Valorization of low-temperature heat: impact of the heat sink on performance and economics

Transcription

1 nd European Conference on Polygeneraton th March- st Aprl, arragona, Spa Felx Zegler Valorzaton of low temperature heat: mpact of the heat sk on performance and economcs pages nn-mm Valorzaton of low-temperature heat: mpact of the heat sk on performance and economcs Felx ZIEGLER echnsche Unverstät Berl, Insttute of Energy Engeerg, K Marchstraße 8, D-587 Berl, Germany Abstract Low-grade heat s avalable everywhere; consequently, the valorzaton of ths heat seems to be attractve terms of economcs. However, rrespectve of the form of energy whch s produced, any valorzaton comes along wth the producton of another stream of waste heat wth even lower value. he dumpg of ths reject heat often turns to be the ssue whch determes cost. hs presentaton wll elaborate on the fluence of the heat sk temperature both on converson effcency and cost. It frst wll gve a frame on a very generc level. hen, an example wll be gven especally for an absorpton coolg system. Keywords Frst cost, operatg cost, thermodynamcs, temperature, characterstc equaton Introducton Valorzaton of low-temperature heat s a broad area. It covers heat recovery by compresson heat pumps, sorpton heat pumps, and heat transformers, as well as converson to cold or mechancal energy. he means to do so are abundant as well: conventonal converson systems use thermodynamc mono-flud cycles (closed steam cycles, open steam cycles, or even gas cycles), or dual-flud cycles such as sorpton coolg processes or sorpton power processes. Some optons whch are state of the art, or techncally feasble, or at least dscusson, are lsted able. able : Optons for valorzaton of low-temperature heat Mono-flud Mult-flud No flud Ar cycle # Ranke cycle Absorpton cycle #,, 5 # Steam jet cycle Adsorpton cycle #,, 5 Pelter cooler #, 5 Strlg cycle Chemcal cycle #,, 5 Magnetocalorc cooler #, Vapor compresson Hybrd sorpton cycle # hermoelectrc generator # cycle Ranke sorpton cycle # #,, 5 Vulleumer cycle # # # Correspondg author: felx.zegler@tu-berl.de, +9 87, +9 5

2 nd European Conference on Polygeneraton th March - st Aprl arragona, Spa he numbers (#,, etc.) whch are lsted able, refer to Fgure, whch the nature of the duty to be fulflled by these cycles s depcted on a temperature scale. he frst am of ths paper s to gve an order to the sad optons and then to elaborate on the mpact of the heat sk, and that of the other temperatures, too. It has to be dstgushed between the mpact on power densty, effcency, and cost. hs wll be done usg generc equatons. In a more techncal approach, absorpton chllers wll be dscussed more detal. Generc thermodynamc approach Optons for revalorsaton hese optons could be dscussed terms of exergy, but we keep usg energy and temperature as descrbg parameters. Frst two deftons or clarfcatons are order: low-temperature heat s heat wth a temperature above ambent (at least two tmes the temperature gradent across a heat exchanger!). he heat sk s defed by the ambent, as well. It may clude humdty, so t may be the dry bulb temperature or the wet bulb temperature. In order not to complcate thgs, ths paper we do not dstgush ths. Fgure schematcally shows the thermodynamc optons; the only scale used s a temperature scale wth temperature rsg from bottom to top. emperature of heat flow work: #: compresson heat pump #: heat-drven heat pump #: power cycle #: heat transformer #5: heat-drven refrgerator drve: upgraded: source: sk: cold: # # # # #5 Fgure : Generc optons to valorse heat of temperature Each box denotes another generc converson process. he words "" or "" are related to the energy flow on the respectve temperature level, enterg or leavg the devce. Box # depcts a compresson heat pump whch upgrades heat from to wth put of mechancal work.

3 nd European Conference on Polygeneraton th March - st Aprl arragona, Spa Process # does the same upgradg, albet wth usg heat of temperature as drve. It depcts a heat drven heat pump. Box # stands for a power cycle whch works between and. Box # represents a heat transformer cycle whch upgrades heat from to wth degradg part of the heat to the heat sk at. Box #5, fally, shows a heat drven refrgerator. So, summarsg, #, #, and # are heat pumps of dfferent nature. In any case, the low-temperature heat source at conveys heat to the box. Energy flows at a hgher level (# to ) or flows at a lower level (#5). he focus of ths paper should be on the processes # to #5 because they have to reject heat to a heat sk at a temperature. However, we wll dscuss processes # and # also. Performance able gves the defton of effcency or and an equaton to determe t the most smple way, whch s to calculate the reversble lmt and multply ths wth a rough measure for thermodynamc qualty, g. A numercal example s gven also, just for orentaton. hs example uses the temperatures from able and a qualty of g=.5. able : Performance of generc valorsaton processes Effcency Example # Work-drven heat pump W g.9 # Heat-drven heat pump g. # Power cycle W g. 6 # Heat transformer g.9 #5 Heat-drven refrgerator g. All these equatons are well-known and wll not be dscussed here. he senstvty of the effcences on the temperatures wll be vestgated by usg the dervatves. able gves the dervatves wth respect to all the relevant temperatures, normalsed wth the respectve effcency. From these equatons t s obvous that, e.g., the mpact of the source temperature,, on the heat pump s always somewhat larger than that of the sk,, the work drven case (#), whereas t s smaller the heat drven case #. For a power plant (#) the mpact of the heat sk,, always s somewhat larger than that of the heat source,. In the case of the heat transformer (#) t s the other way round, aga. hs s understood easly, as a shft the termedate temperature changes temperature lft and temperature thrust of the process at the same tme. For the same reason, the mpact of the heat sk the case of refrgeraton (#5) s the largest one. In order to quantfy these fdgs, the dervatves accordg to able are plotted agast the heat sk temperature for a set of other temperatures (see able ) Fgures to 6. he absolute value of the dervatves s shown. he dashed les dsplay negatve dervatves.

4 nd European Conference on Polygeneraton th March - st Aprl arragona, Spa able : Relatve change or effcency due to a change one temperature or, dervatve wth respect to... # # # # #5 able : Set temperatures accordg to Fgure emperature level Value [ C Dervatve wth regard to [ C Fgure : Relatve change of the of a compresson heat pump (#) wth temperatures

5 nd European Conference on Polygeneraton th March - st Aprl arragona, Spa he mpact of the temperatures on the of a compresson heat pump (Fgure ) between and s the larger, the smaller the temperature lft, ( - ), to be accomplshed s. It s the order of some %/K for realstc temperatures. he dfference between the mpact of the two temperatures s margal. Dervatve wth regard to [ C Fgure : Relatve change of the of a heat drven heat pump (#) wth temperatures For heat drven heat pumps (#, Fgure ), the mpact of the temperatures on the s the same order of magntude as for a compresson heat pump. However, the fluence of the drvg temperature s the smallest and does not vary much. For termedate temperatures, the mpact of the sk s the strongest, as dscussed before. Dervatve wth regard to [ C Fgure : Relatve change of the effcency of a power staton (#) wth temperatures 5

6 nd European Conference on Polygeneraton th March - st Aprl arragona, Spa For a power staton whch s operated by low temperature heat (#, Fgure ), the mpact of the temperatures s reverse as compared to Fgure, naturally. Dervatve wth regard to [ C Fgure 5: Relatve change of the of a heat transformer (#) wth temperatures An unusual result s found for the heat transformer (Fgure 5): the relatve mpact of the hgh temperature heat sk temperature does not change wth temperature. herefore, t s comparably small for small heat source temperatures, but for hgh heat source temperatures t becomes mportant. hen however, all dervatves are the order of %. 8 6 Dervatve wth regard to [ C Fgure 6: Relatve change of the of a heat drven refrgerator (#5) wth temperatures 6

7 nd European Conference on Polygeneraton th March - st Aprl arragona, Spa he most mportant result may be found Fgure 6 for the refrgerators (#5): all dervatves are ab a factor of larger than for the other processes (be aware that the scale of the ordate s doubled!). So, t may be stated that waste heat drven chllers are most senstve to the respectve temperatures. he mpact of the heat sk temperature s by far the largest. We wll elaborate on these fdgs a later chapter. Before we do so, we use the equatons from above for another short dscusson wth the focus on frst cost. Impact on frst cost It s very well known that low effcency drves operatg cost. However, low effcency also drves frst cost: the amount of heat whch has to be put through an energy converson system, of course, depends on ts effcency. Especally processes whch are drven by lowtemperature heat the cost for heat exchange becomes a decsve ssue. In able 5 equatons for a specfc cost rato are gven whch s defed as the rato of the overall heat turnover to the useful energy (whch may be heat or work): () USE hese equatons may be combed wth the equatons for effcency able ; then the dervatves able can be appled. hs wll not be exemplfed here because t s a straghtforward exercse. It shall be suffcent to state that those temperatures whch have a large mpact on effcency wll have a large mpact on cost, also. able 5: Specfc cost rato: relatve heat turnover # Work-drven heat pump Relatve heat turnover Example (see able ).8 # Heat-drven heat pump # Power cycle W # Heat transformer #5 Heat-drven refrgerator It s terestg to note that the relatve heat turnover the case of the heat drven heat pump (#) does not depend on the. In all other cases, the turnover of heat can only and wll be reduced by creasg effcency. he numercal examples drastcally show the problem of producg power from low-temperature heat: as the effcency of the power plant wll be relatvely small, the turnover of heat as compared to the power put wll be large. he heat pumps (# and ), from ths pot of vew, deftely show the best result. So we can conclude at ths stage that valorzaton of waste heat by pumpg t to a useful, hgher temperature level may be the most attractve opton. 7

8 nd European Conference on Polygeneraton th March - st Aprl arragona, Spa Absorpton chllers he dscusson up to now, of course, suffers from the fact that the specfc features of the processes whch are used do not show up the fundamental thermodynamc relatonshps. herefore, order to check the valdty, a more appled approach wll be shown now. he performance of absorpton chllers can be presented most easly wth usg the characterstc equatons. he coolg power,, as well as the drvg heat put,, can be represented as a lear functon of a temperature functonal, the characterstc temperature functon t, whch, turn, depends on the mean temperatures of the external heat carrers, drvg heat t, coolg water t, and chlled water t : t at () bt ct S M t () S M t () he beneft of ths representaton s the fact that the mpact of the temperatures s drectly seen. As an example a sgle-effect LBr absorpton chller wth a nomal coolg capacty of kw shall be used. In order to brg cost to the play the heat flows are normalsed by a frst cost of, for ths devce. hs, of course, s not the real prce of the chller but t s the rght order of magntude. It renders a specfc prce of /kw of coolg capacty. he costspecfc heat flows (W/ ) then are gven by: q s m t (5) q s m t (6) he consequently s the rato q q s s m m t t (7) he coeffcents are gven able 6 [. he coeffcent b gves the mpact of the heat sk. It, obvously s the largest one, and t s ab double the sze as the others. he same order of magntude resulted from the generc approach (Fgure 6) also. he respectve characterstc curves are shown Fgure 8. he vertcal le marks the desgn pot of the chller wth a coolg capacty of W/ at a characterstc temperature dfference of ab K. Any changes temperatures may be seen as fluencg coolg power or specfc cost, respectvely. able 6: Coeffcents for characterstcs of an absorpton chller Coeffcent a b c s m s m Value.8.5.9W/.W/ K.W/.5W/ K 8

9 q [W/, nd European Conference on Polygeneraton th March - st Aprl arragona, Spa Nomal pot q,5 q, t [K Fgure 7: Characterstc curves of a sgle-effect absorpton chller In order to see the fluence of the temperatures on heat flows and the, aga the dervatves have to be calculated. he results for the heat flows are gven able 7. he mpact of the temperatures on the drvg heat are stronger than on the coolg power. he fluence of the heat sk temperature s the largest of the three. able 7: Dervatves of the specfc heat flows wth respect to the temperatures q a m.76 -b m -.5 c m. t q a m.9 -b m -.8 c m.5 t he mpact of the temperatures on the heat flows s almost lear, but t s a non-lear mpact on the. Moreover, the relatve mpact s more terestg than the absolute one. herefore, the relatve fluence of each temperature on relatve coolg capacty and s plotted agast the cost-specfc coolg power q Fgures 8 and 9. Aga, a negatve value of the dervatve s dcated by a dashed le. he nomal pot s marked by a vertcal le. he mpact of the temperatures on specfc power s the order of 5%/K (drvg heat), 8%/K (chlled water), and over %/K (heat sk) the nomal pot. It creases strongly when the specfc power s reduced. hs happens the case of part load, or the case of the characterstc temperature dfference beg small. In ths case, the requred heat exchange area s relatvely large, the chller wll be expensve, and the senstvty on the temperatures wll be hgh. 9

10 nd European Conference on Polygeneraton th March - st Aprl arragona, Spa q q t 5 Nomal pot Dervatve wth regard to... t 5 t,,6,,,8 q [W/ t Fgure 8: Senstvty of the specfc coolg power on the temperatures he mpact on the s sgnfcantly less, as long as the specfc load s not too small. hs can be seen Fgure 7 as well as Fgure 9, where the mpact of the temperatures on the s plotted agast the specfc coolg load, aga. Once more, the dervatve wth respect to the heat sk temperature, t, s the largest. 5 t Dervatve wth regard to... t t Nomal pot t,,6,,,8 q [W/ Fgure 8: Senstvty of the on the temperatures

11 nd European Conference on Polygeneraton th March - st Aprl arragona, Spa Concluson From the fundamental relatonshps whch have been presented ths communcaton t can be concluded that the mpact of the temperature and nature of the heat sk on performance and economcs the feld of valorzaton of low-temperature heat s predomant - except, of course, the case of smple heat pumps. In all other cases the heat flow to ths sk accounts for a large fracton of the energetc turnover. For the sake of effcency, the drvg temperature dfference must be small whch turn necesstates large heat transfer areas. Heat pumps seem to be the most cost-effcent devces for valorzaton of low-temperature heat. Of course a rsg ambent or heat sk temperature any case reduces effcency. hs effect s especally large for heat drven coolg maches. hese devces have been studed more detal usg the approach of the characterstc functons. he mpact of the heat sk temperature on heat flows (capacty) and performance () s ab twce as large as that of the other temperatures. It can be stated that the research whch s dedcated to ths feld does not match the overall mportance wth the area of energy engeerg. Nomenclature a,b,c: Coeffcents [- : Coeffcent of Performance [- g: hermodynamc qualty [- M: Coeffcent [kw/k m: Coeffcent [W/ K : Heat flow [kw q: Specfc heat flow [W/ S: Coeffcent [kw s: Coeffcent [W/ : emperature (process) [K t: emperature (heat carrer) [K W: Mechancal power [kw : Effcency [- : Relatve heat turnover [- Reference [ Kühn, A., Zegler, F. 5, "Operatonal results of a kw absorpton chller and adaptaton of the characterstc equaton", Proceedgs of the Internatonal Conference Solar Ar Condtong, October 5, Bad Staffelste.