12th International Symposium on District Heating and Cooling

The <strong>12th</strong> <strong>International</strong> <strong>Symposium</strong> on District Heating and Cooling,September 5 th to September 7 th , 2010, Tallinn, Estoniawill increase with increasing supply temperatures,which is not modelled here.The exergoeconomic analysis does take into accountthe increasing exergy requirements for systems withlower surface areas. Consequently, 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 and 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 calculations. As a result, the linedoes not slope up as strongly with increasing f-factoras the line pertaining to the classical analysis. Going tohigher f-factors, eventually all heat will be deliveredunder 60 °C, and all heat provided will be free. Going tolower f-factors, eventually all heat will be supplied attemperatures over 60 °C and the green line willcoincide with the blue classical analysis line. The heatunder 60 °C free analysis does not show an optimumand would suggest minimizing the f-factor. Like theclassical analysis the economic analysis suggests thatcapital cost are dominant.Figure 3 shows the effect of introducing a carbon tax of$30/tonCO2eq on the exergoeconomic analysis. It isclear that the carbon tax leads to higher annual costand lower f-factors for the same systems, both causedby the increased exergy cost. Both lines show anoptimum for an f-factor in the range 0.71–0.73, but forthe case without carbon tax the corresponding surfacearea is lower than for the case with carbon tax. Thismakes sense as increasing heat and exergy cost meana shift to a system with higher surface areas and lowerheat and exergy requirements. As figure 3 shows, thecapital and O&M cost as a fraction of total cost (andconsequently also the exergy cost as a fraction of totalcost) remain in the same range.Annual cost ($)$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 carbon tax Carbon tax $30/tCO2Fig. 3. Relation between f-factor and annual cost radiatorsystem, with and without carbon tax.Alternative designs – cross-flow heat exchangersystemFigure 4 shows the results for the system with crossflowheat exchangers. Note again that the jump inannual cost at an f-factor around 0.78 is due to theincrease in district heating pipe diameter. As for theradiator system, the classical analysis shows a steepslope with increasing f-factors as capital cost aredominant and lower exergy requirements do nottranslate into cost savings. Again the classical analysiswould lead us to minimize the surface area (with thesame limitations as applied to the radiator).Annual cost ($)$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-economic analysis Heat under 60C free analysisFig. 4. Relation between f-factor and annual cost crossflowheat exchanger system, no carbon tax.The exergoeconomic analysis shows a downwardsloping line. This is caused by the reduced capital costand O&M cost compared to the radiator system andthus increased importance of exergy cost as fraction ofthe total cost. An increase in cost due to surface area ismore than offset by a decrease in exergy cost.Contrary to the radiator system, though, theexergoeconomic analysis does not show a clearoptimum, although it clearly levels off at higherf-factors. It is interesting to note here that the classicalanalysis and the exergoeconomic analysis lead tocontradictory recommendations as to optimization.The analysis with free heat under 60 °C shows a linegradually sloping up, though far less pronounced 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 carbon tax on theexergoeconomic analysis. As for the radiator systemthe carbon tax means higher annual cost and lowerf-factors for the same system due to increased exergycost. As there is not a clear optimum in either line, wecan not conclude that the optimum f-factor is the samefor both. However, it is clear that both level off in thehigher f-factors range.51