The <str<strong>on</strong>g>12th</str<strong>on</strong>g> <str<strong>on</strong>g>Internati<strong>on</strong>al</str<strong>on</strong>g> <str<strong>on</strong>g>Symposium</str<strong>on</strong>g> <strong>on</strong> <strong>District</strong> <strong>Heating</strong> <strong>and</strong> <strong>Cooling</strong>,September 5 th to September 7 th , 2010, Tallinn, Est<strong>on</strong>iawill increase with increasing supply temperatures,which is not modelled here.The exergoec<strong>on</strong>omic analysis does take into accountthe increasing exergy requirements for systems withlower surface areas. C<strong>on</strong>sequently, there is a minimumannual cost (for an f-factor in the range 0.71–0.73).Going to lower f-factors, exergy cost significantlyincrease, which results in increasing annual overallcost. Going to higher f-factors, the annual cost increaseagain because the decreasing exergy cost are morethan offset by the increase in capital <strong>and</strong> O&M cost.The analysis discounting heat under 60 °C does takethe temperature level of energy supplied into accountwhile determining costs, though there is no explicitprice for exergy in the calculati<strong>on</strong>s. As a result, the linedoes not slope up as str<strong>on</strong>gly with increasing f-factoras the line pertaining to the classical analysis. Going tohigher f-factors, eventually all heat will be deliveredunder 60 °C, <strong>and</strong> all heat provided will be free. Going tolower f-factors, eventually all heat will be supplied attemperatures over 60 °C <strong>and</strong> the green line willcoincide with the blue classical analysis line. The heatunder 60 °C free analysis does not show an optimum<strong>and</strong> would suggest minimizing the f-factor. Like theclassical analysis the ec<strong>on</strong>omic analysis suggests thatcapital cost are dominant.Figure 3 shows the effect of introducing a carb<strong>on</strong> tax of$30/t<strong>on</strong>CO2eq <strong>on</strong> the exergoec<strong>on</strong>omic analysis. It isclear that the carb<strong>on</strong> tax leads to higher annual cost<strong>and</strong> lower f-factors for the same systems, both causedby the increased exergy cost. Both lines show anoptimum for an f-factor in the range 0.71–0.73, but forthe case without carb<strong>on</strong> tax the corresp<strong>on</strong>ding surfacearea is lower than for the case with carb<strong>on</strong> tax. Thismakes sense as increasing heat <strong>and</strong> exergy cost meana shift to a system with higher surface areas <strong>and</strong> lowerheat <strong>and</strong> exergy requirements. As figure 3 shows, thecapital <strong>and</strong> O&M cost as a fracti<strong>on</strong> of total cost (<strong>and</strong>c<strong>on</strong>sequently also the exergy cost as a fracti<strong>on</strong> of totalcost) remain in the same range.Annual cost ($)$2,750,000$2,700,000$2,650,000$2,600,000$2,550,000$2,500,000$2,450,000$2,400,000$2,350,000$2,300,000$2,250,000$2,200,0000.63 0.65 0.67 0.69 0.71 0.73 0.75 0.77 0.79 0.81 0.83 0.85 0.87f-factor (-)No carb<strong>on</strong> tax Carb<strong>on</strong> tax $30/tCO2Fig. 3. Relati<strong>on</strong> between f-factor <strong>and</strong> annual cost radiatorsystem, with <strong>and</strong> without carb<strong>on</strong> tax.Alternative designs – cross-flow heat exchangersystemFigure 4 shows the results for the system with crossflowheat exchangers. Note again that the jump inannual cost at an f-factor around 0.78 is due to theincrease in district heating pipe diameter. As for theradiator system, the classical analysis shows a steepslope with increasing f-factors as capital cost aredominant <strong>and</strong> lower exergy requirements do nottranslate into cost savings. Again the classical analysiswould lead us to minimize the surface area (with thesame limitati<strong>on</strong>s as applied to the radiator).Annual cost ($)$2,200,000$2,100,000$2,000,000$1,900,000$1,800,000$1,700,000$1,600,000$1,500,000$1,400,0000.65 0.67 0.69 0.71 0.73 0.75 0.77 0.79 0.81 0.83f-factor (-)Classical analysis Exergo-ec<strong>on</strong>omic analysis Heat under 60C free analysisFig. 4. Relati<strong>on</strong> between f-factor <strong>and</strong> annual cost crossflowheat exchanger system, no carb<strong>on</strong> tax.The exergoec<strong>on</strong>omic analysis shows a downwardsloping line. This is caused by the reduced capital cost<strong>and</strong> O&M cost compared to the radiator system <strong>and</strong>thus increased importance of exergy cost as fracti<strong>on</strong> ofthe total cost. An increase in cost due to surface area ismore than offset by a decrease in exergy cost.C<strong>on</strong>trary to the radiator system, though, theexergoec<strong>on</strong>omic analysis does not show a clearoptimum, although it clearly levels off at higherf-factors. It is interesting to note here that the classicalanalysis <strong>and</strong> the exergoec<strong>on</strong>omic analysis lead toc<strong>on</strong>tradictory recommendati<strong>on</strong>s as to optimizati<strong>on</strong>.The analysis with free heat under 60 °C shows a linegradually sloping up, though far less pr<strong>on</strong>ounced thanthe classical analysis line. Like the classical analysisline it would indicate that lower surface areas wouldoptimize this system.Figure 5 shows the effect of a carb<strong>on</strong> tax <strong>on</strong> theexergoec<strong>on</strong>omic analysis. As for the radiator systemthe carb<strong>on</strong> tax means higher annual cost <strong>and</strong> lowerf-factors for the same system due to increased exergycost. As there is not a clear optimum in either line, wecan not c<strong>on</strong>clude that the optimum f-factor is the samefor both. However, it is clear that both level off in thehigher f-factors range.51
The <str<strong>on</strong>g>12th</str<strong>on</strong>g> <str<strong>on</strong>g>Internati<strong>on</strong>al</str<strong>on</strong>g> <str<strong>on</strong>g>Symposium</str<strong>on</strong>g> <strong>on</strong> <strong>District</strong> <strong>Heating</strong> <strong>and</strong> <strong>Cooling</strong>,September 5 th to September 7 th , 2010, Tallinn, Est<strong>on</strong>iaAnnual cost ($)$2,500,000$2,400,000$2,300,000$2,200,000$2,100,000$2,000,000$1,900,000$1,800,000$1,700,000$1,600,0000.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82No carb<strong>on</strong> taxf-factor (-)Carb<strong>on</strong> tax $30/tCO2Fig.5. Relati<strong>on</strong> between f-factor <strong>and</strong> annual cost crossflowheat exchanger system, with <strong>and</strong> without carb<strong>on</strong> tax.From the foregoing, it is clear that useful comparis<strong>on</strong>scan be made using this methodology. The results fromexergoec<strong>on</strong>omic analyses can significantly deviatefrom those obtained with a classical analysis. Which ofthe two is the more relevant <strong>on</strong>e will depend <strong>on</strong> thesituati<strong>on</strong>. For n<strong>on</strong>-integrated systems, the classicalanalysis may be the <strong>on</strong>e to follow, but for integratedenergy systems, which are expected to become more<strong>and</strong> more important, the temperature level of heatbecomes important, <strong>and</strong> the exergoec<strong>on</strong>omic analysisseems more appropriate. Using the f-factor will help infinding optimum soluti<strong>on</strong>s, especially for exergoec<strong>on</strong>omicanalyses.Variati<strong>on</strong>s in external factors, such as fuel costs orGovernment / utility incentives could change the shapeof the curves to make the minimum more pr<strong>on</strong>ounced.CONCLUSION AND SUGGESTIONS FOR FURTHERWORKFrom the results of testing the methodology ofexergoec<strong>on</strong>omic optimizati<strong>on</strong> using the f-factor, it isclear that it is a useful tool to determine the effects ofdifferent heating technologies <strong>and</strong> heat transfer surfacesizes of these technologies <strong>on</strong> the annual overalloperati<strong>on</strong>al costs. This is especially true if the heatingsystem is integrated with other energy systems. It isalso true if the temperature level of the heat isimportant for another reas<strong>on</strong>. The methodology can beused to make informed choices regarding technologiesto be used for heating homes or buildings <strong>and</strong>regarding the size of these technologies.To c<strong>on</strong>tinue this development work, it is recommendedthat more practical c<strong>on</strong>siderati<strong>on</strong>s will be incorporatedinto the models <strong>and</strong> analyses. Increasing temperaturesdo not just cost more in terms of exergy but also inmore expensive materials, <strong>and</strong> steam based districtheating systems are c<strong>on</strong>siderably more expensive thanhot water based systems. Heat losses from the pipelinewere small but may need to be c<strong>on</strong>sidered in a followupstudy. Including passive heating of houses by solarradiati<strong>on</strong>, plug loads <strong>and</strong> occupancy gains will alsoimprove model predicti<strong>on</strong>s. Also mixed systemscombining heating technologies <strong>and</strong> possibly includingother technologies such as under-floor heating providefurther opportunities to optimize system cost.In additi<strong>on</strong>, the applicati<strong>on</strong> of the methodologydeveloped in this study should be applied to a heatpump, where the variati<strong>on</strong>s in COP with supplytemperature would be included. This would result in theability to match the heating equipment to the heatpump, resulting in an optimum operati<strong>on</strong>.ACKNOWLEDGEMENTDuring this work the authors have had very fruitfulc<strong>on</strong>versati<strong>on</strong>s with many colleagues: Mikhail Sorin,Evgueniy Entchev, Libing Yang, Ibrahim Dincer, HajoRibberink <strong>and</strong> Kirby Wittich. These discussi<strong>on</strong>s helpedfocus the work <strong>and</strong> stimulated further thinking in thisinteresting area of science. This is to thank all thosewho spent their valuable time listening <strong>and</strong> providingvaluable comments.REFERENCES[1] G. Wall, ―Exergy <strong>and</strong> Morals‖, in Sec<strong>on</strong>d lawanalysis of energy systems: towards the 21stcentury, E. Sciubba, M.J. Moran Eds, Circus,Roma (1995), ISBN 88-86662-0-9, pp. 21-29.[2] D. Schmidt, ―Design of Low Exergy Buildings –Method <strong>and</strong> a Pre-Design Tool‖, in <str<strong>on</strong>g>Internati<strong>on</strong>al</str<strong>on</strong>g>Journal of Low Exergy <strong>and</strong> Sustainable Buildings,Vol. 3 (2003), pp. 120-126.[3] A. Valero, L. Serra & J. Uche, ―Fundamentals ofExergy Cost Accounting <strong>and</strong> Thermoec<strong>on</strong>omics.Part I: Theory‖, in Journal of Energy ResourcesTechnology, Vol. 128 (2006), pp. 1-8.[4] G. Tsatsar<strong>on</strong>is, ―Applicati<strong>on</strong> of Thermoec<strong>on</strong>omicsto the Design <strong>and</strong> Synthesis of Energy Plants‖, inExergy, Energy System Analysis, <strong>and</strong>Optimizati<strong>on</strong>, [ed. Christos A. Fr<strong>on</strong>gopoulos], inEncyclopedia of Life Support Systems (EOLSS),developed under auspices of the Unesco, EolssPublishers, Oxford, UK (2007).[5] G. Temir, D. Bilge, ―Thermoec<strong>on</strong>omic analysis of atrigenerati<strong>on</strong> system‖ in Applied ThermalEngineering, Vol. 24 (2004), pp. 2689-2699.[6] Clean Energy Project Analysis – RETScreenEngineering & Cases Textbook, 3 rd editi<strong>on</strong>,RETScreen <str<strong>on</strong>g>Internati<strong>on</strong>al</str<strong>on</strong>g>, Natural ResourcesCanada, Varennes (2005).52
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