47:. Thus, the Carnot method is a form of an exergetic allocation method. It uses mean heat grid temperatures at the output of the process as a calculation basis. The Carnot method's advantage is that no external reference values are required to allocate the input to the different output streams; only endogenous process parameters are needed. Thus, the allocation results remain unbiased of assumptions or external reference values that are open for discussion.
449:
declines. Exergy does not only consider energy but also energy quality. It can be considered a product of both. Therefore any energy transformation should also be assessed according to its exergetic efficiency or loss ratios. The quality of the product "thermal energy" is fundamentally determined by
378:
The reciprocal value of the fuel factor (f-intensity) describes the effective efficiency of the assumed sub-process, which in case of CHP is only responsible for electrical or thermal energy generation. This equivalent efficiency corresponds to the effective efficiency of a "virtual boiler" or a
512:
The main application area of this method is cogeneration, but it can also be applied to other processes generating a joint products, such as a chiller generating cold and producing
1060:
EN 15316-4-5:2017 Energy performance of buildings - Method for calculation of system energy requirements and system efficiencies - Part 4-5: District heating and cooling
678:
describes the backward transformation. A reversible transformation is assumed, in order not to favour any of the two directions. Because of the exchangeability of
454:
describes how much of the fuel's potential to generate physical work remains in the joint energy products. With cogeneration the result is the following relation:
204:
In heating systems, a good approximation for the upper temperature is the average between forward and return flow on the distribution side of the heat exchanger.
994:
Tereshchenko, Tymofii; Nord, Natasa (2015-02-05), "Uncertainty of the allocation factors of heat and electricity production of combined cycle power plant",
437:
Next to the efficiency factor which describes the quantity of usable end energies, the quality of energy transformation according to the
1054:
613:
has to be solved, which is possible with a lot of adequate tuples. As second equation, the physical transformation of product
1048:
A novel exergy-based concept of thermodynamic quality and its application to energy system evaluation and process analysis
249:
137:: allocation factor for electrical energy, i.e. the share of the fuel input which is allocated to electricity production
516:
which could be used for low temperature heat demand, or a refinery with different liquid fuels plus heat as an output.
334:
To obtain the primary energy factors of cogenerated heat and electricity, the energy prechain needs to be considered.
546:
is a factor for rating the relevant product in the domain of primary energy, or fuel costs, or emissions, etc.
143:: allocation factor for thermal energy, i.e. the share of the fuel input which is allocated to heat production
970:
1034:
Allocating carbon dioxide emissions from cogeneration systems: descriptions of selected output-based methods
975:
438:
63:
for the thermal energy H (useful heat) respectively, can be calculated accordingly to the first and second
27:, end energy) in joint production processes that generate two or more energy products in one process (e.g.
1047:
1084:
1033:
1040:
64:
1066:, 2018-12-11. Annex V, C. Methodology, b) and Annex VI, B. Methodology, d)
1079:
965:
450:
the mean temperature level at which this heat is delivered. Hence, the exergetic efficiency η
220:
or - if more thermodynamic precision is needed - the logarithmic mean temperature is used
8:
1007:
244:
If process steam is delivered which condenses and evaporates at the same temperature, T
1064:
Directive (EU) 2018/2001 on the promotion of the use of energy from renewable sources
960:
44:
1089:
1036:, Journal of Cleaner Production, Volume 16, Issue 2, January 2008, p. 171–177.
1011:
1003:
1057:, Energy systems - Combined heat and power - Allocation and evaluation, Juli 2008.
1063:
59:
which is needed to generate the combined product electrical energy W (work) and a
43:) is used as the distribution key. For heat this potential can be assessed the
24:
1073:
955:
692:, the assessment of the two sides of the equation above with the two factors
32:
950:
28:
1016:
1039:
Andrej
Jentsch: The Carnot-Method for Allocation of Fuel and Emissions,
513:
423:: effective efficiency of electricity generation within the CHP process
31:
or trigeneration). It is also suited to allocate other streams such as
766:
If we put this into the first equation, we see the following steps:
442:
429:: effective efficiency of heat generation within the CHP process
446:
40:
503:= exergetic efficiency of the virtual electricity-only process
260:
The fuel intensity or the fuel factor for electrical energy f
39:
or variable costs. The potential to provide physical work (
432:
706:
should therefore result in an equivalent outcome. Output
509:= exergetic efficiency of the virtual heat-only process
475:
The allocation with the Carnot method always results in:
23:
is an allocation procedure for dividing up fuel input (
549:evaluation of the input = evaluation of the output
1071:
993:
497:= exergetic efficiency of the combined process
268:is the relation of specific input to output.
201:: upper temperature, superior (useful heat)
524:Let's assume a joint production with Input
172:: Total heat, fuel or primary energy input
519:
379:"virtual generator" within the CHP plant.
189:(Carnot factor for electrical energy is 1)
1015:
599:are known. An equation with two unknowns
370:: primary energy factor of the used fuel
50:
329:
195:: lower temperature, inferior (ambient)
433:Performance factor of energy conversion
373:
1072:
1008:10.1016/j.applthermaleng.2014.11.019
720:shall be the same as the amount of
250:saturated steam of a given pressure
13:
1026:
650:is the transformation factor from
14:
1101:
1043:, Vol 12 II, 2015, p. 26-28.
1050:, dissertation, TU Berlin, 2010.
1002:, Amsterdam: Elsevier: 410–422,
441:is also important. With rising
987:
255:
1:
1053:Verein Deutscher Ingenieure:
981:
976:Second law of thermodynamics
7:
996:Applied Thermal Engineering
971:Nicolas Léonard Sadi Carnot
944:
16:Energy allocation procedure
10:
1106:
248:is the temperature of the
1055:VDI-Guideline 4608 Part 2
574:The factor for the input
627:and vice versa is used.
520:Mathematical derivation
581:and the quantities of
264:resp. thermal energy f
65:laws of thermodynamics
51:Fuel allocation factor
966:Joint product pricing
330:Primary energy factor
535:and a second output
374:Effective efficiency
885:) or respectively f
734:and evaluated with
528:and a first output
181:: Carnot factor 1-T
164:W: electrical work
1041:EuroHeat&Power
1085:Energy conversion
961:Power loss factor
45:Carnot efficiency
1097:
1046:Andrej Jentsch:
1021:
1020:
1019:
991:
55:The fuel share a
1105:
1104:
1100:
1099:
1098:
1096:
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1070:
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1029:
1027:Further reading
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992:
988:
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739:
732:
727:generated from
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713:evaluated with
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166:H: useful heat
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695:
688:
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674:
667:
664:, the inverse
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60:
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52:
49:
34:
25:primary energy
15:
9:
6:
4:
3:
2:
1102:
1091:
1088:
1086:
1083:
1081:
1078:
1077:
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1052:
1049:
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1042:
1038:
1035:
1031:
1030:
1018:
1017:11250/2581526
1013:
1009:
1005:
1001:
997:
990:
986:
977:
974:
972:
969:
967:
964:
962:
959:
957:
956:Variable cost
954:
952:
949:
948:
942:
941:
933:
926:
918:
910:
863:
840:
817:
794:
767:
764:
742:
740:
733:
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719:
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705:
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684:
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670:
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649:
642:
628:
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619:
612:
605:
598:
591:
584:
580:
572:
550:
547:
545:
541:
534:
527:
517:
515:
510:
473:
455:
448:
444:
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430:
380:
371:
335:
327:
296:
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202:
173:
144:
118:
91:
68:
66:
48:
46:
42:
38:
30:
26:
22:
21:Carnot method
1080:Cogeneration
1032:Marc Rosen:
999:
995:
989:
951:Cogeneration
935:
928:
920:
913:
911:
864:
841:
818:
795:
768:
765:
743:
735:
728:
721:
714:
707:
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693:
686:
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672:
665:
658:
651:
644:
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629:
621:
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586:
582:
575:
573:
551:
548:
543:
536:
529:
525:
523:
511:
474:
456:
436:
381:
377:
336:
333:
297:
270:
259:
203:
174:
145:
119:
92:
69:
67:as follows:
54:
29:cogeneration
20:
18:
439:entropy law
256:Fuel factor
1074:Categories
982:References
514:waste heat
37:-emissions
556:· I = f
283:= 1 / (η
945:See also
234:) / ln(T
74:= (1 · η
1090:Pricing
800:· I = f
773:· I = f
495:x,total
479:x,total
459:x,total
443:entropy
427:th, eff
421:el, eff
411:= 1 / f
401:th, eff
394:= 1 / f
384:el, eff
120:Note: a
831:/I + η
592:, and
447:exergy
218:) / 2
105:) / (η
78:) / (η
41:exergy
912:with
756:) = f
657:into
417:with
364:with
352:PE,th
339:PE,el
159:= H/Q
150:= W/Q
927:and
897:/ (η
873:/ (η
850:· (η
839:/I)
827:· (O
804:· (O
785:· (η
748:· (η
699:and
685:and
606:and
507:x,th
501:x,el
491:with
487:x,th
483:x,el
413:F,th
396:F,el
368:PE,F
360:PE,F
356:F,th
347:PE,F
343:F,el
314:/ (η
300:F,th
273:F,el
266:F,th
262:F,el
226:= (T
210:= (T
175:and
131:with
97:= (η
19:The
1012:hdl
1004:doi
905:· η
901:+ η
893:· f
889:= η
881:· η
877:+ η
869:= f
858:· η
854:+ η
846:= f
835:· O
823:= f
812:· O
808:+ η
789:× O
781:+ f
777:· O
760:· O
752:· O
666:1/η
638:· O
634:= η
620:in
568:· O
564:+ f
560:· O
485:= η
481:= η
469:· η
465:+ η
461:= η
407:/ a
403:= η
390:/ a
386:= η
358:· f
354:= f
345:· f
341:= f
322:· η
318:+ η
310:= η
306:/ η
302:= a
291:· η
287:+ η
279:/ η
275:= a
128:= 1
124:+ a
113:· η
109:+ η
101:· η
86:· η
82:+ η
1076::
1010:,
1000:76
998:,
940:/I
934:=
925:/I
919:=
909:)
903:21
891:21
879:21
862:)
856:21
833:21
816:)
810:21
793:)
787:21
750:21
741:.
675:12
668:21
647:21
636:21
585:,
542:.
471:th
463:el
445:,
409:th
405:th
392:el
388:el
326:)
324:th
316:el
308:th
304:th
295:)
293:th
285:el
281:el
277:el
252:.
242:)
240:RF
238:/T
236:FF
232:RF
230:-T
228:FF
216:RF
214:+T
212:FF
185:/T
157:th
148:el
141:th
135:el
126:th
122:el
117:)
115:th
107:el
103:th
95:th
90:)
88:th
80:el
76:el
72:el
61:th
57:el
33:CO
1014::
1006::
938:2
936:O
931:2
929:η
923:1
921:O
916:1
914:η
907:2
899:1
895:i
887:2
883:2
875:1
871:i
867:1
865:f
860:2
852:1
848:1
844:i
842:f
837:2
829:1
825:1
821:i
819:f
814:2
806:1
802:1
798:i
796:f
791:2
783:1
779:1
775:1
771:i
769:f
762:2
758:2
754:2
746:1
744:f
738:1
736:f
731:2
729:O
724:1
722:O
717:2
715:f
710:2
708:O
703:2
701:f
696:1
694:f
689:2
687:O
682:1
680:O
673:η
671:=
661:1
659:O
654:2
652:O
645:η
640:2
632:1
630:O
624:2
622:O
617:1
615:O
610:2
608:f
603:1
601:f
596:2
594:O
589:1
587:O
583:I
578:i
576:f
570:2
566:2
562:1
558:1
554:i
552:f
544:f
539:2
537:O
532:1
530:O
526:I
505:η
499:η
493:η
477:η
467:c
457:η
452:x
425:η
419:η
399:η
382:η
366:f
350:f
337:f
320:c
312:c
298:f
289:c
271:f
246:s
224:s
222:T
208:s
206:T
199:s
197:T
193:i
191:T
187:s
183:i
179:c
177:η
170:F
168:Q
161:F
155:η
152:F
146:η
139:a
133:a
111:c
99:c
93:a
84:c
70:a
35:2
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