heat loss to the surroundings which is set manually:

Ḣ i − Ḣ u − ˙Q loss = 0 (3.16)

The pressure loss over the burner is set manually by the pressure increase

∆p (which will always be negative):

p o = p i + ∆p (3.17)

49


3. COMPONENT DESCRIPTION

3.5 Condenser - COND

Figure 3.5: Condenser component. Refrigerant enters at ”r,i” and leaves at ”r,o”. ”c,i” and

”c,o” are the cooling water in- and outlet respectively.

In the Condenser the refrigerant (H 2 O) comes in as either superheated

gas, saturated gas or in the two-phase region. The cooling water facilitates

a phase change of the refrigerant which comes out of the condenser

as a liquid. (The refrigerant can not be subcooled, since the outlet enthalpy

is found by the stem quality (and pressure)).

In case the refrigerant comes in as saturated steam or in the two phase region,

the calculation of closest approach temperature difference and heat

exchanger effectiveness will be straight forward. But if the refrigerant

comes in as superheated steam (which is the case in this model), things

become a little more complicated:

By far the most likely point for ∆T min to appear is where the

refrigerant becomes saturated steam, but in theory ∆T min could also

appear at the refrigerant inlet (se figure 3.6). So to make sure that the

(closest) approach temperature difference is not specified at a wrong

point, ∆T min is calculated in both inlet, outlet, and midpoint (saturated

gas) 2 .

∆T minr,i = T r,i − T c,o (3.18)

∆T minr,o = T r,o − T c,i (3.19)

∆T minmp = T r,mp − T c,mp (3.20)

The effectiveness is equally complicated. Since the closest approach

temperature difference occurs at the midpoint, the effectiveness must

either be specified between the refrigerant inlet and the midpoint or

between the refrigerant outlet and the midpoint.

2 In reality ∆T minmp should be specified, but EES crashes when this is attempted, so

instead ∆T minr,o is given (a little too high), so that ∆T minmp reaches the relevant value.

∆T minr,i should not be given explicitly, since it depends very much on the degree of

superheating at the refrigerant inlet.

50


3.5. Condenser - COND

T [° C ]

ΔT min ,r ,i

T r ,o

ΔT min ,r ,o

ΔT min ,mp T c ,o

T c ,i

T r ,i

˙Q[kW ]

Figure 3.6: Condenser: Approach temperature differences are calculated both in the ends and at

the middle to make sure that the one being given as a parameter actually is the smallest of them.

The problem can be viewed as having two heat exchangers - one

for the superheated region, and one for the two-phase region. Both

effectiveness are calculated, and the larger of them is the one to be

specified (if not the closest approach temperature difference is specified

instead):

ɛ SH = T r,i − T r,mp

T r,i − T c,mp

(3.21)

ɛ 2P = T c,mp − T c,i

T r,mp − T c,i

(3.22)

Where SH = Super Heated region, and 2P = Two-Phase region.

The refrigerant midpoint temperature (T r,mp ) is calculated from the

saturation temperature at the given pressure. The cooling water

midpoint temperature (T c,mp ) is calculated from an energy balance

between refrigerant inlet and midpoint:

(h c,o − h c,mp ) · ṁ c = (h r,i − h r,mp ) · ṁ r (3.23)

The amount of heat to be removed by the cooling circuit is calculated

by the energy balance, which includes a loss to the surroundings ( ˙Q loss ),

which should be zero (adiabatic component) or positive (heat loss to the

51


3. COMPONENT DESCRIPTION

surroundings).

Ḣ r,i + Ḣ c,i = Ḣ r,o + Ḣ c,o + ˙Q loss (3.24)

The mass balance is specified for the refrigerant as well as the coolant.

ṁ r,o = ṁ r,i (3.25)

ṁ c,o = ṁ c,i (3.26)

The pressure losses (given as a negative pressure increases) are defined

as two different ∆p parameters:

p r,o = p r,i + ∆p r (3.27)

p c,o = p c,i + ∆p c (3.28)

52


3.6. Desorber - DES

3.6 Desorber - DES

In the desorber the weak water-LiBr solution enters (either sub cooled or

saturated liquid) and is mixed with the solution in the desorber, which

is heated up by the heating water circuit. Hereby the refrigerant (water)

is evaporated, and strong solution LiBr (which is saturated) is returned

towards the absorber. See figure 3.7.

Figure 3.7: Desorber component. Weak solution (ws,i) enters the desorber and is heated by the

heating water (h,i and h,o). Refrigerant in gas phase (r,o) is sent out through an outlet at the

top, while the strong solution (ss,o) leaves at the bottom of the desorber.

The desorber is made up by a reservoir of solution in which some

heat exchanger tubes with the warm heating water run. On top there is a

gas phase of refrigerant. In the model it is assumed that the temperature

is the same throughout the liquid phase and the gas phase. So when

the weak LiBr solution enters the reservoir, it instantly becomes perfectly

mixed with the rest of the liquid phase.

It is also assumed that the outlet temperature of the refrigerant

(superheated steam) is the same as the outlet temperature of the solution,

after all, the water has been evaporated from the solution (at which point

they must have the same temperature), and no heating or cooling is

assumed to happen to the gas after the evaporation (hence T ss,o = T r,o ),

see figure 3.8.

Since it is assumed that the temperature of the solution is the same

throughout the desorber, only the heating water changes temperature.

Hence the closest approach temperature difference appears between

the outlet temperature of the heating water (T h,o ) and the mutual

temperature of the refrigerant and solution (T ss,o = T r,o ):

∆T minr,o = T h,o − T ss,o (3.29)

Since only the heating water changes temperature during the heat

exchange process, the effectiveness will be based on the heating water

53


3. COMPONENT DESCRIPTION

T [° C ]

T h , i

T h , o

ΔT min ,r ,o

T ss , o

T r ,o

T ws ,i

˙Q[kW ]

Figure 3.8: Desorber: The solution/gas temperature is assumed to be constant throughout the

desorber. So the closest approach temperature difference will be between the heating water outlet

and the common solution temperature.

heat capacity flow:

ɛ = T h,i − T h,o

T h,i − T ss,o

(3.30)

The amount of heat to be added by the heating circuit is calculated by

the energy balance, which includes a loss to the surroundings ( ˙Q loss ),

which should be zero (adiabatic component) or positive (heat loss to the

surroundings).

Ḣ ws,i + Ḣ h,i = Ḣ r,o + Ḣ ss,o + Ḣ h,o + ˙Q loss (3.31)

A mass balance is made for H 2 O as well as LiBr (total inlet = total outlet):

ṁ r,o + ṁ ss,o = ṁ ws,i (3.32)

ṁ ss,o · w ss,o = ṁ ws,i · w ws,i (3.33)

were w is the concentration of LiBr in the solution. The pressure losses

(given as a negative pressure increases) are defined as three different ∆P

parameters:

p r,o = p ws,i + ∆p r (3.34)

p ss,o = p ws,i + ∆p ss (3.35)

p h,o = p h,i + ∆p h (3.36)

54


3.7. Evaporator - EVAP

3.7 Evaporator - EVAP

Figure 3.9: The evaporator has two sets of inlet and outlet: refrigerant (r,i and r,o) and chilled

water (chill,i and chill,o).

In the evaporator heat is transferred from an external circuit of

chilling water to the refrigerant. It is assumed that the refrigerant is in

the two-phase region when it enters the evaporator. The refrigerant in

the outlet can either be saturated gas or in the two-phase region.

The closest approach temperature difference is defined as the temperature

difference between the chilled water outlet and the refrigerant inlet,

see figure 3.10.

T [° C ]

T chill , o

T r ,i

ΔT min ,r ,i

T chill ,i

T r ,o

EVAP

˙Q[kW ]

Figure 3.10: Evaporator: The closest approach temperature difference is at the refrigerant inlet.

∆T minr,i = T chill,o − T r,i (3.37)

The effectiveness is determined by the chilled water because it has the

lowest heat capacity flow; both media are water, but the refrigerant

55


3. COMPONENT DESCRIPTION

undergoes a phase transition which by far gives a higher heat capacity

flow.

ɛ = T chill,i − T chill,o

T chill,i − T r,i

(3.38)

The chilling power of the evaporator is calculated by the enthalpy

change of the chilling water. This change is determined by the energy

balance. The heat ingress from the surroundings defined by the

parameter ˙Q loss , should be either zero or a negative number.

˙Q = Ḣ chill,i − Ḣ chill,o (3.39)

Ḣ r,i + Ḣ chill,i = Ḣ r,o + Ḣ chill,o + ˙Q loss (3.40)

The mass balance is specified for the refrigerant as well as the chilling

water cycle.

ṁ r,o = ṁ r,i (3.41)

ṁ chill,o = ṁ chill,i (3.42)

The pressure losses (given as a negative pressure increases) are defined

as two different ∆P parameters:

p r,o = p r,i + ∆p r (3.43)

p c,o = p c,i + ∆p chill (3.44)

56


3.8. Heat Exchanger - HEX

3.8 Heat Exchanger - HEX

Beside the heat exchangers implicitly appearing in the absorber, condenser

and evaporator, three different heat exchanger components (HEXes)

exist:

• Gas-Gas HEX appearing in the SOFC subsystem.

• Water-Gas HEX for transferring heat from the exhaust gas to

heating circuits.

• Solution HEX for internal heat exchange between strong and weak

LiBr solution.

Figure 3.11: Heat exchangers (all counter flow). Types: Gas-Gas, Water-Gas, and Solution

heat exchangers

T [° C ]

T hot , i

ΔT min ,hot ,i

T hot , o

T cold ,o

ΔT min ,hot ,o

T cold ,i

HEX

˙Q[kW ]

Figure 3.12: Heat Exchangers: Closest approach temperature difference can appear in either

end.

57


3. COMPONENT DESCRIPTION

The general working principle is the same for all of them - only the media

differ. None of the media experience phase changes, so the definition of

approach temperature differences and efficiencies are straight forward.

The effectiveness is calculated in both ends, and the larger of them is

the valid one. Approach temperature differences are also calculated in

both ends, and the smaller of them is the closest approach temperature

difference.

The indices are different for the three heat exchanger types, but the

general way of determining approach temperature difference of a hot

and a cold stream is:

∆T mincold,i = T hot,o − T cold,i (3.45)

∆T mincold,o = T hot,i − T cold,o (3.46)

The effectiveness for the cold and the hot stream respectively are defined

as:

ɛ cold = T cold,o − T cold,i

T hot,i − T cold,i

(3.47)

ɛ hot = T hot,o − T hot,i

T cold,i − T hot,i

(3.48)

An energy balance is specified for each heat exchanger, including the

possibility for specifying a heat loss to the surroundings ( ˙Q loss ):

Ḣ cold,i + Ḣ hot,i = Ḣ cold,o + Ḣ hot,o + ˙Q loss (3.49)

For the Gas-Gas HEX and Water-Gas HEX, the specific enthalpies are

calculated from the temperature and pressure, but for the Solution Hex,

the enthalpy function is only valid for saturated liquid. So in the latter,

the specific heat capacity has been calculated (at the saturated state) for

the given temperature and concentration. It has then been assumed that

c p doesn’t change with temperature in the sub cooled area:

h j = h(T = T j , p = p j ) (GGHE X & W GHE X ) (3.50)

∆h i→o = c p (T = T sat , w = w i ) · (T o − T i ) (SHE X ) (3.51)

The mass balance is specified for the two flows.

ṁ cold,o = ṁ cold,i (3.52)

ṁ hot,o = ṁ hot,i (3.53)

58


3.8. Heat Exchanger - HEX

The pressure losses (given as a negative pressure increases) are defined

as two different ∆P parameters:

p cold,o = p cold,i + ∆p cold (3.54)

p hot,o = p hot,i + ∆p hot (3.55)

59


3. COMPONENT DESCRIPTION

3.9 Mixer - MIX

There are three mixer components:

• one for exhaust gas (from the SOFC)

• one for the LiBr solution (in the ABS)

• one for the water/steam (in the ABS)

They all work the same basic way, just with different species.

No chemical reaction takes place in the mixer, so the mass flow of each

species (j) out is the sum of the two mass flows of that species into the

component.

ṁ o,j = ṁ i ,1,j + ṁ i ,2,j (3.56)

The mixer is adiabatic, but since the temperature in the two inlets can be

different, an energy balance is applied to calculate the temperature in the

outlet.

Ḣ o = Ḣ i ,1 + Ḣ i ,2 (3.57)

The pressure at the two inlets can be different (due to other components

in the system), so the component includes two different pressure loss

parameters (of which none may be positive).

p o = p i ,1 + ∆p 1 (3.58)

p o = p i ,2 + ∆p 2 (3.59)

60


3.10. Pre Reformer - PR

3.10 Pre Reformer - PR

Figure 3.13: Pre Reformer component

The most important function of the pre reformer is to break down

large carbon chains into methane, hydrogen, and carbon oxides. All the

components in the model have, however, only been made to accept 7

different species (not including other hydro carbons than C H 4 ). So in this

model, the pre reformer only reforms methane into carbon oxides and

hydrogen by the ”Reforming” and ”Water Gas Shift” process:

C H 4 + H 2 O → CO + 3H 2

CO + H 2 O ⇋ CO 2 + H 2

∆H ◦ f

∆H ◦ f

kJ

= +206,10

mol

kJ

= −41,16

mol

(3.60)

(3.61)

The degree to which these two reactions occur, is set by the two

parameters ´´FR´´ (Fraction of Reforming) and ”FW” (Fraction of Water

gas shift). FR determines how many times the reforming process runs

per molecule of C H 4 that is sent into the pre reformer:

F R =

ṙre f

ṅ C H4 ,i

(3.62)

FW determines how many times the water gas shift reaction runs per

molecule of CO present after the reforming process

FW =

ṙ W GS

ṙ re f + ṅ CO,i

(3.63)

Since reforming is endothermic while water gas shift is exothermic, the

temperature can either raise or fall during reformation, depending on

how large FW and FR are relative to each other. The pressure loss is

given by the parameter ∆p.

p o =p i + ∆p (3.64)

61


3. COMPONENT DESCRIPTION

The energy balance includes the heat loss to the surroundings, which is

set manually by the parameter ˙Q loss :

Ḣ 2 = Ḣ 1 − ˙Q loss (3.65)

62


3.11. Pump - PUMP

3.11 Pump - PUMP

Figure 3.14: LiBr solution pump

The pump increases the pressure of the LiBr solution which is

assumed incompressible. The enthalpy of the corresponding isentropic

process is calculated from the density at the inlet and the pressure

difference:

∆h i s = ∆p

ρ i

(3.66)

The actual enthalpy change is determined by the isentropic efficiency of

the pump:

∆h = ∆h i s

η

(3.67)

The heat capacity, which is evaluated at the inlet is used to determine the

temperature at the outlet where the solution is sub cooled (which means

that the LiBr function is incapable of evaluating the temperature):

T o = T i + ∆h

c p,i

(3.68)

The pumping power is calculated from the actual enthalpy change:

Ẇ = m˙

i ∆h (3.69)

The enthalpy flow at the outlet is calculated from the pumping power

and the heat losses to the surroundings by the energy balance:

Ḣ o = Ḣ i +Ẇ − ˙Q loss (3.70)

The mass is conserved and the composition remains the same:

ṁ o = ṁ i (3.71)

w o = w i (3.72)

63


3. COMPONENT DESCRIPTION

3.12 Solid Oxide Fuel Cell - SOFC

Figure 3.15: SOFC component

The SOFC is modeled as a number of stacks (n st ack ) each consisting of

a number of cells (n cell ). Electricity wise the cells are connected in series.

This means that the voltage of the stack will be n cell times bigger than

the cell voltage. The total power of the SOFC is just the number of stacks

times the power of each stack:

Ẇ SOFC = n st ack ·Ẇ st ack (3.73)

Ẇ st ack = n cell I cell V cell (3.74)

Gas flow wise the stacks can be connected in parallel or in series. If

the stacks are in series, they can use a higher percentage of the fuel,

since cell number two will be fed with the exhaust from the first cell.

In parallel connection, however, the power will be bigger, since each cell

gets its own gas. And since SOFCs are still quite expensive, the extra fuel

utilization of the series connection is probably not enough to compensate

for the lower electricity generation per kg fuel cell. So in the model the

stacks are coupled in parallel.

The model has an anode side, where all the fuel, water and CO 2 is

sent in, and a cathode side, where the air is sent in. The air is modeled as

consisting of 79% Nitrogen and 21% Oxygen (volume fraction).

Some of the heat generated by the chemical reactions in the SOFC can

be set to be lost to the surroundings ( ˙Q loss ), whereas the rest will lead

to a temperature increase of the gasses at the outlet. In reality the outlet

temperature of the anode side is different from that of the cathode side,

but since the model is zero dimensional the temperature distribution in

the cell has not been calculated, and the outlet temperatures have instead

been set equal to each other.

64


3.12. Solid Oxide Fuel Cell - SOFC

The temperature into the SOFC must be in the region 650 ◦ C to 700 ◦ C

since the catalyst must be hot enough for the electrochemical reaction to

take place. At the same time the temperature must not be too high either,

since that will significantly increase the degradation of the cell. So the

exhaust temperature must be around 750 ◦ C to 800 ◦ C.

When calculating certain variables in the cell, such as ASR and Gibbs free

energy, the mean temperature of the cell must be used. This has been set

to 30 ◦ C below the outlet temperature of the cell, since this seems to give

data consistent with that of the Topsoe Fuel Cell models.

3.12.1 Chemical reactions

The fuel cell can run on three different fuels: C H 4 , CO, and H 2 . When

recycling and/or pre reforming is used, all of those will be present at the

inlet of the SOFC (anode side).

Three chemical reactions take place. First all the C H 4 is transformed by

internal steam reforming (which is an endothermal reaction):

C H 4 + H 2 O → CO + 3H 2

∆H ◦ f

= +206,10

kJ

mol

(3.75)

In the Water Gas Shift reaction (WGS) the Carbon monoxide and water

is turned into Carbon dioxide and Hydrogen (which is an exothermal

reaction):

CO + H 2 O ⇋ CO 2 + H 2

∆H ◦ f

= −41,16

kJ

mol

(3.76)

The electrochemical reaction transforms hydrogen and oxygen into

water, and is the only reaction generating electricity in the fuel cell.

H 2 + 1 2 O 2 ⇋ H 2 O

∆H ◦ f

= −241,82

kJ

mol

(3.77)

At the same time a chemical equilibrium is assumed to exist in the

cell between the species in the WGS reaction (CO, CO 2 , H 2 , and

H 2 O). The equilibrium constant (K W GS is determined from the average

65


3. COMPONENT DESCRIPTION

cell temperature and the free Gibbs energy of the species in the

electrochemical reaction.

K W GS = ṅCO 2 ṅ H2

ṅ CO ṅ H2 O

(3.78)

K W GS = e −∆g

RTav (3.79)

∆g = (g CO2 + g H2 ) − (g CO + g H2 O) (3.80)

One more equation comes from the assumption that the C H 4 is not present

at the outlet (meaning that reforming runs 100%).

The last equation is given by the fuel Utilization factor U f , which is an

input parameter. This factor states how much H 2 is used in the electrochemical

reaction (ṙ Elk ) divided by the much H 2 that would be available

for the electrochemical reaction, if all the C H 4 and CO in the anode inlet

was reformed and water gas shifted into H 2 :

U f =

ṙ Elk

4ṅ C H4,i + ṅ CO,i + ṅ H2,i

(3.81)

Together with the conservation of mass (for each element), this is enough

to determine composition of the outlet gas. Nitrogen and oxygen leaves

the SOFC at the cathode side, whereas all other species leaves on the

anode side.

OC ratio

If the concentration of Carbon atoms at the anode side of the SOFC

becomes too large relative to the concentration of Oxygen atoms on

the anode side, there is a risk that Carbon will deposit in the cell (this

includes the O- and C- content in all the different species at the anode

side). So it is desirable that there is at least twice as much Oxygen as

Carbon [25].

The ratio is controlled by altering the degree of anode recycling, since

more recycling means more Oxygen atoms into the anode side (from CO,

CO 2 , and H 2 O). So it is desired that OC r atio ≧ 2:

ṅ C H4 ,ai + ṅ CO,ai + ṅ CO2 ,ai

OC r atio =

ṅ CO,ai + 2ṅ CO2 ,ai + 2ṅ H2 O,ai + 2ṅ O2 ,ai

(3.82)

66


3.12. Solid Oxide Fuel Cell - SOFC

The electrochemical process

Equation 3.77 is a redox-reaction which can be split op into to halfreactions

for anode (oxidation) and cathode (reduction) respectively.

H 2 +O 2− → H 2 O + 2e − (anode) (3.83)

1

2 O 2 + 2e − → O 2− (cathode) (3.84)

”The free Gibbs energy” or ”the chemical potential” is an expression for

the maximum possible ”non-expansion work” (e.g. electrical work) a

chemical reaction can give. The (free) Gibbs energy can be expressed as:

g = h − Ts (3.85)

where ”h” is the molar specific enthalpy, ”T ” is the absolute temperature,

and ”s” is the molar specific entropy. The Gibbs energy is only

determined for the electrochemical reaction (equation 3.77), since this

is the only reaction creating electrical power in the cell (the reforming

and WGS does not contribute to the electrical power generation). The

Gibbs energy must be evaluated at the actual (average) temperature in

the cell according to [33]. As mentioned earlier, the average temperature

is assumed to be a little (30 ◦ C) below the exhaust temperature of the cell.

The Gibbs energy per mole of H 2 is found as:

∆g c = g H2 O(T av ) − g H2 (T av ) − 1 2 g O 2

(T av ) (3.86)

The temperature in the parentheses state the temperature which the

Gibbs energy is evaluated at. The ideal theoretical voltage that can be

obtained by the cell is given by the Nernst potential (V Ner nst ), which

depends on Faraday’s constant (F = 96485,3 C ), the number of electrons

mol

per reaction (two), the Gibbs free energy of the reaction, and the partial

pressure of the three species participating in the electrochemical reaction.

The bigger the concentration of the reactants, and the smaller the

concentration of the products, the bigger the Nernst potential will be.


V Ner nst = − ∆g c

2F − RT

2F ln ⎜


p H2

p 0

p H2 O

p 0


pO2

p 0



⎠ (3.87)

67


3. COMPONENT DESCRIPTION

Losses

There are always losses in real processes, and the actual voltage of the

cell will hence be smaller than the theoretical Nernst voltage. The real

cell voltage becomes:

V cell = V Ner nst − i d · ASR (3.88)

With i d being the current density (current per cell area) A/m 2 and ASR

being the Area Specific Resistance Ωm 2 . The ASR is meant to include the

four kinds of losses which appear in the fuel cell [23]:

• Ohmic resistance: There is a certain resistance in the electrodes,

which will decrease when the temperature of the cell is increased.

• Fuel cross over and internal currents: If there is a leakages a little

part of the fuel might be wasted by passing through the electrolyte

so the chemical reaction occurs at the cathode side whereby no

electricity is generated from its reaction. Since the electrolyte has

a finite electrical resistance a small current can pass through it.

• Activation losses: It takes a certain amount of energy (electrochemical

potential) to make the electrochemical reaction happen. The rate

of the reaction on the surface of the catalyst depends on the current

density and the temperature. A high temperature will result in low

activation loss.

• Concentration loss: There is a resistance against diffusion of the

reactants (H 2 and O 2 ) as well as the product H 2 O [33], which

depends on their concentrations. The more reactants, and the less

products, the smaller the concentration loss will be.

So in reality the ASR depends on the Temperature of the cell, the

current density and the concentrations. In this report is does, however

only depend on the temperature of the cell. The ASR function has

been constructed by fitting an exponential curve to measurements from

Topsoe Fuel Cell and multiplying it with a factor a little different from 1,

in order to prevent classified data from being published.

ASR = 0,0280e −0,0083·T SOFC ,av

Ωm 2 (3.89)

So if the current draw is large, the cell voltage will be low and visa versa.

68


3.12. Solid Oxide Fuel Cell - SOFC

Current and power

The electric current will be proportional to the mole flow of the reacted

Hydrogen, the number of electrons per mole Hydrogen, and Faraday’s

constant. And the current becomes:

I SOFC =ṅ H2 ,c 2F (3.90)

i d = I SOFC

A cell

(3.91)

The electrical gross power of the cell will then be:

Ẇ SOFC = V SOFC I SOFC (3.92)

A control volume is put around the SOFC component, and the first law

of thermodynamics is applied on this. Potential and kinetic energy is

neglected, so the energy balance becomes as follows:

Ḣ i − Ḣ o −Ẇ SOFC − ˙Q loss = 0 (3.93)

Ḣ i and Ḣ o are the total enthalpy flow rates for in- and out-lets (cathode

plus anode). Hereby the enthalpy and hence temperature at the outlet

can be determined. ˙Q loss is the heat lost directly to the surroundings.

Pressure losses

The pressure losses in the anode and cathode can be different, and are set

by the parameters ∆p a and ∆p c .

p a,o =p a,i + ∆p SOFC ,a (3.94)

p c,o =p c,i + ∆p SOFC ,c (3.95)

69


3. COMPONENT DESCRIPTION

3.13 Splitter - SP

There are three splitter components:

• one for exhaust gas (from the SOFC)

• one for the LiBr solution (in the ABS)

• one for the water/steam (in the ABS)

They all work the same basic way, just with different species.

No chemical reaction takes place in the splitter, so the mass flow of each

species (j) into the component is the sum of the two mass flows of that

species out the component. The fraction of the inlet flow which goes to

the first outlet is termed α (and the fraction for the other outlet then becomes

(1-α)):

ṁ o,1,j = ṁ i ,j α (3.96)

ṁ o,2,j = ṁ i ,j (1 − α) (3.97)

The mixer is adiabatic and hence the temperature of the two outlet are

equal to the inlet temperature:

T o,1 = T i (3.98)

T o,2 = T i (3.99)

The pressure at the two outlets can be different (due to other

components in the system), so the splitter includes two different pressure

loss parameters (of which none may be positive).

p o,1 = p i + ∆p 1 (3.100)

p o,2 = p i + ∆p 2 (3.101)

70


3.14 Cooling Tower - TOWER

3.14. Cooling Tower - TOWER

Removing heat (at a temperature not too far from the ambient temperature)

to the surrounding air can be somewhat difficult, expensive and

energy consuming (and perhaps water consuming). Three popular solutions

exist:

air,o

air,o

air,o

DRY

WET

SEMI

w,add

w,add

w,o

FAN

air,mp

air,i

w,i

w,o

FAN

air,mp

air,i

w,i

w,o

FAN

air,mp

air,i

w,i

Figure 3.16: The three variants of the Cooling Tower component. w = water, i = inlet, o = outlet,

mp = midpoint (after fan at the air side) and w.add = water addition.

• A Dry Cooling Tower, which only consumes power for driving

a fan to send ambient air over tubes containing the fluid to be

cooled. A dry cooler can, however only cool down the fluid to a

temperature above the ambient temperature.

• A Wet Cooling Tower, which utilizes the enthalpy of evaporation

of water for cooing the fluid. The water and air is in direct contact,

which increases the heat transfer. Furthermore, by using this

component it is possible to cool down the fluid to below ambient

temperature. A wet tower has the advantage, that it consumes

(less) power for driving a fan than a dry tower, since a smaller air

flow is needed, but on the downside it has a water consumption to

make up for the water lost in evaporation.

• A semi-wet Cooler mixing the two types above by spraying a water

mist over the tubes of the dry cooling tower to use the enthalpy of

evaporation. This has the advantage that more water can be added

during hot weather, while the cooler can run in dry cooling mode

during cold weather. But since the fluid inside the tubes and the air

71


3. COMPONENT DESCRIPTION

is not in direct contact there will be a temperature difference (over

the tubes), and the outlet temperature of the fluid will be higher

than for the Wet Cooling Tower.

In this project only the Dry Cooling Tower and the Wet Cooling

Tower will be investigated and modeled since they constitute the two

extremities.

3.14.1 Dry Cooling Tower - TOWERd

The heat transmission of the dry tower works exactly as the general heat

exchanger component (see section 3.8 page 57). The only new thing is

that the cold fluid is humid air with a humidity at the inlet equal to that

of the ambient air, while the outlet air has the same absolute humidity as

inlet air (i.e. the relative humidity changes).

T [° C ]

T w ,o

T w ,i

ΔT min ,w , i

ΔT min ,w , o

T air , o

T air ,i

TOWERd

˙Q[kW ]

Figure 3.17: Dry Tower: ∆T min,w,o (left side) specifies how much larger the water outlet

temperature is than the (ambient) air inlet temperature. ∆T min,w,i (right side) specifies how

much colder the outlet air is relative to the water inlet temperature

.

The electricity consumption of the fan in the tower is calculated by

the volume flow of the air times the (explicitly given) pressure loss in the

72


3.14. Cooling Tower - TOWER

tower divided by the efficiency of the fan:

Ẇ f an = ∆p · ˙V air,i

η f an

(3.102)

The energy balance of the component includes the fan power (since

it must be assumed that all of the power sent into the fan will be

transformed into heat in the air):

Ḣ air,i + Ḣ w,i +Ẇ f an = Ḣ air,o + Ḣ w,o (3.103)

The variable (W Q r atio ) expresses how much power the fan consumes relative

to how big a cooling service the tower delivers to the water circuit,

since this provides an easy way to compare the power consumption to

that of commercial dry coolers.

W Q r atio =

Ẇ f an

˙Q cool

(3.104)

˙Q cool = Ḣ w,i − Ḣ w,o (3.105)

3.14.2 Wet Cooling Tower - TOWERw

The Wet Tower also has air at ambient temperature and humidity coming

in at the inlet, but since water is evaporated, the outlet temperature

of water and air is lower than for the Dry Tower (for a given ambient

temperature).

The tower is made in three steps:

1. Compression of the inlet air

2. Evaporation of water.

3. Addition of water to make up for the evaporation water loss.

1. First the fan slightly compresses the air (to produce the air flow), which

increases the pressure and temperature of the air (while the absolute

humidity is kept constant):

Ẇ f an = ∆p · ˙V air,i

η f an

(3.106)

73


3. COMPONENT DESCRIPTION

air,mp

air,i

ΔTmin,a,o

w,i

w,o

wb

air,o

w,o

Figure 3.18: WET Tower: The fan increases the temperature of the air (air,i → air,mp), this

process has been exaggerated on the figure, since the temperature increase in reality is quite

small. The water outlet temperature lays at a point ɛ wb down from air,mp to wb. The air does

not follow the path of the arrow from air,mp to wb on its way to saturation. The arrow only

shows how the water outlet temperature is found. The air becomes saturated at the temperature:

T air,o = T w,i − ∆T min,a,o , which should be in the range T w,o


3.14. Cooling Tower - TOWER

The air could ideally come out at a temperature equal to the water inlet

temperature, but due to resistances, heat transports, mixing etc. the real

outlet temperature of the air is expected to be somewhat lower. This is

modeled by means of the approach temperature difference ∆T minair,o :

∆T minair,o = T w,i − T air,o (3.108)

3. Since some of the water in the water circuit has been lost to the air

during the evaporation process, some new water is added (ṁ add ).

A mass balance is made for each of the steps for both the water flow

and air flow. The overall mass balances becomes:

ṁ w,o = ṁ w,i (3.109)

ṁ air,o = ṁ air,i + ṁ w,add (3.110)

An energy balance is also added for each step:

Ḣ air,i +Ẇ f an = Ḣ air,mp pressurizing (3.111)

Ḣ air,mp + Ḣ w,i = Ḣ air,o + Ḣ w,mp evaporation (3.112)

Ḣ w,mp + Ḣ w,add = Ḣ w,o water side refill (3.113)

The variable (W Q r atio ) expresses how much power the fan consumes

relative to how big a cooling service the tower delivers to the water

circuit.

W Q r atio =

Ẇ f an

˙Q cool

(3.114)

˙Q cool = Ḣ w,i − Ḣ w,o (3.115)

75


3. COMPONENT DESCRIPTION

3.15 Expansion valve - VA/VB

Figure 3.19: The expansion valve has a single inlet and outlet.

The expansion valve reduces the pressure of the incoming fluid. If the

heat loss to the surroundings is zero, the process is isenthalpic.

Ḣ 2 = Ḣ 1 − ˙Q loss (3.116)

The mass is conserved and the composition remains the same.

ṁ o = ṁ i (3.117)

w o = w i (3.118)

The pressure difference is governed by other components, and thus no

pressure loss is defined for the valves.

There are two different types of valves - one for refrigerant (water)

and one for water-LiBr solution. The latter has two variants. The

difference of the three valves will be described in the following

subsections.

3.15.1 Expansion valve for refrigerant - VA

This valve handles pure water only and hence it can be assumed that

the outlet of the valve will always end up inside the two-phase region as

long as the entering fluid is saturated liquid.

3.15.2 Expansion valve for LiBr solution - VB

Calculating the enthalpy at the outlet is always straight forward, since

the only enthalpy change in the component comes from ˙Q loss (which will

often be set to zero). But the temperature at the outlet can be difficult to

find, since the LiBr function only works for saturated liquid.

The fluid in the LiBr solution circuit will not always be saturated

liquid when entering the expansion valves. Thus there are three

76


3.15. Expansion valve - VA/VB

possibilities - the fluid can either end up as sub cooled liquid, as saturated

liquid, or in the two-phase region. In order to handle this, two different

variants of valves have been modeled. (If the fluid outlet is saturated

liquid, both models are valid).

Sub cooled outlet

First the saturation temperature at the outlet pressure (and concentration)

is found. Then the heat capacity (evaluated at the saturated state) is

used in order to calculated the actual temperature at the outlet:

T o = T sat + h o − h sat

c p,sat

(3.119)

In order to make sure that this variant is the one to use, it is necessary to

check that the outlet state is in fact subcooled. This is done by ∆h chk,SC

which is defined as:

∆h chk,SC = h sat − h o (3.120)

If ∆h chk,SC is positive the outlet is sub cooled and the component variant

is valid. If ∆h chk,SC is negative, the other variant of VB must be used.

Two-phase outlet

This variant is to be used if the enthalpy at the outlet is larger than the

saturation enthalpy at the outlet pressure and concentration. ∆h chk,2P is

used to check this (notice that it is defined oppositely of ∆h chk,SC ):

∆h chk,2P = h o − h sat (3.121)

If ∆h chk,2P is positive this component variant is valid and the outlet

temperature is set equal to the saturation temperature at the outlet

pressure:

T o = T sat (3.122)

77


C H A P T E R

4

SYSTEM DESCRIPTION

4.1 General

The components described in the previous chapter have been assembled

in order to make a model of SOFC system integrated with an absorption

cooling unit, see figure 4.1. The system can be divided into subsystems:

SOFC subsystem, absorption subsystem and cooling tower.

The absorption cycle can be either a Singe Stage or a Double Stage. In

addition it is possible to supply the double stage cycle with heat input in

two different points - this is called Dual Heat. Enlarged layout diagrams

of all three system configurations are seen in appendix G page 293.

Each of the subsystems will be described in the following sections as

well as the three different system configurations. Also the value of the

most important parameters and assumptions will be stated.

In general all heat losses of the components to the surroundings are

assumed to be zero 1 .

The closest approach temperature difference for heat exchangers

is estimated to be 5 ◦ C for liquid-liquid, 10 ◦ C for Condensers (which

are liquid-liquid/gas), 15 ◦ C for liquid-gas and 25 ◦ C for gas-gas heat

exchangers.

The fluid in the external heat transfer circuits is water and the

1 The wet/dry cooling towers are an exception - their purpose is to reject heat to the

surroundings.

79


4. SYSTEM DESCRIPTION

8

SPG 10

20

1 1-α

WGHEX

1

α 7

43

CH4, add, in

6

GGHEX1 9

GGHEX2

0

42 41

COND2

71

70

78

2 MIXG 3

4

5 ANODE

DES2

1

33 34

21

1 PR

10

79

SOFC

BURN

18

22

CH4, in

SPG α

SHEX

2

CATHODE 2

WGHEX

80 77

12 13

14 15 16

72

2

1-α

GGHEX4

GGHEX3

81

76

BLOW

11

1

17

MIXG

34

Air, in

2

PUMP

22 20 19

VA2

VB2

19

31

2

21

23

82

73 75

1-α

32

28

MIXR

α

SPL

1

WGHEX

50

1

58

3

DES1

57

59

MIXL

27 24 Flue gas, out

COND1

1

51

82

35 36

SHEX

Domestic Hot Water

60 1 57

Saturated air

47

52

61

56

VA1

VB1

PUMP

1

Water add

38

TOWER

46

53

49

EVAP

48

54

62

ABSO

36 37

55

39

37

FAN

45

Atmospheric air

Chilled Water

Figure 4.1: Diagram of SOFC-ABS system in Double Stage, Dual Heat configuration. The

SOFC subsystem is located in the upper left corner. The ABS subsystem is located at the

righthand side. The names of the components are listed in the nomenclature page xxii.

pressure in all of them is assumed to be 2000 kPa (to ensure liquid phase).

A complete list of parameters is given in appendix C.1 page 233. Further

explanation regarding the choice of parameters can be seen in D.1 page

271.

80


4.2. SOFC subsystem

4.2 SOFC subsystem

4.2.1 Fuel pretreatment and recirculation

At point 1 the fuel which is methane (C H 4 ) 2 is fed into a heat exchanger

(GGHEX1) where it is preheated, see figure 4.2.

Normally the fuel is natural gas coming from a supply grid or

pressurized storage, so it is assumed that the pressure of the gas is

sufficiently high to overcome the pressure losses in the system. It

is assumed that the temperature of the fuel is equal to the reference

temperature of 25 ◦ C. The mass flow rate of methane corresponds to an

enthalpy flow of 100kW 3 .

8

GGHEX1

9

SPG

1

α

10

1-α

7

GGHEX2

6

CH4, add, in

0

1

CH4, in

Air, in

2

11

MIXG

1

BLOW

1

3

PR

4

ANODE

SOFC

SPG α

CATHODE 2

12 13

14 15 16

1-α

GGHEX4

GGHEX3

23

22

20

5

19

10

BURN

17

18

MIXG

2

19

Figure 4.2: Diagram of SOFC subsystem (zoom of figure 4.1) which consists of gas-gas heat

exchangers (GGHEX), a pre reformer (PR), mixers (MIXG), splitters (SPG), a Solid Oxide Fuel

Cell stack (SOFC) and a catalytic burner (BURN).

At point 2, the fuel is mixed with the recirculated gas coming from

point 9 in the mixer component (MIXG) before it enters the pre reformer

(PR) in point 3.

2 Natural gas contains mainly methane but also higher order hydrocarbons. For

simplicity it has been assumed that only methane is present.

3 Based on lower heating value

81


4. SYSTEM DESCRIPTION

Pre reformer

Since there is not chemical equilibrium in the pre reformer [25], the degree

to which reforming and water gas shift happens in the pre reformer

can not be calculated easily and is hence determined by two parameters,

which have been set to give partial pressures of the different species at

the outlet approximately equal to the values of the TOFC model.

The parameter ”F R” (fraction of reforming) determines how much of the

incoming methane (at point 3) which is reformed (see equation 3.62 page

61).

”FW ” (fraction of water gas shift reaction) determines how much of

the CO after the reforming reaction 4 which reacts in the water gas shift

reaction, see equation 3.65 page 62.

F R is set to 0,14, while FW is set to 0,6. With these values the

following happens to the volume flow from the pre reformer inlet (point

3) to the outlet (point 4):

1) H 2 is approximately doubled.

2) CO is reduced by 50%.

3) CO 2 is increased by 15%.

These numbers are all quite close to the TOFC model.

After the pre reformer (point 4) the fuel heated to 690 ◦ C by GGHEX2

before it enters the SOFC stack in point 5.

Recirculation

The exhaust gas from the SOFC anode (point 6) is sent back to the hot

side of both GGHEX2 (point 7) and GGHEX1 (point 8) for heat recovery.

In order to make the model more flexible when parameters are varied, the

effectiveness (ɛ) of these two heat exchangers are set equal to each other

instead of giving the closest approach temperature difference (∆T min ) for

one of them.

The splitter (SPG1) is controlled by the parameter α SPG1 dictating the

4 In reality the two reactions occur simultaneously, but it is assumed that the

reforming reaction run to end before the water gas shift reaction starts

82


4.2. SOFC subsystem

fraction which is recirculated to point 9. The standard value for α SPG1 is

set to 0,62 (62% recirculation) since this corresponds to an OC ratio just

above 2. The OC ratio is the ratio of oxygen and carbon molecules at the

SOFC anode inlet (point 5) (see equation 3.82 page 66).

Normally a blower is needed to recirculate the exhaust gases from the

SOFC anode (the pressure is higher in point 3 than in point 9), but to

simplify the system this blower has been neglected. This is done by allowing

a positive 5 pressure loss in MIXG1 from point 9 to point 3.

4.2.2 Air inlet

Atmospheric air (79% N 2 and 21% O 2 , by volume) at reference temperature

and pressure (T re f =25 ◦ C and p re f =100kPa) enter the blower (BLOW1) at

point 11.

The blower has an isentropic efficiency 6 of 60%. This value is

dependent on the size of the blower, especially small scale blowers have

a low efficiency. However, this has been neglected since only larger

systems are considered and it is assumed that blowers in this scale has

the same isentropic efficiency independent of the system size.

In the blower the pressure of the air is only slightly increased

to a pressure corresponding to the pressure losses in the successive

components (the absolute pressure after the blower is 122kPa). The

pressure loss of each component is an estimate based on data from TOFC.

Since all the gasses in the model are ideal the losses in the gas system only

influence the blower power. All pressure losses are listed in appendix C.1

page 233.

Air pre heating

The air must be preheated before it enters the SOFC stack to obtain an

inlet temperature of 690 ◦ C. This is done by heat recovery of the exhaust

gases. The system has the opportunity to do this air preheating in two

steps:

First the air is preheated by the low temperature exhaust gas

via GGHEX4 from point 12 to point 13. This is an extra feature

5 The pressure loss is defined as a negative value

6 See definition in equation 3.10 page 48

83


4. SYSTEM DESCRIPTION

which increases system performance and therefore called Additional Air

Preheating.

Afterwards the air is preheated by high temperature exhaust gas by

GGHEX3 to a temperature of 690 ◦ C before it enters the SOFC cathode

inlet point 14.

4.2.3 SOFC stack

The specified cell area of 0,0228 m 2 makes the SOFC the only component

in the model having a physical size. The number of cells per stack has

been set to 60. However these value does not affect system efficiency or

system size - the number of stacks in the system is variable and will depend

on the enthalpy flow of the fuel input 7 . So the cell area and number

of cells are only specified to have some kind of relation to real systems.

The fuel utilization factor (U f ) is set 70% which is a typical value for fuel

cell systems [25]. Together with the fuel input of 100kW and recirculation

factor of 0,62 this gives the current of the system. Instead of the fuel input

of 100kW the current draw could have been specified, but when the fuel

input is kept constant, the cooling and heating powers become easier to

evaluate during the parameter investigations in chapter5.3.

The current density (i d ) is a parameter which determines how much

the SOFC is loaded (regulation). The value of 3000 A/m 2 is an estimate

based on data from TOFC. The fuel input determines the size of the system

(100kW fuel input). These two factors give the number of stacks,

which becomes 20,15. Instead of the current density the number of stacks

n st ack ) could be specified, but it is impractical to have more than one extensive

parameter.

The two inlets at the SOFC are assumed to have equal temperature, and

the two outlets have the same temperature. ∆T min,SOFC determines the

temperature increase from inlet (point 5 and 14) to the outlet (point 6

and 15). ∆T min,SOFC has a value of 90 ◦ C which is a typical value of fuel

cells today [25]. It is important that the limits of minimum temperature

at the inlet and maximum temperature at the outlet are not violated, as

described in section 3.12 page 64.

7 Alternatively the current draw could have be specified or the number of stacks

(since the current density is also given)

84


4.2. SOFC subsystem

The air utilization factor is defined as the fraction of the oxygen input

at the cathode side of the SOFC component which is consumed:

U air = ṅSOFC ,cat,i ,O 2

− ṅ SOFC ,cat,o,O2

ṅ SOFC ,cat,i ,O2

= ṅ14,O 2

− ṅ 15,O2

ṅ 14,O2

(4.1)

4.2.4 Exhaust gas

The air which is not consumed in the SOFC stack (point 15) is split by

SPG2. α SPG2 defines how much of the air is sent to the burner inlet, point

16. The exhaust gas (containing excess fuel) from the SOFC is sent to the

burner fuel inlet point 10.

It is also possible to bypass the pretreatment of the fuel and the SOFC

by adding fuel to the burner directly at point 0 if more heat and less

electricity is wanted. The parameter FuelBP Ratio determines the fraction

of the total fuel input which is sent directly to the burner circumventing

the rest of the SOFC system. This option, though, is only used for a

single simulation, so normally FuelBP Ratio = 0. More details are given

in section 5.3.3 page 130.

λ BURN ,i is the air excess ratio of the burner inlet (point 0, 10 and 16)

defined as:

λ BURN ,i = 2ṅ i ,C H 4

+ 0,5ṅ i ,H2 + 0,5ṅ i ,CO

ṅ i ,O2

(4.2)

λ BURN ,i is set to 1,5 which is common for combustors. This implicitly

sets the value of α SPG2 such that the right amount of air is bypassed the

burner (point 17). The bypassing air is mixed with the exhaust gas from

the burner (point 18) in MIXG2. The gas is returned to the hot side of

GGHEX3 (point 19) before it leaves the SOFC subsystem in point 20.

After some of the energy in the exhaust gas has been utilized in the

absorption cycle, the gas is returned to the SOFC subsystem entering at

point 22. Heat is transferred via GGHEX4 to the inlet air and the exhaust

gas leaves at point 23.

85


4. SYSTEM DESCRIPTION

4.3 Absorption Single Stage

The exhaust gas from the SOFC subsystem enters the water-gas heat

exchanger (WGHEX2) in point 21 and leaves in point 22, see figure 4.3.

Heat is transferred by a closed loop of water to the desorber (DES1)

heating inlet point 31. The temperature T 31 is set to 85 ◦ C (parameter

for the single stage only). The temperature change in the heating loop

(∆T h,DES1 ) is 5 ◦ C corresponding to a temperature in point 32 of 80 ◦ C for

the single stage.

22

21

WGHEX

2

32

31

50

DES1

58

59

52

35

COND1

36

51

60

61

SHEX

1

57

56

VA1

VB1

PUMP

1

53

49

EVAP

48

54

62

36

ABSO

37

55

Chilled Water

Figure 4.3: Diagram of single stage absorption subsystem (zoom of full diagram in appendix

G page 293) composed of an absorber (ABSO), a condenser (COND1), a desorber (DES1), an

evaporator (EVAP), a pump, a solution heat exchanger (SHEX), a water-gas heat exchanger

(WGHEX2), and two valves (VA1 and VB1).

In reality the WGHEX2 and DES1 would have been integrated as one

unit since the water circuit was only introduced due to flexibility in the

modeling work. So in reality there would only be one (Water-Gas)HEX

and hence only one ∆T min between the exhaust gas and fluid in DES2. So

∆T min,DES1,r,o has been set to zero. This way ∆T min,W GHE X 2,w,i = 15 covers

the overall closest approach temperature difference.

86


4.3. Absorption Single Stage

4.3.1 Refrigerant cycle

The superheated refrigerant in point 51 is condensed in COND1 until

a condition of saturated liquid is reached (qu COND1,r,o = 0) in point 52.

The high pressure in the condenser is determined by the cooling water

temperature and the ∆T min of the condenser.

The evaporation temperature is given by the temperature of the

cooling circuit and ∆T min,COND1,r,o = 10 ◦ C 8 .

The refrigerant is led through expansion valve VA1 to point 53. The

low pressure in the evaporator (EVAP) is set so the temperature of the

chilled water obtains the desired temperature (T 49 = 6 ◦ C) for the given

closest approach temperature difference (between T 49 and T 53 ), which

is ∆T min,EV AP,r,i = 5 ◦ C. The temperature difference of the chilled water

leaving the evaporator (point 49) and the returned water in point 48

(∆T chill,EV AP ) is assumed to be 5 ◦ C 9 .

4.3.2 Solution cycle

When the refrigerant leaves the evaporator in point 54 as saturated

gas (qu EV AP,r,o = 1) it is absorbed by the strong LiBr solution (rich in

LiBr) entering at point 62 in the absorber. The heat is removed by the

cooling water entering at point 36 and leaving at point 37. Together

with the pressure, T 37 determines the concentration of the weak solution

which leaves at point 55, via the closest approach temperature difference

∆T min,ABSO,s,o = 5 ◦ C (Difference between T 55 and T 37 ).

The weak solution is pressurized by a canned pump (PUMP1) which

is assumed to have an efficiency of 0,5 (point 56). Next the solution

is preheated in SHEX1 before entering DES1 in point 57. The strong

solution leaving the desorber in point 59 transfers heat to the weak

solution in SHEX1 (point 60-61) and expands in VB1 before entering the

absorber.

8 EES has problems running if ∆T min,COND1,r,o is given explicitly, so in praxis

∆T min,COND1,r,o is given to 12,5 ◦ C in the standard parameter configuration, and

monitored and changed during investigations, so that ∆T min,COND1,r,o remains at 10 ◦ C

9 It is assumed that the water is sent to a cold water storage with a temperature of

10 ◦ C and that the air temperature for the air coming out of an air conditioning should

be about 15 ◦ C. Similar temperatures are used in [19] and [34].

87


4. SYSTEM DESCRIPTION

4.3.3 Pumping factor

The pumping factor is defined as the mass flow ratio of the weak solution

and the refrigerant[18]:

PF = ṁ55

ṁ 51

(4.3)

For the standard configuration PF = 12,75. This number should not be

too high since it increases the amount of LiBr solution circulated per kW

of cooling which increases desorber heating, absorber cooling and pump

power.

88


4.4 Absorption Double Stage

4.4. Absorption Double Stage

The double stage absorption cycle is similar to the single stage cycle

described in previous section. Thus only the additional components and

changes of parameters will be described in this section. All state points

refers to figure 4.4.

20

WGHEX

1

43

COND2

71

33 34

21

70

79

42

DES2

41

78

72

80

81

SHEX

2

77

76

52

35

COND1

36

51

PUMP

VA2

VB2

2

82

73 75

1-α

32 31

MIXR

α

SPL

1

50

1

58

MIXL

1

59

82

60

61

DES1

SHEX

1

57

56

57

VA1

VB1

PUMP

1

53

49

EVAP

48

54

62

36

ABSO

37

55

Chilled Water

Figure 4.4: Diagram of double stage absorption subsystem (zoom of full diagram in appendix G

page 293). It is similar to the single stage cycle with addition of an extra condenser (COND2),

desorber (DES2), two mixers (MIXR and MIXL), a pump, a splitter (SPL) and two valves (VA2

and VB2).

The exhaust gas is sent through WGHEX1 (point 20 and point 21).

As for the single stage cycle, WGHEX1 and DES2 are modeled as two

components (but considered as one) which means that ∆T min,DES2,r,o = 0.

89


4. SYSTEM DESCRIPTION

The temperature difference between point 41 and point 42 (∆T h,DES2 ) is

5 ◦ C like for DES1. The temperature of DES2 is 150 ◦ C (point 70 and 79).

The high pressure refrigerant is sent to COND2 inlet (point 71). Like

for COND1 in the single stage cycle configuration, the refrigerant is both

de-superheated and condensed in COND2. Thus the closest approach

temperature difference is found somewhere between point 71 and point

72. Due to limitations in the model it is not possible to set this parameter

directly and instead ∆T min,COND2,r,o is set to 12,5 ◦ C. This corresponds to

∆T min,COND2,mp being 10 ◦ C.

The heat from COND2 is removed by the heat transferring loop (point

31 to point 34) and supplied to low temperature desorber DES1. The loop

is modeled as a water circuit, but in a real double stage unit, COND2 and

DES1 would be integrated as one component.

The saturated liquid refrigerant (qu 72 = 0) is expanded in VA2 point

72 before it is mixed with superheated refrigerant from DES1 point 50 in

MIXR1. The quality of the refrigerant outlet is between zero and one in

point 51.

Unlike COND2, the refrigerant entering COND1 is not superheated.

Thus the closest approach temperature difference exists at the inlet in

point 51 (compared to the temperature in point 36) but the value is still

10 ◦ C. The heat from COND2 is removed by the cooling circuit (point 35

and point 36)

The refrigerant is expanded in VA1 (point 53), then evaporated (point

54), and absorbed in the absorber exactly the same way as in the single

stage cycle. The difference occurs after the weak solution is preheated in

SHEX1 in point 57. In the double stage system only some of the solution

is sent to DES1 but the remaining part is pressurized further by PUMP2

(point 76) and preheated in SHEX2 (point 77) before it enters DES2 (point

78). The strong solution is cooled in SHEX2 (point 80 to 81), expanded in

VB2 and mixed with the strong solution coming from DES1 in MIXL1.

Since the temperature in point 50 is not set as a parameter (as it is the

case for the single stage cycle), another relation is given:

ṁ 70

ṁ 78

= ṁ50

ṁ 58

(4.4)

This relation determines the fraction of solution which is sent to the

DES2. It also implies that concentration of the weak and strong solution

will be the same for the two solutions in the two circuits (w 55 = w 75

90


4.4. Absorption Double Stage

and w 59 = w 79 ). This has been done for two reasons. First of all it

gives a value of T 50 = 78 ◦ C which is quite close to optimum. Secondly

if other parameters like the temperature of the high pressure desorber

is increased then T 50 will increase as well and thereby remain near

optimum for the given T 70 .

91


4. SYSTEM DESCRIPTION

4.5 Absorption Double Stage, Dual Heat

20

WGHEX

1

43

72

COND2

71

33 34

22

34

WGHEX

2

21

42

70

79

80

81

DES2

SHEX

2

41

77

76

78

52

35

COND1

36

VA2

31

VB2

73

82

75

MIXR

32

α

1

51

MIXL

1

50

59

82

60

61

DES1

SHEX

1

57

56

58

57

PUMP

2

1-α

SPL

1

VA1

VB1

PUMP

1

53

49

EVAP

48

54

62

36

ABSO

37

55

Chilled Water

Figure 4.5: Diagram of double stage absorption subsystem with dual heat (zoom of full diagram

in appendix G page 293). The cycle is similar to the double stage cycle - the difference is that

heat is transferred from the exhaust gas to the absorption cycle at two points (via WGHEX1 and

WGHEX2).

Another attempt to increase the production of cooling is to make a

configuration which is a combination of the single and the double stage

cycle, see figure 4.5. Basically it is a double stage cycle where heat is

transferred from the exhaust gas to the absorption cycle twice (dual heat).

In the configuration without Air Preheat, the exhaust gas from

WGHEX1 in point 21 is 165 ◦ C so only some of the heat from the exhaust

gas is used for the cooling cycle. So in order to use more of the heat from

92


4.5. Absorption Double Stage, Dual Heat

the exhaust gas it is sent through WGHEX2 (hot side) so it is cooled down

to around 90 ◦ C at point 22. This extra heat is sent into DES1 through the

external circuit (point 31, 32, 33 and 34) 10 . In this way more of the heat of

the exhaust gas can be used, although part of it goes directly into the low

temperature desorber and hence doesn’t benefit from the Double Stage

setup.

10 In a real application these three components could be integrated as one and the

heat could be transferred in parallel rather than in series, which would change the

involved temperatures a little, but this has not been investigated further.

93


4. SYSTEM DESCRIPTION

4.6 Cooling Tower

28

WGHEX

3

23

MIXR

1

50

32

DES1

31

27

Domestic Hot Water

24

Saturated air

47

Flue gas, out

52

35

COND1

36

51

MIXL

1

59

82

60

61

SHEX

1

57

56

VA1

VB1

PUMP

1

Water add

38

TOWER

46

53

49

EVAP

48

54

62

36

ABSO

37

55

39

37

FAN

45

Atmospheric air

Chilled Water

Figure 4.6: Diagram of cooling system and hot water production (zoom of figure 4.1). The

cooling tower removes waste heat from the absorber (ABSO) and the condenser (COND1). The

remaining heat in the exhaust gas is used for hot water production.

As described in section 4.3, heat must be removed from the condenser

(COND1) and the absorber (ABSO) by a heat transferring fluid (water).

It has been decided to connect COND1 and ABSO in series. According

to Scandinavian Energy Group [27] the condenser is normally ”before” the

absorber for cooling units (for heat pumps it is always the opposite). This

corresponds to the series connection of COND1 and ABSO (point 35, 36

and 37) in figure 4.6.

The temperature difference of the Tower inlet (point 37) and outlet

(point 39) is estimated to be ∆T c,TOW ER1 = 5 ◦ C. In praxis this is

controlled by the water mass flow in the external circuit. The COP

generally increases if ∆T c,TOW ER1 is reduced (the absorber and condenser

becomes colder), but since the water flow increases, pumping work

and component geometry is enlarged which requires more energy and

increases the price of the condenser and absorber.

The water is cooled by the ambient air (at T amb ) which enters the

tower at point 45, is pressurized by the FAN (point 46) and then

94


4.6. Cooling Tower

discharged in point 47. The cooling tower is either a dry tower (dry

cooler) or a wet tower, as described in section 3.14 page 71.

The parameter configuration for these two towers are different and

will be described separately in the next two paragraphs.

4.6.1 Wet Tower

The ambient air has a temperature of 30 ◦ C when the wet tower is used.

Since the water and air is mixed this allows a much lower CATD than for

a tube heat exchanger and it is thus estimated to be ∆T min,TOW ER1,a,o,wet =

3 ◦ C. This way the temperature of the discharged air (T 47 ) is almost in the

middle of the water outlet temperature (T 39 ) and water inlet temperature

(T 37 ).

According to [14] the ”wet bulb” Tower efficiency is typically around

0,75, so this has been assumed also to be the case here giving a water

outlet temperature of 22 ◦ C when the inlet air is 30 ◦ C and the relative

humidity is 40%.

4.6.2 Dry Tower

Ideally the dry tower should use the same ambient temperature as the

wet tower (30 ◦ C), but this gives a condenser and absorber temperature

so high that the model can not run at all. So it has been necessary to use a

lower ambient temperature for the dry tower although it gives a slightly

unfair advantage when comparing it to the wet tower. A temperature of

18 ◦ C has been chosen, since this is just below where COP ABS,f uel starts

to decrease rapidly (at 20 ◦ C the system will barely run), so the unfair

temperature advantage is minimized as much as possible.

The Approach Temperature Difference between water inlet (T 37 ) and

air outlet (T 47 ) is estimated to be: ∆T min,TOW ER1,a,o,dr y = 8 ◦ C.

4.6.3 Hot Water

Most of the energy in the exhaust gas is utilized in the absorption cycle

and for air preheating (eventually additional air preheating is used in

GGHEX4). In point 23 temperature of the exhaust gas is rather low

95


4. SYSTEM DESCRIPTION

(below 100 ◦ C), but high enough for heating domestic hot water.

exhaust gas is discharged to the surroundings at point 24.

The

Fresh water is entering the water-gas heat exchanger (WGHEX3) in

point 27. It is assumed that the water comes from a supply line which

has the same temperature as the surroundings 11 (T amb ). This water is

heated to a temperature of 65 ◦ C 12 in point 28.

It is assumed that the consumption follows the production of hot

water or that the water can be stored in a thermal stratification heat

storage, so the water inlet temperature of WGHEX3 remains constant.

11 for buried pipes the temperature could be much lower.

12 Recommended maximum temperature to avoid scald and high enough to avoid

bacteria growth in storage tanks.

96


4.7. System calculation

4.7 System calculation

Most calculations are done in the respective component modules as

described in chapter 3, but calculations concerning more than one

component (or just very simple components - merely consisting of an

efficiency) have been places in the main system file. These calculations

will be described in the following sections.

Inverter

The power produced by the SOFC (Ẇ SOFC ) is delivered by direct current

(DC), but for many applications alternating current (AC) is more desirable.

It is assumed that the other components in the system (blower, fan and

pumps) are driven by AC power.

An inverter converts DC to AC which introduces a power loss. The

efficiency of the inverter is specified by η inver t which is estimated to 95%.

4.7.1 Efficiencies

When looking at the system it is convenient to know how much energy

that is available in each point of the gas stream (fuel, air and exhaust gas).

For this the ”energy flow rate”, ∆Ḣ, is used 13 . It is defined as how much

enthalpy the gas contains in a given point relative to when it is totally

combusted at the reference temperature (T re f = 25 ◦ C, in non-condensed

state):

∆Ḣ j = Ḣ j − Ḣ f ull y combusted at Tre f

(4.5)

∆Ḣ is calculated in point 0 to 24 (figure 4.1 page 80). The sum of all

incoming gases to the system (point 0, 1 and 11) is called ∆Ḣ i .

SOFC

The gross AC and the net AC power delivered by the SOFC stack (without

deductions for ABS pump or cooling tower fan) is calculated respectively

13 Caution! This has another reference than the normal enthalpy flow rate Ḣ as

defined in equation 3.1 page 43

97


4. SYSTEM DESCRIPTION

as:

Ẇ AC = Ẇ SOFC · η inver t (4.6)

Ẇ SOFC ,SOLO = Ẇ AC −Ẇ BLOW 1 (4.7)

The electrical efficiency of the SOFC subsystem alone - disregarding

electricity consuming components in the rest of the components in the

system - then becomes:

η SOFC ,el,SOLO = ẆSOFC ,SOLO

∆Ḣ i

(4.8)

Absorption chiller

The performance of the absorption cycle (per kW heat consumption) is

determined as:

COP ABS =

˙Q Chill,EV AP

˙Q tr ans,W GHE X 1 + ˙Q tr ans,W GHE X 2

(4.9)

where ˙Q tr ans,W GHE X is the amount of heat transferred into the absorption

cycle (through WGHEX1 and WGHEX2). This COP is comparable to

COP’s found in the literature of absorption system.

System

The electrical net efficiency of the entire system takes the power

consumption of all components into account:

Ẇ sys,net = Ẇ AC −Ẇ BLOW 1 −Ẇ PU MP1 −Ẇ PU MP2 −Ẇ F AN (4.10)

η sys,el ,net =

Ẇ sys,net

∆Ḣ i

(4.11)

The chilling Coefficient Of Performing is defined as kW chilling power

output per kW fuel (methane) input into the entire system:

COP ABS,f uel = ˙Q Chill,EV AP

∆Ḣ i

(4.12)

98


4.7. System calculation

This definition has the advantage that the COP implicitly takes into

account how much heat the absorption unit receives from the exhaust

gas (more heat means more cooling power). So it tells how much cooling

power per fuel input the system generates, which is the important thing

from a system perspective, where the ”regular” COP ABS only tells part of

the story).

The hot water efficiency is defined as kW water heating per kW fuel

(methane) input into the entire system:

η HW = ˙Q tr ans,W GHE X 3

∆Ḣ i

(4.13)

The total ”efficiency” 14 is found as the sum of useful power (electrical,

heating and cooling) or the sum of two efficiencies and COP:

Ẇ sys,net + ˙Q Chill,EV AP + ˙Q tr ans,W GHE X 3

η sys,tot =

(4.14)

∆Ḣ i

η sys,tot = η sys,el ,net +COP ABS,f uel + η HW (4.15)

Since η sys,el ,net and η HW are defined as positive quantities for energy

going out of the system, whereas COP ABS,f uel is positive for energy going

into the system, η sys,tot can be above 1 and should hence be used with

caution. (If one imagine that ∆Ḣ i = 100kW and ˙Q Chill,EV AP is 50kW, then

the system will contain 150kW, which could be used for generating up

to maximum 150kW of electricity and hot water. This would give an

electrical efficiency of η sys,el,net = 50kW+150kW

100kW

= 2).

14 Since energy input at low temperature (the chilling power) is not included in the

denominator, η sys,tot can be above one and therefore by definition is not an efficiency

although this name will be used in lack of better.

99


4. SYSTEM DESCRIPTION

4.8 Verification of Model

All variables in the model have been assigned units. EES has a feature

to check units automatically. This has been carried out and no unit

problems were found 15 .

4.8.1 Energy balance

The conservation of energy must be fulfilled for all energy systems. In

order to verify the model, an energy balance around the entire system

has been made:

EB tot =∆Ḣ i − ∆Ḣ W GHE X 3,g ,o − Ḣ air,i − Ḣ air,o + ˙Q Chill,EV AP (4.16)

− ˙Q HW + Ḣ w,add +Ẇ BLOW +Ẇ F AN +Ẇ PU MP1

+Ẇ PU MP2 −Ẇ SOFC = 0

where ∆Ḣ W GHE X 3,g ,o is the enthalpy flow of discharged exhaust gas,

Ḣ air,i and Ḣ air,o is the enthalpy flow of the air into the cooling tower

and out of it, and Ḣ w,add is the enthalpy of the fresh water added to the

cooling tower.

4.8.2 Check of heat exchangers

Most of the heat exchangers are defined by a Closest Approach Temperature

Difference. This can however introduce an error if the chosen parameter

for the approach temperature difference is not the closest one - in that

case the real closest approach temperature can then become negative

(whereby ɛ exceeds one).

To avoid this error a variable ”ɛ M AX ” has been introduced. It simply

finds the largest effectiveness of all the heat exchangers in the system.

This way it is not necessary to monitor the effectiveness of all the heat

exchangers during simulation as long as ɛ M AX does not exceed 1,0.

15 Due to a bug in the external function ”CP_LiBrH2O.LIB” (the unit of c p is set

to kJ

kg and not kJ

kgK

), so the unit check feature finds 15 unit problems - all related to

CP_LiBrH2O.LIB. These have been checked manually and no error was found.

100


4.9. Validation of Model

4.9 Validation of Model

During the development of the model, the output (results) has been

compared to other models as well as measured data. Rules of thumb

have also been taken into account. In some cases additional variables

have been introduced in order to validate the model and will be

described in the following.

4.9.1 SOFC

In the standard parameter configuration the increase of the temperature

from the inlet to the outlet of the fuel cell (∆T SOFC ) is 90 ◦ C. The fuel

utilization factor U f is 0,7 and the current density isi d = 3000 A . The

m 2

fraction of reforming in the pre reformer (F R) is 0,14. The air utilization

factor (U air ) which is dependent on ∆T SOFC , U f and F R is calculated to

0,16 which is quite close to that of the TOFC models [25].

Recycling

The fraction of anode recycling α SPG1 is 0,62. This deviates less than

5% from an equivalent SOFC system modeled by TOFC. And the gas

composition at the SOFC anode outlet matches the TOFC model.

Blower power

A rule of thumb says that the blower consumes 10% of the produced

power [25]. Ẇ Blower is 5,5kW which corresponds to 10% of Ẇ SOFC ,SOLO

(see definition in equation 4.6 and 4.7 page 98), while the TOFC models

the fraction is in the range of only 5-8% of the net power.

Since the SOFC system in this project is integrated with an absorption

cooling unit, more heat exchangers are applied and hence it is expected

that the total pressure loss of the exhaust gases must be higher. Taking

this into account the blower power consumption seems to be reasonable.

101


4. SYSTEM DESCRIPTION

SOFC net efficiency

The net electrical efficiency of the SOFC subsystem, η SOFC ,el,SOLO (the

definition is shown in equation 4.8 page 98) is 54% which is a bit higher

than that of the TOFC models. This might partly be due to a higher

current density in the model of this project.

4.9.2 Absorption cycle

Some general recommendation (rules of thumb) about operation of

absorption cycles are given by SEG (Scandinavian Energy Group) [27].

These are valid for a single cycle only, but have been used in order

to validate the components in the absorption cycle (under single stage

configuration).

∆T EV AP,ABSO is the temperature difference of the absorber cooling

water outlet (T 37 ) and the evaporator chilling outlet (T 49 ). ∆T COND,DES

is the temperature difference of the condenser (COND1) cooling water

outlet (T 36 ) and the desorber (DES1) solution outlet (T 59 ).

∆T EV AP,ABSO = T 37 − T 49 (4.17)

∆T COND,DES = T 36 − T 59 (4.18)

∆T CFG,C HK = ∆T COND,DES − ∆T EV AP,ABSO (4.19)

∆T CFG,C HK must be a positive quantity and is typically approximately

20 ◦ C. At the standard parameter configuration in single cycle mode

(using additional reheating and wet tower cooling) ∆T CFG,C HK is 35 ◦ C

(∆T EV AP,ABSO = 21 ◦ C and ∆T COND,DES = 56 ◦ C) which is higher than the

typical value.

Part of the reason can be the relatively low condenser and absorber

temperatures provided by the wet cooling tower. If these temperatures

are increased by 5 ◦ C, ∆T CFG,C HK will decrease to 26 ◦ C. But no matter

how the temperature of DES1, COND1, EVAP or ABSO is set in the

model, ∆T CFG,C HK can not be brought to reach 20 ◦ C. This however is very

likely caused by the chosen values of CATD in the desorber, condenser,

evaporator and absorber.

102


4.9. Validation of Model

Distribution of heat rejection

The heat from the absorption cycle is removed by the condenser and the

absorber and according to [27] the distribution should be as follows:

˙Q ABSO = 56%

˙Q COND = 44%

For the single cycle at standard parameter configuration with

additional air pre heat and wet tower the heat removed by the absorber

and the condenser is ˙Q ABSO = 31,1kW (53%) and ˙Q COND = 27,7kW (47%)

respectively.

So in the model a slightly bigger fraction of the heat is removed by the

condenser. The reason is the same as described in the previous section

- low condenser/absorber temperature. If this is increased by 5 ◦ C, COP

will drop to about 0,7 and the fraction of the heat rejected by the absorber

will be 56%.

COP

According to [27], COP ABS should be between 0,70 and 0,75 almost independent

of the temperatures (and load). At the standard configuration,

the model gives a COP ABS of 0,80 which is a little higher than expected.

But this can be due to the assumptions that the heat losses as well as

pressure losses of the components have been neglected. Also the low

condenser/absorber temperature will increase the COP ABS .

Taking the above into consideration it is concluded that the temperature

levels of the absorption cycle and the general behavior of the absorption

model seems to be reasonable.

103


C H A P T E R

5

SIMULATION AND RESULTS

5.1 Basic absorption cooling

COND

1

HEAT

DES

COOLING

9

7

2

SHEX

3

VA

EVAP

4

11

12

VB

ABSO

PUMP

6

5

CHILLED WATER

COOLING

Figure 5.1: Diagram of single stage absorption cycle

In this section the single stage absorption cycle will be simulated

in order to demonstrate the general behavior of an absorption cycle,

independently of the rest of the system. Therefore the cooling tower is

105


5. SIMULATION AND RESULTS

eliminated by choosing ”manual” in the control panel of the EES model.

Instead, inlet temperatures and temperature differences of the condenser

and absorber are given explicit. The basic parameter configuration is

though the same as for the standard single cycle with cooling tower in

order to make it easier to compare.

The four temperatures of the desorber, condenser, evaporator and

absorber will be varied one at the time and presented in four separate

figures. These temperatures correspond to point 1, 2, 4 and 5 in figure

5.1. They temperatures will be shown in upper x-axis of the graphs.

A temperature change with reference to the standard parameter

configuration for each of the four temperatures is introduced and shown

on the lower x-axis on four graphs. As far as possible the four

temperatures will be varied 10 ◦ C up and down.

COP ABS (equation 1.1, page 8) is the most important indicator of how

the stand alone cycle performs. In each figure COP ABS , the pressures

(high and low) and the concentrations of the strong and weak LiBr

solution will be plotted (w ss and w ws ).

5.1.1 Changing the desorber temperature

The desorber temperature is equivalent to the temperature at which heat

is supplied to the absorption cycle 1 . Changing the desorber temperature

does not affect the high or the low pressure, see figure 5.2A.

On the other hand, the concentration of the strong solution (strong in

LiBr) flowing from the absorber to the desorber (see figure 5.1) is affected

by T DES . Since the high pressure is constant and the temperature of

the desorber is changed, it implies that the concentration of the strong

solution must change as well in order to keep the solution and vapor in

equilibrium (saturated liquid).

When the desorber temperature drops, w ss decreases as well, see

figure 5.2A. If the temperature decreases 10 ◦ C (corresponding to a

desorber temperature of 70 ◦ C) w ss becomes almost equal to w ws .

This means that the pumping factor (mass flow of LiBr solution in

the absorber-desorber cycle relative to the flow of generated refrigerant)

1 To avoid change in the amount of heat supplied, ˙Q HE AT,DES is given explicit for this

particular simulation. T min,W GHE X 2,w,i is set free.

106


5.1. Basic absorption cooling

Figure 5.2: A: T DES is the desorber temperature. ∆T DES is the change of the desorber

temperature relative to the standard parameter configuration (80 ◦ C). w ss and w ws is the

concentration of the strong and weak LiBr-solution on mass basis. p Hi g h and p Low is the

pressure at the condenser and evaporator respectively B: PF is the Pumping factor, which is

the ratio between the mass flow of the weak solution (ṁ ws ) and refrigerant (ṁ r ).

becomes very large as seen in figure 5.2B. This is the reason why COP ABS

drops rapidly at the left hand side of the graph of figure 5.2A.

There is no clear optimum for the desorber temperature with respect

to COP ABS - the curve is rather flat. So it seems there is no reason to

raise the desorber temperature above 80 ◦ C for the chosen parameter

configuration. In the following it will be examined why the COP

has a flat optimum at so low a temperature (rather than continuously

increasing with temperature like so many other thermodynamic cycles

do).

Changing the solution heat exchanger

At the standard parameter configuration ∆T min,SHE X = 5 ◦ C (ɛ SHE X = 0,9).

To find out why the COP optimum is flat it is now investigated what

happens if SHEX is either not present (ɛ SHE X = 0) or if the heat is ideally

transferred (∆T min,SHE X = 0). In figure 5.3A COP ABS is plotted as function

of ∆T DES for the three cases mentioned above.

107


5. SIMULATION AND RESULTS

Figure 5.3: A: Comparison of COP ABS for 1: a system without solution heat exchanger, 2:

at standard parameter configuration (∆T min,SHE X = 5 ◦ C) and 3: with ideal heat exchanging

(∆T min,SHE X = 0). B: The curves with dotted markers show the heat capacity flow of the weak

and strong solution. The curves with triangular markers show ∆T min at each end of the SHEX.

No SHEX

If the SHEX is not present, COP ABS will increase as long as T DES increases,

only limited by the maximum concentration of w ss (which is about 75%,

see appendix B.4 page 231). The explanation is that before evaporation

can take place, each kg of solution entering the desorber from the

absorber has to be heated up from 31 ◦ C (T ABSO ) to T DES which requires

energy without creating refrigerant. So it is an advantage to evaporate

as much water per kg of LiBr solution as possible. And this is done by

having a large difference in concentration between ws and ss (i.e. a high

desorber temperature).

Ideal SHEX

For the ideal SHEX (∆T min,SHE X = 0) COP ABS will have an optimum at

T DES = 72 ◦ C. At this point the difference in concentration of the strong

and weak solution is very small, which leads to a very large pumping

factor (PF), see figure 5.2B.

108

The reason why the SHEX makes a lower temperature more advanta-


5.1. Basic absorption cooling

geous seems to be the following:

When the desorber temperature is 72 ◦ C (optimum) the concentration

of the strong solution is only slightly higher than that of the weak

solution so the mass flow of the two flows is almost identical. This means

that the heat capacity flow (Ċ = ṁ · c p ) becomes almost equal as seen in

figure 5.3B

Now that Ċ is almost the same for both flows, ∆T min,SHE X will be

around zero in both ends of the SHEX as seen in figure 5.3B. This means

that when the weak solution comes out of the SHEX and enters the

desorber, it is already at the same temperature as the rest of the desorber

(72 ◦ C). This way all of the heat supplied to the desorber can be used to

evaporate refrigerant (water) from the solution instead of ”wasting” part

of it on heating up the weak solution entering the desorber.

If the desorber temperature was now increased to 80 ◦ C the weak

solution would only be 75 ◦ C when entering the desorber since the ∆T min

at the strong solution inlet would be 5 ◦ C even though the ∆T min at the

weak solution inlet is 0 ◦ C. So in that case some of the heat supplied to

the desorber would be needed for heating up the incoming solution to

80 ◦ C before evaporation could begin. Hence the desorber temperature

should not be too high.

Conclusion on Desorber Temperature

The investigations show that when the SHEX is omitted, a high desorber

temperature is an advantage since it minimizes the energy required for

heating up refrigerant into the desorber before evaporation can begin.

But the better the SHEX is, the more advantageous it becomes to use

a lower desorber temperature, since the SHEX can then do all of the ”pre

heating” of the weak solution whereby all energy input into the desorber

can be used for evaporating the refrigerant.

5.1.2 Changing condenser temperature

When the temperature of the condenser increases, the pressure increases

as well because the condensation mainly takes place in the two phase

region where pressure and temperature are dependent, see figure 5.4.

Since the temperature of the desorber is kept constant and the

pressure is equal to the condenser pressure, the concentration of the

109


5. SIMULATION AND RESULTS

Figure 5.4: T COND is the condenser temperature (upper x-axis). ∆T COND is the change of the

condenser temperature (lower x-axis). w ss and w ws is the concentration of the strong and weak

LiBr-solution on mass basis. p Hi g h and p Low is the pressure at the condenser and evaporator

respectively (right y-axis)

strong LiBr-solution (w ss ) must decrease in order to keep the solution

at equilibrium, see appendix B.4.2 page 232.

As w ss decreases it approaches w ws as seen in figure 5.4. If T COND

increases to 42 ◦ C the concentration of the strong and weak solution

becomes equal and COP ABS drops rapidly since no refrigerant is sent to

the condenser.

COP ABS has no optimum with respect to ∆T COND within the simulated

range - the condenser temperature should just be as low as possible.

But since the curve is almost flat on the left hand side of the graph, it

can be concluded that a condenser temperature of about 30 to 35 ◦ C is

sufficiently low for the given parameter configuration (of the single cycle

configuration).

110


5.1.3 Changing evaporator temperature

5.1. Basic absorption cooling

Figure 5.5: T EV AP is the evaporator temperature (upper x-axis) which must be above 0 ◦ C to

avoid freezing of the refrigerant (water). ∆T EV AP is the change of the evaporator temperature

(lower x-axis). w ss and w ws is the concentration of the strong and weak LiBr-solution on mass

basis. p Hi g h and p Low is the pressure at the condenser and evaporator respectively (right y-axis)

The evaporator temperature is proportional to the temperature at

which the chilling is supplied. It has a lower limit since the refrigerant is

water. This allows the standard evaporator temperature to be decreased

by only 1 ◦ C relative to the standard parameter configuration - the gray

area in figure 5.5 indicates the non-valid area.

When the evaporator temperature (T EV AP ) increases, the low pressure

(p low ) increases as well since T EV AP and p low are dependent in the two

phase region (see figure 5.5).

The pressure in the absorber is determined by the pressure in the

evaporator. An increase of p low thus decreases the concentration of the

weak solution (w ws ) because the temperature of the absorber is kept

constant while the solution must be in equilibrium.

111


5. SIMULATION AND RESULTS

COP ABS does not reach an optimum in the investigated temperature

range. It is evident that the performance increases with increasing

evaporator temperature, but the cooling also becomes less valuable as

the temperature increases. At 19 ◦ C the COP ABS reaches 0,88, but at

this temperature chilling could almost be provided by the cooling tower

directly, which would be much cheaper.

5.1.4 Changing absorber temperature

Figure 5.6: T ABSO is the absorber temperature (upper x-axis). ∆T ABSO is the change of the

evaporator temperature relative to the standard absorber temperature (lower x-axis). w ss and

w ws is the concentration of the strong and weak LiBr-solution on mass basis. p Hi g h and p Low

is the pressure at the condenser and evaporator respectively (right y-axis)

The heat from the absorber must be removed at a temperature

which is not too high. T ABSO does not affect the high or low pressure

which are constant, see figure 5.6. But an increase of T ABSO will affect

the concentration of the weak solution (w ws ) which will increase until

it reaches w ss at T ABSO = 41 ◦ C. At this temperature COP ABS drops

dramatically. The reasons for the shape of COP ABS is mainly the same

112


5.1. Basic absorption cooling

as described in section 5.1.1 about the desorber (now it is just the

strong solution concentration which is constant, and the weak solution

concentration which is changed).

So T ABSO and T DES should be adjusted relative to each other to give

the optimum performance. One should remember that since the heat

is rejected to the surroundings, T ABSO is to a certain extend determined

by the ambient temperature, so the concentration difference is probably

easiest to adjust by changing T DES . This would in praxis be done by

changing the flow rate of the LiBr solution relative to the heat input into

the desorber.

5.1.5 Summing up the general behavior of the

absorption cycle

In table 5.1 the characteristics of the absorption cycle is summed up. ↑

symbols an increase for the current variable. The ↕ for COP ABS in line one

indicates that the optimum is near the standard parameter configuration

value of T DES .

Table 5.1: General behavior of a single stage absorption cycle.

Temperature Pressure Concentration Performance

T DES ↑ ⇒ - ⇒ w ss ↑ ⇒ COP ABS ↕

T COND ↑ ⇒ p COND ↑ ⇒ w ss ↓ ⇒ COP ABS ↓

T EV AP ↑ ⇒ p EV AP ↑ ⇒ w ws ↓ ⇒ COP ABS ↑

T ABSO ↑ ⇒ - ⇒ w ws ↑ ⇒ COP ABS ↓

113


5. SIMULATION AND RESULTS

5.2 System configurations

In the previous section with the single cycle mostly COP ABS was used

(i.e. the ratio of cooling power and high temperature heat input into the

absorption cycle). This was typically around of 0,8 for Single Stage and

around 1,4 for Double Stage.

In the following sections primarily COP ABS,f uel will be used since this

shows how much cooling power the system provides per kW of fuel into

the system (which remains constant at 100kW). This is done because the

important thing for system optimization is how much cooling the system

produces in the end (it doesn’t help that COP ABS is increased by

a certain tweak if the heat flow into the absorption unit is at the same

time reduced by a greater factor, so that the cooling power as a total

drops). COP ABS,f uel will typically be around 0,4-0,5 corresponding to

40kW-50kW of cooling per 100kW of fuel input.

Three different aspects will be examined regarding the overall system

configuration:

• Single Stage (SS) vs Double Stage (DS) vs Double Stage with Dual

Heat (DH).

• Air Preheating (AP) vs No Air Preheat (-).

• Dry Cooling Tower (d) vs Wet Cooling Tower (w).

First SS, DS, and DH will be compared for AP and ”-AP” (all using a wet

cooling tower 2 ). Once the best of these six combinations has been chosen,

the two types of cooling towers will be compared. A figure with all 12

combinations can be seen in appendix E.1.1 (page 276).

For each figure in the following, the color convention will be as follows:

Blue represents COP ABS,f uel : the amount of cooling power generated

per fuel input (kW/kW).

Black represents η el ,sys,net : the amount of net electricity generated per

fuel input (kW/kW).

2 The same tendencies are observed when the dry tower is used, just with

COP ABS,f uel at a lower level

114


5.2. System configurations

Red represents η HW : the amount of energy used for hot water heating

per fuel input (kW/kW).

Since the fuel input is 100kW, each percent point of efficiency is equivalent

to 1kW.

5.2.1 Single, Double, Dual Heat (+/- Air Preheat)

No Air Preheat

From figure 5.7A it can be seen that if no air preheat is used, a pure

double stage cycle doesn’t deliver more cooling than a single cycle. This

is because of two opposite tendencies.

• The COP based on the heat flow into the desorber of the absorption

unit increases from 0,8 to 1,4.

• The heat flow itself is reduced since less energy can be extracted

from the exhaust gas of the SOFC (SS: T 22 =95 ◦ C, DS: T 22 =165 ◦ C,

while T 20 =246 ◦ C in both cases). So the Single Stage receives 29kW,

whereas the Double Stage receives only 16kW.

The two tendencies happen to almost exactly counterweigh each

other at the given parameter configuration (the cooling power is 23,3kW

for SS and 22,7kW for DS).

So the pure Double Stage doesn’t offer any more cooling power than

the Single Stage, although it does leave more energy in the exhaust gas,

which can be used for hot water production (23kW vs 10kW).

When the Dual Heat configuration is applied, DES2 still receives the

same amount of heat as for the Double Stage (16kW) by cooling down

the exhaust gas to 165 ◦ C. But now the exhaust gas is cooled down further

(to 95 ◦ C) in WGHEX2, so an additional 13kW is sent into DES1. This

significantly raises COP ABS,f uel which becomes 0,34. So the Dual Heat

input raises the cooling by 11kW, although the hot water production is

reduced from 23kW to 10kW. Since cooling, however, is assumed to be

115


5. SIMULATION AND RESULTS

more valuable than hot water 3 , the Dual Heat configuration is the best

solution when no air preheat is used.

eta | COP

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.10

No Air Preheat

0.23

0.23 0.23

0.10

0.34

0.53 0.53 0.52

eta_HW

COP_ABS,fuel

eta_sys,el,net

eta | COP

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

With Air Preheat

0.06

0.26

0.07

0.46

0.07

0.38

0.53 0.52 0.52

eta_HW

COP_ABS,fuel

eta_sys,el,net

0.1

0.1

0.0

SSw- DSw- DHw-

0.0

SSwA DSwA DHwA

Figure 5.7: A+B: Comparison of system configurations. SS = Single Stage, DS = Double Stage,

DH = Dual Heat. w = Wet cooling tower, d = Dry cooling tower. A = with Air preheat, - = no

air preheat

Air Preheat

Figure 5.7B: When Air Preheat is applied (by adding GGHEX4) much of

the energy remaining in the exhaust gas after the absorption unit can be

used to heat up the inlet air for the SOFC. This reduces the need for heat

transmission in GGHEX3 and hence T 20 is increased. So this way more

energy can be transferred to DES2 (DES1 for Single Stage).

The COP ABS,f uel doesn’t change so much for Single Stage, since it already

uses much of the exhaust gas energy to begin with.

Dual Stage, however, benefits very much from the air preheating, since

T 20 is increased from 246 ◦ C to 326 ◦ C. So now DES2 receives 33kW instead

of only 16kW when no Air Preheat is used.

3 why else use the Absorption cooling unit in the first place - if hot water was more

valuable, all the waste heat should just be used for hot water production

116


5.2. System configurations

Dual Heat also receives 33kW, but only 19kW is sent in through DES2

while the other 14kW goes directly into DES1 which is much less efficient

than DES2.

Conclusion about Air Preheat

When Air Preheat is not used, the Dual Heat configuration is superior.

But when Air Preheat is used, the pure Double Stage becomes even better

than Dual Heat.

Using the Air Preheat means that one more gas-gas heat exchanger

(GGHEX4) is needed, which will increase the price of the system. But

when GGHEX4 is added, GGHEX3 can be made somewhat smaller, since

it doesn’t have to supply so much heat. So this will partially compensate

for the extra cost of GGHEX4. Furthermore by using Double Stage rather

than Dual Heat, WGHEX2 can be omitted. So the price of DSwA and

DHw- will probably not be too far apart.

Hence it has been chosen solely to look at Double stage with Air

Preheat from now on.

5.2.2 Wet vs Dry cooling and ambient temperature

In the rest of the optimization/investigation process in this chapter, a

figure will be shown with the electrical efficiency (black), the absorption

cycle COP (blue) and the hot water efficiency (red). Sometimes another

figure will be presented to the right of this to help explain the observed

behavior.

It is examined in which interval of the ambient temperature the

absorption process will run, and how the ambient temperature affects

the performance of the system:

COP ABS,f uel

First it should be noticed from figure 5.8A that when the system uses the

dry tower it will only run when the ambient temperature is below 20 ◦ C,

and it is only effective when the temperature is below 18 ◦ C. If, on the

other hand, the wet tower is used, the system can be run at temperatures

up to 39 ◦ C (figure 5.8B).

117


5. SIMULATION AND RESULTS

Figure 5.8: Efficiencies and COP for Double Stage system with standard parameter

configuration. A: Dry Tower. The grey area is where the system is not able to run. B: Wet

Tower

So there is very little idea in using the absorption cooling unit in

conjunction with a dry tower - the ambient temperature has to be so low

for this to work, that the cooling service could probably just as well be

provided by blowing the ambient air over the product which needed the

cooling service. Furthermore air conditioning is rarely needed when the

ambient temperature is below 20 ◦ C, so a dry tower does not seem to be

usable for the double stage ABS unit 4

When the wet tower it used, the cooling COP increases somewhat

when the ambient temperature is decreased (see blue curve in figure

5.8B), but not at all as much as would have been the case for an electrical

air conditioner. But in very hot climates, the limit at around 38-40 ◦ C

could be a problem. It might be rare for so high a temperature to occur,

but when it does, air conditioning would be absolutely crucial.

Further investigations, however, show that if the temperature of

the high pressure desorber is increased, the condenser and absorber

temperature can be increased, whereby the system will be able to operate

4 A single stage ABS unit would be better as using a dry tower since the desorber

temperature of this is normally around 80 ◦ C, so it could be raised without any problem -

thereby making it possible to use a higher absorber and condenser temperature as well.

118


5.2. System configurations

in a hotter climate. If T DES2 is increased from 150 ◦ C to 190 ◦ C the limit of

the ambient temperature is increased from around 40 ◦ C to 50 ◦ C for the

wet tower. For the dry tower, the limit is increased from 20 ◦ C to 30 ◦ C.

But in order to avoid corrosion in the desorber, 150 ◦ C is generally

considered to be the maximum allowed desorber temperature [27]. So

for the very hot climate applications (>40 ◦ C) an option could be to use

more expensive more corrosion resistant desorber materials and increase

its temperature, or a single cycle could be used, which of course would

be cheaper but less efficient. The same tendencies go for the dry tower.

η sys,el ,net

For the dry tower, the electrical efficiency (black curve in figure 5.8A) is

quite steady except when the ambient temperature becomes high, which

leads to an efficiency increase due to lower cooling tower fan power since

the tower needs less cooling when the evaporator cooling production

decreases.

For the wet tower (figure 5.8B) the electrical efficiency increases

steadily with the ambient temperature. This is because of the following:

when the air temperature is high (and the relative humidity constant

at 40%), one kg of air can absorb a bigger amount of water since the

absolute humidity difference between the air inlet and the (saturated)

outlet becomes larger. This means that the air flow through the cooling

tower is lower at high ambient temperatures thereby reducing the fan

power consumption.

η HW

The hot water heating(η HW , red curve in figure 5.8) is bigger for low

ambient temperatures than for high ambient temperatures. But this is

because the temperature of the water to be heated up is assumed to be the

same as the ambient temperature. So when the ambient temperature is

low, the exhaust gas can be cooled down to a lower temperature whereby

more energy is transferred to the water.

5.2.3 ∆T min,Tower

The influence of the closest approach temperature difference on the two

different types of towers is examined in appendix E.1.3.1 page 280.

119


5. SIMULATION AND RESULTS

5.3 Partial optimization of STD parameters

In this section the standard (STD) parameters of the DSwA system

configuration (Double Stage, Wet Tower + Air Preheat) are partial

optimized.

5.3.1 Outer conditions

Evaporator temperature

The temperature level of the evaporator outlet (T EV AP ) is now investigated.

In a normal electrical air conditioner, the COP is strongly depen-

Figure 5.9: The outlet temperature of the cooling water (point 49) is 6 ◦ C in the standard

parameter configuration, and since ∆T min = 5 ◦ C this gives a temperature inside the evaporator

of 1 ◦ C. When T EV AP,w,o is increased, the temperature inside the evaporator increases by the same

amount.

dent on the evaporator temperature. But for the absorption unit it has

a much smaller effect (figure 5.9). When the evaporator outlet temperature

is increased from 5 ◦ C to as much as 30 ◦ C (the ambient temperature),

COP ABS,f uel is only increased 21% (9,5 percent points). So from

120


5.3. Partial optimization of standard parameters

this it can be concluded that an absorption cooling unit should preferably

be used to cool down things to low temperatures where electrical

units loose a bigger fraction of their COP - it is not good for just cooling

things a few degrees. But since the refrigerant is water, it is impossible to

get much lower than 5 ◦ C for a water-LiBr absorption unit (otherwise the

water freezes), so there is a quite sharp lower limit.

Relative humidity

The influence of the relative air humidity is now examined. The ambient

temperature is kept at 30 ◦ C:

Figure 5.10: A): The COP and efficiencies are shown together with the water consumption of

the cooling tower. B (right side): The green curves show the temperature of the air in and out of

the cooling tower. The blue curves show the temperature of the water in and out of the tower.

As can be seen from the dark blue curve in figure 5.10B, the model

of the cooling tower predicts a decrease of the water outlet temperature

when the relative humidity is decreased. This is because the wet bulb

temperature is reduced.

Figure 5.10A shows that from a COP perspective, it is most beneficial

if the ambient air is as dry as possible since the water can thereby

121


5. SIMULATION AND RESULTS

be cooled down to a lower temperature. But the water consumption

(kg/s per kW fuel input) raises considerably when the relative humidity

decreases. This is mainly because the water is cooled down to a lower

temperature which increases the need of heat removal by evaporation.

The slight increase in η sys,el,net for an increase in humidity comes from

a lower FAN power consumption (less cooling for the ABSO and COND1

is needed and less air is sent through the tower).

Furthermore with the standard parameter configuration the system

becomes very ineffective at generating cooling when the relative humidity

exceeds 0,7 (at 30 ◦ C ambient temperature). So in hot damp climates it

could be a problem to run the system.

Figure 5.11: The curves with the triangles show what happens if the temperature of the high

pressure desorber is increased from 150 ◦ C (STD parameter config.) to 160 ◦ C which is seen to be

an advantage for high humidity only

But it turns out that increasing the desorber temperature can remedy

this problem. So if the desorber temperature is just increased from 150

to 160 ◦ C, the maximum limit for the relative humidity is increased from

70% to 90% as seen in figure 5.11. The electrical efficiency and hot water

efficiency remains virtually unaffected by the desorber temperature.

122

Raising the desorber temperature is however only an advantage for


5.3. Partial optimization of standard parameters

damp or hot conditions - if the relative humidity is below 45% at an

ambient temperature of 30 ◦ C then the lower desorber temperature gives

a better COP.

5.3.2 Desorber temperatures

The temperature inside each desorber is assumed to be uniform i.e. the

outlet temperature of the refrigerant and the strong solution is the same

since the temperature is uniform everywhere inside the desorber.

The desorber temperatures influences the saturation concentration of

the LiBr-solution, and hence the temperatures can only be altered in a

certain interval for the model to work - one constraint is that the strong

solution has to be stronger than the weak solution.

The temperature of the high pressure desorber will be described first,

since this is more simple than the low pressure desorber.

Desorber 2

In most thermodynamic cycles a system will perform best when the

supplied heat is at a temperature as high as possible. So one would

expect that it would be beneficial to use a desorber temperature as high

as possible. But this turns out not to be the case. In fact the COP has

a maximum for a desorber temperature around 150 ◦ C (for the chosen

parameter configuration!) as can be seen in figure 5.12A. This is actually

quite fortunate since it fits very well with the limit of 150 ◦ C due to the

corrosion rate in the desorber.

There are several reasons for this. First of all the concentration of

the weak and strong LiBr solution should be neither too close neither

too far apart as explained in section 5.1. Secondly the amount of heat

being reused from COND2 to DES1 can be seen to have an optimum

around 150 ◦ C and a drastic decrease below 130 ◦ C (see orange curve in

figure 5.12B). The heat flow into DES2 is constant though, since a higher

T DES2 will increase T 22 , thereby preheating the SOFC inlet air even more

in GGHEX4 so that GGHEX3 will take less energy from the exhaust gas.

And this way T 20 will increase just as much as T 22 (purple and red curve).

123


5. SIMULATION AND RESULTS

Figure 5.12: A: Efficiencies and COP. B: The red and purple curves show the temperature before

and after heat supply to the absorption unit. The brown curve shows how much heat the high

temperature desorber receives, and the green curve shows how much heat DES1 receives (from

COND2).

Desorber 1

The temperature of the low pressure desorber (DES1) is somewhat

restricted by the temperature of the high pressure desorber (DES2).

When T DES2 =150 ◦ C, T DES1 must be between 68 ◦ C and 88 ◦ C for the system

to operate. From figure 5.13A it can be seen that the optimum of the blue

COP curve is rather flat though, so the exact temperature is not so critical

for the performance.

In the standard configuration, the temperature of DES1 is not given

explicitly since the system will not be able to run if e.g. T DES2 is altered

too much while T DES1 remains constant. Instead the ratio of the mass

flow rate of the refrigerant out of the desorber and the mass flow rate of

solution into the desorber is set equal for the two desorbers:

ṁ 50

ṁ 58

= ṁ70

ṁ 78

(5.1)

This is the same as saying that the difference between the strong

and weak LiBr-solution is the same for two desorbers. And figure

124


5.3. Partial optimization of standard parameters

Figure 5.13: A+B In the standard parameter configuration the temperature of the low pressure

desorber is set at the temperature where the strong solutions out of DES1 and DES2 are equal

(intersection of red lines on the right figure). But by removing this equation an giving T DES1

explicitly, this can be changed to see how it affects the performance of the system.

5.13B shows that the intersection of the two red concentration curves

actually gives a desorber temperature quite close to the optimum for

COP ABS,f uel .

5.3.3 SOFC subsystem

Now some of the parameters in the SOFC subsystem are investigated. As

mentioned earlier: the anode and cathode side of the SOFC has the same

inlet temperature and the same outlet temperature.

Changing ∆T SOFC

A high temperature increase over the fuel cell (∆T SOFC ) is desirable

for several reasons. One of the reasons is that it reduces the required

air flow through the fuel cell thereby decreasing the blower power

consumption. But ∆T SOFC can in practice not be too high, since a higher

125


5. SIMULATION AND RESULTS

outlet temperature of the cell will increase degradation while the inlet

temperature can not be lowered too much if the reactions are to take

place at an acceptable rate. New materials might however change this

in the future so it is now investigated how ∆T SOFC affects the system.

The cell inlet temperature is kept constant at 690 ◦ C, so only the outlet

temperature changes.

Figure 5.14: A The white area is where the SOFCs can run today. The light grey area is what

is likely to become possible in the near future. The dark grey area is probably longer out in the

future. B The green curve is the heat consumption of DES2. The Brown curves are the temp.

before and after heat supply to DES2.

From figure 5.14A it is seen that the electrical efficiency will benefit

from a higher ∆T SOFC . In the cells used today, ∆T SOFC can not be much

higher than 90 ◦ C, but in the near future it is likely to become possible to

increase that number to 120 ◦ C [25], so this should increase the electrical

efficiency from 0,51 to 0,55 (an 8% increase).

The COP of the absorption unit remains virtually unaffected. Since

the difference between T 20 and T 22 (brown curves) increases, one might

expect the absorption unit to generate more cooling. But the temperature

difference increase is accompanied by a decrease in exhaust gas mass

flow, so the heat supply to DES2 (green line) remains almost constant.

126


5.3. Partial optimization of standard parameters

Figure 5.15: A Blower Power and Air Utilization in the SOFC. B Nernst potential, cell voltage

and Area Specific Resistance.

Figure 5.15A+B shows why the electrical efficiency changes - three

things occur when the outlet temperature of the cell increases:

1. The blower power consumption (black curve) decreases because of

a smaller air flow (green line: big air utilization = small air flow).

2. The Nernst potential (grey curve) decreases which in itself reduces

the cell voltage.

3. But at the same time the Area Specific Resistance (blue curve)

decreases. From figure 5.15B it can be seen that the ASR decrease

is more dominant than the Nernst potential drop, so as a total, the

cell voltage increases (brown curve).

Changing T SOFC ,in

Now the inlet temperature of the SOFC is examined. ∆T SOFC is kept

constant, so when the inlet temperature is increased x degrees, so is the

outlet temperature. Again, it is hard to get the inlet temperature much

lower than 650 ◦ C if the chemical reactions are to take place.

127


5. SIMULATION AND RESULTS

Figure 5.16: A+B It is not possible to run the cell with a voltage (brown curve) of less than

0,7kW, since the Nickel will then be oxidized. So at the standard parameter configuration, the

inlet temperature can not be lower than 650 ◦ C although it becomes possible if the current draw

is reduced).

From figure 5.16A it is seen, that the electrical efficiency is increasing

with the temperature of the SOFC inlet. As can be seen in figure 5.16B,

this is due to two of the three factors mentioned in the section concerning

∆T SOFC :

1. The Nernst potential (grey curve) decreases which in itself reduces

the cell voltage.

2. At the same time the Area Specific Resistance (blue curve)

decreases. Since the ASR decrease is more dominant than the

Nernst potential drop, so as a total, the cell voltage (brown curve)

increases.

This time the blower power does not change since the air flow is constant.

The COP of the absorption cooling unit decreases with T SOFC ,i , since

less energy is available in the exhaust gas when the electrical efficiency

of the SOFC is increased.

128


Anode recycling (α SPG1 )

5.3. Partial optimization of standard parameters

There are several reasons for using anode recycling. First of all it supplies

water for the pre reformer. But it also means that more the fuel is used,

since some of the fuel that didn’t react the first time through the SOFC

will react next time. This way more of the fuel will be used even though

the fuel utilization factor from the SOFC point of view remains constant

at U f =0,7 (it just means that every time the fuel is sent through the cell

70% of it will be used in the electrochemical reaction).

There is, however, a downside by the anode recycling. The

concentration of the species CO, CO 2 , H 2 , and H 2 O is affected by the

recycling . Generally the concentration of the reaction products are

increased, which makes both the Nernst potential and the cell voltage

decreases when the anode cycling fraction is increased (grey and brown

curve in figure 5.17B).

Figure 5.17: A+B The OC ratio (green) should be above 2 to avoid carbon depositing, so the

recycling fraction should not be below 0,6.

From figure 5.17A it can be seen that the increased use of the fuel in

the SOFC more than compensates for the drop in cell voltages, so elec-

129


5. SIMULATION AND RESULTS

tricity wise it is a good idea to increase the anode recycling 5 . It can also

be seen from the green line in figure 5.17B that the recycling fraction can

not be below 0,6, since the OC ratio at the anode inlet will then fall below

2, which would leat to carbon depositing.

The COP of the absorption unit decreases with increased anode recycling.

This is mainly due to the SOFC using a bigger fraction of the energy

in the fuel to produce electricity, thereby leaving less heat for the absorption

cooling unit. So although the electricity generation raises when

the recycling is increased, the decrease in COP ABS,f uel is about twice as

big. So for each kW electricity gained, 2kW cooling is lost.

SOFC load (i d )

In certain situations, such as during a heat wave, it might be desirable to

generate as much cooling as possible even if it would severely lower the

electricity production. In such cases more of the energy in the fuel could

be used for the absorption unit and less for the SOFC system. Given a

fixed number (and size) of stacks, this can be done in two ways, which

will be compared in the following:

1. Lowering U f : All fuel is still sent through the SOFC. But less

current is drawn, and hence the utilization factor decreases, leaving

more fuel for the burner.

2. Fuel Bypass: Only some of the fuel is sent through the SOFC, while

the rest is fed directly to the burner (completely bypassing the fuel

cell). The utilization factor of the fuel cell remains constant at 0,7.

Figure 5.18 compares the two methods. When Fuel Bypassing (2) is

used, the current density can go all the way from 0 to 3000A/m 2 6 .

But in case (1) where all the fuel has to go through the SOFC, the

current density may not fall below 2100A/m 2 . Because when all the fuel is

sent through the pre reformer and fuel cell, most of it is reformed, which

5 The model does, however, not include blower power for the recycling blower, but

since the anode side volume flow is quite small, it should not consume especially much

power

6 It has been chosen to monitor the current density, since it is easily comparable to

fuel cells of other sizes due to its independence of size

130


5.3. Partial optimization of standard parameters

Figure 5.18: Triangular markers (Case 1) is when all the fuel is sent through the cell (and U f

varies). Round markers (Case 2) is when some of the fuel is by passed the SOFC and fed directly

to the burner (U f remains constant).

is an endothermic reaction. But the exothermic electrochemical reaction

only occurs at a rate corresponding the current draw, and the exothermic

water gas shift is not enough to make up for the heat consumption of the

endothermic reforming. Furthermore the heat generation due to ASR

loss decreases when the current draw is minimized. So when i d goes

below 2100A/m 2 , the fuel cell will lack heat, and its inlet temperature has

to be higher than the outlet temperature now that the chemical reactions

sum up to be endothermic

It can, however be seen from figure 5.18 that for current densities

over 2100A/m 2 , sending all the fuel through the Fuel cell gives the best

η sys,el ,net (while COP ABS,f uel is almost identical). But for current densities

below 2100A/m 2 it is necessary to bypass some of the fuel directly to the

burner.

Method 1 is more efficient, but only method 2 can be used for lower

current densities. Both these ways of increasing cooling power at the

expense of electrical power will now be examined:

131


5. SIMULATION AND RESULTS

Method 1: Lowering U f

The size and number of stacks is held constant, and the fuel input

remains at 100kW into GGHEX1, but the fuel utilization factor varies

with the current density.

Figure 5.19: A+B: The x-axis now represents the Utilization factor, the corresponding current

density can be seen as the green line. The results are only valid for U f > 0,35 since below this

value the SOFC will not generate enough heat to maintain its temperature throughout the cell

Figure 5.19B shows what happens when all the fuel is sent through

the SOFC and the current density is varied:

When more current is drawn, the fuel utilization increases. But the

Nernst potential (grey curve) drops because of the higher concentration

of products and lower concentration of reactants for the electrochemical

reaction. The cell voltage (brown curve) is further decreased, since

the increased current density will lead to a bigger voltage loss (V cell =

V Ner nst − ASR · i d ). It is seen from η sys,el ,net (black curve) in figure 5.19A

that these two tendencies approximately counterweigh each other in the

region 0,6< U f


5.3. Partial optimization of standard parameters

that it is an advantage to decrease fuel utilization to around 0,55 (by

having a current density at around 2600A/m 2 ), since this increases

the cooling power significantly without any considerable decrease in

electrical power production.

Method 2: Fuel Bypass

The size and number of stacks is held constant 7 , and the total fuel

input remains 100kW, although some of it goes directly into the burner.

The Fuel utilization factor remains 0,7 so when no fuel is bypassed the

fuel cell, the current density is 3000A/m 2 . When the current density is

decreased, the fuel bypass will go up in order to keep the fuel utilization

factor at 0,7.

Figure 5.20: The green curve shows the fuel bypass fraction - how big a part of the total fuel

input which is sent directly into the burner.

The green line in figure 5.20 shows how big a fraction of the total fuel

input which is sent directly into the burner without going through the

fuel cell first.

7 The system size is 20,15 stacks since this corresponds to the standard configuration

- of course the number of stacks will have to be an integer in reality.

133


5. SIMULATION AND RESULTS

As expected, η sys,el ,net decreases when the current density is reduced,

and below 300A/m 2 the electricity generation is not even enough to cover

the blower, fan, and pump power consumption.

But as desired, the COP of the absorption unit increases, resulting

in COP ABS,f uel approaching COP ABS (which is 1,4) when all the fuel is

bypassed the fuel cell. COP ABS,f uel will never actually reach COP ABS ,

since some of the fuel input into the burner will end up going out the

system at point 24.

So during high cooling demand, 100kW of fuel can give 130kW 8 of

cooling instead of giving the usual 38kW cooling and 52kW electricity.

Thus by sacrificing 1kW of electricity, 1,8kW of cooling can be gained.

There are however two drawbacks:

1. If the absorption cooling unit should be able to generate 130kW of

cooling, all of its components have to be much bigger, than if 38kW

is maximum 9 .

2. From an energy point of view it would be more beneficial to

maintain the high electricity production during cooling peak

demand, and instead use the generated electricity to drive an

electrical air conditioning unit where COP is typically in the range

of 3-4. Of course the savings in fuel would have to be held up

against the extra cost of the electrical unit minus the extra cost of

buying a bigger absorption cooling unit.

So to sum up: if only a little more cooling is needed, the current draw

can just be minimized thereby lowering the fuel utilization factor thereby

leaving more heat for the absorption unit. If on the other hand a lot

more cooling is needed some fuel can be sent directly into the burner.

The latter method also makes it possible to maintain a high electricity

generation while generating more cooling by adding fuel to the burner

without diminishing the fuel flow into GGHEX3.

The best solution does however seem to be using the generated

electricity from the SOFC to run an electrical air conditioner.

8 it is not possible to go below i d = 300A/m 2 since there is not enough electrical

power to drive the blower.

9 in the zero dimensional model it is not possible to see what effect an increased

flow will have on components of a given size, so the calculated COP is based on the

components varying in size with the cooling power.

134


5.3. Partial optimization of standard parameters

5.3.4 Closest Approach Temperature Differences (∆T min )

In this section, the effect of the closest approach temperature difference

∆T min of the various heat exchangers will be investigated. In theory

∆T min can approach 0 but in praxis there will always be undesired

losses, mixing, resistances and heat transmission in the direction of the

tubes/plates. Hence the real values will be above zero. Since heat

transmission in a liquid is generally better than in a gas, the standard

closest approach temperature has been set differently for the different

heat exchanger groups (depending on the phase of the fluid). Thus each

group of heat exchanger will be investigated separately in the following.

Water-Water Heat exchangers

This group includes the evaporator, absorber, desorber2 10 and the

internal LiBr solution heat exchangers. These are all liquid-liquid with

a standard ∆T min of 5 ◦ C. All of them are now investigated in the range

from 0 to 16 ◦ C: As expected, the system performs better if more efficient

exchangers (lower ∆T min ) are used. The tendency is, however, not as

pronounced as one might have expected. From figure 5.21 it is seen that

the evaporator, absorber and SHEX1 are the most important of the waterwater

heat exchangers. The cooling power output increases around 3-

4% when ∆T min is reduced from 5 ◦ C to 0 ◦ C. If ∆T min is increased, the

absorber suddenly becomes the most sensitive, and above 10 ◦ C it heavily

decreases the COP.

When it comes to value for money, it looks like it would be beneficial

to buy a more efficient SHEX1 and a less efficient SHEX2, since COP

is about three times more sensitive to SHEX1 than SHEX2. Of course

SHEX1 is almost twice as big as SHEX2, since it contains the flow of

both desorbers, so decreasing its ∆T min will probably be about twice as

expensive as for SHEX2 per degree Celsius, but the gain would also be

three times as large.

CATD of DES2 is seen to have very limited effect on the COP, so it

doesn’t really matter if the water circuit (point 41 to 43) is used or if

WGHEX1 and DES2 were instead integrated.

10 ∆ T,min,DES1 is not examined since WGHEX2 and COND2 are assumed always to

be integrated. ∆ T,min,DES2 on the other hand could be relevant, if the absorption cooling

unit was originally indirect fired.

135


5. SIMULATION AND RESULTS

Figure 5.21: The influence of the Closest Approach Temperature for the liquid-liquid HEXes on

the COP (STD value is 5 ◦ C). The electrical efficiency is not shown since it remains virtually

constant.

Condensers (Heat exchangers)

The two condensers have liquid water inside the tubes, whereas the

refrigerant on the outside is in the 2phase region (changing from higher

gas quality to lower gas quality (saturated water)). So these heat

exchangers must be more efficient than water-gas heat exchangers but

less effective than water-water heat exchangers. Hence their standard

∆T min is 10 ◦ C. They are also investigated from 0 to 16 ◦ C: As can be seen

from figure 5.22, both condensers are far less sensitive to ∆T min than the

water-water heat exchangers, and actually the system does not benefit

from having a more efficient Condenser.

Condenser 1 is a little more sensitive to ∆T min and as this increases,

the slope of the curve becomes more negative. But when it is compared to

the black line for the absorber in figure 5.21 an interesting fact is revealed.

It turns out that the absorber curve is considerably steeper than the

Condenser1 curve (figure 5.22). This shows than the temperature level

136


5.3. Partial optimization of standard parameters

Figure 5.22: The influence of the Closest Approach Temperature for the condensers on the COP

(STD value is 10 ◦ C). The electrical efficiency remains virtually constant.

is more important for the absorber than for Condenser1. In the cooling

tower circuit the condenser has been connected before the absorber

which means that COND1 will be colder than ABSO (since this order

is the normal for absorption cooling machines according to [27]). But as

these curves show, it would be more beneficial to connect them in the

other order so that the absorber becomes colder than the condenser.

To investigate this, simulations were made with the ABSO and

COND1 in the opposite order, but it turned out that it did not give a

higher COP. 11 . It was hence chosen not to use that configuration anyway.

Water-Gas Heat exchangers

The blue curve in figure 5.23 show how COP ABS,f uel depends on the

CATD of WGHEX1 (Water gas heat exchanger supplying the absorption

11 When the temperature of the two components were changed at the same time they

affected each others optimum and the COP dependency on the exact temperature.

137


5. SIMULATION AND RESULTS

Figure 5.23: The influence of the Closest Approach Temperature for the Water-Gas HEXes on

the COP (STD value is 15 ◦ C). The electrical efficiency remains virtually constant. The brown

and green line is the temperature of the exhaust gas before and after heat supply to DES2.

unit with heat). If WGHEX1 becomes less effective (increase of ∆T min )

T 21 will increase but so will T 20 due to the air preheating in GGHEX4

(which means less heat transmission in GGHEX3) 12 .

Gas-Gas Heat exchangers

The GGHEX 1,2, and 3 have not been investigated, since their ∆T min

is not given explicitly. GGHEX 1 and 2 have the same (unspecified)

effectiveness. GGHEX3 is fed with the temperatures at point 13,14, and

19, so ∆T min can not be specified. So only GGHEX4 will be examined

here. GGHEX4 reuses some of the exhaust gas heat after the absorption

unit to preheat the fuel cell inlet air, which means that GGHEX3 can leave

more of the exhaust gas energy for the absorption unit. So as expected

COP ABS,f uel will increase then GGHEX4 becomes more effective, whereas

12 WGHEX2 is not used in the standard configuration, end WGHEX3 will be

examined in section 5.3.6 page 140

138


5.3. Partial optimization of standard parameters

Figure 5.24: The influence of the Closest Approach Temperature for the Air Pre heater

(GGHEX4) on the COP (STD value is 25 ◦ C). The electrical efficiency remains virtually

constant.

the hot water generation will fall, since there is less energy in the exhaust

gas at point 23.

It appears that GGHEX4 is one of the most important heat exchangers

(when it comes to COP variation). When its ∆T min is decreased 50%

(from 25 ◦ C to 12,5 ◦ C), COP ABS,f uel increases from 45,6% to 48,9%. The

second most important heat exchanger (the evaporator) only increases

the COP ABS,f uel from 45,6% to 46,5% when its ∆T min is decreased 50%

(from 5 ◦ C to 2,5 ◦ C).

So cutting ∆T min in halves will give 3,6 percent points for GGHEX4

and only 0,9 percent point for the evaporator. And if GGHEX4 is made

more efficient, GGHEX3 can be made less efficient, since T 14 must remain

constant.

139


5. SIMULATION AND RESULTS

5.3.5 ∆T for external circuits

The difference between the highest and lowest temperature in each of

the external cycles, has been set to 5 ◦ C as standard. They have been

investigated but they only give rise to a slight change in COP, so the

graphs and their description has been placed in appendix E.1.2 page 277.

5.3.6 Hot Water

∆ T,min WGHEX3

WGHEX3 uses the last of the energy in the exhaust gas to heat up

water, which for instance could be used as domestic hot water in a hotel.

The CATD of WGHEX3 is now investigated (it has, of course, only an

influence in the hot water production, not on the absorption unit).

Figure 5.25: The red lines shows how much heat is transferred to the how water when the

WGHEX3 becomes more or less efficient. The water flow into the WGHEX 3 is adjusted so the

Closest Approach Temperature Difference is the same in both ends - hence the outlet temperature

of the water is influenced as well at the amount of energy extracted from the exhaust gas.

140


5.3. Partial optimization of standard parameters

When ∆T min,W GHE X 3 is decreased, a bigger amount of the energy left

in the exhaust gas can be used to water heating, and furthermore the

temperature to which the water can be heated increases (se figure 5.25).

In the investigation ∆T min has been given the same value in both ends

of the HEX, but in a real system their relationship will be controlled by

the amount of water sent into the HEX (a big water flow means that the

smallest ∆T min will occur at the gas outlet and vice versa). So if ∆T min is

e.g. 15 ◦ C the temperature of the water doesn’t necessarily have to be 67 ◦ C

as shown in the figure. By sending more water through, ∆T min would be

smallest at the gas outlet end, yielding a smaller water outlet temperature

(e.g. to avoid the guests on a hotel from being burned on the hot water

from the tap).

It can be seen from the red curve, that ideally 40% more hot water

could be produced if there were no losses in the HEX (∆T min = 0 rather

than 15 ◦ C).

141


5. SIMULATION AND RESULTS

5.4 Sensitivity Analysis

In the previous sections some of the most important/interesting parameters

have been examined thoroughly for different of values. In the following

section spider diagrams will be shown for a larger range of parameters,

subdivided in 4 groups: Closest Approach Temperature Differences,

Pressure Losses, Heat Losses, and (other) Key Parameters. For

each group the effect on the electrical efficiency will be shown on the left

graph, and COP ABS,f uel on the right graph. All of the spider diagrams are

for the standard system configuration (Double Stage, Wet Tower, with

Air Preheat).

The Y-axis show the percent increase of the COP (so a COP increase

from 50% to 51% corresponds to 2% on the y-axis). The x-axis generally

shows the percent increase in the input parameters for the standard

configuration, although for the pressure losses in the absorption cycle,

the standard parameter inputs are 0. So for these pressure loses the

percent change is of the absolute pressure in that component. The heat

loss is also 0 in the standard parameter configuration, so here it has been

chosen to let the x-axis go from 0 to 1kW while the fuel input is kept at

100kW.

The y-axis has the same range in all (but one) of the figures (-5% to

5%). This makes it easier to compare the effect of the different groups

of parameters, although it does of course make it harder to see the exact

value of the less important groups - but again: if all parameters in a group

has a very small effect on COP and η sys,el,net their exact value doesn’t

matter much. The only exception is the group ”Key Parameters”, which

has an y-axis going from (-10% to 10%) since some of those parameters

are particularly sensitive.

5.4.1 Closest Approach Temperature Difference

These temperatures have been estimated only based on the type of fluids

in each heat exchanger (water-water, gas-gas etc.), so they are relatively

uncertain, and it is not unlikely that they can be two times as big as

estimated or only half as big (x-values going from -50% to +100%).

142


5.4. Sensitivity Analysis

ηsys,el,net increase

∆T min : Electrical efficiency

5%

4%

3%

2%

1%

0%

-100% -50% 0% 50% 100%

-1%

-2%

-3%

-4%

-5%

∆T min increase

ABSO,s,o

COND2,r,o

EVAP,r,i

GGHEX4,c,o

SHEX1,ws,i

SHEX2,ws,i

TOWER,a,o,wet

WGHEX1,w,i

WGHEX3,w,i

COPABS,fuel increase

∆T min : COP

5%

4%

3%

2%

1%

0%

ABSO,s,o

COND2,r,o

EVAP,r,i

GGHEX4,c,o

SHEX1,ws,i

SHEX2,ws,i

TOWER,a,o,wet

WGHEX1,w,i

WGHEX3,w,i

-100% -50% 0%

-1%

50% 100%

-2%

-3%

-4%

-5%

∆T min increase

Figure 5.26: The relative influence of the Closest Approach Temperatures on η el ,sys,net and

COP ABS,f uel . The reason that some of the influential curves only ranges from -49% to 99% on

the x-axis is to make the lines hidden below them visible.

η sys,el ,net

The most important CATD (see figure 5.26A) is that of the cooling tower

(-3,5%) since a higher ∆T min means a lower air outlet temperature, which

requires more air flow (and more fan power). GGHEX4 only has a slight

influence (0,5%) because it changes the cooling power and hence the

blower power for the cooling tower.

COP ABS,f uel

The CATD is most important for the GGHEX4 (-15%). The second most

important is the evaporator (-5%) then comes the SHEX1 (-4%) (see

figure 5.26B). So if any of the ”heat exchanger components” should be

improved, those three are the most important.

5.4.2 Pressure Losses

Generally the components in the SOFC system and all the heat exchangers

involving exhaust gas only influence the electrical efficiency (since

a bigger pressure loss leads to a bigger blower power consumption), so

143


5. SIMULATION AND RESULTS

these are only included in the figure with the electrical efficiency (figure

5.27A). The components in the ABS system generally only affect the cooling

power so these are only included in the figure with the COP (figure

5.27B).

ηsys,el,net increase

SOFC system Pressure Losses: El. efficiency

5%

4%

3%

2%

1%

0%

∆pBurn,i,2

∆pGGHEX3,c

∆pGGHEX3,h

∆pGGHEX4,c

∆pGGHEX4,h

∆pMIXG2,i,1

∆pSPG2,o,1

∆pWGHEX1,g

∆pWGHEX2,g

∆pWGHEX3,g

-50% -30% -10% 10% 30% 50%

-1%

-2%

-3%

-4%

-5%

Increase of ∆p (relative to std parameter cfg.)

COPABS,fuel increase

ABS unit Pressure Losses: COP

5%

4%

3%

2%

1%

0%

-10% -5% 0% 5% 10%

-1%

-2%

-3%

-4%

-5%

Increase of ∆p compared to absolute pressure

∆pABSO,r

∆pABSO,s

∆pCOND1,r

∆pCOND2,r

∆pDES1

∆pSHEX1,ss

∆pDES2

∆pSHEX1,ws

∆pEVAP,r

∆pMIXL1,1

∆pMIXL1,2

∆pMIXR1,1

∆pMIXR1,2

∆pSHEX2,ss

∆pSHEX2,ws

Figure 5.27: A Note that the left figure shows the components of the SOFC system and exhaust

gas. These components have a pressure losses to begin with, so the x-axis shows the percentage

increase of this value. B The right figures shows the components of the ABS system. They do not

have a pressure loss to begin with (it is zero as standard). So for these the percentage increase of

the loss (x-axis) is of the absolute pressure in the given component.

η sys,el ,net

The pressure losses in the SOFC system have been approximated to

values from the TOFC models, so they are assumed to be relatively

reliable, and hence they are assumed to lay within +/- 50% of the

standard parameter value.

It can be seen that all the pressure losses are relatively insignificant

- the most influential is the Burner and GGHEX3, which can change the

electrical efficiency one percent (0,5 percent point), see figure 5.27A. The

reason why these have a bigger influence than the other pressure losses

is, that the standard loss is 4kPa in both of these (while the pressure

loss is smaller for each of the other components) which means that if

144


5.4. Sensitivity Analysis

the pressure loss is increased by 50%, it means a larger increase in kPa

than for the other components.

COP ABS,f uel

In the standard parameter configuration the pressure losses of the

absorption unit components have been neglected. Hence it is not possible

to talk about increasing the pressure loss by a certain percentage. So

another way had to be found, and since the absolute pressure changes

very much (from 0,65kPa in the evaporator to 120kPa in the high

temperature desorber) it has been chosen to let the pressure loss be a

percentage of the total (absolute) pressure in each component. It has

been chosen to use 10% and the values are only plotted on the positive

x-axis, since a negative x-axis would suggest a pressure increase for the

components where the standard pressure loss is zero.

For the absorption cycle the most important components are seen to

be the evaporator and absorber (figure 5.27B). COP ABS,f uel is decreased

a little less than 1,5% if the pressure loss of EVAP and ABSO is 0,066kPa

(10% of the total pressure which is 0,66kPa). And these components even

have the disadvantage, that the volume flow of fluid in them is quite

large, since the low pressure increases the specific volume of the gas.

But again the influence on COP is quite small relative to e.g. CATD

and some of the parameters to come in the next subsection.

5.4.3 Heat Losses

η sys,el ,net

It is seen that the heat losses generally have a very limited effect on

the electrical efficiency with the exception of the SOFC, which actually

increases the net generated electricity by almost 1%, see figure 5.28A.

This is because less cooling of the SOFC is needed, so less air is sent

through the blower, which diminishes blower power consumption.

COP ABS,f uel

The absorption unit generally suffers when heat losses occur, since it

means less energy for evaporating the refrigerant in the desorbers. The

difference between the different components (see figure 5.28B) occur

145


5. SIMULATION AND RESULTS

Heat Losses: Electrical efficiency

5%

4%

3%

BURN

DES1

DES2

PR

SHEX1

SHEX2

SOFC

Heat Losses: COP

5%

4%

3%

BURN

DES1

DES2

PR

SHEX1

SHEX2

SOFC

ηsys,el,net increase

2%

1%

0%

-1.0 -0.5 0.0 0.5 1.0

-1%

-2%

-3%

-4%

-5%

Component heat loss [kW]

COPABS,fuel increase

2%

1%

0%

-1.0 -0.5 0.0 0.5 1.0

-1%

-2%

-3%

-4%

-5%

Component heat loss [kW]

Figure 5.28: Component heat loss vs A: η sys,el ,net . B: COP ABS,f uel . A+B: None of the

components have been given a heat loss in the standard parameter configuration, so it is not

possible to talk about a percentage increase in heat loss. Hence it has been chosen to see what

happens if 1kW of heat is lost to the surroundings in some selected components (the total fuel

input into the system is still 100kW).

because of the following: When heat is lost before DES2 it reduces the heat

input into both desorbers whereas heat lost after DES2 will only reduce

the heat input into the low temperature desorber.

5.4.4 (Other) Key Parameters

The last group concerns a range of different parameters mainly concerning

the SOFC system. Many of the parameters themselves have been

estimated, so their value is associated with a significant degree of uncertainty.

For each of them it has been estimated to the best extend of the

authors capability how much the true value may be below or above the

chosen parameter value (in appendix D.2 page 272 it is described how

these values have been chosen). Then these two values have been used

to define the interval in which each parameter is plotted in the spider diagram

in figure 5.29. So from these spider diagrams three things can be

read:

146


5.4. Sensitivity Analysis

1. The x-value in each end of a curve shows how much the real input

is (at most) likely to deviate from the chosen parameter value.

2. The y-value in each end of a curves shows how much the COP

or electrical efficiency will change if the x-value is as far from the

standard parameter value as the interval allows.

3. The slope of each curve shows how much the COP or electrical

efficiency will change if the given input parameter changes 1%.

ηsys,el,net increase

Key Parameters: Electrical efficiency

10%

8%

6%

4%

2%

0%

-100% -50% 0% 50% 100%

-2%

-4%

-6%

-8%

-10%

Paramter increase

ASR

∆pTower,air,wet

∆TSOFC,av

ηWB,Tower

FR

FW

id

ηFAN

ηBLOWER

COPABS,fuel increase

Key Parameters: COP

10%

8%

6%

4%

2%

0%

-100% -50% 0% 50% 100%

-2%

-4%

-6%

-8%

-10%

Parameter increase

ASR

∆pTower,air,wet

∆TSOFC,av

ηWB,Tower

FR

FW

id

ηFAN

ηBLOWER

Figure 5.29: A range of different parameters are changed and the effect on η el,sys,net (A) and

COP ABS,f uel (B) is plotted. Note that the y-axis scale has been increased to 10% (from 5% in

the previous figures).

η sys,el ,net

The current density (blue curve in figure 5.29A) doesn’t change so much

in itself, but each percent change has a very big influence on the electrical

efficiency, so it becomes the overall most important parameter so it seems

to be a good idea to buy a little more cells per kW of fuel input (this will

decrease current density).

The ASR (black) also has a very big influence on the efficiency despite

a limited uncertainty on the input (x-) value. The pressure loss of

147


5. SIMULATION AND RESULTS

the cooling tower(orange) is also seen to have a big influence (due to

increased FAN power consumption) mostly because the input value is

associated with a large uncertainty. The temperature at which ASR is

evaluated (T SOFC ,out − ∆T SOFC ,av ) is also significant. And the isentropic

efficiency of the blower (turquoise) has a big influence on the blower

power.

COP ABS,f uel

The COP generally shows the opposite tendency, see figure 5.29B. The

things which are good for electrical efficiency are bad for COP and vice

versa. The only exceptions are cooling tower pressure loss (which is

neutral for COP) and an increased fraction of reforming (FR) in the pre

reformer, which seems to be bad for COP as well as η.

148


5.5 Total optimization of system

5.5. Total optimization of system

Now where all the different parameters of the standard parameter

configuration have been investigated it is time to optimize the system

(Double Stage, Wet Tower + Air Preheat). Four things will be viewed:

1. The values of the ABS subsystem (mainly ∆T min and T DES ) will be

adjusted/improved.

2. The current (density) draw will be optimized to give the optimum

combination of electricity and cooling.

3. Future Case: What happens if the SOFC tolerate a higher

temperature at the outlet.

5.5.1 Absorption subsystem

In the standard parameter configuration all the heat exchangers in the

absorption cooling subsystem were given a ∆T min depending only on

the phase of the fluids going through them (liquid-liquid = 5 ◦ C, liquidliquid/gas

= 10 ◦ C, and liquid-gas = 15 ◦ C). From the investigations in

the previous sections it was seen that the components in the following

list were the most important for the COP (none of them had any

significant influence on electrical efficiency. The list shows how much

the COP ABs,f uel is increased when ∆T min for the component is halved.

(The number in the parenthesis shows the standard value of the ∆T min .

Ċ r atio is the heat capacity flow ratio):

1. GGHEX4: 8,7% (∆T min =25 ◦ C, ɛ=0,77, NTU=2,4) Ċ r atio = 0,78

2. SHEX1: 2,4% (∆T min =5 ◦ C, ɛ=0,87, NTU=5,0) Ċ r atio = 0,88

3. EVAP: 1,6% (∆T min =5 ◦ C, ɛ=0,50, NTU=0,7) Ċ r atio = 0

4. ABSO: 1,6% (∆T min =5 ◦ C, ɛ=0,40, NTU=0,5) Ċ r atio = 0 13

5. SHEX2: 1,5% (∆T min =5 ◦ C, ɛ=0,87, NTU=5,0) Ċ r atio = 0,89

13 The temperature distribution throughout the absorber is not known, so it has

been assumed that it is uniform (equal to the solution outlet temperature) in the entire

absorber. This corresponds to the solution/refrigerant having an infinite heat capacity

flow compared to the external cooling water. Hence Ċ r atio is assumed to be zero.

149


5. SIMULATION AND RESULTS

Efficiency vs NTU for counterflow HEX

ε

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0,0

C_ratio = 0

C_ratio = 0,25

C_ratio = 0,50

C_ratio = 1,00

0 1 2 3 4 5

NTU

Figure 5.30: The figure shows the relation between ɛ (effectiveness) and NTU (Number of

Transfer Units) for a counterflow heat exchanger.

The correlation between NTU and ɛ for a counter flow heat exchanger

can be seen in figure 5.30. (GGHEX4 and the SHEXes are assumed to be

counterflow, and the EVAP and ABSO has a heat capacity flow ratio of 0

which means that the flow ɛ-NTU relation is unaffected by the flow configuration

and only depends on NTU).

It is seen that the SHEXes have the largest relative sizes (a large NTU

means that the HEX is large relative to the (smallest) heat capacity flow).

Hence it is easiest (and cheapest) to improve the heat exchangers which

have a low NTU number. So the SHEXes will not be improved further,

whereas the GGHEX, EVAP and ABSO can be improved. The list below

show the values used in the optimization.

1. GGHEX4: 8,7% (∆T min =9,4 ◦ C, ɛ=0,9, NTU=5,0) Ċ r atio = 0,78

2. SHEX1: 2,4% (∆T min =5 ◦ C, ɛ=0,87, NTU=5,0 Ċ r atio = 0,88)

3. EVAP: 1,6% (∆T min =2,7 ◦ C, ɛ=0,65, NTU=1,0)Ċ r atio = 0

4. ABSO: 1,6% (∆T min =1,8 ◦ C, ɛ=0,65, NTU=1,0) Ċ r atio = 0

5. SHEX2: 1,5% (∆T min =5 ◦ C, ɛ=0,87, NTU=5,0) Ċ r atio = 0,89

Since GGHEX4 is very important, it has been decided that a very good

HEX should be used (NTU=5). For the evaporator and absorber the NTU

150


5.5. Total optimization of system

is only set to 1. The reason that it is not set to 5 as for some of the other

components is that it would give a ∆T min of less than 1 ◦ C and that just

doesn’t seem realistic.

It was seen in section 5.3.2 page 123 that the system performed best if

T DES2 as well as T DES1 was lowered a little relative to the standard parameter

configuration. So this have been done now (with the new ∆T min s applied),

and it turns out that the ideal value of the desorber temperatures

is T DES1 = 67 ◦ C and T DES2 = 133 ◦ C.

Figure 5.31: A: Optimized parameters (∆T min for ABSO, EVAP, GGHEX4 and T DES1+2 ). B:

The Tradeoff factor shows how many kW of cooling which can be gained by sacrificing 1kW of

electricity (regulated by the current draw).

Figure 5.31A shows how much the optimized parameters improved

the system. COP ABS,f uel is increased 5 to 10 percent points depending

on the current density, while the electrical efficiency remains virtually

unaffected. Only the hot water production decrees a little with the

optimized parameters.

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5. SIMULATION AND RESULTS

5.5.2 Current density

The next point is to decide how much current to draw from the system.

As figure 5.31A shows, there is a very flat optimum for the electrical

efficiency around a current density of 3000A/m 2 . The cooling power is,

however, largest for small current draws. And around 3000A/m 2 the

gradient of the COP is not at all as flat as the electrical efficiency. So

when the current density is decreased, more cooling is gained while only

a little electricity is lost.

So the question is where the optimal tradeoff between electricity and

cooling lays. The optimum is found by the following reasoning: if

more cooling is needed this can be done by using some of the generated

electricity in a normal electrical air conditioner to create cooling. These

generally have a COP of 3-4 for the conditions of the case (ambient

temperature of 30 ◦ C and a produced cooling water at 6 ◦ C). This implies

that electricity is 3-4 times more valuable than cooling. For simplicity

it is here assumed that a supplementary electrical air conditioning unit

already is present for peak load, backup etc. so the electricity can directly

be used to generate cooling. Figure 5.31B shows the tradeoff factor

between cooling and electricity.

It is seen that when i d = 2700A/m 2 , the tradeoff factor is 3,4 meaning

that when the electricity generation is decreased 1kW (by lowering i d )

then 3,4kW of cooling is gained. So optimum is seen to be at a current

density of 2700A/m 2 .

Furthermore it can be seen from figure 5.31B that the total ”efficiency”

of the system exceeds 1,0 (i.e. the total output of electricity plus heat

plus cooling exceeds the fuel input). And the smaller the current density,

the larger this total ”efficiency” becomes. This also makes sense since it

would be equal to COP ABS (=1,45) if all the energy of the fuel was sent

directly into the desorber of the absorption cooling subsystem.

The first two columns of figure 5.32 show how much the efficiencies

and COP has been improved by going from the standard parameter

configuration to an optimized situation (with better ABSO, EVAP,

GGHEX4, optimized T DES1+2 and current draw). The electrical power

has fallen 2 kW (per 100kW fuel input), and the hot water generation

has fallen 4kW, but the cooling power has increased 13kW. The fall in

electrical power is mainly due to the current density being decreased

from 3000A/m 2 to 2700A/m 2 in order to reach the optimum tradeoff

between electricity and cooling.

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5.5. Total optimization of system

eta | COP

Standard vs Optimized parameters

1,2

1,1

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0,0

0,07

0,46

0,03

0,52 0,50

0,03

0,59 0,51

eta_HW

COP_ABS,fuel

eta_sys,el,net

0,55

Standard Optimized Optimized

ΔT_SOFC=120

Figure 5.32: All bars are for the Double stage with Air Preheat. The right and middle columns

are both for the optimized system, where i d has been optimized by aiming for a tradeoff factor

between cooling and electricity of 3,4.

With the new ∆T min = 11 ◦ C for the additional air preheat (GGHEX4),

the total gain of using air preheat is 14kW (59kW with air preheat vs

45 kW for the same parameters without air preheat (not shown in the

figure)).

5.5.3 Future: ∆T SOFC = 120 ◦ C

It is now investigated what will happen if it in the future becomes

possible to use a 120 ◦ C temperature span over the fuel cell (i.e. inlet

temperature is kept constant while outlet temperature is increased from

780 ◦ C to 810 ◦ C).

As seen in figure 5.32 the electricity generation increases 5kW while

the cooling power decreases 8kW 14 . From a cooling perspective this

14 the current density has been adjusted to give the same tradeoff factor between

153


5. SIMULATION AND RESULTS

might sound like bad news, since cooling power does decrease by 8kW.

But the additional 5kW of electricity can be used to generate around 5kW

·3,4 = 17kW of cooling with a normal electrical air conditioner. So it is

definitely worthwhile to increase the SOFC outlet temperature.

cooling and electricity (3,4) as in the ”Optimized” situation. This gives a current density

of 3000A/m 2

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C H A P T E R

6

CASES AND ECONOMICS

6.1 Air conditioning of hotels

In chapter 2 three different market segments - APU, CHP and DG - were

examined and it was concluded that Distributed Generation (DG) was

the best one for integrating a SOFC system with an absorption chilling

unit 1 . A hotel was seen to be an interesting industry for applying DG

technology because the demand of electricity, air conditioning and hot

water to some extend matches the supply of the SOFC-ABS.

In section 2.4 it was concluded that a system combined of a SOFC-

ABS is more profitable in a climate where AC is needed all year (Hot

Climate) compared to a climate where it is only required part of the year

(Normal Climate).

In this chapter potential geographical locations for a SOFC-ABS unit

will be discussed, the water consumption of the cooling tower will be

evaluated, and the assumptions in the economical calculations will be

compared to the results of the thermodynamical model.

better

1 APU for ships also looked promising but it was concluded that DG was slightly

155


6. CASES AND ECONOMICS

Three geographical locations are investigated:

1. Hotel in The Seychelles - Climate with high humidity.

2. Hotel in Bangkok - Climate with very high humidity.

3. Hotel in Las Vegas - Climate with low humidity.

The investigations are based on the double stage system configuration

with optimized parameters as described in section 5.5.

6.2 High humidity climate

6.2.1 Seychelles

The Seychelles is a group of islands located northeast of Madagascar

(about 1600 km east of Kenya). The primary industry is tourism [37]

and thus it is expected that a lot of hotels exist. Additionally the primary

energy supply is based on oil, and the government wants to shift towards

a more sustainable energy source. These two circumstances makes the

Seychelles a potentially attractive market for a SOFC-ABS system.

Figure 6.1: Weather data for Port Victoria, Seychelles. Average condition. Table taken from [6].

The Climate in the Seychelles is quite humid (see the average weather

condition data from Port Victoria in figure 6.1). The data is taken from

156


6.2. High humidity climate

BBC Home Weather web page [6]. The relative humidity is in the range

74-79% and the temperature is also quite stable in the range of 24-29 ◦ C

with peaks up to 33 ◦ C.

To evaluate the behavior of the SOFC-ABS system in different

climates the performance has been plotted as function of the ambient

temperature, see figure 6.2. The relative humidity (φ) is kept constant

at 80%. When the humidity is high, it is an advantage to use a higher

temperature for DES2. So a desorber temperature of 150 ◦ C has been

used. This is sufficient for ambient temperatures up to 32 ◦ C when the

relative humidity is 80%, so for most of the days this will suffice for

the Seychelles. For the few days with a temperature above 32 ◦ C, the

desorber temperature must be increased as discussed in the next section.

Figure 6.2: The relative humidity is φ = 0,8. The desorber temperature is kept at 150 ◦ C. The

water consumption corresponds to a fuel input of 100kW.

6.2.2 Bangkok

In Thailand tourism is important for the economy of the country (about

6% of GDP) [38]. So it looks like Thailand could be a potential market for

SOFC-ABS integrated systems.

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6. CASES AND ECONOMICS

Data from Bangkok is shown in figure 6.3 to illustrate the climate of

the middle part the country. The relative humidity varies a lot and is

more extreme than in the Seychelles: The relative humidity is up to 94% 2 ,

and the temperature is normally in the range of 20-35 ◦ C but can be as

high as 41 ◦ C.

Figure 6.3: Weather data for Bangkok, Thailand. Average condition. Table taken from [3].

Keeping these climate data in mind, the COP of the system (blue

line with round dots in figure 6.4A) shows that it is not sufficient to

use a desorber temperature (DES2) of 150 ◦ C since COP ABS,f uel decreases

drastically at about 30 ◦ C. Thus it has been necessary to increase T DES2 3 in

order to extend the range of the ambient temperature at which the system

can operate (blue line with triangular markers in figure 6.4A). When the

temperature of DES2 is increased, the ambient temperature can be up to

about 40 ◦ C, but the high ambient temperature does significantly decrease

COP ABS .

The biggest problem though is that DES2 is exposed to a temperature

of up to 190 ◦ C which is much higher than the recommended maximum

temperature of 150 ◦ C according to [27] (see brown curve market with

triangles in figure 6.4B). Thus it should not be expected that a standard

absorption unit can operate under this high temperature due to corrosion

problems.

2 The most extreme values of the humidity is likely to be caused by fluctuating

temperature, so it is assumed that the humidity is not above 0,9 during daytime.

3 The desorber temperature of DES1 has been changed as well since its optimum

value depends on the temperature of DES2.

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6.2. High humidity climate

Figure 6.4: A: The relative humidity is φ = 0,9. B: The desorber temperature is either kept

at 150 ◦ C (moderate humidity) or varied (VAR.)(very high humidity). The water consumption

corresponds to a fuel input of 100kW.

It might be possible to design a desorber which is capable to operate

at this high temperature by means of more corrosion resistant materials,

but it is out of the scope of this report to investigate this further.

The above results show that it is more complicated to implement a

system of SOFC integrated with absorption air conditioning in a climate

like the one in Bangkok than the one in the Seychelles. This should be

taken into account when potentially new markets are considered.

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6. CASES AND ECONOMICS

6.3 Low humidity climate

6.3.1 Las Vegas

Tourism and gaming is the major industry of Las Vegas which is located

in the Mojave Desert, Nevada, USA. The city has had more than 39

million visitors a year (2007) [36]. So one can imagine that hotels are

in demand in this area.

Figure 6.5: Weather data for Las Vegas, USA. Average condition. Table taken from [5].

The climate reflects the location in the desert - dry and very hot

during the summer although colder during winter (see table in figure

6.5). So air conditioning is mostly needed during the late spring, summer

and fall.

In this area the relative humidity is around 40% (see figure 6.6) so

the desorber temperature is set equal to that of the optimized parameter

configuration (T DES2 = 133 ◦ C). The figure shows that the system is

efficient up to 40 ◦ C in contrast to the humid climates (φ = 0,8−0,9) where

the ambient temperature had to be below 30 ◦ C for a maximum desorber

temperature of 150 ◦ C. For the dry climate the maximum allowable

ambient temperature is 42 ◦ C, which is just enough to cope with the

maximum average temperature in Las Vegas 6.5.

A problem might occur when the ambient temperature reaches the

peak temperature in July and August (46 ◦ C), but the relative humidity is

160


6.3. Low humidity climate

Figure 6.6: The relative humidity is φ = 0,4. The ambient temperature is varied for the system

with optimized parameter configuration. ṁ is the water consumption of the wet cooling tower.

low in this period - around 20% 4 . The system has been simulated under

these conditions which showed that even at 48 ◦ C the COP ABS,f uel is still

above 0,5 (see appendix E.2 page 283).

6.3.2 Water consumption

Another important difference between a dry and a humid climate is

the consumption of water in the cooling tower. In the case with high

humidity (see figure 6.4B) the water consumption is in the order of 0,03 kg

s

(corresponding to approximately 950 m3

year )5 . In the dry climate (φ = 0,4)

the water consumption is 0,06 kg

s

(figure 6.6) - twice that of the humid

4 The relative humidity ranges from 14 to 32% in July/Aug, but when the

temperature is at its highest (during the day), the relative humidity is generally at the

lowest. So during peak temperature the humidity in Las Vegas should not be above

20%

5 Assuming the system runs at full load all year around. Fuel input of 100kW.

161


6. CASES AND ECONOMICS

climate. So the annually water consumption for the cooling tower is up

to about 1900 m3 if the system is running at full load 24/7.

year

The price and the availability of water depends very much on local

conditions. It is out of the scope of this report to investigate the exact

circumstances. Instead a rough estimate of the expenses of water has

been made and compared to the monetary value of the electrical power

produced by the SOFC in order to assess the proportions of the water

consumption. The calculations are found in appendix D.3 (page 273).

The price of water is assumed to be 10 DKK 6 and electricity is assumed

m 3

to be 2 DKK 7 kWh

. For the humid climate (φ = 0,9) the expense of water is about

1% of the value of electricity produced 8 . For the dry climate (φ = 0,4) the

expense is about 2%. If the water price doubled and the electricity price

was reduced by 50%, the expense of water would be about 4% and 8% of

the value of electricity produced for the wet and dry climate respectively.

So these rough calculations show that the water consumption might

play an important role if the SOFC-ABS system was to be implemented

in an area where fresh water is in short supply. Thus it is important to

address this issue when new markets are considered.

6 The price is inspired by fresh water price for households in Denmark without taxes,

and does not include water treatment.

7 Based on Danish prices including all taxes.

8 Generally it is assumed that the electric efficiency of the SOFC is 0,5 and that the

system is operated at full load all year.

162


6.4. Economics

6.4 Economics

When the profitability calculations in chapter 2 regarding the hotel were

made, the thermodynamical EES model was not yet created, and hence

the efficiencies, COP etc. had to be estimated - partially by looking at

similar commercial products.

It is now examined how the assumptions used in the Hotel case fit

with the results of the EES model.

W [kW] | Q [kW]

1000

900

800

700

600

500

400

300

200

100

0

EES model vs Hotel Case assumption

141

141

268 292

399 406

Hotel Calculations

Hot Water Heating

Cooling Power

Electricical Power

Optimized Model

Figure 6.7: The left bar shows the generation of electricity, cooling and heating in the Hotel

Case calculations for the Hot Climate (based on estimated η el and COP). The right bar shows the

output of the optimized EES model for the same fuel input (800kW). The hot water production

has been set to 141kW as in the hotel calculations 9 .

In the hotel case ”Hot Climate” the natural gas consumption was

800kW in order to generate enough electricity for the hotel. So the fuel

input into the optimized EES model has been set to 800kW as well. In

the hotel case it was decided that the total demand of domestic hot water

(141kW) should come from the waste heat. So in the EES model the ABS

unit has only been allowed to use so big a fraction of the waste heat, that

there was enough heat left to generate 141kW of hot water 10 .

10 In all the previous EES simulations, the ABS unit has been allowed to extract as

much energy from the exhaust gas as possible go generate a bigger amount of cooling

and a smaller amount of hot water.

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6. CASES AND ECONOMICS

It can be seen from figure 6.7 that the assumed electricity, cooling,

and hot water production (for a fuel input of 800kW) lays quite close

to the ultimate values generated by the optimized EES model. The net

electricity generation is almost identical while the cooling generation

is about 10% bigger in the EES model. So if anything, the estimations

of efficiencies and COP in the hotel case economics have been a little

conservative.

It must however be remembered that many of the parameters in the

EES model are subjected to a significant uncertainty. So just because

the values of the Hotel case economics are close to those of the EES

model, it doesn’t prove that they are 100% correct. It just means that the

economical calculations and the thermodynamical model are congruent.

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C H A P T E R

7

DISCUSSION

In this chapter major findings of this project will be listed and discussed.

7.1 The thermodynamical model

The investigations of the SOFC-ABS system showed that the COP of the

ABS unit did not depend so strongly on the evaporator temperature

as it would for an electrical air conditioner. Thus, one can conclude

that a water-LiBr ABS unit seem more advantageous relative to an

electrical unit when the required cooling temperature is low. But since

the refrigerant of the ABS unit is water, the temperature of the chilled

water must be above 0 ◦ C. So it seems that the water-Libr ABS unit has

the biggest advantage when the required cooling temperature is around

5-10 ◦ C.

The optimizations in chapter 5 showed that for a 100kW fuel input in

a SOFC-ABS system it should be possible to obtain approximately:

• 50kW of electricity.

• 59kW of cooling.

• 3kW of heat for hot water production.

• 112kW total (Sum of all services).

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7. DISCUSSION

The conditions for this were a forward/return temperature of the

chilled water of 11 ◦ C/6 ◦ C, an ambient air temperature of 30 ◦ C, a relative

humidity of 40%, and a wet tower for cooling absorber and condenser.

The choice of a wet cooling tower was made because the investigations

showed that the absorber and condenser temperature is quite critical.

If these temperatures become too high relative to the desorber temperature,

the system will not be able to operate. When the temperature

of DES2 is 150 ◦ C, the system will only run if the water temperature out

of the cooling tower (T 39 is below 28 ◦ C). So when the dry cooling tower

of the model 1 is used, the ambient temperature may not be above 20 ◦ C.

The wet tower would tolerate an ambient temperature of around 38 ◦ C at

40% air humidity.

The wet tower does however have the disadvantage of a water

consumption of about 0,06kg/s (1900m 3 /y) for a fuel input of 100 kW. This

is quite a lot and could be a problem for areas with water shortage. The

amount of water is a very rough estimate due to following: The model

of the cooling tower is quite simple and hence not completely accurate

and the data for temperature and humidity are average values (a varying

profile of both temperature and humidity might give a different result).

Two solutions could help to reduce the water consumption:

1. First of all if the desorber temperature could be increased it would

be possible to use a higher temperature for condenser and absorber.

If T DES2 is increased from 150 ◦ C to 190 ◦ C, T 35 can be increased by

10 ◦ C so the dry tower can run at an ambient temperature of 30 ◦ C.

This does however increase the corrosion rate of the desorber, so

new or more expensive materials would have to be used 2 .

2. A semi-wet cooling tower could be used which is basically a dry

tower where water can be sprayed over the tubes when extra

cooling is needed. This way the amount of water being evaporated

can be controlled more accurate so the tower only uses enough

water to bring the temperature down to an acceptable level and

not to a unnecessarily low level. And during colder days the tower

can run purely as a dry tower.

1 ∆T min of the dry tower is set to 8 ◦ C in both ends

2 According to [27] it should be avoided to use desorber temperatures above 150 ◦ C

in order to avoid desorber corrosion

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7.1.1 Accuracy and sensitivity

7.1. The thermodynamical model

A lot of different parameters have been set in the EES model, and all

of them are subjected to a certain amount of uncertainty. It has been

attempted to estimate these as exact as possible, but in a zero dimensional

model, it is not possible to calculate values such as ∆T min or pressure

losses or heat losses. So a sensitivity analysis has been carried out in

section 5.4 page 142. This showed that no single parameter 3 could change

the value of the electrical efficiency or COP by more than 6% 4 . Of course

several parameters could be wrong at the same time (with many of them

pulling in the same direction), so the total output of the model can of

course vary more than just the 6%.

But the electrical efficiency is quite close to that of the TOFC models.

This is partly because a lot of parameters such as ASR, reforming fraction,

and pressure losses have been approximated those of the TOFC models,

although the ASR in the EES model only depends on the cell temperature

and not of the partial pressures or current density. So the fuel cell part of

the model should give relatively realistic values.

The ABS unit in the optimized system gives a COP (based on the heat

input into the desorber) of 1,4 to 1,5 depending on ambient conditions

etc. During the market research only one commercial dual stage

absorption unit was found. This was the Chinese ”Broad BCT23” which

had a COP of 1,1. But this unit was actually the cheapest absorption

cooling unit per kW of cooling for systems of that size. So it is likely that

the quite low COP is due to cheap materials and inefficient design.

Other theoretical models ([20]) have suggested a COP of around 1,3.

So the model of this project seems to be a little optimistic, which might

be due to the neglecting of pressure losses and heat losses. The SHEXes

of the model have also been set to a quite efficient level (∆T min = 5 ◦ C

corresponding to a NTU of 5), since it turned out that they were some of

the most sensitive heat exchangers.

3 other than the current density, which is a variable controlled by the operator and

hence not a normal ”fixed” parameter.

4 For the most important parameters it has been individually estimated how much

the value of each parameter could be off compared to that of a true system. This was

typically between 10% and 100%.

167


7. DISCUSSION

7.2 Economical considerations

In chapter 2 (page 19) the economical potential in different applications

were viewed, keeping in mind that some crude assumptions have been

made. First of all only average consumption and production has been

viewed i.e. assuming that electricity can be bought and sold to the

electrical grid for the same price as long as the net export is zero. The

costs and losses associated with the storage of cooling and heating have

also been neglected - assuming that the cooling need remains constant

throughout each day. The degradation of the SOFC has not been taken

into account either - it has been assumed, that it keeps its performance

throughout the lifetime.

The reality is likely to be much less favorable than the above assumptions

suggest, so the economical potential found in the calculations is

likely to be too optimistic. But as mentioned before, they are mostly

meant to show the overall tendencies and find out which applications

that seem to have most potential.

7.2.1 Auxillary Power Unit (APU)

Truck APU

The combination of SOFC and heat driven cooling turned out not to be

a good match for trucks. This was partly because the air conditioning

need (3kW) is larger than the electricity need (2kW) and because the

commercially available Sorption unit had a nominal heat consumption

of 12,5kW and a COP of only 0,4.

So the only way it could become a decent match is if small (3kW) ABS

units in the future are made as a double cycle with a COP of around the

1,4-1,5 of the model. With this COP 2kW of waste heat could produce

around 3kW of cooling, which would be just the required amount.

Of course this means that either an additional electrical AC should be

installed for cooling the truck during the driving time or the APU should

run during daytime as well although the generated electricity would

probably not be needed. A third variant could be to let the ABS unit

receive heat from the exhaust gas of the main engine during driving. But

mounting a heat exchanger in the truck exhaust system would probably

be expensive, and the soot deposits would be likely to inhibit effective

heat transfer. So this option would not be so straight forward.

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7.2. Economical considerations

Furthermore one of the producers of absorption air conditioning units

claim that they are fairly sensitive to the inclination of the floor [7]. So

during acceleration, braking, turning and hill driving a truck is likely to

impose unfavorable inclinations and accelerations to the unit.

So still the conclusion is that the truck APU market doesn’t look too

promising for the SOFC-ABS combination. There might however be a

potential in cooling cold rooms in cargo trucks, but this has not been

investigated here.

Ship APU

Mounting an ABS unit on an existing SOFC unit for air conditioning on a

ship seemed to be an economical advantage with a payback time of less

than 2 years if the system were to run at least 40% of the time. The results

were fairly sensitive to the diesel price, SOFC efficiency and usage time

fraction - changing one of these by 10% meant that the yearly savings

would change by around 12%.

The calculations did not take the installation, piping and maintenance

costs into account. But since a 10% increase of the purchase price of

the ABS unit only decreases the yearly savings by around 3,5% the

profitability would only decrease around 35% if the installation, piping,

and maintenance costs turned out to be as large as the purchase price of

the ABS unit itself.

It must also be remembered that the calculations only examined

whether it is profitable to mount an ABS unit on an existing SOFC unit. It

has not been calculated if the SOFC unit itself is an advantage to use in

the first place 5 .

7.2.2 Micro Combined Heat and Power (µCHP)

µCHP - Air conditioning

The idea to use SOFC in conjunction with hot water heating and a heat

driven air condition unit in a private house did not look so promising

with the heat driven cooling units on the market today as the smallest one

5 Ship diesel engines are quite efficient, so there might not be so big a gain on

efficiency by swapping the auxiliary diesel engine with a SOFC.

169


7. DISCUSSION

giving 5kW of Cooling for 12,5kW of driving heat. Even if a small ABS

unit cold be made with a COP of 1,5 as in the model, the approximately

1kW of waste heat (assuming 1kW SOFC electricity production) would

only generate 1,5kW of cooling. And this is only around 1/3 of the

estimated cooling need for a normal house in a hot climate.

So for private homes the SOFC-ABS solution doesn’t seem realistic

unless the SOFC is over dimensioned in order to sell the surplus

electricity generation to the electricity grid or used for other purposes

like an electric car.

µCHP - Refrigerators

Using the waste heat of the SOFC for driving a refrigerator was

another option. But it turned out that heat driven refrigerators cost

around 11.000DKK while a normal class A++ electrical refrigerator costs

4.000DKK. And since the electricity consumption of the latter is only

around 200kWh/year, the electricity savings only amounted to around

400DKK/year, so with a discount factor of 5%, the pay back time will be

around 50 years 6 . This even assumes that the electricity for the electrical

refrigerator is bought from the electrical grid (2DKK/kWh), but if a

SOFC unit is purchased anyway, the cost of the electricity would be even

cheaper meaning an even longer pay back time for the absorption cooling

refrigerator.

Of course much of the price difference between the ABS refrigerator

and the electrical refrigerator is due to the ABS unit being produced in

much smaller numbers. So if ABS refrigerators became more common

the price might approach that of electrical units. But on the other hand

installation and piping costs for the ABS unit have not been included in

the calculations and this will pull in the opposite direction.

All in all there seems to be no potential for combining a SOFC with

ABS refrigerators in private homes.

6 With a discount factor of 0% the pay back time will be 18years ((11.000-

4.000)DKK/y/400DKKDKK/y), but with a discount factor of 5% the savings in the last

years become very small when discounted.

170


7.2.3 Distributed Generation (DG)

DG - Hotel

7.2. Economical considerations

A favorable DG application is a hotel in a warm or hot climate, where

electricity and air conditioning as well as domestic hot water production

is needed. Other applications might fit the supply of electricity and

cooling even better e.g. manufacturing. However, the demand for

electricity and cooling for manufacturing applications is much harder to

estimate in general since they are much more diversified.

The economical calculations showed that for a hotel with 230 rooms

in a hot climate, with a SOFC-system price of 2.700DKK/kW and a

ABS price of 3.700DKK/kW, the total expense of gas, electricity, air

conditioning units and SOFC in the assumed component lifetime of 10

years would be approximately:

• 27mio DKK for grid electricity supply + electrical air conditioning

• 15mio DKK for SOFC electricity + electrical air conditioning

• 14mil DKK for SOFC electricity + ABS air conditioning

SOFC

So by far the biggest savings (12mio DKK) would come from the

SOFC itself with pay back time would be around 1 year. This does

however depend very much on the gas price and electricity price of

0,20DKK/kWh and 0,75DKK/kWh respectively. If, for instance, the

gas price was increased to 0,38DKK/kWh, the SOFC would never be

profitable (with an electrical efficiency of 0,5), since it would be cheaper

to import the electricity.

The price of the SOFC is also important although not as much as

one might expect. If the SOFC price is 12.000 DKK/kW instead of the

assumed 2.700DKK/kW, the pay back time will increase from 1 year to

3 years (figure 2.5 page 34). The investment would still look profitable,

but if the gas or electricity at the same price changed a little, the pay

back time might approach the life time of the system. And it should be

remembered that the SOFC price is very uncertain, since the technology

today is at a state where there is no real large scale production, and the

reliability/stamination of the cell is not satisfactory either.

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7. DISCUSSION

This leads to the next uncertainty - the lifetime which has been

assumed to be 10 years. This is a lot longer than what is possible today.

But as seen in figure 2.7 (page 36), the profitability doesn’t depend so

much on lifetime. So even if it is just 5 years, the gains from using the

SOFC is less than 10% smaller than if the lifetime was 10 years.

It must also be remembered that for all the calculations (of both SOFC,

ABS, and ECH) installation and maintenance costs have been neglected.

But even if these costs sum up to be as large as the purchase price of

SOFC unit during its 10 years lifetime, the pay back time of the SOFC

system will increase from around 1 to 1,5 years.

The model has been made as steady state and the selling and buying

prices of electricity have been assumed equal in the calculations in lack

of better data. In reality the sale price is likely to be lower than the

purchase price, but since the cost of the SOFC was seen not to have so

big an influence on the profitability, it might be a good idea to buy a unit

50% larger than average load, so it could be regulated up and down.

ABS unit

The ABS unit would give an extra gain of around 1,5 mil. DKK during

its 10 years expected lifetime which is quite good considering that the

additional purchase price of the ABS unit is only around 0,5 mil. DKK. 7 .

This way the pay back time of the ABS unit becomes around 1,5 years

for the hot climate, assuming the purchase price is 3700DKK/kW. If the

price were doubled, the pay back time would be 6 years. But the ABS

units are (in contrast to SOFCs) already on the market today, and the

estimated price is hence much more accurate than the estimated price of

the SOFC. There are however not so many suppliers of ABS units, and

very few of them make double stage units, so the price is still somewhat

uncertain, and one could imagine that it would decrease if the market

grew.

But as mentioned, the installation and maintenance costs have been

neglected for all units. If maintenance and installation costs for the ABS

sums up to be the same as the purchase price for the unit (during its 10

years lifetime), the pay back time of the ABS unit will increase from 1,5

7 The actual price of the ABS unit is 1mio DKK, but the supplementary ECH unit

can be smaller than if no ABS were used, so the cost of the ECH decreases from 1,4mio

DKK to 0,9mio DKK

172


7.2. Economical considerations

to 6 years 8 . So before it is decided to make such a system, the installation

and maintenance costs should be established.

One disadvantage of the ABS AC unit is that when the ambient

temperature raises, so does the need for air conditioning, but at the same

time the COP of the ABS unit decreases. So during very hot periods,

this can give rise to a lack of cooling unless the ABS units is originally

overdimensioned 9 . This is however not so much a problem in the hotel

case where a supplementary electrical air conditioner is already present

since the ABS unit can only generate about 1/3 of the required cooling

due to the restricted amount of waste heat.

Just as for the SOFC the ABS unit has only been modeled as steady

state assuming that it runs at full load all the time. But since there was

only enough waste heat in the SOFC exhaust gas to generate around 1/3

of the entire cooling demand of the hotel, the ABS unit should be able to

run as base load all the time, and the supplementary ECH should be used

to regulate the total cooling production. So the steady state assumption

should not give so big an error on the ABS unit.

ABS vs Hot water production

In the economical calculations for the hotel, it has been assumed that all

the hot water production should be done by using waste heat from the

exhaust gas. This was done partly to make it easier to compare it to the

”naked” SOFC system, case B (with no ABS, so there was plenty of heat

for the hot water production), and partly because generating hot water

from the exhaust gas only takes a heat exchanger, whereas generating

cooling takes a much more expensive ABS unit.

But if the hotel is placed in a hot climate, the hot water heating

could quite inexpensively be done by solar heating panels because the

required temperature for the domestic hot water is so low - around 60 ◦ C

compared to the approximately 150 ◦ C needed for the ABS unit. And

when additional air preheating is used in the SOFC-ABS system, the ABS

unit can use almost all of the waste heat. If the ABS unit is allowed to

8 This is under the assumption that the installation and maintenance cost of the ECH

is the same regardless of whether an ABS unit is installed - after all there will be an ECH

in either case - the only difference is a 35% reduction in size of the ECH if an ABS is also

installed.

9 Or it could just be tolerated that the indoor temperature raises a couple of degrees

during heat waves (as long as there is some air conditioning, the consequences of a heat

wave should not be life threatening for anyone)

173


7. DISCUSSION

extract as much of the waste heat as it can, there will only be enough

waste heat left to make 3kW of hot water per 100kW fuel input (see figure

5.32 page 153). This means that almost all of the waste heat can be used

in the ABS unit. So if domestic hot water heating is to be made from the

SOFC exhaust gas then the cooling production will decrease a lot, and for

each kW the hot water production is decreased, approximately 1,5kW of

cooling can be made (since COP ABS = 1,48).

Hotel locations

One of the really good places to use the SOFC-ABS would be at the

Seychelles. First of all the primary industry for this group of islands is

tourism so there are a lot of hotels. Secondly their primary energy source

is oil which the government wants to replace which is an advantage for

the SOFC. Thirdly the climate is perfect for using the ABS air conditioning:

the average temperature is between 24 and 30 degrees all year, creating

a certain need for air conditioning all year round. And since the

average temperature rarely exceeds 33 ◦ C, the absorption unit is capable

of running just about all the time with a desorber temperature of no more

than 150 ◦ C which is the maximum ambient temperature that can be used

with this desorber temperature is only 33 ◦ C since the relative humidity is

around 80%.

Bangkok could at first glance also be a potential place for the SOFC-ABS.

The temperature is a couple of degrees higher than for the Seychelles during

summer (increasing the air conditioning need). But since the maximum

temperature is higher, and the climate is very humid (up to 90%

relative humidity), the desorber temperature will have to be increased

up to 190 ◦ C for the system to even run at this ambient temperature. So

fairly expensive materials are likely to be needed in order to minimize

the corrosion rate of the Desorber (and probably also SHEX), meaning

that Bangkok after all might not be the best place to use the absorption

cooling unit after all.

Las Vegas has even higher maximum temperatures (up to 46 ◦ C), but since

the air humidity is much lower than in Bangkok, the system will run at

temperature up to 48 ◦ C at a desorber temperature of 150 ◦ C. So this makes

for a much better place to put the SOFC-ABS unit - especially since there

are a lot of hotels and casinos which needs air condition and electricity.

Although in this climate, the water consumption could be a problem.

174


7.2. Economical considerations

As mentioned earlier: the simple model of the cooling tower as

well as the climate data (only average and extremes values) makes the

simulation of varying the climate uncertain. The exact results should

hence be used with caution, but the tendencies in three cases are still

valid.

Heat waves/peak load

As mentioned the optimization showed that for 100kW of fuel input,

50kW of electricity and 59kW of cooling (and 3kW of hot water) could

be generated. If during a heat wave one wishes to make as much cooling

as possible regardless of the effect on electricity, approximately 130kW of

cooling and 0kW of electricity could be generated by sending most of the

fuel directly into the burner - only feeding the SOFC with enough fuel to

generate electricity needed for the blower.

This might at first glance look like an easy way to increase the cooling,

but there are two drawbacks:

• First of all, more cooling could be generated by the same amount

of fuel by running the SOFC-ABS system at the normal optimized

operating point (Ẇ el = 50kW and ˙Q cooling = 59kW ) and just use

the 50kW of electricity in an electrical air conditioner (with an

estimated COP of 3,5). This would give a cooling power of

59kW+50kW·3,4=230kW which is much more than the 130kW

obtained by the fuel by pass.

• Secondly, if the ABS unit should be able to cope with a cooling

power of 130kW, it had to be heavily over dimensioned for the

normal load (59kW), which would significantly increase the cost.

And since the waste heat from the SOFC is only enough to supply

the hotel with half its average cooling demand it would most likely

have a supplementary ECH anyway. So it would be cheaper to let

the ECH be a little over dimensioned and let this take care of the

peak load during heat waves.

175


7. DISCUSSION

7.3 Other considerations

The steady state assumption has made the modeling work more

simple (less time consuming) but as mentioned a lot of estimations

and assumptions have been made in order to make the model work.

This however has introduced a lot of uncertainties in the calculated

performance and the economics.

The profile of the demand of electricity, cooling and hot water

(throughout the day and year 10 ) has been assumed to be constant which

is a very crude assumption. How, and how much these demands will

vary is hard to say, but it might have significant impact on the system.

A way to cope with the varying demand of cooling and hot water

would be to introduce storages. These would to some extend make

the production of cooling and hot water constant, but they would also

introduce additional losses, investment and maintenance costs which

have not been taken into account. The required capacity of the storages

depends very much on the demand profiles. And the size also has an

impact on the losses to the surroundings, so finding the best storage size

is a matter of economical optimization.

Another issue is the interplay with the rest of the energy system. It has

been assumed that electricity can be exported to the grid at any time the

local demand for electricity is below the production of the SOFC. How

the electricity system copes with this depends very much on the type of

electricity generation (power stations etc.).

For a system with a lot of renewable intermitted electricity generation

(e.g. wind turbines and photovoltaic) it would probably not be the best

match to use the SOFC as base load. From a system manager point

of view it would be much better to use the SOFC only when there

is not enough electricity production from the renewable sources. I.e.

the electricity production of the SOFC should followed the electricity

prices (which often are correlated to demand minus the production of

intermitted capacity). But that solution would not be good for the SOFC-

ABS combination, since the ABS unit would only be able to run when

the SOFC was active, so the savings from the ABS unit would be smaller

relative to the purchase price of the system.

10 for the ”Normal Climate” is has however been assumed that the cooling need only

arises during summer, and that it is zero during the 6 winter months

176


C H A P T E R

8

CONCLUSION

System configuration

It turned out that a double stage configuration for the ABS unit could

give a cooling power of around 59kW of cooling per 100kW fuel input

in contrast to the only 26kW of cooling that was obtained with the single

stage.

An additional air preheating (GGHEX4) turned out to give 14kW of

extra cooling for the double stage with the optimized parameters, so this

must be considered a very worthwhile addition.

The model showed that it was almost essential to use a wet cooling

tower. If a dry cooling tower was used, the ABS unit could only

run at ambient temperatures below 20 ◦ C for a desorber temperature of

150 ◦ C. If the desorber temperature was increased to 190 ◦ C, the ambient

temperature could be up to 30 ◦ C, but this would increase corrosion of

the desorber significantly. Since air conditioning is not so necessary

when the ambient temperature is much below 30 ◦ C, the conclusion of

the absorber/condenser-cooling was that the tower had to be wet or at

least semi-wet, whereby the amount of water used for evaporation could

be controlled to fit the need.

Critical components for good performance

The investigations showed that the most critical heat exchangers with

respect to the system COP were: the internal water-LiBr heat exchangers

(SHEX1+2), the evaporator (EVAP) and the air pre heater (GGHEX4).

177


8. CONCLUSION

So by looking at how the effectiveness depends on NTU, these heat

exchangers were optimized to what could reasonably be expected to be

possible.

The sensitivity analysis showed that the pressure loss and heat loss

of the components in the ABS unit were not so influential, so neglecting

these were probably not a significant source to uncertainty.

The temperature of the evaporator turned out not to be as important

as one would expect for a cooling device. If the temperature of the cooled

fluid out of the evaporator is increased from 5 ◦ C to 30 ◦ C the amount of

generated cooling only increases by 1/5. So compared to an electrical

unit, the ABS is most advantageous for low temperatures (where the

COP of an ECH decreases more rapidly). But of course the temperature

may not be below 0 ◦ C for water-LiBr ABS unit since the water would

freeze.

Performance

When the model was optimized with respect to the different temperatures

and the effectiveness of heat exchangers etc. the following performance

was obtained for a 100kW fuel (methane) input:

• 50kW of electricity.

• 59kW of cooling.

• 3kW of heat for hot water production.

• 112kW total (Sum of total services).

If instead the waste heat had been used for hot water production only,

the system would have given less than 100kW of total services (i.e. 50kW

of electricity and approximately 45kW of hot water). So by utilizing

the ABS unit, the amount of total services per kW fuel input has been

increased, and furthermore the value of the cooling is often higher than

that of heating.

Market segments, Economics and Climate

The market investigations indicated a potential economical advantage by

using a SOFC-ABS system in two of the three market segments:

178


For the APU segment a SOFC-ABS system could be placed on a ship

to generate electrical power and produce air conditioning. The rough

calculations suggested a pay back time of the ABS unit of around 2 years.

For the DG segment the calculations indicated a potential for using a

SOFC-ABS system in a hotel with supply of electricity, air conditioning

and hot water. The location should preferably be a climate which is

hot all year and has a low air humidity as well. This way a cooling

demand is present all year so the ABS unit will have a lot of operating

hours, and it would be possible to run the ABS unit at high temperatures

(up to 48 ◦ C for φ=0,2). In a hot and humid climate (φ=0,8), the ABS

unit would only work at ambient temperatures up to 33 ◦ C unless the

desorber temperature was raised above 150 ◦ C, which would require

special desorber materials. So this makes the dry climate a better choice.

In the case study following examples of locations were concluded to

be attractive for using a SOFC-ABS in a hotel:

• Las Vegas: Many hotels, a relative humidity of around 40% (less

during high temperature) and a very high ambient temperature

during summer (op to 46 ◦ C) leads to a large air conditioning need,

although the cooling need in the winter half of the year is modest.

• The Seychelles: Many hotels and an abient temperature of around

30 ◦ C leads to an air conditioning need throughout the year. There

is a high humidity - around 80%, but that is not a problem for the

ABS unit as long as the ambient temperature does not exceed 33 ◦ C.

The economical calculations indicated that the pay back time of the

SOFC and ABS unit for a hotel in a hot climate would be around 1

year and 1,5 year respectively. But this did not include installation and

maintenance costs, and it has been based on average values (assuming

that the purchase/sales price of the electricity from/to the electrical grid

would be the same, as long as the net export of electricity was zero). In

reality the sales price is likely to be lower than the purchase price.

The neglected installation and maintenance costs have significant

influence on the pay back time, so the economical calculations might

be too optimistic. Especially the installation and maintenance costs of

the ABS unit were seen to have a high impact on profitability. If the

installation and maintenance costs during the 10 year lifetime summed

up to be as high as the original purchase price the pay back time would

increase from 1,5 to 6 years.

179


8. CONCLUSION

Furthermore the system has been modeled as steady state which adds

to the uncertainty of the economical calculations.

In hot climates it might be a good idea to utilize as much of the waste

heat as possible for cooling instead of hot water, which can be produced

cheaper by other means, e.g. solar collectors. Each kW of waste heat can

give around 1,5kW of cooling but only about 1kW of hot water.

Sum up

The project has shown that integrating a SOFC with an absorption

cooling unit should be a thermodynamically good match, and the market

investigations suggest that for certain applications there could be an

economical potential as well. But before a specific market area is chosen,

more detailed economical calculations should be made, and the time

variation of demand for electricity, cooling and hot water should be taken

into account.

180


C H A P T E R

9

FURTHER WORK

Some ideas for further work could be:

1. Conduct an exergy analysis of the entire system.

2. Time series for electricity, cooling and heating could be made and

different purchase and selling price for electricity could be used.

3. A Storage (cooling/heating) could be made to account for the

variations, and the cost and losses of this could be calculated.

4. Improve the modeling of the cooling tower component.

5. It could be investigated which materials are normally used for the

desorbers, which new materials could be used, and what maximum

temperature these would be able to tolerate.

6. A triple or quadruple stage water-LiBr ABS unit could be modeled

and integrated with a SOFC.

7. The reduction in CO2 mitigation for the system could be examined,

since this provides an insensitive other than the purely economical.

8. The economical calculations could be improved by gathering

information about installation costs, maintenance costs etc.

9. A ammonia-water ABS units could be modeled.

10. The SOFC ABS system could be compared to a Solar heating/cooling

system.

181


9. FURTHER WORK

11. The system could be compared to a gas engine driven generator

with ABS or a micro turbine with ABS.

12. More cases could be investigated, e.g. the ammonia-water

absorption unit applied for industrial freezing.

13. Analysis of how the SOFC-ABS system interact with the surrounding

energy system (e.g. national electricity supply system).

182


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search=RGE%20400 (feb 19, 2010)

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print.php (February 18, 2010)

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BIBLIOGRAPHY

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F53D95F7-36FF-477A-AD71-35C64DEDAFA4/0/

Analyseforuds%C3%A6tninger20072016.pdf, (June 15,

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literature_CRES.doc (feb 19, 2010)

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ng_pri_sum_dcu_SCA_a.htm http://www.ens.dk/

da-DK/Info/TalOgKort/Statistik_og_noegletal/

Maanedsstatistik/Documents/Energistatistik%

202008.pdf (February 18, 2010)

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[23] Larminine, James et al.: Fuel Cell Systems Explpained. Wiley, (2003).

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jpg&imgrefurl=http://www.nordeainvest.dk/

Nyheder/Nyheder%2B2009/Ugens%2BPerspektiv%

2B2009/20082009%2BOptimisme%2Bp%25C3%25A5%2Br%

25C3%25A5varemarkederne/1142802.html&usg=__

1vQEq1C1rbLKso8m2OD8SRX1lms=&h=459&w=699&sz=

82&hl=da&start=7&um=1&itbs=1&tbnid=73TJWdJD-_

0OkM:&tbnh=91&tbnw=139&prev=/images%3Fq%3Dh%25C3%

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26tbs%3Disch:1 (June 15, 2010).

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business_areas/apu.aspx, (June 16, 2010).

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business_areas/dg.aspx, (June 16, 2010).

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186


Appendices

187


A P P E N D I X

A

MARKET INVESTIGATION

189


A. MARKET INVESTIGATION

A.1 Market Investigation Appendix -

Introduction

Some of the quite important prices in the calculations are those of oil,

natural gas and electricity. Since fossil fuels are slowly being depleted,

while CO2 emission become more and more unpopular, the price of

electricity as well as gas is likely to increase in the coming years. It is

however very difficult to give an accurate estimate of the future price

development (in 2003 it was for instance estimated that the oil price from

2003 to 2025 would lay between $20 and $35 per barrel [9], which is quite

far from the $140/barrel[24] which was reached during the financial

crisis 2007/2008). And since the rest of the numbers in the calculations

are also quite uncertain, it has been assumed in this report, that the

electricity prices, gas prices, and diesel prices will just increase with the

rate of the inflation.

190


A.2. APU appendix

A.2 APU appendix

A.2.1

A.2.1.1

Ship APU appendix

Assumptions

• All prices are ex VAT.

• Discount rate 5%

• Diesel oil price 4,50DKK/l

• Heating value 42,7MJ/kg

• Density 840kg/m3

• Full load hours per year 4380

• SOFC efficiency 0,5

• Absorption cooling power = 20kW

• COP elec.ac = 3,6

• Usage time fraction = 0,5

• Electricity for electrical chiller is made by the SOFC (price 0,60DKK

per kWh)

• Electrical AC price: Enviromax 20kW = 61,000DKK

• Absorption AC price: Robour = 10,000DKK/kW * 20kW =

200,000DKK (incl. hexes)

• Absorption AC electrical consumption 1,0kW

• No service needed on either refrigerator

A usage time fraction is set to 50% of the time, since it is assumed that

the SOFC will generate electricity for the ship almost all the time (both

sailing and docking), and that it is big enough to deliver enough heat for

the absorption air condition to run all the time. But there is probably not

always a need for air conditioning - for instance the ships some time sail

in cold climates.

191


A. MARKET INVESTIGATION

No cost for distribution piping or user-side heat exchangers has been

included, since this equipment is assumed to be the same whether an

absorption air conditioner or an electrical air conditioner is used.

192


Aircondition 20kW ship. SOFC+ABS vs SOFC+ECH

(prices are excl. VAT)

Electrical Aircondition COP = 3,6 (4kW heat, 3,5kW cooling)

Ship SOFC runs 50% of the time

Elec price ship:

1,13 DKK/kWh

Assuming that the SOFC is big enough to supply enough waste heat for the ABS at all time

Diesel oil price 4,23DKK/l

Heating value 42,7MJ pr kg

Density 840kg/m3

SOFC el eff 0,4

Price pr l Density Heat value Heating value Price pr MJ kWh/MJ Price pr kWh_d

DKK/L kg/L MJ/kg MJ/L DKK/MJ kWh/MJ DKK/kWh

4,50 0,84 42,7 35,9 0,125 0,28 0,452

Usage fraction 0,50 Price pr kWh_EL

Full load hours 4380 DKK/kWh

Electricity price 4945 DKK/y/kW 1,129

Normal Heat pump AC, electricity from SOFC

Enviromax 20 kW 61128 DKK (excl. VAT)

Coooing power 20 kW

Discount rate 5,0%

year Purchase Electricity Net payment NPV_i NPV tot Annuity

0 61'128 61'128 61'128 61'128

1 98'891 98'891 94'182 155'310 163'075

2 98'891 98'891 89'697 245'006 131'766

3 98'891 98'891 85'426 330'432 121'337

4 98'891 98'891 81'358 411'790 116'130

5 98'891 98'891 77'483 489'273 113'010

6 98'891 98'891 73'794 563'067 110'934

7 98'891 98'891 70'280 633'347 109'455

8 98'891 98'891 66'933 700'280 108'349

9 98'891 98'891 63'746 764'025 107'491

10 98'891 98'891 60'710 824'736 106'807

11 98'891 98'891 57'819 882'555 106'250

12 98'891 98'891 55'066 937'621 105'787

13 98'891 98'891 52'444 990'065 105'398

14 98'891 98'891 49'947 1'040'012 105'066

15 98'891 98'891 47'568 1'087'580 104'780

9

193


Absorpton unit (free waste heat)

Price ABS 10'000 DKK/kW Including HEXes, Robur 16,9kW = 170,000DKK

Cooling power 20 KW

electrical consomp 1,03 kW

year Purchase Electricity Net payment NPV_i NPV tot Annuity

0 200'000 200'000 200'000 200'000

1 5'091 5'091 4'848 204'848 215'091

2 5'091 5'091 4'618 209'466 112'652

3 5'091 5'091 4'398 213'864 78'533

4 5'091 5'091 4'188 218'052 61'493

5 5'091 5'091 3'989 222'041 51'286

6 5'091 5'091 3'799 225'839 44'494

7 5'091 5'091 3'618 229'457 39'655

8 5'091 5'091 3'446 232'903 36'035

9 5'091 5'091 3'282 236'185 33'229

10 5'091 5'091 3'125 239'310 30'992

11 5'091 5'091 2'976 242'286 29'169

12 5'091 5'091 2'835 245'121 27'656

13 5'091 5'091 2'700 247'821 26'382

14 5'091 5'091 2'571 250'392 25'296

15 5'091 5'091 2'449 252'841 24'359

Savings by using Absorption

year Purchase Electricity Net payment NPV_i NPV tot Annuity

0 -138'872 0 -138'872 -138'872 -138'872 0

1 0 93'800 93'800 89'333 -49'539 -52'016

2 0 93'800 93'800 85'079 35'540 19'114

3 0 93'800 93'800 81'028 116'568 42'805

4 0 93'800 93'800 77'169 193'738 54'636

5 0 93'800 93'800 73'495 267'232 61'724

6 0 93'800 93'800 69'995 337'227 66'440

7 0 93'800 93'800 66'662 403'889 69'800

8 0 93'800 93'800 63'487 467'377 72'313

9 0 93'800 93'800 60'464 527'841 74'262

10 0 93'800 93'800 57'585 585'426 75'815

11 0 93'800 93'800 54'843 640'269 77'081

12 0 93'800 93'800 52'231 692'500 78'132

13 0 93'800 93'800 49'744 742'244 79'016

14 0 93'800 93'800 47'375 789'619 79'770

15 0 93'800 93'800 45'119 834'739 80'421

Positive NPV means that Absorption chiller is advantageous

9

194


Sensitivity analysis

The effect on the 10 years anuity difference is investigated

-9,75 0 9,75

Increase (%) x: -10 0 10

y- y0 y+ ∆y-/y0 ∆y+/y0

Purchase price ABS 78'170 75'815 73'225 3,1 0,0 -3,4

Purchase price EAC 75'096 75'815 76'607 -0,9 0,0 1,0

Diesel price 67'288 75'815 85'195 -11,2 0,0 12,4

Efficiency SOFC 85'195 75'815 67'288 12,4 0,0 -11,2

Usage time fraction 67'288 75'815 85'195 -11,2 0,0 12,4

Discount rate 76'210 75'815 75'376 0,5 0,0 -0,6

Sensitivity analysis of Ship ABS vs ECH

15

Annuity increase [%]

10

5

0

-10 -5 0 5 10

-5

-10

-15

Increase in variables [%]

Purchase price ABS

Purchase price EAC

Diesel price

Efficiency SOFC

Usage time fraction

Discount rate

An incrase in y-value means, that the advantage of using the absorption refrigerator becomes even larger.

The electricity price and anual electricity consumption are exactly on top of each other as could be expected

195


A. MARKET INVESTIGATION

A.3 CHP appendix

A.3.1

Assumptions

• All prices are incl VAT since it is seen from the consumer viewpoint,

and electricity etc. is incl VAT.

• Electrical refrigerator (Bosch energy class A++) price = 3.999DKK

Footnote[Bosch KGV 36X27 225l refrigeration and 91liter freezer].

• Absorption refrigerator (RGE 400 from Åbybro camping og fritid

224L + 76L) price = 11.000DKK.

• Electrical refrigerator electricity consumption = 208kWh/y.

• Absorption refrigerator electricity consumption = 0kWh/y.

• Electricity price 2 DKK/kWh (Danish prices).

• No service needed on either refrigerator.

• No price for a HEX between the SOFC exhaust gas and the

refrigerator has been included, so in reality this might add an extra

cost for the absorption refrigerator.

• Discount factor 5% per year.

196


Refrigerators for private end users (incl VAT)

Discount rate

Annually el. cons.

El. price

5,00%

208,00 kWh

2,00 DKK/kWh (incl. VAT)

Electrical Refrigerator (A++)

Bosch KGV 36X27 225l refritiation and 91liter freezer

year Purchase Electricity Net payment NPV_i NPV tot Annuity

0 3'999 3'999 3'999 3'999

1 416 416 396 4'395 4615

2 416 416 377 4'773 2567

3 416 416 359 5'132 1884

4 416 416 342 5'474 1544

5 416 416 326 5'800 1340

6 416 416 310 6'110 1204

7 416 416 296 6'406 1107

8 416 416 282 6'688 1035

9 416 416 268 6'956 979

10 416 416 255 7'211 934

11 416 416 243 7'454 897

12 416 416 232 7'686 867

13 416 416 221 7'907 842

14 416 416 210 8'117 820

15 416 416 200 8'317 801

16 416 416 191 8'508 785

17 416 416 181 8'689 771

18 416 416 173 8'862 758

19 416 416 165 9'026 747

20 416 416 157 9'183 737

21 416 416 149 9'333 728

22 416 416 142 9'475 720

23 416 416 135 9'610 712

24 416 416 129 9'739 706

25 416 416 123 9'862 700

26 416 416 117 9'979 694

27 416 416 111 10'091 689

28 416 416 106 10'197 684

29 416 416 101 10'298 680

30 416 416 96 10'394 676

10'975

197


Absorption Refrigerator

RGE 400 from Åbybro camping og fritid 224L + 76L

The absorption refrigerator doesn't use any electricity

year Purchase Electricity Net payment NPV_i NPV tot Annuity

0 10'975 10'975 10'975 10'975

1 0 0 10'975 11524

2 0 0 10'975 5902

3 0 0 10'975 4030

4 0 0 10'975 3095

5 0 0 10'975 2535

6 0 0 10'975 2162

7 0 0 10'975 1897

8 0 0 10'975 1698

9 0 0 10'975 1544

10 0 0 10'975 1421

11 0 0 10'975 1321

12 0 0 10'975 1238

13 0 0 10'975 1168

14 0 0 10'975 1109

15 0 0 10'975 1057

16 0 0 10'975 1013

17 0 0 10'975 973

18 0 0 10'975 939

19 0 0 10'975 908

20 0 0 10'975 881

21 0 0 10'975 856

22 0 0 10'975 834

23 0 0 10'975 814

24 0 0 10'975 795

25 0 0 10'975 779

26 0 0 10'975 763

27 0 0 10'975 750

28 0 0 10'975 737

29 0 0 10'975 725

30 0 0 10'975 714

198


Absorption - electrical A++ refrigerator

year Purchase Electricity Net payment NPV_i NPV tot Annuity

0 -6'976 0 -6'976 -6'976 -6'976 0

1 0 416 416 396 -6'580 -6909

2 0 416 416 377 -6'202 -3336

3 0 416 416 359 -5'843 -2146

4 0 416 416 342 -5'501 -1551

5 0 416 416 326 -5'175 -1195

6 0 416 416 310 -4'865 -958

7 0 416 416 296 -4'569 -790

8 0 416 416 282 -4'287 -663

9 0 416 416 268 -4'019 -565

10 0 416 416 255 -3'764 -487

11 0 416 416 243 -3'521 -424

12 0 416 416 232 -3'289 -371

13 0 416 416 221 -3'068 -327

14 0 416 416 210 -2'858 -289

15 0 416 416 200 -2'658 -256

16 0 416 416 191 -2'467 -228

17 0 416 416 181 -2'286 -203

18 0 416 416 173 -2'113 -181

19 0 416 416 165 -1'949 -161

20 0 416 416 157 -1'792 -144

21 0 416 416 149 -1'642 -128

22 0 416 416 142 -1'500 -114

23 0 416 416 135 -1'365 -101

24 0 416 416 129 -1'236 -90

25 0 416 416 123 -1'113 -79

26 0 416 416 117 -996 -69

27 0 416 416 111 -884 -60

28 0 416 416 106 -778 -52

29 0 416 416 101 -677 -45

30 0 416 416 96 -581 -38

Positive NPV means that Absorption refrigerator is advantageous 0

Approximation of wast heat needed for the absorption refrigerator

Electrical refrigerator:

Electricity consumption 208 kWh/y A++ refrigerators use 208kWh/y

COP_ECH 2 The COP of a normal refrigerator is assumed to be 2

Cooling energy

416 kWh/y

Absorption refrigerator:

COP_ABS 0,25 The COP of a small platen cycle unit is around 0,25

Heat energy

1664 kWh/y

Heat power (avg)

0,190 kW

Estimation of electrical refrigerator COP

T_H T_C COP_carnot

AC 318 288 9,6

Refrigiator 303 263 6,6 199


Sensitivity analysis

The effect on the 10 years anuity difference is investigated

-9,8 0 9,8

Increase (%) x: -10 0 10

y- y0 y+ ∆y-/y0 ∆y+/y0

Purchase price ABS -358 -487 -630 -26 0 29

Purchase price El-unit -535 -487 -436 10 0 -10

Electricity price -525 -487 -446 8 0 -8

Anual electricity consump -525 -487 -446 8 0 -8

Discount rate -468 -487 -509 -4 0 5

Sensitivity analysis of refrigiator ABS vs ECH

30

20

Annuity increase [%]

10

0

-10 -5 0 5 10

-10

-20

-30

Increase in variables [%]

Purchase price ABS

Purchase price El-unit

Electricity price

Anual electricity consump

Discount rate

An incrase in y-value means, that the disadvantage of using the ABS refrigerator becomes even larger.

The electricity price and anual electricity consumption are exactly on top of each other

200


Pay back time

ABS refregiator price PB Time

4000 0

4500 1,4

5000 2,7

6000 5,7

7000 9,2

8000 13,5

9000 19

10000 26

11000

12000

15000

12000

Pay Back Time for absorption refrigerator

ABS refrigerator Purchase

Price [DKK]

10000

8000

6000

4000

2000

0

0 5 10 15 20 25

Pay Back Time [years]

The price of the normal refrigerator is 4000Dkk, so if the absorption refrigerator matches that price

the pay back time will be zero

201


A. MARKET INVESTIGATION

A.4 DG appendix

In order to see whether there was a match between SOFC waste heat,

absorption cooling heat demand and hot water heat demand, the Gas

consumption and the electricity consumption was obtained for a typical

18.000m 2 Hotel with 230 rooms in three different American states [13].

This data did however not specify how much of the gas was used

for space heating and how much for hot water heating. And neither

did it specify how much of the electricity was used for electrical air

conditioning and how much for lighting etc. So the fraction for these

things was approximated by using data for the energy consumption of

the total hotel and lodging industry in the US [13].

This meant that 65% of the gas use is assumed to be for space heating,

and 35% for hot water, while 27% of the electricity is for Air conditioning

and 73% is for other equipment (including refrigeration). The cooling

demand is then estimated by assuming a COP of 4 for the electrical air

conditioning and multiplying this with the electricity use for air conditioning.

These numbers now represent what in this report is called ”normal climate”.

A hot climate has then been approximated by assuming that the

cooling demand (kWh/y) is twice that of the normal climate (since air

condition will run all year), and that no energy is needed for space heating

anymore, whereas the hot water heating consumes the same power

as in the normal climate.

Somewhere in the report the annuity has been used, elsewhere NPV is

used. This is because of the following:

The annuity is preferable for the so called chain investments which is

when a new identical unit is bought as soon as the old one is worn down.

Imagine you have the following two options: A) will give a total NPV of

1mio DKK during a lifespan on 1 year, whereas B) will give a total NPV

of 3 mil. DKK during a life span of 6 years. Option B will have the highest

NPV, but if a new unit is purchased each time the old one is worn up,

option A will give 1 mil. DKK per year, whereas option B will only give

0,5mio DKK per year (both continuing year after year). So option A is to

prefer although option B has the highest NPV per investment cycle.

202

The problem with the annuity is that it can not be calculated for 0


A.4. DG appendix

years, so if the pay back time is less than 1 year, it becomes impossible to

calculate the Pay Back Time by interpolating between 0 and 1 year.

The NPV is excellent to compare two investments with the SAME lifespan

or two mutually exclusive investments which can only be made

once. The benefit of the NPV is that it shows directly how much the

investment will return in present time money. But it is not good for chain

investments. But in contrast to annuity, it has a value (equal to the purchase

price) for t=0years.

203


From the "CHP in the Hotel and Casino market Sectors" report

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"

but the "average kW" has been chosen in order to give the reader a better feeling of how big the power consumptions are relative to a SOFC or ABS unit of a given kW size.

Hotel example

1kWh equals 3412 Btu

(Indfyrede effekter)

Unit/Place Average Anaheim Las Vegas Minneapolis

Climate Mild Hot Cold

Rooms 230 230 230

Square meters m2 18.115 18.115 18.115

Anual El. use MWh 3.131 3.548 2.960

Anual gas use Milion Btu 7.836 8.780 19.660

Anual gas use MWh 2.297 2.573 5.762

El Peak kW 745 840 832

El avg kW 367 357 405 338

El min kW 250 260 240

Gas av kW 405 262 294 658

Gas + El total, avg 771 619 699 996

Total Lodging industry

AC, el ind 10^9 Btu/y 55

Space Heating 10^9 Btu/y 118

Water Heating 10^9 Btu/y 63

Lignting 10^9 Btu/y 45

Other 10^9 Btu/y 40

Cooking 10^9 Btu/y 19

Office Eqipment 10^9 Btu/y 15

Ventilation 10^9 Btu/y 15

Refrigiation 10^9 Btu/y 14

Electricity total 10^9 Btu/y 203

AC fraction - 0,27

Other el fraction - 0,73

Gas total 10^9 Btu/y 181

Space heat frac - 0,65

Water heat frac - 0,35


Total lodging pr Hotel (calculated)

Space heating (1=yes, 0=no) 0 1 0 1 0 1

Aircondition (1=normal, 2=all year) 2 1 2 1 2 1

AC running time (fraction of year) 1 0,5 1 0,5 1 0,5

ECH ECH FC+HotW FC+HotW FC+AC+HotW FC+AC+HotW

Hot climate Normal clim. Hot climate Normal clim. Hot climate Normal clim.

Waste heat driven: average - - HotW HotW AC+HotW AC+HotW

AC, electricity kW 199 99 199 99 199 99

Other electricity kW 267 267 267 267 267 267

Space Heating kW 0 264 0 264 0 264

Water Heating kW 141 141 141 141 141 141

Total kW 607 771 607 771 607 771

EL use (excl cool) kWe 267 267 267 267 267 267

COP (prev) Electrial Chiller 4 4 4 4 4 4

Cooling use (Q_c) kWt 795 397 795 397 795 397

Heat use (Q_h) kWt - - 141 141 141 141

Fractions EL = 1 1 1 1 1

Cooling 2,97 1,49 2,97 1,49

Heating 0,5 0,5 0,5 0,5

Heat exchanger eff 0,8 0,8 0,8 0,8

SOFC eff (LHV) 0,5 0,5 0,5 0,5

COP_ABS 1,3 1,3

Cooling from ABS(yearly average) 268 104

ABS size summer production 268 208

Cooling from ECH (yearly average) 795 397 795 397 526 293

ECH size summer production 795 795 795 795 526 587

Power consumption ECH 199 99 199 99 132 73

Total electricity need 466 367 466 367 399 341

El import from net 466 367 0 0 0 0

SOFC size = av el power 466 367 399 341

Gas for SOFC and space heating 141 405 932 997 798 945

Gas for SOFC only 798 681


Hotel with 230 rooms and 18000 m^2 Arbsorption Chiller

Assumptions

Default values

COP_ECH 4,0 4 USD/Dkr 5,3

COP_ABS 1,3 1,3 GBP/Dkk 8,5

eta_SOFC 0,5 0,5

Gas price kr/kWh 0,20 0,2 California, commercial

Electricity pr kr/kWh 0,75 0,75 California, commercial

SOFC Price kr/kW 2650 2650 $500/kW

ABS Price kr/kW 3670 3'670 Broard price pr kW corected which is the size correlation seen for WEGRACAL ABS units

ECH Price kr/kW 1798 1798 P_(Enviromax 20 kW) * 0,5 (half kW price for a 250kW unit compared to the 20kW)

Storage price/Cooling price 0,00 Storage size factor 0,50

Discount 0,050 Hot climate Normal clim. Hot climate Normal clim. Hot climate Normal clim.

- - HotW HotW ABS+HotW ABS+HotW

SOFC eff (LHV) 0,0 0,0 0,5 0,5 0,5 0,5

COP_ABS 0,0 0,0 0,0 0,0 1,3 1,3

Cooling from ABS(yearly average) 268 104

ABS size 268 208

Cooling from ECH (yearly average) 795 397 795 397 526 293

ECH size 795 795 795 795 526 587

Power consumption ECH 199 99 199 99 132 73

Total electricity need 466 367 466 367 399 341

El import from net 466 367 0 0 0 0

SOFC size = av el power 466 367 399 341

Gas for SOFC and space heating 141 405 932 997 798 945


Electricity + Electrical Chiller, HOT

kW kWh/y

P_gas 141 1'233'534

P_el 466 4'082'246

P_el, SOFC

P_ECH 795

P_ABS

Year Electricity Gas ECH Net payment NPV_i NPV_akk Anuity

0 1'428'754 1'428'754 1'428'754 1'428'754

1 3'061'685 246'707 3'308'392 3'150'849 4'579'603 4'808'583

2 3'061'685 246'707 3'308'392 3'000'809 7'580'411 4'076'782

3 3'061'685 246'707 3'308'392 2'857'913 10'438'324 3'833'042

4 3'061'685 246'707 3'308'392 2'721'822 13'160'146 3'711'317

5 3'061'685 246'707 3'308'392 2'592'211 15'752'358 3'638'398

6 3'061'685 246'707 3'308'392 2'468'773 18'221'130 3'589'881

7 3'061'685 246'707 3'308'392 2'351'212 20'572'342 3'555'308

8 3'061'685 246'707 3'308'392 2'239'250 22'811'592 3'529'451

9 3'061'685 246'707 3'308'392 2'132'619 24'944'211 3'509'403

10 3'061'685 246'707 3'308'392 2'031'065 26'975'276 3'493'422

11 3'061'685 246'707 3'308'392 1'934'348 28'909'624 3'480'398

12 3'061'685 246'707 3'308'392 1'842'236 30'751'860 3'469'591

13 3'061'685 246'707 3'308'392 1'754'511 32'506'371 3'460'491

14 3'061'685 246'707 3'308'392 1'670'963 34'177'333 3'452'730

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

The ABS only runs all year. The cooling power is all year equal to the sommer power of the "sommer Case"

SOFC runs all the time 24/7

kW kWh/y

P_gas 932 8'164'493

P_el, SOFC 466

P_el, import 0 0 Electricity is imported from the grid to cover the extra need for the ECH

P_ECH 795

P_ABS

Year Electricity GAS for FC ECH SOFC ABS Storage Net payment NPV_i NPV_akk Anuity

0 1'428'754 1'234'926 2'663'680 2'663'680 2'663'680

1 0 1'632'899 1'632'899 1'555'141 4'218'821 4'429'762

2 0 1'632'899 1'632'899 1'481'087 5'699'908 3'065'439

3 0 1'632'899 1'632'899 1'410'559 7'110'467 2'611'025

4 0 1'632'899 1'632'899 1'343'390 8'453'857 2'384'088

5 0 1'632'899 1'632'899 1'279'419 9'733'276 2'248'141

6 0 1'632'899 1'632'899 1'218'494 10'951'770 2'157'690

7 0 1'632'899 1'632'899 1'160'470 12'112'240 2'093'235

8 0 1'632'899 1'632'899 1'105'210 13'217'450 2'045'028

9 0 1'632'899 1'632'899 1'052'581 14'270'031 2'007'652

10 0 1'632'899 1'632'899 1'002'458 15'272'489 1'977'857

11 0 1'632'899 1'632'899 954'722 16'227'211 1'953'576

12 0 1'632'899 1'632'899 909'259 17'136'470 1'933'429

13 0 1'632'899 1'632'899 865'961 18'002'431 1'916'463

14 0 1'632'899 1'632'899 824'725 18'827'156 1'901'994

15 0 1'632'899 1'632'899 785'452 19'612'608 1'889'524


SOFC + Water heating + ABS, Cooling ALL YEAR

Sofc running full year, netimport electricity = 0

A storage will take care of the daily variation of cooling demand

No room heating. Hot water is made by the SOFC waste heat

Part of the cooling is made by the ABS, and the rest by the ECH

Cooling need ALL YEAR (30 Celcius all year)

The ABS runs all year (thereby nu waste heat is wasted)

The SOFC delivers to the ABS all the time, and no real seasonal variation in el-in/export

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

SOFC runs all the time 24/7

kW kWh/y

P_gas 798 6'988'834

P_el, SOFC 399

P_el, import 0 0

P_ECH 526

P_ABS 268

Year Electricity GAS for FC ECH SOFC ABS Storage Net payment NPV_i NPV_akk Anuity

0 946'210 1'057'101 984'971 0 2'988'282 2'988'282 2'988'282

1 0 1'397'767 1'397'767 1'331'206 4'319'488 4'535'462

2 0 1'397'767 1'397'767 1'267'816 5'587'304 3'004'879

3 0 1'397'767 1'397'767 1'207'443 6'794'747 2'495'089

4 0 1'397'767 1'397'767 1'149'946 7'944'693 2'240'497

5 0 1'397'767 1'397'767 1'095'187 9'039'880 2'087'984

6 0 1'397'767 1'397'767 1'043'035 10'082'915 1'986'510

7 0 1'397'767 1'397'767 993'367 11'076'282 1'914'201

8 0 1'397'767 1'397'767 946'064 12'022'345 1'860'119

9 0 1'397'767 1'397'767 901'013 12'923'358 1'818'188

10 0 1'397'767 1'397'767 858'108 13'781'466 1'784'763

11 0 1'397'767 1'397'767 817'245 14'598'711 1'757'523

12 0 1'397'767 1'397'767 778'329 15'377'040 1'734'921

13 0 1'397'767 1'397'767 741'266 16'118'305 1'715'887

14 0 1'397'767 1'397'767 705'967 16'824'272 1'699'655

15 0 1'397'767 1'397'767 672'350 17'496'622 1'685'665


16000

Pay Back Time: Entire System (SOFC+ABS)

14000

SOFC Price [DKK/kW]

12000

10000

8000

6000

4000

2000

0

Normal Climate

Hot Climate

0 1 2 3 4 5

Time [years]

10000

ABS Price [DKK/kW]

9000

8000

7000

6000

5000

4000

3000

2000

1000

0

Pay Back Time: Absorption Cooling Unit (ABS)

Normal Climate

Hot Climate

0 2 4 6 8 10 12

Time [years]


Electricity + Electrical Chiller, Cooling Normal climate

kW kWh/y

P_gas 405 3'543'962

P_el, SOFC

P_el 367 3'212'000

P_ECH 795

P_ABS

Year Electricity Gas ECH Net payment NPV_i NPV_akk Anuity

0 1'428'754 1'428'754 1'428'754 1'428'754

1 2'409'000 708'792 3'117'792 2'969'326 4'398'080 4'617'984

2 2'409'000 708'792 3'117'792 2'827'930 7'226'010 3'886'183

3 2'409'000 708'792 3'117'792 2'693'266 9'919'276 3'642'443

4 2'409'000 708'792 3'117'792 2'565'016 12'484'292 3'520'718

5 2'409'000 708'792 3'117'792 2'442'872 14'927'164 3'447'799

6 2'409'000 708'792 3'117'792 2'326'545 17'253'708 3'399'282

7 2'409'000 708'792 3'117'792 2'215'757 19'469'465 3'364'709

8 2'409'000 708'792 3'117'792 2'110'245 21'579'710 3'338'852

9 2'409'000 708'792 3'117'792 2'009'757 23'589'467 3'318'804

10 2'409'000 708'792 3'117'792 1'914'054 25'503'521 3'302'823

11 2'409'000 708'792 3'117'792 1'822'909 27'326'430 3'289'799

12 2'409'000 708'792 3'117'792 1'736'104 29'062'533 3'278'992

13 2'409'000 708'792 3'117'792 1'653'432 30'715'965 3'269'892

14 2'409'000 708'792 3'117'792 1'574'697 32'290'662 3'262'131

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

The ABS only runs in the summer. No cooling needed at winter time

SOFC runs all the time 24/7

During summer there will be a net import of electricity (for the ECH), and during winter a net exp

kW kWh/y

P_gas 997 8'734'429

P_el, SOFC 367

P_el, import 0 0 Electricity is imported from the grid to cover the extra need for the ECH

P_ECH 795

P_ABS

Year Electricity GAS for FC ECH SOFC ABS Storage Net payment NPV_i NPV_akk Anuity

0 1'428'754 971'667 2'400'420 2'400'420 2'400'420

1 0 1'746'886 1'746'886 1'663'701 4'064'121 4'267'327

2 0 1'746'886 1'746'886 1'584'477 5'648'598 3'037'843

3 0 1'746'886 1'746'886 1'509'026 7'157'623 2'628'341

4 0 1'746'886 1'746'886 1'437'167 8'594'791 2'423'833

5 0 1'746'886 1'746'886 1'368'731 9'963'521 2'301'322

6 0 1'746'886 1'746'886 1'303'553 11'267'074 2'219'810

7 0 1'746'886 1'746'886 1'241'479 12'508'553 2'161'726

8 0 1'746'886 1'746'886 1'182'361 13'690'914 2'118'283

9 0 1'746'886 1'746'886 1'126'058 14'816'973 2'084'601

10 0 1'746'886 1'746'886 1'072'436 15'889'409 2'057'751

11 0 1'746'886 1'746'886 1'021'368 16'910'777 2'035'870

12 0 1'746'886 1'746'886 972'731 17'883'508 2'017'714

13 0 1'746'886 1'746'886 926'411 18'809'919 2'002'424

14 0 1'746'886 1'746'886 882'296 19'692'215 1'989'386

15 0 1'746'886 1'746'886 840'282 20'532'497 1'978'148


SOFC + Water heating + ABS, Cooling SUMMER ONLY

Sofc running full year, netimport electricity = 0

A storage will take care of the daily variation of cooling demand

Room heating will always be made by gas - only hot water is made by the SOFC waste heat

Part of the cooling is made by the ABS, and the rest by the ECH

Cooling SUMMER ONLY

The ABS only runs in the summer. No cooling needed at winter time

The SOFC delivers to the ABS at summer, and wastes heat in the winter.

During summer there will be a net import of electricity (for the ECH), and during winter a net exp

SOFC runs all the time 24/7

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

kW kWh/y

P_gas 945 8'279'206

P_el, SOFC 341

P_el, import 0 0

P_ECH 587

P_ABS 208

Year Electricity GAS for FC ECH SOFC ABS Storage Net payment NPV_i NPV_akk Anuity

0 1'055'066 902'812 762'773 0 2'720'651 2'720'651 2'720'651

1 0 1'655'841 1'655'841 1'576'992 4'297'643 4'512'525

2 0 1'655'841 1'655'841 1'501'897 5'799'539 3'119'021

3 0 1'655'841 1'655'841 1'430'378 7'229'917 2'654'888

4 0 1'655'841 1'655'841 1'362'265 8'592'182 2'423'097

5 0 1'655'841 1'655'841 1'297'395 9'889'577 2'284'243

6 0 1'655'841 1'655'841 1'235'614 11'125'191 2'191'857

7 0 1'655'841 1'655'841 1'176'775 12'301'967 2'126'024

8 0 1'655'841 1'655'841 1'120'739 13'422'705 2'076'785

9 0 1'655'841 1'655'841 1'067'370 14'490'075 2'038'610

10 0 1'655'841 1'655'841 1'016'543 15'506'618 2'008'178

11 0 1'655'841 1'655'841 968'136 16'474'754 1'983'377

12 0 1'655'841 1'655'841 922'034 17'396'789 1'962'800

13 0 1'655'841 1'655'841 878'128 18'274'917 1'945'470

14 0 1'655'841 1'655'841 836'312 19'111'229 1'930'692

15 0 1'655'841 1'655'841 796'488 19'907'717 1'917'955


Hot climate SOFC + ABS + HW vs pure El

Must be updated manually!

NO SOFC SOFC + ABS + HW ------------------------------------------------------------------------------------------------

SOFC pris DKK/kW

Year 1'000 2'000 2'650 4'000 6'000 8'000 10'000 15'000

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1 1 1 2 2 3 3 5

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

Must be updated manually!

Delta NPV_10 SOFC + ABS + HW - (SOFC + HW) ------------------------------------------------------------------------------------------------

ABS pris DKK/kW

Year 2'000 2'450 3'000 3'670 5'000 6'000 7'000 8'000 10'000

0 123'538 2'751 -144'877 -324'715 -681'708 -950'123 -1'218'538 -1'486'954 -2'023'784

1 347'473 226'686 79'058 -100'780 -457'773 -726'188 -994'603 -1'263'019 -1'799'849

2 560'745 439'958 292'329 112'491 -244'501 -512'917 -781'332 -1'049'747 -1'586'578

3 763'860 643'074 495'445 315'607 -41'386 -309'801 -578'216 -846'631 -1'383'462

4 957'304 836'517 688'889 509'050 152'058 -116'357 -384'773 -653'188 -1'190'019

5 1'141'536 1'020'749 873'121 693'282 336'290 67'875 -200'541 -468'956 -1'005'787

6 1'316'995 1'196'208 1'048'580 868'741 511'749 243'334 -25'082 -293'497 -830'328

7 1'484'099 1'363'312 1'215'683 1'035'845 678'853 410'437 142'022 -126'393 -663'224

8 1'643'245 1'522'458 1'374'830 1'194'992 837'999 569'584 301'169 32'753 -504'077

9 1'794'813 1'674'026 1'526'398 1'346'560 989'567 721'152 452'737 184'321 -352'509

10 1'939'164 1'818'377 1'670'748 1'490'910 1'133'918 865'502 597'087 328'672 -208'159

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

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

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

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

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

PB time

0,0 0,7 1,5 3,2 4,7 6,2 7,8 11,5


Assumptions

SOFC price = 2650kr/kW

10 years lifetime

Electricity can be im/exported at same price as long at netexport < 0

no gas for room heating

Cooling ALL YEAR

Cooling in Sommer only

Annuity_5 Annuity_10 Annuity_15 Annuity_5 Annuity_10 Annuity_15

EL 3'638'398 3'493'422 3'446'041 3'447'799 3'302'823 3'255'442

SOFC+WH 2'248'141 1'977'857 1'889'524 2'301'322 2'057'751 1'978'148

SOFC+WH+ABS 2'087'984 1'784'763 1'685'665 2'284'243 2'008'178 1'917'955

HOT climate.

Annual price for all energy equipment + gas and electricity use

Normal climate.

Annual price for all energy equipment + gas and electricity use

Annuity price [DKK/y]

4'000'000

3'500'000

3'000'000

2'500'000

2'000'000

1'500'000

1'000'000

Annuity_5

Annuity_10

Annuity_15

Annuity price [DKK/y]

4'000'000

3'500'000

3'000'000

2'500'000

2'000'000

1'500'000

1'000'000

Annuity_5

Annuity_10

Annuity_15

500'000

500'000

0

EL SOFC+WH SOFC+WH+ABS

0

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

Sensitivity analysis

The effect on the 10 years anuity difference is investigated

HOT climate

Summer only (not shown in report)

(SOFC + WH + ABS) - (SOFC + WH)

(SOFC + WH + ABS) - (SOFC + WH)

Positive values => ABS is advantageous

Positive values => ABS is advantageous

Delta NPV Delta Anuity Delta NPV Delta Anuity

0 -324'602 0 -320'231 0

1 -100'667 -105'700 -233'522 -245'198

2 112'605 60'559 -150'942 -81'177

3 315'720 115'935 -72'294 -26'547

4 509'164 143'590 2'609 736

5 693'396 160'157 73'944 17'079

6 868'855 171'180 141'883 27'953

7 1'035'959 179'034 206'587 35'702

8 1'195'105 184'909 268'209 41'498

9 1'346'673 189'464 326'897 45'991

10 1'491'024 193'094 382'791 49'573

11 1'628'500 196'053 436'022 52'492

12 1'759'431 198'508 486'719 54'914

13 1'884'126 200'576 535'002 56'954

14 2'002'884 202'339 580'986 58'693

15 2'115'986 203'859 624'780 60'193


Hot climate

Increase (Delta NPV_10) -10 0 10

Electricity price 1'491'024 1'491'024 1'491'024

Gas price 1'325'967 1'491'024 1'672'586

Discount rate 1'531'779 1'491'024 1'447'734

COP_ECH 1'656'193 1'491'024 1'334'841

COP_ABS 1'381'390 1'491'024 1'606'966

eta_SOFC 2'066'664 1'491'024 1'018'709

SOFC price 1'474'858 1'491'024 1'508'806

ECH price 1'447'156 1'491'024 1'539'278

ABS price 1'580'567 1'491'024 1'392'527

-10 0 10

Net Present Value increase [%]

Sensitivity analysis: SOFC+HW+ABS vs SOFC+WH

Electricity price 0 0 0

Gas price -11 0 12

-20

Discount rate 3 0 -3

COP_ECH 11 0 -10

-30

COP_ABS -7 0 8

eta_SOFC 39 0 -32

Increase in variables [%]

SOFC price -1 0 1

ECH price -3 0 3 A positive value of e.g. 5% means, that after 10 years, the difference in NPV will

ABS price 6 0 -7 be 5% higher (in favour of the ABS solution)

30

20

10

0

-10 -5 0 5 10

-10

ECH price

COP_ABS

Electricity price

COP_ECH

Discount rate

Gas price

eta_SOFC

SOFC price

ABS price


A.5 Absorption cooling unit prices

A.5. Absorption cooling unit prices

219


Prices of absorption cooling units

Name Rotarica Rotarica CHEM SorTech AG SorTech AG EAW Cooling Tech

Model Splar 045 Splar 045v AAdC ACS 08 ASC 15 WEGRACAL 15 Cooltech 5

Refrigerant water water water ammonia

Ab/adsorbent silica gel silica gel LiBr water

Providing heat yes yes no

Cooling power, nom Q_C kW 4,5 4,5 5,0 8 15 15 17,6

Cooling power interval [Q_C] kW 2->8 2->8 5->11 10->23

Electrical power P kW 0,4 1,11 0,5 0,007 0,014 0,3 1,3

Heat Consumption Q_D kW 12,5 13 25 21,1 25,9

COP COP 0,7 0,7 0,4 0,6 0,6 0,71 0,68

T_hotw (i/o) T_Hw C 90 90 72->65 72->65 Gas

T_cool,fwd TC_o C 12 12 15 15 11 7,2

T_cool,return TC_I C 12 12 18 18 17 12,8

T_condenser T_Cond C 32->27 32->28 30-->36

HEX Warm included no no no yes

HEX Cold included no no no no

HEX Hot, (hot water) included yes yes yes no

HEX Hot, (gas burner) included no no no yes

HEX Hot, (exhaust gas) included no no no no

Lager

kWh

(kg) m kg 240 280 295 590 650 475

Price @ 1unit (excl VAT) kr 114'800 169'900 111'154 139'920

Price @ 1000units (excl VAT) kr 93'280

Price pr kW @ 1unit (excl VAT) DKK/kW 0 0 14'350 11'327 7'410 7'950

Price pr kW @ 1000units (excl VAT) DKK/kW 0 0 0 0 0 5'300

HEX Warm included DKK 45'000 65'000 65'000 0

HEX Cold included DKK 3'796 7'118 7'118 8'352

HEX Hot, (exhaust gas) included DKK 3'164 5'932 5'013 6'141

Total ext eq. (excl VAT) DKK 0 0 0 51'960 78'050 77'131 14'494

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

SC 5 TM 10 GAHP-AR BCT23 WEGRACAL 50 WEGRACAL 80 WEGRACAL 140 WEGRACAL200 Model

water water ammonia water water water water water Refrigerant

LiBr LiCl water LiBr LiBr LiBr LiBr LiBr Ab/adsorbent

yes yes yes Providing heat

17,6 20 16,9 23 54 83 140 200 Cooling power, nom

Cooling power interval

0,043 0,11 0,87 1,80 3,4 3,4 3,4 3,4 Electrical power

25,1 29,4 25,3 20,8 72,0 111 187 267 Heat Consumption

0,7 0,68 0,67 1,11 0,75 0,75 0,75 0,75 COP

88 Gas Gas 86-->71 86-->71 86-->71 86-->71 T_hotw (i/o)

7 17 [7] 7,2 7 9 9 9 9 T_cool,fwd

12,5 12,7 14 15 15 15 15 T_cool,return

30 [20] 27-->32 27-->32 27-->32 27-->32 T_condenser

no no no yes no no no no HEX Warm included

no no no no no no no no HEX Cold included

yes yes (no) yes (84%) yes yes yes yes HEX Hot, (hot water) included

no no yes yes (100%) no no no no HEX Hot, (gas burner) included

no no no yes (98%) no no no no HEX Hot, (exhaust gas) included

60 Lager

420 740 380 700 2250 2900 3400 4300 (kg)

143'600 111'900 92'504 119'360 379'453 436'485 598'777 684'306 Price @ 1unit (excl VAT)

93'250 0 0 0 0 0 0 Price @ 1000units (excl VAT)

8'159 5'595 5'474 5'190 7'027 5'259 4'277 3'422 Price pr kW @ 1unit (excl VAT)

0 4'663 0 0 0 0 0 0 Price pr kW @ 1000units (excl VAT)

65'000 75'217 65'000 0 191'803 294'809 497'268 710'383 HEX Warm included

8'352 9'491 8'020 10'915 25'626 39'388 66'438 94'912 HEX Cold included

5'956 6'979 6'006 0 17'084 26'259 44'292 63'275 HEX Hot, (exhaust gas) included

79'308 91'687 79'026 10'915 234'514 360'456 607'998 868'569 Total ext eq. (excl VAT)

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

900'000

800'000

143'600

700'000

Price [DKK]

600'000

500'000

400'000

300'000

200'000

100'000

0

ECH vs ABS vs ADS

9'000

15'000 12'400 16'000 50'865 58'510 8'000 80'265 91'730

12'500

7'000

ECH

ABS

Adsorption

0 50 100 150 200

Cooling capacity [kW]

Price [DKK/kW]

6'000

5'000

4'000

3'000

2'000

1'000

0

Prices pr kW for different ABS brands

ABSorption

0 50 100 150 200 250

Cooling capacity [kW]

The marked investigation showed the following prices for different cooling capacities for electrical chillers (ECH), absorption units (ABS) and Adsorption units.

The reason for the large spread for kW price (right figure) of the low sizes is that it is different brands og different performance and quality, hence the development of the

kW price can not be attributed solely to the size of the unit, and for establishing the size-kW-price correlation, the price dependency of the WEGSECAL ABS units is

used (see next page)


Prices of WEGRACAL absorption cooling units of different size

Model WEGRACAL 15 50 80 140 200

Capacity kW 15 54 83 140 200

Mass kg 650 2250 2900 3400 4300

Catalog price Euro 14'900 50'865 58'510 80'265 91'730

Price ex VAT Dkr 111'154 379'453 436'485 598'777 684'306

Euro exchange rate 7,46

Data comes from:

http://www.easy-server.org/ebg_neu/Klimaanlage/preislistekwkk.pdf

The WEGRACAL data has been used to get a correlation between size and price for absorption cooling units

since they are all the same manufacturer, the price difference must be due to size only (and not

Quality, performance, stamination etc).

WEGRACAL Absorption coolnig unit

800'000

Price

700'000

600'000

Price [DKK]

500'000

400'000

300'000

200'000

100'000

0

0 50 100 150 200 250

Cooling power [kW]

WEGRACAL Absorption coolnig unit

Price [DKK]

5'000

4'500

4'000

3'500

3'000

2'500

2'000

1'500

1'000

500

0

Mass

0 50 100 150 200 250

Cooling power [kW]


A. MARKET INVESTIGATION

A.6 Gas and electricity prices

224


Retail gas prices

2008

prices

2008

prices

39,48 GJ/1000 m^3 (LHV)

5,41 DKK/USD

0,02831685 m^3/cubic foot

DKK/kWh

Residential Industry Commercial

Residential Industry Commercial

Taiwan USD/1000 Cubic Feet 0,00 0,00 0,00

Singapore USD/1000 Cubic Feet 0,00 0,00 0,00

Malaysia USD/1000 Cubic Feet 0,00 0,00 0,00

California 12,74 10,71 11,72 USD/1000 Cubic Feet 0,22 0,19 0,20

Hawaii 44,75 26,74 39,01 USD/1000 Cubic Feet 0,78 0,47 0,68

US avg. 13,68 9,58 11,99 USD/1000 Cubic Feet 0,24 0,17 0,21

2008

prices

2008

prices

USD/m^3 DKK/m^3DKK/GJ DKK/MWH DKK/kWh

Taiwan 0,00 0,00 0,00 0,00 0,00

Singapore 0,00 0,00 0,00 0,00 0,00

Malaysia 0,00 0,00 0,00 0,00 0,00

California 0,45 2,43 61,65 221,95 0,22

Hawaii 1,58 8,55 216,56 779,60 0,78

US avg. 0,48 2,61 66,20 238,32 0,24

Retail natural gas price

0,90

0,80

0,70

0,60

Residential

Industry

Commercial

DKK/kWh

0,50

0,40

0,30

0,20

0,10

0,00

Taiwan Singapore Malaysia California Hawaii US avg.

http://tonto.eia.doe.gov/dnav/ng/ng_pri_sum_dcu_nus_a.htm

http://www.ens.dk/da-DK/Info/TalOgKort/Statistik_og_noegletal/Maanedsstatistik/Documents/Energistatistik%202008.pdf

http://www.xe.com/ucc/convert.cgiAmount=1&From=USD&To=DKK&image.x=41&image.y=13&image=Submit

http://www.onlineconversion.com/volume.htm

http://www.eia.doe.gov/emeu/cabs/taiwan.html#gas

http://www.eia.doe.gov/dnav/ng/ng_pri_sum_dcu_SCA_a.htm

225


Retail electricity prices

Exchange rate in DKK

TWD USD

0,1687 5,41

2007

prices

2009

prices

In DKK/kWh

Residential Industry Commercial Currency Residential Industry Commercial

Taiwan 2,5855 1,8331 n/a TWD/kWh 0,44 0,31 n/a

Singapore 4,4842 3,5121 n/a TWD/kWh 0,76 0,59 n/a

Malaysia 2,301 2,2201 n/a TWD/kWh 0,39 0,37 n/a

California 14,08 11,43 13,93 Uscent/kWh 0,76 0,62 0,75

Hawaii 26,45 20,49 24,35 Uscent/kWh 1,43 1,11 1,32

US avg. 11,76 6,68 10,22 Uscent/kWh 0,64 0,36 0,55

Retail electricity price

1,60

1,40

1,20

Residential

Industry

Commercial

DKK/kWh

1,00

0,80

0,60

0,40

0,20

0,00

Taiwan Singapore Malaysia California Hawaii US avg.

sources:

US

Taiwan

http://www.eia.doe.gov/cneaf/electricity/epm/table5_6_a.html

http://www.etaiwannews.com/etn/print.php

226


A P P E N D I X

B

DIAGRAMS AND PLOTS

227


B. DIAGRAMS AND PLOTS

B.1 GAX diagram

Figure B.1: Diagram of GAX cycle. Taken from [20].

228


B.2. Double stage diagram

B.2 Double stage diagram

COND2

21

HEAT

DES2

29

27

22

SHEX

2

23

VA2

31

32

VB2

PUMP

2

26

25

2

COND1

COOLING

1

MIXR

0

10

MIXL

9

DES1

SHEX

1

α

8

SPL

1-α

7

3

VA1

EVAP

4

11

12

VB1

ABSO

PUMP

1

6

5

CHILLED WATER

COOLING

Figure B.2: Diagram of double stage absorption cycle.

229


B. DIAGRAMS AND PLOTS

B.3 Closed adsorption cycle

Figure B.3: Diagram of closed adsorption cycle - two-bed system. Taken from [35].

230


B.4. Property plots

B.4 Property plots

B.4.1

Phase diagram of water-LiBr-solution

Figure B.4: Only states of solution of water and LiBr applies for the absorption cycle.

Precipitation must be avoided to avoid blocks in tubes and damage of the machine.

231


B. DIAGRAMS AND PLOTS

B.4.2

p-T diagram of water-LiBr-solution

Figure B.5: p-T diagram of water-LiBr. w is the concentration of the LiBr-solution (on mass

basis).

232


A P P E N D I X

C

EES

C.1 Parameter configuration

This is the optimized parameter configuration. The standard parameter

configuration is very similar and only parameters which are different

from the optimized one are shown with blue numbers.

FUEL CELL related

α SPG1 = 0,62 [·]

λ Bur n;i = 1,5 [·]

A cell = 0,0228 [ m 2]

ASR = 280 · exp ( −0,0083 · T SOFC ;av

)

· 10

−4 [ Ω · m 2]

F R = 0,14 [·]

FW = 0,6 [·]

∆ Ḣ f uel = 100 [kW ]

i d = 2700 [ A/m 2] 3000

n cell = 60 [·]

U f = 0,565 [·] 0,70

Effectiveness

ɛ GGHE X 1;c = ɛ GGHE X 2;c [·]

233


C. EES

Efficiencies

SOFC

η inver t = 0,95 [·]

η i s;BLOW 1 = 0,60 [·]

General

η blower ;TOW ER1 = 0,4 [·]

η wb;TOW ER1 = 0,75 [·]

ABS

η PU MP1 = 0,5 [·]

η PU MP2 = 0,5 [·]

Mass flows at inlet - [CH 4 ; CO ; CO 2 ; H 2 ; H 2 O ; N 2 ; O 2 ]

SOFC

ṁ 1; 1..7 = [ṁ i ; 0; 0; 0; 0; 0; 0] kg

s

ṁ 11; 1..5

= [0; 0; 0; 0; 0]

kg

s

Burner additional fuel input

ṁ Bur ni ;3 ; 1..7 = [ ṁ bur n;add ; 0; 0; 0; 0; 0; 0 ] kg

s

FuelBP Ratio = 0,0 [·]

234


C.1. Parameter configuration

Humidity

φ TOW ERair ;i

= 0,4 [·]

Pressure - Absolute

p re f = 100 [kPa]

SOFC

p BLOW 1i = p re f

[kPa]

General

p W GHE X 3g ;o

= p re f

[kPa]

p W GHE X 3w;i = 1000 [kPa]

ABS

p DES1h;i = 2000 [kPa]

p COND1c;i = 2000 [kPa]

p EV APc;i = 2000 [kPa]

p DES2h;i = 2000 [kPa]

Pressure loss of components

SOFC

∆ p;BURN ;i ;1 = −8 [kPa]

∆ p;BURN ;i ;2 = −1 [kPa]

∆ p;GGHE X 1;h = −1 [kPa]

235


C. EES

∆ p;GGHE X 1;c = −1 [kPa]

∆ p;GGHE X 2;h = −1 [kPa]

∆ p;GGHE X 2;c = −1 [kPa]

∆ p;GGHE X 3;h = −4 [kPa]

∆ p;GGHE X 3;c = −4 [kPa]

∆ p;GGHE X 4;c = −2 [kPa]

∆ p;GGHE X 4;h = −2 [kPa]

∆ p;M I XG1;i ;1 = −0,1 [kPa]

∆ p;M I XG2;i ;1 = −0,1 [kPa]

∆ p;PR = −5 [kPa]

∆ p;SOFC ;ano = −1 [kPa]

∆ p;SOFC ;cat = −3 [kPa]

∆ p;SPG1;o;1 = −0,1 [kPa]

∆ p;SPG1;o;2 = −0,1 [kPa]

∆ p;SPG2;o;1 = −0,1 [kPa]

∆ p;SPG2;o;2 = −0,1 [kPa]

General

∆ p;TOW ER1;w = 0 [kPa]

∆ p;W GHE X 1;g = −2 [kPa]

∆ p;W GHE X 1;w = 0 [kPa]

∆ p;W GHE X 2;g = −2 [kPa]

∆ p;W GHE X 2;w = 0 [kPa]

∆ p;W GHE X 3;g = −2 [kPa]

∆ p;W GHE X 3;w = 0 [kPa]

∆ p;TOW ER1;air ;dr y = 0,15 [kPa]

∆ p;TOW ER1;air ;wet = 0,15 [kPa]

236


C.1. Parameter configuration

ABS

∆ p;ABSO;1 = 0 [kPa]

∆ p;ABSO;2 = 0 [kPa]

∆ p;ABSO;c = 0 [kPa]

∆ p;COND1;r = 0 [kPa]

∆ p;COND1;c = 0 [kPa]

∆ p;COND2;r = 0 [kPa]

∆ p;COND2;c = 0 [kPa]

∆ p;DES1;r = 0 [kPa]

∆ p;DES1;s = 0 [kPa]

∆ p;DES1;h = 0 [kPa]

∆ p;DES2;r = 0 [kPa]

∆ p;DES2;s = 0 [kPa]

∆ p;EV AP;r = 0 [kPa]

∆ p;EV AP;c = 0 [kPa]

∆ p;M I X R1;1 = 0 [kPa]

∆ p;M I X R1;2 = 0 [kPa]

∆ p;M I X L1;1 = 0 [kPa]

∆ p;M I X L1;2 = 0 [kPa]

∆ p;SHE X 1;ws = 0 [kPa]

∆ p;SHE X 1;ss = 0 [kPa]

∆ p;SHE X 2;ws = 0 [kPa]

∆ p;SHE X 2;ss = 0 [kPa]

Heat loss of components

SOFC

˙Q loss;BLOW 1 = 0 [kW ]

237


C. EES

˙Q loss;Bur n = 0 [kW ]

˙Q loss;PR = 0 [kW ]

˙Q loss;SOFC = 0 [kW ]

General

˙Q loss;W GHE X 1 = 0 [kW ]

˙Q loss;W GHE X 2 = 0 [kW ]

˙Q loss;W GHE X 3 = 0 [kW ]

˙Q loss;W W HE X 1 = 0 [kW ]

ABS

˙Q loss;ABSO = 0 [kW ]

˙Q loss;COND1 = 0 [kW ]

˙Q loss;COND2 = 0 [kW ]

˙Q loss;DES1 = 0 [kW ]

˙Q loss;DES2 = 0 [kW ]

˙Q loss;EV AP = 0 [kW ]

˙Q loss;PU MP1 = 0 [kW ]

˙Q loss;PU MP2 = 0 [kW ]

˙Q loss;SHE X 1 = 0 [kW ]

˙Q loss;SHE X 2 = 0 [kW ]

˙Q loss;V A1 = 0 [kW ]

˙Q loss;V A2 = 0 [kW ]

˙Q loss;V B1 = 0 [kW ]

˙Q loss;V B2 = 0 [kW ]

238


C.1. Parameter configuration

Qualities

qu COND1r ;o

= 0 [·]

qu COND2r ;o

= 0 [·]

qu EV APr ;o

= 1 [·]

Temperatures

T re f = 25 [C ]

T Bur ni ;3

= T re f [C ]

T amb;dr y = 18 [C ]

T amb;wet = 30 [C ]

SOFC

T GGHE X 1c;i = T re f [C ]

T BLOW 1i = T re f [C ]

T SOFCano;i = 690 [C ]

T SOFCcat;i = T SOFCano;i [C ]

T W GHE X 3w;i = T amb [C ]

T W GHE X 3w;o = 65 [C ]

T DES2s;o = 133 [C ] 150

ABS

T DES1;h;i = 67 [C ] 78

T EV APc;o = 6,0 [C ]

T amb;evap = T amb − T EV APc;o [C ]

Temperature changes

239


C. EES

SOFC

∆ T ;SOFC ;av = 30 [C ]

∆ T ;SOFC = 90 [C ]

General

∆ T ;c;TOW ER1 = 5 [C ]

ABS

∆ T ;chill;EV AP = 5 [C ]

∆ T ;h;DES1 = 5 [C ]

∆ T ;h;DES2 = 5 [C ]

∆ T ;min

∆ T ;min;DES1;r ;o = 0 [C ]

∆ T ;min;DES2;r ;o = 0 [C ]

Liquid-Liquid HEXES

∆ T ;min;ABSO;s;o = 1,8 [C ] 5

∆ T ;min;SHE X 1;ws;i = 5 [C ]

∆ T ;min;SHE X 2;ws;i = 5 [C ]

∆ T ;min;EV AP;r ;i = 2,7 [C ] 5

240

Liquid-Gas/liquid HEXES

∆ T ;min;COND1;r ;o;S = 12,5 [C ]


C.1. Parameter configuration

∆ T ;min;COND1;r ;o;D = 10 [C ]

∆ T ;min;COND2;r ;o = 15 [C ] 12,5

(∆ T ;min;COND2;r ;o is set so ∆ T ;min;COND2;mp = 10[C ] in both STD and OPTI)

Gas/liquid HEXES

∆ T ;min;W GHE X 1;w;i = 15 [C ]

∆ T ;min;W GHE X 2;w;i = 15 [C ]

∆ T ;min;W GHE X 3;w;i = 15 [C ]

Gas-Gas HEXES

∆ T ;min;GGHE X 4;c;o = 9,4 [C ] 25

TOWERs

∆ T ;min;TOW ER1;a;o;wet = 3 [C ]

∆ T ;min;TOW ER1;a;o;dr y = 8 [C ]

∆ T ;min;TOW ER1;a;i ;dr y = ∆ T ;min;TOW ER1;a;o [C ]

241


C. EES

C.2 Results - Standard parameter configuration

ABSO c;i = 36 ABSO c;o = 37

ABSO r ;i = 54 ABSO s;i = 62

ABSO s;o = 55

AddPreHeat$ = ‘On’

Air Fuel Ratio;m = 92,78 [-] Air Fuel Ratio;n = 8,355 [-]

Air i = 11 [-] α SPG1 = 0,62 [-]

α SPG2 = 0,0461 [-]

ASR = 0,00005542 [ Ω·m 2] α SPL1 = 0,4351 [-]

A cell = 0,0228 [ m 2]

BLOW 1 i = 11 BLOW 1 o = 12

Bur n i ;1 = 10 [-] Bur n i ;2 = 16 [-]

Bur n i ;3 = 0 Bur n o = 18 [-]

COND1 c;i = 35 COND1 c;o = 36

COND1 r ;i = 51 COND1 r ;o = 52

COND2 c;i = 33 COND2 c;o = 34

COND2 r ;i = 71 COND2 r ;o = 72

COP ABS = 1,412 [-] COP ABS;f uel = 0,4556 [-]

COP ABS;heat = 0,7657 [-] C p M I X L1;o = 1,912 [ k J/kg-K ]

C p pump1;i = 1,978 [ k J/kg-K ] C p pump1;o = 1,978 [ k J/kg-K ]

C p pump2;i = 2,037 [ k J/kg-K ] C p pump2;o = 2,037 [ k J/kg-K ]

C p SHE X 1;hi = 1,912 [ k J/kg-K ] C p SHE X 2;hi = 1,987 [ k J/kg-K ]

∆ h;C HK ;min = 13,63 [ k J/kg ] ∆ Ḣ f uel = 100

∆ Ḣ i = 100 [kW ] ∆ h;M I X L1;chk = 13,63 [ k J/kg ]

∆ h;V B1;chk = 11,61 [ k J/kg ] ∆ h;V B2;chk = 24,12 [ k J/kg ]

∆ p;ABSO;1 = 0 [kPa]

∆ p;ABSO;2 = 0 [kPa]

∆ p;ABSO;c = 0 [kPa]

∆ p;BURN ;i ;1 = −8 [kPa]

∆ p;BURN ;i ;2 = −1 [kPa]

∆ p;COND1;c = 0 [kPa]

∆ p;COND1;r = 0 [kPa]

∆ p;COND2;c = 0 [kPa]

∆ p;COND2;r = 0 [kPa]

∆ p;DES1;h = 0 [kPa]

∆ p;DES1;r = 0 [kPa]

∆ p;DES1;s = 0 [kPa]

∆ p;DES2;h = 2,776 × 10 −17 [kPa] ∆ p;DES2;r = 0 [kPa]

∆ p;DES2;s = 0 [kPa]

∆ p;EV AP;c = 0 [kPa]

∆ p;EV AP;r = 0 [kPa]

∆ p;GGHE X 1;c = −1 [kPa]

∆ p;GGHE X 1;h = −1 [kPa] ∆ p;GGHE X 2;c = −1 [kPa]

∆ p;GGHE X 2;h = −1 [kPa] ∆ p;GGHE X 3;c = −4 [kPa]

∆ p;GGHE X 3;h = −4 [kPa] ∆ p;GGHE X 4;c = −2 [kPa]

∆ p;GGHE X 4;h = −2 [kPa] ∆ p;M I XG1;i ;1 = −0,1 [kPa]

∆ p;M I XG1;i ;2 = 9,1 [kPa] ∆ p;M I XG2;i ;1 = −0,1 [kPa]

∆ p;M I XG2;i ;2 = −1,1 [kPa] ∆ p;M I X L1;1 = 0 [kPa]

∆ p;M I X L1;2 = 0 [kPa]

∆ p;M I X R1;1 = 0 [kPa]

242


C.2. Results - Standard parameter configuration

∆ p;M I X R1;2 = 0 [kPa]

∆ p;PR = −5 [kPa]

∆ p;PU MP1 = 4,05 [kPa]

∆ p;PU MP2 = 74,44 [kPa]

∆ p;SHE X 1;ss = 0 [kPa]

∆ p;SHE X 1;ws = 0 [kPa]

∆ p;SHE X 2;ss = 0 [kPa]

∆ p;SHE X 2;ws = 0 [kPa]

∆ p;SOFC ;ano = −1 [kPa]

∆ p;SOFC ;cat = −3 [kPa]

∆ p;SPG1;o;1 = −0,1 [kPa] ∆ p;SPG1;o;2 = −0,1 [kPa]

∆ p;SPG2;o;1 = −0,1 [kPa] ∆ p;SPG2;o;2 = −0,1 [kPa]

∆ p;TOW ER1;air = 0,15 [kPa] ∆ p;TOW ER1;air ;dr y = 0,15 [kPa]

∆ p;TOW ER1;air ;wet = 0,15 [kPa] ∆ p;TOW ER1;w = 0 [kPa]

∆ p;W GHE X 1;g = −2 [kPa] ∆ p;W GHE X 1;w = 0 [kPa]

∆ p;W GHE X 2;g = −2 [kPa] ∆ p;W GHE X 2;w = 0 [kPa]

∆ p;W GHE X 3;g = −2 [kPa] ∆ p;W GHE X 3;w = 0 [kPa]

∆ T ;CFG;C HK = 34,17 [C ] ∆ T ;chill;EV AP = 5 [C ]

∆ T ;COND;DES = 54,88 [C ] ∆ T ;c;ABSO = 3,397 [C ]

∆ T ;c;COND1 = 1,498 [C ] ∆ T ;c;COND2 = 5 [C ]

∆ T ;c;TOW ER1 = 5 [C ] ∆ T ;EV AP;ABSO = 20,71 [C ]

∆ T ;h;DES1 = 5 [C ] ∆ T ;h;DES2 = 5 [C ]

∆ T ;min;ABSO;s;o = 5 [C ] ∆ T ;min;COND1;mp = 7,067 [C ]

∆ T ;min;COND1;r ;i = 8,502 [C ] ∆ T ;min;COND1;r ;o = 10 [C ]

∆ T ;min;COND1;r ;o;D = 10 [C ] ∆ T ;min;COND1;r ;o;S = 12,5 [C ]

∆ T ;min;COND2;mp = 10,24 [C ] ∆ T ;min;COND2;r ;i = 66,8 [C ]

∆ T ;min;COND2;r ;o = 15 [C ] ∆ T ;min;DES1;r ;o = 0 [C ]

∆ T ;min;DES2;r ;o = 0 [C ] ∆ T ;min;EV AP;r ;i = 5 [C ]

∆ T ;min;EV AP;r ;o = 10 [C ] ∆ T ;min;GGHE X 1;c;i = 443,1 [C ]

∆ T ;min;GGHE X 1;c;o = 96,12 [C ] ∆ T ;min;GGHE X 2;c;i = 151,6 [C ]

∆ T ;min;GGHE X 2;c;o = 90 [C ] ∆ T ;min;GGHE X 3;c;i = 186,6 [C ]

∆ T ;min;GGHE X 3;c;o = 148,7 [C ] ∆ T ;min;GGHE X 4;c;i = 27,89 [C ]

∆ T ;min;GGHE X 4;c;i ; = 27,89 [C ] ∆ T ;min;GGHE X 4;c;o = 25 [C ]

∆ T ;min;GGHE X 4;c;o; = 25 [C ] ∆ T ;min;SHE X 1;ws;i = 5 [C ]

∆ T ;min;SHE X 1;ws;o = 8,98 [C ] ∆ T ;min;SHE X 2;ws;i = 5 [C ]

∆ T ;min;SHE X 2;ws;o = 13,91 [C ] ∆ T ;min;TOW ER1;a;i ;dr y = 3 [C ]

∆ T ;min;TOW ER1;a;o = 3 [C ] ∆ T ;min;TOW ER1;a;o;dr y = 8 [C ]

∆ T ;min;TOW ER1;a;o;wet = 3 [C ] ∆ T ;min;W GHE X 1;w;i = 15 [C ]

∆ T ;min;W GHE X 1;w;i ; = 15 [C ] ∆ T ;min;W GHE X 1;w;o = 171,6 [C ]

∆ T ;min;W GHE X 1;w;o; = 171,6 [C ] ∆ T ;min;W GHE X 2;w;i = 81,8 [C ]

∆ T ;min;W GHE X 2;w;i ; = 15 [C ] ∆ T ;min;W GHE X 2;w;o = 81,8 [C ]

∆ T ;min;W GHE X 3;w;i = 15 [C ] ∆ T ;min;W GHE X 3;w;o = 17,02 [C ]

∆ T ;SOFC = 90 [C ] ∆ T ;SOFC ;av = 30 [C ]

DES1 h;i = 31 DES1 h;o = 32

DES1 i = 58 DES1 r ;o = 50

DES1 s;o = 59 DES2 h;i = 41

243


C. EES

244

DES2 h;o = 42 DES2 i = 78

DES2 r ;o = 70 DES2 s;o = 79

EB SOFC ;sys = −16,18 [kW ] EB tot = −0,00000 [kW ]

ɛ ABSO = 0,4045 [-] ɛ COND1;2P = 0,2933 [-]

ɛ COND1;SH = −1,891 × 10 −13 [-] ɛ COND2;2P = 0,3176 [-]

ɛ COND2;SH = 0,8473 [-] ɛ DES1 = 1 [-]

ɛ DES2 = 1 [-] ɛ EV AP = 0,5 [-]

ɛ GGHE X 1 = 0,765 [-] ɛ GGHE X 1;c = 0,765 [-]

ɛ GGHE X 1;h = 0,1278 [-] ɛ GGHE X 2 = 0,765 [-]

ɛ GGHE X 2;c = 0,765 [-] ɛ GGHE X 2;h = 0,6386 [-]

ɛ GGHE X 3 = 0,7757 [-] ɛ GGHE X 3;c = 0,7757 [-]

ɛ GGHE X 3;h = 0,7481 [-] ɛ GGHE X 4 = 0,7736 [-]

ɛ GGHE X 4;c = 0,7736 [-] ɛ GGHE X 4;c; = 0,7736 [-]

ɛ GGHE X 4;h = 0,7494 [-] ɛ GGHE X 4;h; = 0,7494 [-]

ɛ M AX = 0,9431 [-] ɛ SHE X 1 = 0,873 [-]

ɛ SHE X 1;ss = 0,873 [-] ɛ SHE X 1;ws = 0,7718 [-]

ɛ SHE X 2 = 0,9431 [-] ɛ SHE X 2;s = 0,9431 [-]

ɛ SHE X 2;ws = 0,8417 [-] ɛ W GHE X 1 = 0,9151 [-]

ɛ W GHE X 1;g = 0,9151 [-] ɛ W GHE X 1;g ; = 0,9151 [-]

ɛ W GHE X 1;w = 0,02831 [-] ɛ W GHE X 1;w; = 0,02831 [-]

ɛ W GHE X 2 = 2,513 × 10 −10 [-] ɛ W GHE X 2;g = 2,513 × 10 −10 [-]

ɛ W GHE X 2;w = 0 [-] ɛ W GHE X 3 = 0,7117 [-]

ɛ W GHE X 3;g = 0,7117 [-] ɛ W GHE X 3;w = 0,6728 [-]

η blower ;TOW ER1 = 0,4 [-] η HW = 0,07184 [-]

η inver t = 0,95 [-] η i s;BLOW 1 = 0,6 [-]

η PU MP1 = 0,5 [-] η PU MP2 = 0,5 [-]

η SOFC ;el ;SOLO = 0,5357 [-] η sys;el ;net = 0,516 [-]

η sys;tot = 1,044 [-] η wb;TOW ER1 = 0,75 [-]

EV AP c;i = 48 EV AP c;o = 49

EV AP r ;i = 53 EV AP r ;o = 54

F R = 0,14 [-] FuelBP Ratio = 0

Fuel i = 1 FW = 0,6 [-]

GGHE X 1 c;i = 1 GGHE X 1 c;o = 2

GGHE X 1 h;i = 7 GGHE X 1 h;o = 8

GGHE X 2 c;i = 4 GGHE X 2 c;o = 5

GGHE X 2 h;i = 6 GGHE X 2 h;o = 7

GGHE X 3 c;i = 13 GGHE X 3 c;o = 14

GGHE X 3 h;i = 19 GGHE X 3 h;o = 20

GGHE X 4 c;i = 12 GGHE X 4 c;o = 13

GGHE X 4 h;i = 22 GGHE X 4 h;o = 23

I = 68,4 [A] input1 = 70


C.2. Results - Standard parameter configuration

input2 = 77 input3 = 79

i d = 3000 [ A/m 2] K W GS = 1,139 [-]

λ Bur n;i = 1,5 [-] λ SOFC ;i = 4,409 [-]

λ SOFC ;o = 12,36 [-] LG r atio;TOW ER1 = 0,6473 [-]

M I XG1 i ;1 = 2 M I XG1 i ;2 = 9

M I XG1 o = 3 M I XG2 i ;1 = 18

M I XG2 i ;2 = 17 M I XG2 o = 19

M I X L1 i ;1 = 59 M I X L1 i ;2 = 82

M I X L1 o = 60 M I X R1 i ;1 = 50

M I X R1 i ;2 = 73 M I X R1 o = 51

ṁ bur n;add = 0 ṁ i = 0,001999 [ kg /s ]

ṁ tr ans;TOW ER1 = 0,04812 [ kg /s ] n cell = 60 [-]

n st ack = 20,15 [-] OC r atio = 2,133 [-]

out put1 = 71 out put2 = 78

out put3 = 80 PR i = 3

PR o = 4 PU MP1 i = 55

PU MP1 o = 56 PU MP2 i = 75

PU MP2 o = 76

p re f = 100 [kPa]

˙Q air ; = 85,93 [kW ] ˙Q Chill;EV AP = 45,56 [kW ]

˙Q c;ABSO = 54,02 [kW ] ˙Q c;COND1 = 23,82 [kW ]

˙Q c;COND2 = 25,93 [kW ] ˙Q c;TOW ER1 = 77,84 [kW ]

˙Q Heat;DES1 = 25,93 [kW ] ˙Q Heat;DES2 = 32,26 [kW ]

˙Q HW = 7,184 [kW ] ˙Q hw; = 7,184 [kW ]

˙Q loss;ABSO = 0 [kW ] ˙Q loss;BLOW 1 = 0 [kW ]

˙Q loss;Bur n = 0 [kW ] ˙Q loss;COND1 = 0 [kW ]

˙Q loss;COND2 = 0 [kW ] ˙Q loss;DES1 = 0 [kW ]

˙Q loss;DES2 = 0 [kW ] ˙Q loss;EV AP = 0 [kW ]

˙Q loss;PR = 0 [kW ] ˙Q loss;PU MP1 = 0 [kW ]

˙Q loss;PU MP2 = 0 [kW ] ˙Q loss;SHE X 1 = 0 [kW ]

˙Q loss;SHE X 2 = 0 [kW ] ˙Q loss;SOFC = 0 [kW ]

˙Q loss;V A1 = 0 [kW ] ˙Q loss;V A2 = 0 [kW ]

˙Q loss;V B1 = 0 [kW ] ˙Q loss;V B2 = 0 [kW ]

˙Q loss;W GHE X 1 = 0 [kW ] ˙Q loss;W GHE X 2 = 0 [kW ]

˙Q loss;W GHE X 3 = 0 [kW ] ˙Q loss;W W HE X 1 = 0 [kW ]

˙Q tr ans;SHE X 1 = 13,58 [kW ] ˙Q tr ans;SHE X 2 = 19,24 [kW ]

˙Q tr ans;W GHE X 1 = 32,26 [kW ] ˙Q tr ans;W GHE X 2 = 0 [kW ]

˙Q tr ans;W GHE X 3 = 7,184 [kW ] ˙Q w;add; = 6,135

SHE X 1 ss;i = 60 SHE X 1 ss;o = 61

SHE X 1 ws;i = 56 SHE X 1 ws;o = 57

SHE X 2 ss;i = 80 SHE X 2 ss;o = 81

SHE X 2 ws;i = 76 SHE X 2 ws;o = 77

245


C. EES

SOFC ano;i = 5 SOFC ano;o = 6

SOFC cat;i = 14 SOFC cat;o = 15

SPG1 i = 8 SPG1 o;1 = 9

SPG1 o;2 = 10 SPG2 i = 15

SPG2 o;1 = 16 SPG2 o;2 = 17

SPL1 i = 57 SPL1 o;1 = 58

SPL1 o;2 = 75

SysC f g $ = ‘Double’

TOW ER$ = ‘WET’ TOW ER1 w;add = 38 [ kg /s ]

TOW ER1 w;i = 37 TOW ER1 w;o = 39

TOW ER air ;i = 45 TOW ER air ;mp = 46

TOW ER air ;o = 47 T 47;aim = 23,77

T 60SHE X = 78,2 [C ] T amb = 30 [C ]

T amb;dr y = 18 [C ] T amb;evap = 24

T amb;wet = 30 [C ] T DES1;h;i = 85 [C ]

T M I X L1;sat60 = 78,2 T re f = 25 [C ]

T SHE X 2;sat81 = 150 [C ] T SOFC ;av = 750 [C ]

T V B1;sat62 = 42,17 [C ] T V B2;sat82 = 78,2 [C ]

T wb;TOW ER1 = 20,04 [C ] T W GHE X 1;g ;o = 165 [C ]

U air = 0,1588 [-] U f = 0,7 [-]

V A1 i = 52 V A1 o = 53

V A2 i = 72 V A2 o = 73

V B1 i = 61 V B1 o = 62

V B2 i = 81

V cell = 0,7514 [V ]

V B2 o = 82

˙V air ;TOW ER1 = 5,205 [ m 3 /s ]

V Ner nst = 0,9177 [V ] V st ack = 45,09 [V ]

W GHE X 1 g ;i = 20 W GHE X 1 g ;o = 21

W GHE X 1 w;i = 42 W GHE X 1 w;o = 43

W GHE X 2 g ;i = 21 W GHE X 2 g ;o = 22

W GHE X 2 w;i = 34 W GHE X 2 w;o = 31

W GHE X 3 g ;i = 23 W GHE X 3 g ;o = 24

W GHE X 3 w;i = 27 W GHE X 3 w;o = 28

W Q R AT IO;TOW ER1 = 0,02507 [-] Ẇ AC = 59,05 [kW ]

Ẇ BLOW 1 = 5,48 [kW ] Ẇ F AN = 1,952 [kW ]

Ẇ PU MP1 = 0,001122 [kW ] Ẇ PU MP2 = 0,01175 [kW ]

Ẇ SOFC = 62,16 [kW ] Ẇ SOFC ;SOLO = 53,57 [kW ]

Ẇ st ack = 3,084 [kW ] Ẇ sys;net = 51,6 [kW ]

246


C.2. Results - Standard parameter configuration

Point T i p i ṁ i qu i h i w i ∆˙

[ ] [ ]

H i

[C ] [kPa] kg /s [-] k J/kg [-] [kW ]

0 25 0 0

1 25 130,3 0,001999 100

2 431,4 129,3 0,001999 102,4

3 459,6 129,2 0,01645 141,3

4 376 124,2 0,01645 141,3

5 690 123,2 0,01645 151,8

6 780 122,2 0,02331 75,69

7 527,6 121,2 0,02331 65,22

8 468,1 120,2 0,02331 62,86

9 468,1 120,1 0,01445 38,97

10 468,1 120,1 0,008857 23,89

11 25 100 0,1855 0

12 54,14 122,2 0,1855 5,48

13 140 120,2 0,1855 21,66

14 690 116,2 0,1855 132

15 780 113,2 0,1786 146

16 780 113,1 0,008234 6,728

17 780 113,1 0,1704 139,2

18 1271 112,1 0,01709 30,61

19 838,7 112 0,1875 169,8

20 326,6 108 0,1875 59,5

21 165 106 0,1875 27,24

22 165 104 0,1875 27,24

23 82,02 102 0,1875 11,06

24 45 100 0,1875 3,876

25

26

27 30 1000 0,0491 126,6

28 65 1000 0,0491 272,9

29

30

31 83,2 2000 1,238 349,9

32 78,2 2000 1,238

33 78,2 2000 1,238

34 83,2 2000 1,238 349,9

247


C. EES

Point T i p i ṁ i qu i h i w i ∆˙

[ ]

[ ]

H i

[C ] [kPa] kg /s [-] k J/kg [-] [kW ]

35 21,81 2000 3,806

36 23,31 2000 3,806

37 26,71 2000 3,806 113,7

38 30 2000 0,04812 127,5

39 21,81 2000 3,806 93,29

40

41 155 2000 1,496

42 150 2000 1,496 633,3

43 155 2000 1,496 654,8

45 30 100 5,88 57,67

46 30,32 100,2 5,88

47 23,71 100 5,928 71,7

48 11 2000 2,179

49 6 2000 2,179

50 78,2 4,708 0,008368 100 2646 0

51 31,81 4,708 0,01923 0,5107 1372 0

52 31,81 4,708 0,01923 0 133,3 0

53 1 0,6571 0,01923 0,05167 133,3 0

54 1 0,6571 0,01923 1 2502 0

55 31,71 0,6571 0,226 0 81,37 0,5595

56 31,71 4,708 0,226 -100 81,37 0,5595

57 62,09 4,708 0,226 -100 141,5 0,5595

58 62,09 4,708 0,09835 -100 141,5 0,5595

59 78,2 4,708 0,08998 0 196,7 0,6115

60 71,07 4,708 0,2068 -100 183,1 0,6115

61 36,71 4,708 0,2068 -100 117,4 0,6115

62 35,91 0,6571 0,2068 -100 117,4 0,6115

70 150 79,15 0,01086 100 2778 0

71 150 79,15 0,01086 100 2778 0

72 93,2 79,15 0,01086 0 390,4 0

73 31,81 4,708 0,01086 0,106 390,4 0

75 62,09 4,708 0,1277 -100 141,5 0,5595

76 62,13 79,15 0,1277 -100 141,6 0,5595

77 136,1 79,15 0,1277 -100 292,2 0,5595

78 136,1 79,15 0,1277 -100 292,2 0,5595

79 150 79,15 0,1168 0 337,3 0,6115

80 150 79,15 0,1168 0 337,3 0,6115

81 67,13 79,15 0,1168 -100 172,6 0,6115

82 65,58 4,708 0,1168 -100 172,6 0,6115

248


C.2. Results - Standard parameter configuration

Point y i ;1 y i ;2 y i ;3 y i ;4 y i ;5 y i ;6 y i ;7

[-] [-] [-] [-] [-] [-] [-]

0

1 1,000 -0,000 -0,000 -0,000 0,000 0,000 -0,000

2 1,000 -0,000 -0,000 -0,000 0,000 0,000 -0,000

3 0,170 0,048 0,229 0,107 0,447 0,000 -0,000

4 0,139 0,027 0,259 0,211 0,363 0,000 -0,000

5 0,139 0,027 0,259 0,211 0,363 0,000 -0,000

6 -0,000 0,058 0,275 0,129 0,538 -0,000 0,000

7 -0,000 0,058 0,275 0,129 0,538 -0,000 0,000

8 -0,000 0,058 0,275 0,129 0,538 -0,000 0,000

9 0,000 0,058 0,275 0,129 0,538 0,000 -0,000

10 0,000 0,058 0,275 0,129 0,538 -0,000 -0,000

11 -0,000 0,000 -0,000 0,000 0,000 0,790 0,210

12 -0,000 0,000 -0,000 0,000 0,000 0,790 0,210

13 -0,000 0,000 -0,000 0,000 0,000 0,790 0,210

14 -0,000 0,000 -0,000 0,000 0,000 0,790 0,210

15 -0,000 0,000 0,000 0,000 -0,000 0,817 0,183

16 -0,000 -0,000 0,000 -0,000 0,000 0,817 0,183

17 0,000 0,000 -0,000 0,000 -0,000 0,817 0,183

18 0,000 -0,000 0,199 0,000 0,398 0,374 0,028

19 0,000 0,000 0,019 0,000 0,038 0,775 0,168

20 0,000 0,000 0,019 0,000 0,038 0,775 0,168

21 0,000 0,000 0,019 0,000 0,038 0,775 0,168

22 0,000 0,000 0,019 0,000 0,038 0,775 0,168

23 0,000 0,000 0,019 0,000 0,038 0,775 0,168

24 0,000 0,000 0,019 0,000 0,038 0,775 0,168

249


C. EES

C.3 Results - Optimized parameter

configuration

ABSO c;i = 36 ABSO c;o = 37

ABSO r ;i = 54 ABSO s;i = 62

ABSO s;o = 55

AddPreHeat$ = ‘On’

Air Fuel Ratio;m = 54,44 [-] Air Fuel Ratio;n = 4,902 [-]

Air i = 11 [-] α SPG1 = 0,62 [-]

α SPG2 = 0,1412 [-]

ASR = 5,54 × 10 −5 [ Ω·m 2] α SPL1 = 0,6199 [-]

A cell = 0,0228 [ m 2]

BLOW 1 i = 11 BLOW 1 o = 12

Bur n i ;1 = 10 [-] Bur n i ;2 = 16 [-]

Bur n i ;3 = 0 Bur n o = 18 [-]

COND1 c;i = 35 COND1 c;o = 36

COND1 r ;i = 51 COND1 r ;o = 52

COND2 c;i = 33 COND2 c;o = 34

COND2 r ;i = 71 COND2 r ;o = 72

COP ABS = 1,484 [-] COP ABS;f uel = 0,5872 [-]

COP ABS;heat = 1,089 [-] C p M I X L1;o = 2,011 [ k J/kg-K ]

C p pump1;i = 2,055 [ k J/kg-K ] C p pump1;o = 2,055 [ k J/kg-K ]

C p pump2;i = 2,115 [ k J/kg-K ] C p pump2;o = 2,115 [ k J/kg-K ]

C p SHE X 1;hi = 2,011 [ k J/kg-K ] C p SHE X 2;hi = 2,013 [ k J/kg-K ]

Ċ SHE X 1;r atio = 0,9005 Ċ SHE X 1;ss = 0,5932

Ċ SHE X 1;ws = 0,6587 Ċ SHE X 2;r atio = 0,8445

Ċ SHE X 2;ss = 0,2176 Ċ SHE X 2;ws = 0,2577

∆ h;C HK ;min = 8,779 [ k J/kg ] ∆ Ḣ f uel = 100

∆ Ḣ i = 100 [kW ] ∆ h;M I X L1;chk = 8,779 [ k J/kg ]

∆ h;V B1;chk = 7,608 [ k J/kg ] ∆ h;V B2;chk = 25,83 [ k J/kg ]

∆ p;ABSO;1 = 0 [kPa]

∆ p;ABSO;2 = 0 [kPa]

∆ p;ABSO;c = 0 [kPa]

∆ p;BURN ;i ;1 = −8 [kPa]

∆ p;BURN ;i ;2 = −1 [kPa]

∆ p;COND1;c = 0 [kPa]

∆ p;COND1;r = 0 [kPa]

∆ p;COND2;c = 0 [kPa]

∆ p;COND2;r = 0 [kPa]

∆ p;DES1;h = 0 [kPa]

∆ p;DES1;r = 0 [kPa]

∆ p;DES1;s = 0 [kPa]

∆ p;DES2;h = 2,776 × 10 −17 [kPa] ∆ p;DES2;r = 0 [kPa]

∆ p;DES2;s = 0 [kPa]

∆ p;EV AP;c = 0 [kPa]

∆ p;EV AP;r = 0 [kPa]

∆ p;GGHE X 1;c = −1 [kPa]

∆ p;GGHE X 1;h = −1 [kPa] ∆ p;GGHE X 2;c = −1 [kPa]

∆ p;GGHE X 2;h = −1 [kPa] ∆ p;GGHE X 3;c = −4 [kPa]

250


C.3. Results - Optimized parameter configuration

∆ p;GGHE X 3;h = −4 [kPa] ∆ p;GGHE X 4;c = −2 [kPa]

∆ p;GGHE X 4;h = −2 [kPa] ∆ p;M I XG1;i ;1 = −0,1 [kPa]

∆ p;M I XG1;i ;2 = 9,1 [kPa] ∆ p;M I XG2;i ;1 = −0,1 [kPa]

∆ p;M I XG2;i ;2 = −1,1 [kPa] ∆ p;M I X L1;1 = 0 [kPa]

∆ p;M I X L1;2 = 0 [kPa]

∆ p;M I X R1;1 = 0 [kPa]

∆ p;M I X R1;2 = 0 [kPa]

∆ p;PR = −5 [kPa]

∆ p;PU MP1 = 3,933 [kPa] ∆ p;PU MP2 = 46,69 [kPa]

∆ p;SHE X 1;ss = 0 [kPa]

∆ p;SHE X 1;ws = 0 [kPa]

∆ p;SHE X 2;ss = 0 [kPa]

∆ p;SHE X 2;ws = 0 [kPa]

∆ p;SOFC ;ano = −1 [kPa]

∆ p;SOFC ;cat = −3 [kPa]

∆ p;SPG1;o;1 = −0,1 [kPa] ∆ p;SPG1;o;2 = −0,1 [kPa]

∆ p;SPG2;o;1 = −0,1 [kPa] ∆ p;SPG2;o;2 = −0,1 [kPa]

∆ p;TOW ER1;air = 0,15 [kPa] ∆ p;TOW ER1;air ;dr y = 0,15 [kPa]

∆ p;TOW ER1;air ;wet = 0,15 [kPa] ∆ p;TOW ER1;w = 0 [kPa]

∆ p;W GHE X 1;g = −2 [kPa] ∆ p;W GHE X 1;w = 0 [kPa]

∆ p;W GHE X 2;g = −2 [kPa] ∆ p;W GHE X 2;w = 0 [kPa]

∆ p;W GHE X 3;g = −2 [kPa] ∆ p;W GHE X 3;w = 0 [kPa]

∆ T ;CFG;C HK = 22,97 [C ] ∆ T ;chill;EV AP = 5 [C ]

∆ T ;COND;DES = 43,68 [C ] ∆ T ;c;ABSO = 3,386 [C ]

∆ T ;c;COND1 = 1,509 [C ] ∆ T ;c;COND2 = 5 [C ]

∆ T ;c;TOW ER1 = 5 [C ] ∆ T ;EV AP;ABSO = 20,71 [C ]

∆ T ;h;DES1 = 5 [C ] ∆ T ;h;DES2 = 5 [C ]

∆ T ;min;ABSO;s;o = 1,81 [C ] ∆ T ;min;COND1;mp = 7,012 [C ]

∆ T ;min;COND1;r ;i = 8,491 [C ] ∆ T ;min;COND1;r ;o = 10 [C ]

∆ T ;min;COND1;r ;o;D = 10 [C ] ∆ T ;min;COND1;r ;o;S = 12,5 [C ]

∆ T ;min;COND2;mp = 10,21 [C ] ∆ T ;min;COND2;r ;i = 61 [C ]

∆ T ;min;COND2;r ;o = 15 [C ] ∆ T ;min;DES1;r ;o = 0 [C ]

∆ T ;min;DES2;r ;o = 0 [C ] ∆ T ;min;EV AP;r ;i = 2,69 [C ]

∆ T ;min;EV AP;r ;o = 7,69 [C ] ∆ T ;min;GGHE X 1;c;i = 457,2 [C ]

∆ T ;min;GGHE X 1;c;o = 105,8 [C ] ∆ T ;min;GGHE X 2;c;i = 142,1 [C ]

∆ T ;min;GGHE X 2;c;o = 90 [C ] ∆ T ;min;GGHE X 3;c;i = 334,8 [C ]

∆ T ;min;GGHE X 3;c;o = 271 [C ] ∆ T ;min;GGHE X 4;c;i = 14,54 [C ]

∆ T ;min;GGHE X 4;c;i ; = 14,54 [C ] ∆ T ;min;GGHE X 4;c;o = 10,1 [C ]

∆ T ;min;GGHE X 4;c;o; = 10,1 [C ] ∆ T ;min;SHE X 1;ws;i = 5 [C ]

∆ T ;min;SHE X 1;ws;o = 8,099 [C ] ∆ T ;min;SHE X 2;ws;i = 5 [C ]

∆ T ;min;SHE X 2;ws;o = 15,99 [C ] ∆ T ;min;TOW ER1;a;i ;dr y = 3 [C ]

∆ T ;min;TOW ER1;a;o = 3 [C ] ∆ T ;min;TOW ER1;a;o;dr y = 8 [C ]

∆ T ;min;TOW ER1;a;o;wet = 3 [C ] ∆ T ;min;W GHE X 1;w;i = 15 [C ]

∆ T ;min;W GHE X 1;w;i ; = 15 [C ] ∆ T ;min;W GHE X 1;w;o = 334,7 [C ]

∆ T ;min;W GHE X 1;w;o; = 334,7 [C ] ∆ T ;min;W GHE X 2;w;i = 76 [C ]

∆ T ;min;W GHE X 2;w;i ; = 15 [C ] ∆ T ;min;W GHE X 2;w;o = 76 [C ]

251


C. EES

∆ T ;min;W GHE X 3;w;i = 15 [C ] ∆ T ;min;W GHE X 3;w;o = 3,673 [C ]

∆ T ;SOFC = 90 [C ] ∆ T ;SOFC ;av = 30 [C ]

DES1 h;i = 31 DES1 h;o = 32

DES1 i = 58 DES1 r ;o = 50

DES1 s;o = 59 DES2 h;i = 41

DES2 h;o = 42 DES2 i = 78

DES2 r ;o = 70 DES2 s;o = 79

EB SOFC ;sys = −9,261 [kW ] EB tot = −0,00000 [kW ]

ɛ ABSO = 0,6516 [-] ɛ COND1;2P = 0,2988 [-]

ɛ COND1;SH = −1,906 × 10 −13 [-] ɛ COND2;2P = 0,3195 [-]

ɛ COND2;SH = 0,8332 [-] ɛ DES1 = 1 [-]

ɛ DES2 = 1 [-] ɛ EV AP = 0,6502 [-]

ɛ GGHE X 1 = 0,7499 [-] ɛ GGHE X 1;c = 0,7499 [-]

ɛ GGHE X 1;h = 0,1299 [-] ɛ GGHE X 2 = 0,7499 [-]

ɛ GGHE X 2;c = 0,7499 [-] ɛ GGHE X 2;h = 0,6352 [-]

ɛ GGHE X 3 = 0,6539 [-] ɛ GGHE X 3;c = 0,6539 [-]

ɛ GGHE X 3;h = 0,6145 [-] ɛ GGHE X 4 = 0,892 [-]

ɛ GGHE X 4;c = 0,892 [-] ɛ GGHE X 4;c; = 0,892 [-]

ɛ GGHE X 4;h = 0,8457 [-] ɛ GGHE X 4;h; = 0,8457 [-]

ɛ M AX = 0,9558 [-] ɛ SHE X 1 = 0,8644 [-]

ɛ SHE X 1;ss = 0,8644 [-] ɛ SHE X 1;ws = 0,7803 [-]

ɛ SHE X 2 = 0,9339 [-] ɛ SHE X 2;s = 0,9339 [-]

ɛ SHE X 2;ws = 0,7887 [-] ɛ W GHE X 1 = 0,9558 [-]

ɛ W GHE X 1;g = 0,9558 [-] ɛ W GHE X 1;g ; = 0,9558 [-]

ɛ W GHE X 1;w = 0,01472 [-] ɛ W GHE X 1;w; = 0,01472 [-]

ɛ W GHE X 2 = 4,542 × 10 −10 [-] ɛ W GHE X 2;g = 4,542 × 10 −10 [-]

ɛ W GHE X 2;w = 1,849 × 10 −15 [-] ɛ W GHE X 3 = 0,905 [-]

ɛ W GHE X 3;g = 0,6121 [-] ɛ W GHE X 3;w = 0,905 [-]

η blower ;TOW ER1 = 0,4 [-] η HW = 0,02752 [-]

η inver t = 0,95 [-] η i s;BLOW 1 = 0,6 [-]

η PU MP1 = 0,5 [-] η PU MP2 = 0,5 [-]

η SOFC ;el ;SOLO = 0,5243 [-] η sys;el ;net = 0,4996 [-]

η sys;tot = 1,114 [-] η wb;TOW ER1 = 0,75 [-]

EV AP c;i = 48 EV AP c;o = 49

EV AP r ;i = 53 EV AP r ;o = 54

F R = 0,14 [-] FuelBP Ratio = 0

Fuel i = 1 FW = 0,6 [-]

GGHE X 1 c;i = 1 GGHE X 1 c;o = 2

GGHE X 1 h;i = 7 GGHE X 1 h;o = 8

GGHE X 2 c;i = 4 GGHE X 2 c;o = 5

GGHE X 2 h;i = 6 GGHE X 2 h;o = 7

252


C.3. Results - Optimized parameter configuration

GGHE X 3 c;i = 13 GGHE X 3 c;o = 14

GGHE X 3 h;i = 19 GGHE X 3 h;o = 20

GGHE X 4 c;i = 12 GGHE X 4 c;o = 13

GGHE X 4 h;i = 22 GGHE X 4 h;o = 23

I = 61,56 [A] input1 = 70

input2 = 77 input3 = 79

i d = 2700 [ A/m 2] K W GS = 1,139 [-]

λ Bur n;i = 1,5 [-] λ SOFC ;i = 2,321 [-]

λ SOFC ;o = 4,037 [-] LG r atio;TOW ER1 = 0,6473 [-]

M I XG1 i ;1 = 2 M I XG1 i ;2 = 9

M I XG1 o = 3 M I XG2 i ;1 = 18

M I XG2 i ;2 = 17 M I XG2 o = 19

M I X L1 i ;1 = 59 M I X L1 i ;2 = 82

M I X L1 o = 60 M I X R1 i ;1 = 50

M I X R1 i ;2 = 73 M I X R1 o = 51

ṁ bur n;add = 0 ṁ i = 0,001999 [ kg /s ]

ṁ tr ans;TOW ER1 = 0,06077 [ kg /s ] n cell = 60 [-]

n st ack = 20,15 [-] OC r atio = 1,919 [-]

out put1 = 71 out put2 = 78

out put3 = 80 PR i = 3

PR o = 4 PU MP1 i = 55

PU MP1 o = 56 PU MP2 i = 75

PU MP2 o = 76

p re f = 100 [kPa]

˙Q air ; = 108,5 [kW ] ˙Q Chill;EV AP = 58,72 [kW ]

˙Q c;ABSO = 67,99 [kW ] ˙Q c;COND1 = 30,31 [kW ]

˙Q c;COND2 = 33,01 [kW ] ˙Q c;TOW ER1 = 98,3 [kW ]

˙Q Heat;DES1 = 33,01 [kW ] ˙Q Heat;DES2 = 39,57 [kW ]

˙Q HW = 2,752 [kW ] ˙Q hw; = 2,752 [kW ]

˙Q loss;ABSO = 0 [kW ] ˙Q loss;BLOW 1 = 0 [kW ]

˙Q loss;Bur n = 0 [kW ] ˙Q loss;COND1 = 0 [kW ]

˙Q loss;COND2 = 0 [kW ] ˙Q loss;DES1 = 0 [kW ]

˙Q loss;DES2 = 0 [kW ] ˙Q loss;EV AP = 0 [kW ]

˙Q loss;PR = 0 [kW ] ˙Q loss;PU MP1 = 0 [kW ]

˙Q loss;PU MP2 = 0 [kW ] ˙Q loss;SHE X 1 = 0 [kW ]

˙Q loss;SHE X 2 = 0 [kW ] ˙Q loss;SOFC = 0 [kW ]

˙Q loss;V A1 = 0 [kW ] ˙Q loss;V A2 = 0 [kW ]

˙Q loss;V B1 = 0 [kW ] ˙Q loss;V B2 = 0 [kW ]

˙Q loss;W GHE X 1 = 0 [kW ] ˙Q loss;W GHE X 2 = 0 [kW ]

˙Q loss;W GHE X 3 = 0 [kW ] ˙Q loss;W W HE X 1 = 0 [kW ]

˙Q tr ans;SHE X 1 = 18,95 [kW ] ˙Q tr ans;SHE X 2 = 15,38 [kW ]

˙Q tr ans;W GHE X 1 = 39,57 [kW ] ˙Q tr ans;W GHE X 2 = 0 [kW ]

253


C. EES

˙Q tr ans;W GHE X 3 = 2,752 [kW ] ˙Q w;add; = 7,748

SHE X 1 ss;i = 60 SHE X 1 ss;o = 61

SHE X 1 ws;i = 56 SHE X 1 ws;o = 57

SHE X 2 ss;i = 80 SHE X 2 ss;o = 81

SHE X 2 ws;i = 76 SHE X 2 ws;o = 77

SOFC ano;i = 5 SOFC ano;o = 6

SOFC cat;i = 14 SOFC cat;o = 15

SPG1 i = 8 SPG1 o;1 = 9

SPG1 o;2 = 10 SPG2 i = 15

SPG2 o;1 = 16 SPG2 o;2 = 17

SPL1 i = 57 SPL1 o;1 = 58

SPL1 o;2 = 75

SysC f g $ = ‘Double’

TOW ER$ = ‘WET’ TOW ER1 w;add = 38 [ kg /s ]

TOW ER1 w;i = 37 TOW ER1 w;o = 39

TOW ER air ;i = 45 TOW ER air ;mp = 46

TOW ER air ;o = 47 T 47;aim = 23,77

T 60SHE X = 69,75 [C ] T amb = 30 [C ]

T amb;dr y = 18 [C ] T amb;evap = 24

T amb;wet = 30 [C ] T DES1;h;i = 85 [C ]

T M I X L1;sat60 = 69,75 T re f = 25 [C ]

T SHE X 2;sat81 = 133 [C ] T SOFC ;av = 750 [C ]

T V B1;sat62 = 36,91 [C ] T V B2;sat82 = 74,67 [C ]

T wb;TOW ER1 = 20,04 [C ] T W GHE X 1;g ;o = 148 [C ]

U air = 0,2434 [-] U f = 0,565 [-]

V A1 i = 52 V A1 o = 53

V A2 i = 72 V A2 o = 73

V B1 i = 61 V B1 o = 62

V B2 i = 81

V cell = 0,7871 [V ]

V B2 o = 82

˙V air ;TOW ER1 = 6,573 [ m 3 /s ]

V Ner nst = 0,9368 [V ] V st ack = 47,23 [V ]

W GHE X 1 g ;i = 20 W GHE X 1 g ;o = 21

W GHE X 1 w;i = 42 W GHE X 1 w;o = 43

W GHE X 2 g ;i = 21 W GHE X 2 g ;o = 22

W GHE X 2 w;i = 34 W GHE X 2 w;o = 31

W GHE X 3 g ;i = 23 W GHE X 3 g ;o = 24

W GHE X 3 w;i = 27 W GHE X 3 w;o = 28

W Q R AT IO;TOW ER1 = 0,02507 [-] Ẇ AC = 55,64 [kW ]

Ẇ BLOW 1 = 3,215 [kW ] Ẇ F AN = 2,465 [kW ]

Ẇ PU MP1 = 0,001598 [kW ] Ẇ PU MP2 = 0,007267 [kW ]

Ẇ SOFC = 58,57 [kW ] Ẇ SOFC ;SOLO = 52,43 [kW ]

Ẇ st ack = 2,907 [kW ] Ẇ sys;net = 49,96 [kW ]

254


C.3. Results - Optimized parameter configuration

Point T i p i ṁ i qu i h i w i ∆˙

[ ] [ ]

H i

[C ] [kPa] kg /s [-] k J/kg [-] [kW ]

0 25 0 0

1 25 130,3 0,001999 100

2 439,2 129,3 0,001999 102,4

3 472 129,2 0,01533 159,3

4 402,9 124,2 0,01533 159,3

5 690 123,2 0,01533 168,7

6 780 122,2 0,0215 103,6

7 545 121,2 0,0215 94,21

8 482,2 120,2 0,0215 91,8

9 482,2 120,1 0,01333 56,92

10 482,2 120,1 0,008169 34,88

11 25 100 0,1088 0

12 54,14 122,2 0,1088 3,215

13 137,9 120,2 0,1088 12,48

14 690 116,2 0,1088 77,45

15 780 113,2 0,1027 83,99

16 780 113,1 0,01449 11,86

17 780 113,1 0,08817 72,13

18 1504 112,1 0,02266 46,74

19 961 112 0,1108 118,9

20 472,7 108 0,1108 53,9

21 148 106 0,1108 14,33

22 148 104 0,1108 14,33

23 68,67 102 0,1108 5,073

24 45 100 0,1108 2,321

25

26

27 30 1000 0,01881 126,6

28 65 1000 0,01881 272,9

29

30

31 72 2000 1,579 303

32 67 2000 1,579

33 67 2000 1,579

34 72 2000 1,579 303

255


C. EES

Point T i p i ṁ i qu i h i w i ∆˙

[ ]

[ ]

H i

[C ] [kPa] kg /s [-] k J/kg [-] [kW ]

35 21,81 2000 4,807

36 23,32 2000 4,807

37 26,71 2000 4,807 113,7

38 30 2000 0,06077 127,5

39 21,81 2000 4,807 93,29

40

41 138 2000 1,852

42 133 2000 1,852 560,4

43 138 2000 1,852 581,7

45 30 100 7,426 57,67

46 30,32 100,2 7,426

47 23,71 100 7,486 71,7

48 11 2000 2,808

49 6 2000 2,808

50 67 4,708 0,01101 100 2625 0

51 31,81 4,708 0,02474 0,5051 1358 0

52 31,81 4,708 0,02474 0 133,3 0

53 3,31 0,7749 0,02474 0,04788 133,3 0

54 3,31 0,7749 0,02474 1 2507 0

55 28,52 0,7749 0,3205 0 64,18 0,5282

56 28,52 4,708 0,3205 -100 64,19 0,5282

57 57,29 4,708 0,3205 -100 123,3 0,5282

58 57,29 4,708 0,1987 -100 123,3 0,5282

59 67 4,708 0,1876 0 152,5 0,5592

60 65,39 4,708 0,2957 -100 153,8 0,5724

61 33,52 4,708 0,2957 -100 89,74 0,5724

62 33,03 0,7749 0,2957 -100 89,74 0,5724

70 133 51,4 0,01374 100 2746 0

71 133 51,4 0,01374 100 2746 0

72 82 51,4 0,01374 0 343,3 0

73 31,81 4,708 0,01374 0,08661 343,3 0

75 57,29 4,708 0,1218 -100 123,3 0,5282

76 57,32 51,4 0,1218 -100 123,4 0,5282

77 117 51,4 0,1218 -100 249,6 0,5282

78 117 51,4 0,1218 -100 249,6 0,5282

79 133 51,4 0,1081 0 298,4 0,5954

80 133 51,4 0,1081 0 298,4 0,5954

81 62,32 51,4 0,1081 -100 156,1 0,5954

82 61,44 4,708 0,1081 -100 156,1 0,5954

256


C.3. Results - Optimized parameter configuration

Point y i ;1 y i ;2 y i ;3 y i ;4 y i ;5 y i ;6 y i ;7

[-] [-] [-] [-] [-] [-] [-]

0

1 1,000 0,000 0,000 0,000 -0,000 0,000 -0,000

2 1,000 0,000 0,000 0,000 -0,000 0,000 -0,000

3 0,170 0,079 0,198 0,172 0,381 0,000 -0,000

4 0,139 0,039 0,248 0,291 0,283 0,000 0,000

5 0,139 0,039 0,248 0,291 0,283 0,000 0,000

6 0,000 0,095 0,239 0,207 0,459 0,000 -0,000

7 0,000 0,095 0,239 0,207 0,459 0,000 -0,000

8 0,000 0,095 0,239 0,207 0,459 0,000 -0,000

9 0,000 0,095 0,239 0,207 0,459 0,000 0,000

10 0,000 0,095 0,239 0,207 0,459 0,000 -0,000

11 -0,000 0,000 0,000 -0,000 -0,000 0,790 0,210

12 -0,000 0,000 0,000 -0,000 -0,000 0,790 0,210

13 -0,000 0,000 0,000 -0,000 -0,000 0,790 0,210

14 -0,000 0,000 0,000 -0,000 -0,000 0,790 0,210

15 0,000 0,000 -0,000 0,000 -0,000 0,833 0,167

16 -0,000 -0,000 0,000 0,000 0,000 0,833 0,167

17 0,000 -0,000 -0,000 0,000 0,000 0,833 0,167

18 0,000 0,000 0,151 0,000 0,303 0,511 0,034

19 0,000 0,000 0,032 0,000 0,064 0,765 0,139

20 0,000 0,000 0,032 0,000 0,064 0,765 0,139

21 0,000 0,000 0,032 0,000 0,064 0,765 0,139

22 0,000 0,000 0,032 0,000 0,064 0,765 0,139

23 0,000 0,000 0,032 0,000 0,064 0,765 0,139

24 0,000 0,000 0,032 0,000 0,064 0,765 0,139

257


C. EES

C.4 Results - Uncertainty propagation (STD)

C.4.1 ∆Tmin

Variable+Uncertainty Partial Derivative % of Uncertainty

COP ABS;f uel = 0,4556 ± 0,03738[-]

∆T ;min;ABSO;s;o = 5 ± 2,5[C ] ∂COP ABS;f uel /∂∆T ;min;ABSO;s;o = −0,002944 3,88 %

∆T ;min;COND1;r ;o;D = 10 ± 5[C ] ∂COP ABS;f uel /∂∆T ;min;COND1;r ;o;D = −0,0008637 1,33 %

∆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 %

∆T ;min;COND2;r ;o = 15 ± 7,5[C ] ∂COP ABS;f uel /∂∆T ;min;COND2;r ;o = −0,0004227 0,72 %

∆T ;min;DES1;r ;o = 0 ± 0[C ] ∂COP ABS;f uel /∂∆T ;min;DES1;r ;o = −0,0002961 0,00 %

∆T ;min;DES2;r ;o = 0 ± 0[C ] ∂COP ABS;f uel /∂∆T ;min;DES2;r ;o = 0,00000817 0,00 %

∆T ;min;EV AP;r ;i = 5 ± 2,5[C ] ∂COP ABS;f uel /∂∆T ;min;EV AP;r ;i = −0,004363 8,51 %

∆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 %

∆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 %

∆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 %

∆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 %

∆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 %

∆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 %

∆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 %

∆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 %

ηHW = 0,07184 ± 0,02776[-]

∆T ;min;ABSO;s;o = 5 ± 2,5[C ] ∂ηHW /∂∆T ;min;ABSO;s;o = −8,809E − 16 0,00 %

∆T ;min;COND1;r ;o;D = 10 ± 5[C ] ∂ηHW /∂∆T ;min;COND1;r ;o;D = −3,795E − 15 0,00 %

∆T ;min;COND1;r ;o;S = 12,5 ± 6,25[C ] ∂ηHW /∂∆T ;min;COND1;r ;o;S = −8,674E − 16 0,00 %

∆T ;min;COND2;r ;o = 15 ± 7,5[C ] ∂ηHW /∂∆T ;min;COND2;r ;o = −2,259E − 17 0,00 %

258


C.4. Results - Uncertainty propagation (STD)

∆T ;min;DES1;r ;o = 0 ± 0[C ] ∂ηHW /∂∆T ;min;DES1;r ;o = 7,115E − 15 0,00 %

∆T ;min;DES2;r ;o = 0 ± 0[C ] ∂ηHW /∂∆T ;min;DES2;r ;o = 0,00007009 0,00 %

∆T ;min;EV AP;r ;i = 5 ± 2,5[C ] ∂ηHW /∂∆T ;min;EV AP;r ;i = −1,172E − 12 0,00 %

∆T ;min;GGHE X 4;c;o; = 25 ± 12,5[C ] ∂ηHW /∂∆T ;min;GGHE X 4;c;o; = 0,001891 72,53 %

∆T ;min;SHE X 1;ws;i = 5 ± 2,5[C ] ∂ηHW /∂∆T ;min;SHE X 1;ws;i = −8,095E − 11 0,00 %

∆T ;min;SHE X 2;ws;i = 5 ± 2,5[C ] ∂ηHW /∂∆T ;min;SHE X 2;ws;i = 9,758E − 15 0,00 %

∆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 %

∆T ;min;TOW ER1;a;o;wet = 3 ± 1,5[C ] ∂ηHW /∂∆T ;min;TOW ER1;a;o;wet = 5,647E − 15 0,00 %

∆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 %

∆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 %

∆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 %

ηsys;el ;net = 0,516 ± 0,008916[-]

∆T ;min;ABSO;s;o = 5 ± 2,5[C ] ∂ηsys;el;net /∂∆T ;min;ABSO;s;o = 0,00006305 0,03 %

∆T ;min;COND1;r ;o;D = 10 ± 5[C ] ∂ηsys;el;net /∂∆T ;min;COND1;r ;o;D = 0,00001514 0,01 %

∆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 %

∆T ;min;COND2;r ;o = 15 ± 7,5[C ] ∂ηsys;el;net /∂∆T ;min;COND2;r ;o = 0,000003054 0,00 %

∆T ;min;DES1;r ;o = 0 ± 0[C ] ∂ηsys;el ;net /∂∆T ;min;DES1;r ;o = 7,689E − 07 0,00 %

∆T ;min;DES2;r ;o = 0 ± 0[C ] ∂ηsys;el ;net /∂∆T ;min;DES2;r ;o = 0,000002356 0,00 %

∆T ;min;EV AP;r ;i = 5 ± 2,5[C ] ∂ηsys;el ;net /∂∆T ;min;EV AP;r ;i = 0,00009601 0,07 %

∆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 %

∆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 %

∆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 %

∆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 %

∆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 %

∆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 %

∆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 %

259


C. EES

∆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 %

260


C.4.2 Miscellaneous parameters

Variable+Uncertainty Partial Derivative % of Uncertainty

COP ABS;f uel = 0,4556 ± 0,1035[-]

C.4. Results - Uncertainty propagation (STD)

ASR = 0,00005542 ± 0,00002771 [ Ω·m 2] ∂COP ABS;f uel /∂ASR = 2616 49,08 %

∆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 %

∆p;TOW ER1;air ;wet = 0,15 ± 0,075[kPa] ∂COP ABS;f uel /∂∆p;TOW ER1;air ;wet = 0,0005637 0,00 %

∆T ;SOFC ;av = 30 ± 15[C ] ∂COP ABS;f uel /∂∆T ;SOFC ;av = −0,0003557 0,27 %

ηblower ;TOW ER1 = 0,4 ± 0,2[-] ∂COP ABS;f uel /∂ηblower ;TOW ER1 = 0,000187 0,00 %

ηi s;BLOW 1 = 0,6 ± 0,3[-] ∂COP ABS;f uel /∂ηi s;BLOW 1 = 0,00009776 0,00 %

ηwb;TOW ER1 = 0,75 ± 0,375[-] ∂COP ABS;f uel /∂ηwb;TOW ER1 = 0,03229 1,37 %

F R = 0,14 ± 0,07[-] ∂COP ABS;f uel /∂F R = −0,0928 0,39 %

FW = 0,6 ± 0,3[-] ∂COP ABS;f uel /∂FW = 0,0064 0,03 %

id = 3000 ± 1500 [ A/m 2] ∂COP ABS;f uel /∂id = 0,00004822 48,86 %

ηHW = 0,07184 ± 0,04285[-]

ASR = 0,00005542 ± 0,00002771 [ Ω·m 2] ∂ηHW /∂ASR = 824,6 28,44 %

∆p;TOW ER1;air ;dr y = 0,15 ± 0,075[kPa] ∂ηHW /∂∆p;TOW ER1;air ;dr y = 1,279E − 08 0,00 %

∆p;TOW ER1;air ;wet = 0,15 ± 0,075[kPa] ∂ηHW /∂∆p;TOW ER1;air ;wet = 2,982E − 13 0,00 %

∆T ;SOFC ;av = 30 ± 15[C ] ∂ηHW /∂∆T ;SOFC ;av = −0,000106 0,14 %

ηblower ;TOW ER1 = 0,4 ± 0,2[-] ∂ηHW /∂ηblower ;TOW ER1 = −6,964E − 10 0,00 %

ηi s;BLOW 1 = 0,6 ± 0,3[-] ∂ηHW /∂ηi s;BLOW 1 = −0,09133 40,89 %

ηwb;TOW ER1 = 0,75 ± 0,375[-] ∂ηHW /∂ηwb;TOW ER1 = 1,374E − 09 0,00 %

F R = 0,14 ± 0,07[-] ∂ηHW /∂F R = 0,08439 1,90 %

FW = 0,6 ± 0,3[-] ∂ηHW /∂FW = −0,006182 0,19 %

id = 3000 ± 1500 [ A/m 2] ∂ηHW /∂id = 0,00001523 28,44 %

ηsys;el ;net = 0,516 ± 0,1288[-]

ASR = 0,00005542 ± 0,00002771 [ Ω·m 2] ∂ηsys;el ;net /∂ASR = −3145 45,77 %

261


C. EES

∆p;TOW ER1;air ;dr y = 0,15 ± 0,075[kPa] ∂ηsys;el ;net /∂∆p;TOW ER1;air ;dr y = 0,000009298 0,00 %

∆p;TOW ER1;air ;wet = 0,15 ± 0,075[kPa] ∂ηsys;el ;net /∂∆p;TOW ER1;air ;wet = −0,1327 0,60 %

∆T ;SOFC ;av = 30 ± 15[C ] ∂ηsys;el;net /∂∆T ;SOFC ;av = 0,0004208 0,24 %

ηblower ;TOW ER1 = 0,4 ± 0,2[-] ∂ηsys;el;net /∂ηblower ;TOW ER1 = 0,05002 0,60 %

ηi s;BLOW 1 = 0,6 ± 0,3[-] ∂ηsys;el;net /∂ηi s;BLOW 1 = 0,09133 4,52 %

ηwb;TOW ER1 = 0,75 ± 0,375[-] ∂ηsys;el;net /∂ηwb;TOW ER1 = −0,05275 2,36 %

F R = 0,14 ± 0,07[-] ∂ηsys;el;net /∂F R = −0,06511 0,13 %

FW = 0,6 ± 0,3[-] ∂ηsys;el;net /∂FW = 0,004777 0,01 %

id = 3000 ± 1500 [ A/m 2] ∂ηsys;el;net /∂id = −0,0000581 45,77 %

262


C.4. Results - Uncertainty propagation (STD)

C.4.3 ∆p for SOFC subsystem

Variable+Uncertainty Partial Derivative % of Uncertainty

COP ABS;f uel = 0,4556 ± 0,000321[-]

∆p;BURN ;i ;1 = −8 ± −8[kPa] ∂COP ABS;f uel /∂∆p;BURN ;i ;1 = −0,0000252 39,45 %

∆p;BURN ;i ;2 = −1 ± −1[kPa] ∂COP ABS;f uel /∂∆p;BURN ;i ;2 = −0,0001575 24,06 %

∆p;GGHE X 1;c = −1 ± −1[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 1;c = −0,0001223 14,52 %

∆p;GGHE X 1;h = −1 ± −1[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 1;h = −0,00009441 8,65 %

∆p;GGHE X 2;c = −1 ± −1[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 2;c = −0,0000729 5,16 %

∆p;GGHE X 2;h = −1 ± −1[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 2;h = −0,00005776 3,24 %

∆p;GGHE X 3;c = −4 ± −4[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 3;c = −0,00001097 1,87 %

∆p;GGHE X 3;h = −4 ± −4[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 3;h = −0,000008776 1,20 %

∆p;GGHE X 4;c = −2 ± −2[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 4;c = −0,000014 0,76 %

∆p;GGHE X 4;h = −2 ± −2[kPa] ∂COP ABS;f uel /∂∆p;GGHE X 4;h = −0,00001118 0,48 %

∆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 %

∆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 %

∆p;PR = −5 ± −5[kPa] ∂COP ABS;f uel /∂∆p;PR = −0,000002214 0,12 %

∆p;SPG1;o;1 = −0,1 ± −0,1[kPa] ∂COP ABS;f uel /∂∆p;SPG1;o;1 = −0,00007397 0,05 %

∆p;SPG1;o;2 = −0,1 ± −0,1[kPa] ∂COP ABS;f uel /∂∆p;SPG1;o;2 = −0,0000502 0,02 %

∆p;SPG2;o;1 = −0,1 ± −0,1[kPa] ∂COP ABS;f uel /∂∆p;SPG2;o;1 = −0,00003108 0,01 %

∆p;SPG2;o;2 = −0,1 ± −0,1[kPa] ∂COP ABS;f uel /∂∆p;SPG2;o;2 = −0,00004615 0,02 %

∆p;W GHE X 1;g = −2 ± −2[kPa] ∂COP ABS;f uel /∂∆p;W GHE X 1;g = −0,000001465 0,01 %

∆p;W GHE X 2;g = −2 ± −2[kPa] ∂COP ABS;f uel /∂∆p;W GHE X 2;g = −3,646E − 07 0,00 %

∆p;W GHE X 3;g = −2 ± −2[kPa] ∂COP ABS;f uel /∂∆p;W GHE X 3;g = −7,671E − 07 0,00 %

ηHW = 0,07184 ± 0,01676[-]

∆p;BURN ;i ;1 = −8 ± −8[kPa] ∂ηHW /∂∆p;BURN ;i ;1 = −1,782E − 10 0,00 %

∆p;BURN ;i ;2 = −1 ± −1[kPa] ∂ηHW /∂∆p;BURN ;i ;2 = −0,002301 1,89 %

263


C. EES

∆p;GGHE X 1;c = −1 ± −1[kPa] ∂ηHW /∂∆p;GGHE X 1;c = −7,258E − 10 0,00 %

∆p;GGHE X 1;h = −1 ± −1[kPa] ∂ηHW /∂∆p;GGHE X 1;h = −4,811E − 14 0,00 %

∆p;GGHE X 2;c = −1 ± −1[kPa] ∂ηHW /∂∆p;GGHE X 2;c = −4,845E − 14 0,00 %

∆p;GGHE X 2;h = −1 ± −1[kPa] ∂ηHW /∂∆p;GGHE X 2;h = 3,862E − 14 0,00 %

∆p;GGHE X 3;c = −4 ± −4[kPa] ∂ηHW /∂∆p;GGHE X 3;c = −0,002301 30,18 %

∆p;GGHE X 3;h = −4 ± −4[kPa] ∂ηHW /∂∆p;GGHE X 3;h = −0,002301 30,18 %

∆p;GGHE X 4;c = −2 ± −2[kPa] ∂ηHW /∂∆p;GGHE X 4;c = −0,002301 7,54 %

∆p;GGHE X 4;h = −2 ± −2[kPa] ∂ηHW /∂∆p;GGHE X 4;h = −0,002301 7,54 %

∆p;M I XG1;i ;1 = −0,1 ± −0,1[kPa] ∂ηHW /∂∆p;M I XG1;i ;1 = −1,426E − 08 0,00 %

∆p;M I XG2;i ;1 = −0,1 ± −0,1[kPa] ∂ηHW /∂∆p;M I XG2;i ;1 = −0,002301 0,02 %

∆p;PR = −5 ± −5[kPa] ∂ηHW /∂∆p;PR = −1,475E − 11 0,00 %

∆p;SPG1;o;1 = −0,1 ± −0,1[kPa] ∂ηHW /∂∆p;SPG1;o;1 = 3,388E − 14 0,00 %

∆p;SPG1;o;2 = −0,1 ± −0,1[kPa] ∂ηHW /∂∆p;SPG1;o;2 = 8,640E − 13 0,00 %

∆p;SPG2;o;1 = −0,1 ± −0,1[kPa] ∂ηHW /∂∆p;SPG2;o;1 = −0,002301 0,02 %

∆p;SPG2;o;2 = −0,1 ± −0,1[kPa] ∂ηHW /∂∆p;SPG2;o;2 = −7,361E − 10 0,00 %

∆p;W GHE X 1;g = −2 ± −2[kPa] ∂ηHW /∂∆p;W GHE X 1;g = −0,002301 7,54 %

∆p;W GHE X 2;g = −2 ± −2[kPa] ∂ηHW /∂∆p;W GHE X 2;g = −0,002301 7,54 %

∆p;W GHE X 3;g = −2 ± −2[kPa] ∂ηHW /∂∆p;W GHE X 3;g = −0,002301 7,54 %

ηsys;el ;net = 0,516 ± 0,01676[-]

∆p;BURN ;i ;1 = −8 ± −8[kPa] ∂ηsys;el;net /∂∆p;BURN ;i ;1 = −4,987E − 09 0,00 %

∆p;BURN ;i ;2 = −1 ± −1[kPa] ∂ηsys;el;net /∂∆p;BURN ;i ;2 = 0,002301 1,89 %

∆p;GGHE X 1;c = −1 ± −1[kPa] ∂ηsys;el;net /∂∆p;GGHE X 1;c = −6,200E − 08 0,00 %

∆p;GGHE X 1;h = −1 ± −1[kPa] ∂ηsys;el;net /∂∆p;GGHE X 1;h = −7,212E − 08 0,00 %

∆p;GGHE X 2;c = −1 ± −1[kPa] ∂ηsys;el;net /∂∆p;GGHE X 2;c = −2,729E − 08 0,00 %

∆p;GGHE X 2;h = −1 ± −1[kPa] ∂ηsys;el;net /∂∆p;GGHE X 2;h = −4,800E − 09 0,00 %

∆p;GGHE X 3;c = −4 ± −4[kPa] ∂ηsys;el;net /∂∆p;GGHE X 3;c = 0,002301 30,18 %

264


C.4. Results - Uncertainty propagation (STD)

∆p;GGHE X 3;h = −4 ± −4[kPa] ∂ηsys;el;net /∂∆p;GGHE X 3;h = 0,002301 30,18 %

∆p;GGHE X 4;c = −2 ± −2[kPa] ∂ηsys;el;net /∂∆p;GGHE X 4;c = 0,002301 7,54 %

∆p;GGHE X 4;h = −2 ± −2[kPa] ∂ηsys;el;net /∂∆p;GGHE X 4;h = 0,002301 7,54 %

∆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 %

∆p;M I XG2;i ;1 = −0,1 ± −0,1[kPa] ∂ηsys;el;net /∂∆p;M I XG2;i ;1 = 0,002301 0,02 %

∆p;PR = −5 ± −5[kPa] ∂ηsys;el;net /∂∆p;PR = −8,231E − 09 0,00 %

∆p;SPG1;o;1 = −0,1 ± −0,1[kPa] ∂ηsys;el;net /∂∆p;SPG1;o;1 = −9,460E − 08 0,00 %

∆p;SPG1;o;2 = −0,1 ± −0,1[kPa] ∂ηsys;el;net /∂∆p;SPG1;o;2 = −4,558E − 07 0,00 %

∆p;SPG2;o;1 = −0,1 ± −0,1[kPa] ∂ηsys;el;net /∂∆p;SPG2;o;1 = 0,002301 0,02 %

∆p;SPG2;o;2 = −0,1 ± −0,1[kPa] ∂ηsys;el;net /∂∆p;SPG2;o;2 = 5,435E − 07 0,00 %

∆p;W GHE X 1;g = −2 ± −2[kPa] ∂ηsys;el;net /∂∆p;W GHE X 1;g = 0,002301 7,54 %

∆p;W GHE X 2;g = −2 ± −2[kPa] ∂ηsys;el;net /∂∆p;W GHE X 2;g = 0,002301 7,54 %

∆p;W GHE X 3;g = −2 ± −2[kPa] ∂ηsys;el;net /∂∆p;W GHE X 3;g = 0,002301 7,54 %

265


C. EES

C.4.4 ∆p for absorption subsystem

Variable+Uncertainty Partial Derivative % of Uncertainty

COP ABS;f uel = −9999 ± 0,004593[-]

∆p;ABSO;1 = −0,01 ± 0,03286[kPa] ∂COP ABS;f uel /∂∆p;ABSO;1 = 0,09195 43,27 %

∆p;ABSO;2 = −0,01 ± 0,03286[kPa] ∂COP ABS;f uel /∂∆p;ABSO;2 = −0,00008428 0,00 %

∆p;COND1;r = −0,01 ± 0,2354[kPa] ∂COP ABS;f uel /∂∆p;COND1;r = 0,002045 1,10 %

∆p;COND2;r = −0,01 ± 3,958[kPa] ∂COP ABS;f uel /∂∆p;COND2;r = 0,0001977 2,90 %

∆p;DES1;r = −0,01 ± 0,2354[kPa] ∂COP ABS;f uel /∂∆p;DES1;r = −0,0001494 0,01 %

∆p;DES2;r = −0,01 ± 3,958[kPa] ∂COP ABS;f uel /∂∆p;DES2;r = 0,00001242 0,01 %

∆p;EV AP;r = −0,01 ± 0,03286[kPa] ∂COP ABS;f uel /∂∆p;EV AP;r = 0,09961 50,79 %

∆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 %

∆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 %

∆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 %

∆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 %

∆p;SHE X 1;ss = −0,01 ± 0,2354[kPa] ∂COP ABS;f uel /∂∆p;SHE X 1;ss = 0,0001362 0,00 %

∆p;SHE X 1;ws = −0,01 ± 0,2354[kPa] ∂COP ABS;f uel /∂∆p;SHE X 1;ws = 0,0002474 0,02 %

∆p;SHE X 2;ss = −0,01 ± 3,958[kPa] ∂COP ABS;f uel /∂∆p;SHE X 2;ss = 0,00005226 0,20 %

∆p;SHE X 2;ws = −0,01 ± 3,958[kPa] ∂COP ABS;f uel /∂∆p;SHE X 2;ws = 0,00009274 0,64 %

ηHW = −9999 ± 4,050 × 10 −11 [-]

∆p;ABSO;1 = −0,01 ± 0,03286[kPa] ∂ηHW /∂∆p;ABSO;1 = 3,388E − 13 0,00 %

∆p;ABSO;2 = −0,01 ± 0,03286[kPa] ∂ηHW /∂∆p;ABSO;2 = −3,524E − 12 0,00 %

∆p;COND1;r = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;COND1;r = 4,506E − 12 0,07 %

∆p;COND2;r = −0,01 ± 3,958[kPa] ∂ηHW /∂∆p;COND2;r = 6,607E − 12 41,69 %

∆p;DES1;r = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;DES1;r = 4,167E − 12 0,06 %

∆p;DES2;r = −0,01 ± 3,958[kPa] ∂ηHW /∂∆p;DES2;r = −5,557E − 12 29,49 %

∆p;EV AP;r = −0,01 ± 0,03286[kPa] ∂ηHW /∂∆p;EV AP;r = −3,795E − 12 0,00 %

266


C.4. Results - Uncertainty propagation (STD)

∆p;M I X L1;1 = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;M I X L1;1 = −4,506E − 12 0,07 %

∆p;M I X L1;2 = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;M I X L1;2 = 6,776E − 14 0,00 %

∆p;M I X R1;1 = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;M I X R1;1 = −4,811E − 12 0,08 %

∆p;M I X R1;2 = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;M I X R1;2 = 9,012E − 12 0,27 %

∆p;SHE X 1;ss = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;SHE X 1;ss = 1,389E − 12 0,01 %

∆p;SHE X 1;ws = −0,01 ± 0,2354[kPa] ∂ηHW /∂∆p;SHE X 1;ws = −3,388E − 13 0,00 %

∆p;SHE X 2;ss = −0,01 ± 3,958[kPa] ∂ηHW /∂∆p;SHE X 2;ss = −4,845E − 12 22,42 %

∆p;SHE X 2;ws = −0,01 ± 3,958[kPa] ∂ηHW /∂∆p;SHE X 2;ws = 2,473E − 12 5,84 %

ηsys;el ;net = −9999 ± 0,000101[-]

∆p;ABSO;1 = −0,01 ± 0,03286[kPa] ∂ηsys;el ;net /∂∆p;ABSO;1 = −0,001982 41,53 %

∆p;ABSO;2 = −0,01 ± 0,03286[kPa] ∂ηsys;el ;net /∂∆p;ABSO;2 = 0,000002275 0,00 %

∆p;COND1;r = −0,01 ± 0,2354[kPa] ∂ηsys;el ;net /∂∆p;COND1;r = −0,00001229 0,08 %

∆p;COND2;r = −0,01 ± 3,958[kPa] ∂ηsys;el ;net /∂∆p;COND2;r = 0,000006445 6,38 %

∆p;DES1;r = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;DES1;r = −0,000006068 0,02 %

∆p;DES2;r = −0,01 ± 3,958[kPa] ∂ηsys;el;net /∂∆p;DES2;r = 0,000001443 0,32 %

∆p;EV AP;r = −0,01 ± 0,03286[kPa] ∂ηsys;el;net /∂∆p;EV AP;r = −0,00217 49,79 %

∆p;M I X L1;1 = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;M I X L1;1 = −0,0000109 0,06 %

∆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 %

∆p;M I X R1;1 = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;M I X R1;1 = −0,00001644 0,15 %

∆p;M I X R1;2 = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;M I X R1;2 = 0,000002001 0,00 %

∆p;SHE X 1;ss = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;SHE X 1;ss = −0,000004218 0,01 %

∆p;SHE X 1;ws = −0,01 ± 0,2354[kPa] ∂ηsys;el;net /∂∆p;SHE X 1;ws = −0,000003342 0,01 %

∆p;SHE X 2;ss = −0,01 ± 3,958[kPa] ∂ηsys;el ;net /∂∆p;SHE X 2;ss = 0,000002051 0,65 %

∆p;SHE X 2;ws = −0,01 ± 3,958[kPa] ∂ηsys;el ;net /∂∆p;SHE X 2;ws = 0,000002563 1,01 %

267


C. EES

C.4.5 ˙Qloss for absorption subsystem

Variable+Uncertainty Partial Derivative % of Uncertainty

COP ABS;f uel = 0,4556 ± 0,03209[-]

˙Qloss;Bur n = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;Bur n = −0,01392 18,82 %

˙Qloss;DES1 = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;DES1 = −0,007894 6,05 %

˙Qloss;DES2 = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;DES2 = −0,014 19,03 %

˙Qloss;PR = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;PR = −0,01403 19,11 %

˙Qloss;SHE X 1 = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;SHE X 1 = −0,008557 7,11 %

˙Qloss;SHE X 2 = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;SHE X 2 = −0,01406 19,21 %

˙Qloss;SOFC = 0 ± 1[kW ] ∂COP ABS;f uel /∂ ˙Qloss;SOFC = −0,01049 10,68 %

ηHW = 0,07184 ± 0,003323[-]

˙Qloss;Bur n = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;Bur n = −2,882E − 10 0,00 %

˙Qloss;DES1 = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;DES1 = −1,016E − 14 0,00 %

˙Qloss;DES2 = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;DES2 = 4,574E − 14 0,00 %

˙Qloss;PR = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;PR = −1,321E − 14 0,00 %

˙Qloss;SHE X 1 = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;SHE X 1 = 3,795E − 14 0,00 %

˙Qloss;SHE X 2 = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;SHE X 2 = −2,473E − 14 0,00 %

˙Qloss;SOFC = 0 ± 1[kW ] ∂ηHW /∂ ˙Qloss;SOFC = −0,003323 100,00 %

ηsys;el;net = 0,516 ± 0,003461[-]

˙Qloss;Bur n = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;Bur n = 0,0006088 3,09 %

˙Qloss;DES1 = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;DES1 = 0,0004529 1,71 %

˙Qloss;DES2 = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;DES2 = 0,0006089 3,09 %

˙Qloss;PR = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;PR = 0,0006089 3,09 %

˙Qloss;SHE X 1 = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;SHE X 1 = 0,0004679 1,83 %

˙Qloss;SHE X 2 = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;SHE X 2 = 0,0006089 3,09 %

˙Qloss;SOFC = 0 ± 1[kW ] ∂ηsys;el ;net /∂ ˙Qloss;SOFC = 0,003174 84,08 %

268


C.5. Guide to EES files

C.5 Guide to EES files

Four versions of the main file have been appended. All of them use the

same sub-files (LIB files) which have also been appended. All 4 versions

are capable of running as single stage, double stage, dual reheat, with

wet tower, dry tower etc.

The reason they are all supplied is that they each contain the

parametric tables with the numeric results of the investigations of the

different sections in the report:

• Single Stage.EES contains all the results for investigating the single

cycle (section 5.1).

• 12Config.EES contains the results for comparing the 12 different

system configurations (section 5.2).

• STD.EES shows the results from the investigations with the

standard parameter configurations (section 5.2 through 5.4).

• OPTI.EES shows the results from the investigations with the

optimized parameter configurations (from section 5.4 through 6.1).

269


A P P E N D I X

D

OTHER

D.1 Explanation of chosen Parameters

In this section the choice of some of the parameters will be explained.

∆T min

The heat exchangers have been described by the Closest Approach

Temperature Difference (∆T min ) which has been estimated since it is not

possible to calculate the UA values in a zero dimensional model. It was

decided to let the ∆T min be 5 ◦ C for all the water-water heat exchangers,

15 ◦ C for all the water-gas heat exchangers, and 25 ◦ C for all the gas-gas

heat exchangers.

Then later in the project investigations could be carried out to see

which of the heat exchangers were important and which ones were not,

and it could then be decided which of the heat exchangers that should be

improved in order to optimize the system.

Pressure losses

The pressure losses of the components in the SOFC part of the system

have been approximated to values used in the models used by Topsoe

Fuel Cell, although the values have been altered a little to prevent

publishing classified data.

271


D. OTHER

The pressure loss of GGHEX4 have been set to half the pressure loss of

GGHEX3. Because those two heat exchangers experience the same mass

flows, but GGHEX4 transfers much less heat, so it is assumed to be much

shorter (reducing pressure loss in tubes / between plates)

Inlet conditions

The water added in the cooling tower is assumed to be at ambient

temperature.

The air and fuel at the inlet of the SOFC were assumed to be 25 ◦ C

(instead of being equal to the ambient temperature). This way the

ambient temperature could be changed to examine its influence on the

cooling tower without having the results ”polluted” by changes from the

SOFC.

D.2 Spider diagram parameter interval choice

272

• ASR: In reality ASR depends on a number of factors such as

temperature, current density, and oxygen partial pressure. In this

model it only depends on temperature. And in different models

from TOFC the value differs somewhat. So it has been estimated

that it is in reality likely to be within +/-20% of the value in the

model.

• ∆p tower,wet : The pressure loss of the cooling tower has been

estimated by looking at how much fan power small commercially

available cooling towers consume relative to the cooling power and

then calculate the pressure loss from this. But in reality the pressure

loss depends on how big the system is physically build relative to

the amount of cooling to be removed. Also the temperature of the

fluids matters. So this way it can vary a lot, and it is hence estimated

that it can be somewhere between double as large and half as large

as the estimated value.

• T SOFC ,in = 690 ◦ C, T SOFC ,out = 780 ◦ C, and T SOFC ,max is probably a

little over 800 ◦ C. So the average temperature must for sure be over

690 and below 800 ◦ C. At the standard parameter configuration it

is 750 ◦ C (∆T SOFC ,av = 30 ◦ C). And with T SOFC ,max > T SOFC ,out , the

average temperature must be closer to T SOFC ,out than to T SOFC ,in .


D.3. Water consumption

Hence it is likely to be between 735 ◦ C and 780 ◦ C (15 ◦ C < ∆T SOFC ,av

< 60 ◦ C))

• η W B,Tower is typically around 0,75 according to [14]. Since 0 equals

no evaporation at all and 1 equals the best possible theoretical

situation, it must be reasonable to assume that the value would not

be outside the interval 0,6 to 0,9.

• FR and FW: These values have been set so the change of the

flow (partial pressure) for the different species in the pre reformer

reassembles the TOFC data. Hence the standard configuration

values must be quite close to reality. FR (0,14) is assumed to be

within [0,1 to 0,2] whereas FW (0,6) is assumed to be within [0,45 to

0,75]

• i d The current density is controlled by the operator, so this can be

set exactly as desired - it is just a matter of buying the right amount

of cells for the desired current draw. As was shown in figure 5.19B

page 132 the current density can not go below 2100Ωm 2 if the fuel

input remains at the 100kW for the given number of cells since

the heat generated in the electrochemical reaction is not enough to

make up for the energy used in the endothermic reforming process.

The current density can not go above 3300Ωm 2 either, since the

voltage falls below 0,7V (0=>Nickel Oxidation).

• The efficiency of the FAN (for the cooling tower) can vary quite

a lot depending on the size of the system (and hence FAN), so

depending on the system size, it is assumed that it can range from

0,3 to 0,6.

• The isentropic efficiency of the blower in the SOFC system should

be relatively exact for the given size (100kW of fuel), since the

blower power consumption fits very well with being 10% of the

net electricity [25]. But it does depend a lot on the size, so it can

be suspected to range from 0,4 to 0,8 if the system is scaled up or

down.

D.3 Water consumption

273


High humidity - low water price, high electricity price

Unit Water Electricity

Consumption kg/s 0,03

Density kg/m^3 1000

Consumption m^3/year 946

Unit price DKK/m^3 10

Fuel input kW 100

Eta_sys,el,net - 0,5

Production kWh/year 438.000

Unit price DKK/kWh 2

Total price DKK 9.461 876.000

Fraction of water expenses and electricity value: 1,1%

High humidity - high water price, low electricity price

Unit Water Electricity

Consumption kg/s 0,03

Density kg/m^3 1000

Consumption m^3/year 946

Unit price DKK/m^3 20

Fuel input kW 100

Eta_sys,el,net - 0,5

Production kWh/year 438.000

Unit price DKK/kWh 1

Total price DKK 18.922 438.000

Fraction of water expenses and electricity value: 4,3%

Low humidity - low water price, high electricity price

Unit Water Electricity

Consumption kg/s 0,06

Density kg/m^3 1000

Consumption m^3/year 1892

Unit price DKK/m^3 10

Fuel input kW 100

Eta_sys,el,net - 0,5

Production kWh/year 438.000

Unit price DKK/kWh 2

Total price DKK 18.922 876.000

Fraction of water expenses and electricity value: 2,2%

Low humidity - high water price, low electricity price

Unit Water Electricity

Consumption kg/s 0,06

Density kg/m^3 1000

Consumption m^3/year 1892

Unit price DKK/m^3 20

Fuel input kW 100

Eta_sys,el,net - 0,5

Production kWh/year 438.000

Unit price DKK/kWh 1

Total price DKK 37.843 438.000

Fraction of water expenses and electricity value: 8,6%

274


A P P E N D I X

E

OPTIMIZATION GRAPHS

275


E. OPTIMIZATION GRAPHS

E.1 Simulations and Results

E.1.1

All 12 Configurations

eta | COP

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

System Configurations

eta_HW

COP_ABS,fuel

eta_sys,el,net

0.07

0.10

0.07

0.26

0.23

0.13

0.09 0.10

0.10 0.06

0.12 0.09

0.46

0.42

0.23 0.26

0.23

0.31

0.35

0.34

0.38

0.15 0.17

0.21

0.51 0.51 0.53 0.53 0.51 0.49

0.53 0.52 0.50 0.49 0.52 0.52

SSd- SSdA SSw- SSwA DSd- DSdA DSw- DSwA DHd- DHdA DHw- DHwA

Figure E.1: Comparison of system configurations

Figure E.1 shows the COP and efficiencies of the 12 different

configurations described by the 4 letters below each column:

1. SS = Single stage, DS = Double Stage, DH = Double Stage Dual

Heat

2. d = Dry Tower, w = Wet Tower

3. A = Air preheat, - = no Air Preheat

276


E.1. Simulations and Results

E.1.2

E.1.2.1

∆T for external circuits

∆T EV AP

The temperature of the chilling water into the evaporator (T 48 ) is set to

11 ◦ C (this value is not changed in this simulation). ∆T min,EV AP is 5 ◦ C so

to prevent the refrigerant (water) from freezing, ∆T EV AP can not be larger

than 6 ◦ C.

Figure E.2

When the temperature increase in the chilling water circuit (∆T EV AP )

is decreased from 5 ◦ C to 1 ◦ C, the COP ABS,f uel is increased a little over 3%

(1,5 percent points), see figure E.2. So there is a little to gain, but since

both the evaporator and the hex at the other end at the external circuit

has to be larger (and hence more expensive) it is probably not one of the

best places to optimize the process.

277


E. OPTIMIZATION GRAPHS

E.1.2.2

∆T DES1

The temperature increase in the external water cycle between DES1, COND2

and WGHEX2 is most relevant when using the reheat configuration. When

the pure double cycle is used, COND2 and DES1 would in reality be integrated

in the same component (hence ∆T DES1 should be zero). It is

however investigated how big an effect it would have on the system if

the heat transmission between DES1, COND2 and WGHEX2 was in fact

made by an external water cycle with a ∆T DES1 .

Figure E.3

It is seen from figure E.3 that as long as ∆T DES1 is below 10 ◦ C, there

is only a very little effect on COP, while η sys,el ,net and η HW t are constant.

E.1.2.3

∆T DES2

WGHEX1 is assumed to be integrated in DES2, but it could also be made

by an external water circuit. In that case the temperature change in

the external circuit (∆T DES2 ) could be varied, and this is done in the

following: It appears from figure E.4 that ∆T DES2 has no influence on

278


E.1. Simulations and Results

Figure E.4

the efficiencies or COP. This is because the closest approach temperature

difference takes place in the water inlet side of the WGHEX1 (15 ◦ C)

whereas the closest approach temperature difference at the water outlet

side is above 100 ◦ C. So when ∆T DES2 is increased, ∆T min,DES2,w,o is just

decreased by the same amount.

279


E. OPTIMIZATION GRAPHS

E.1.3

Towers

The influence of the Closest Approach Temperature Difference on the

two different types of towers is now investigated.

E.1.3.1 ∆ T,min,Tower

Figure E.5

The COP ABS,f uel (blue curve in figure E.5) is heavily dependent on

the ∆ T,min when the DRY Tower is used because a large ∆ T,min,Tower

will give a large absorber and condenser temperature. The electrical

efficiency of the system (black curve) raises a little when ∆ T,min,Tower is

increased, but that is merely due to lower FAN power consumption when

the absorption cooling unit becomes less efficient and this way needs less

low quality heat removed.

For the WET Tower the COP ABS,f uel (figure E.6A) is unaffected by

the ∆ T,min . This is because the (somewhat simple) model of the wet

tower only uses the air inlet conditions and tower (wet bulb) efficiency to

determine the water outlet temperature. So the water outlet temperature

is not affected by the ∆ T,min (hence COP is unaffected).

280


E.1. Simulations and Results

Figure E.6: A: Efficiencies, COP, and water consumption. B: Air temperatures and fan power.

The air outlet temperature, however, is directly dependent on ∆ T,min .

So when the ∆ T,min,Tower is increased the air outlet temperature falls

(orange curve in figure E.6B). This means that more water will be

consumed (lost through evaporation) since each kg of the outlet air

carries less energy out of the system (T air,out < T air,in , so some of the

evaporation energy will be used to cool down the air). Furthermore

since the airflow increases, the FAN power consumption will rise (brown

curve). So the electrical efficiency will decrease significantly.

281


E. OPTIMIZATION GRAPHS

E.1.3.2

∆ T,Tower

∆ T,Tower is the difference between point 37 and 39. And since T 39 is given

by the cooling tower and ambient conditions, ∆ T,Tower will effectively

control T 37 . In a physical system this is done by regulating the water flow

in the circuit point 35 to 39. In lack of exact numbers, it has been assumed

that the outlet temperature of the air remains at the same relative position

between the water in- and outlet of the tower (green curve relative to the

two blue lines in figure E.7B). This seemed more realistic than keeping

∆T min constant at the 3 ◦ C, which would have made the air outlet become

colder than the water outlet for ∆ T,Tower < 3.

Figure E.7: A: Efficiencies, COP, and water consumption. B: Air and water temperatures.

T air,in = T 45 ,T air,out = T 47 ,T water,in = T 37 and T water,out = T 39 .

As can be seen in figure E.7, the COP of the absorption unit increases

when ∆ T,Tower is reduced because T 39 is decreased. But the fan power

rises considerably mainly because of the increased air flow, which comes

from the increased amount of water evaporated. Hence the electrical

efficiency decreases.

282


E.2. Cases

E.2 Cases

E.2.1

Extreme low relative humidity

Figure E.8: The relative humidity is only φ = 0,2. The ambient temperature is varied for the

system with optimized parameter configuration. ṁ is the water consumption of the wet cooling

tower.

283


A P P E N D I X

F

LITERATURE

F.1 Scandinavian Energy Group Aps.

285


SEG

Scandinavian Energy Group Aps.

Mulige anvendelser af absorptionskøling

Absorptionskøling evner i grundprincippet at tage varme fra to temperaturniveauer (en lavtemperatur energikilde

og en højtemperatur energikilde) og aflevere hele varmemængden ved en mellemtemperatur. For at processen

skal være mulig skal denne mellemtemperatur ligge tættest på lavtemperatur energikilden

Grafisk fremstillet kan det se ud som følger :

Temperatur akse

Varmetilførsel ved høj temperatur

Varmetilførsel ved lav temperatur

Varmeafgivelse ved mellemtemperatur

286

VEGENDALVEJ 18 APS REG. NR. 206388

P.O. BOX 143 SE-NR. 16073105

DK-7700 THISTED BANK: NORDEA A/S

PHONE: +45-96 19 53 22 DK-7700 THISTED

FAX: +45-96 19 53 23 DENMARK


SEG

Scandinavian Energy Group Aps.

En mere uddybende beskrivelse er angivet i følgende hvor de reelle begrænsninger er beskrevet mere detaljeret.

1. Da kølemidlet er vand kan der ikke opereres med temperaturer under 0 °C. I praksis er det uden specielle

foranstaltninger dog ikke realistisk at køre med udgangstemperaturer på det kølede vand fra

fordamperen på under 6 °C da der skal være en rimelig margin mellem driftstemperatur og

frysevagtstemperaturen der generer sikkerhedsstop.

2. Af hensyn til begrænsning af indre korrosion laver man normalt ikke driftstemperaturer på generatoren

på over 150 °C.

3. Højere temperaturforskel mellem fordamper og absorber kræver højere LiBr koncentration. Den

maksimale koncentration der kan tolereres svarer til ca. 40 °C i temperaturforskel. For at opnå den

nødvendige LiBr koncentration uden for store hedeflader kræves der en temperaturforskel mellem

kondensatorudgang og generator som typisk er 20 °C hørere end temperaturforskellen mellem fordamper

og absorber (udgangstemperaturer).

4. Varmeafgivelsen kommer desuden ikke fra ét sted, men i stedet fra to steder i processen som ikke

nødvendigvis har samme temperaturniveau. Varmen genereres nemlig både i absorberen der absorbere

dampene fra fordamperen (ca. 56 % af varmeafgivelsen) og kondensatoren der kondenserer dampene fra

generatoren (ca. 44 % af varmeafgivelsen). Kølevandet til de to varmeafgivere er normalt koblet i serie så

de fremstår som én kilde, men andre koblinger er også muligt. På varmepumper (højtemperatur maskiner

som laver fjernvarme) er absorberen altid koblet før kondensatoren. På kølemaskiner (lavtemperatur

maskiner som laver vand til køleformål) er koblingen normalt modsat.

5. Energimæssigt udgør lavtemperatur energikilden 70-75 % af højtemperatur energikilden. Da vands

fordampningsvarme er dominerende i forhold varmekapaciteten (henført til nogle graders

temperaturvariation) er dette forhold næsten uafhængigt af driftstemperaturer og belastning for en given

maskine.

6. Absorptions varm