Effect of Internal Heat Recovery in Ammonia-Water Absorption Cooling Cycles: Exergy and Structural Analysis

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1 Int. J. of Thrmodynamcs Vol. (No. ), pp. 7-7, March 00 ISSN ffct of Intrnal Hat Rcovry n mmona-watr bsorpton oolng ycls: xrgy and Structural nalyss tr Bor *, Brhan Hagos brslass, Marc Mdrano, Mqul Nogués, partmnt of Mchancal ngnrng, Unvrsty of Rovra Vrgl, Tarragona, Span hon: (+) 77 -mal: tr.bor@urv.nt; Brhan.brslass@urv.nt, R Innovacó oncurrnt, Unvrstat d Llda Llda, Span -mal: mmdrano@d.udl.cat; mnogus@d.udl.cat bstract Frst and scond law analyss hav bn conductd for thr low tmpratur drvn ammona-watr absorpton coolng cycls wth ncrasng ntrnal hat rcovry. Basd on th rsults of xrgy analyss th structural analyss has bn achvd. Th obtand offcnts of Structural Bonds (SB) consdr how th rrvrsblty of th whol cycl s affctd by a chang n th rrvrsblty rlatd to an ffcncy mprovmnt of a sngl componnt. Trnds for th dffrnt confguratons ar smlar, whl quanttatv dffrncs among th man hat xchangrs ar consdrabl. Th hghst valus of th SB ar found for th rfrgrant hat xchangr. lso th vaporator, th condnsr, th gnrator and th absorbr show valus hghr than unty. Th lowst SB s ar obtand n th soluton hat xchangr. In gnral, SB s dcras wth ncrasng ffcncy. That mans that for vry ffcnt hat xchangrs, a furthr mprovmnt looks lss attractv. Th dphlgmator s an xcpton as t shows a sngularty of th SB valu du to ts complx ntractons wth th othr componnts. Onc th SB s ar obtand for th man componnts, thy can b usd n th structural mthod of th thrmoconomc optmsaton. Ths mthod nabls us to fnd th optmum dsgn of a componnt n a straghtforward calculaton. Kywords: bsorpton cycl, ammona-watr, xrgy analyss, structural analyss.. Introducton ombnng thrmodynamcs and conomcs, th thrmoconomc or xrgoconomc analyss can b achvd (Kotas, ; Bjan t al., ; l-sayd, 00). Th objctv of xrgoconomc optmzaton s th mnmzaton of th total cost, manly composd of captal and nrgy costs. In th fld of rfrgraton thrmoconomc analyss was appld ntally to comprsson cycls (Wall, 8; ntc d'ccada t al., 8; ngç t al., ; Frrr t al., 00; ntc d'ccada t al., 00; Zhang t al., 00) and latr to absorpton cycls (Tozr t al., ; Sahn t al., 00; Msra t al., 00; Msra t al., 00; Msra t al., 00; KzIlkan t al., 007). On mthodology usd n xrgoconomc optmsaton s th structural mthod ntroducd by Byr (70 and 7). It s basd on structural coffcnts, whch show how local rrvrsblts n th componnts affct th ovrall rrvrsblty rat of th cycl. Th coffcnt of structural bonds (SB) of a componnt k, whch s obtand by varaton of a paramtr x, s dfnd as SB k; I = t I k x= var whr I s th rrvrsblty rat of componnt k, and k I t s th rrvrsblty rat of th whol cycl. Structural coffcnts show how th rrvrsblty of th whol cycl and a sngl componnt ar rlatd. If a slght dcras n th rrvrsblty of on componnt du to an ncrasd * orrspondng author () ffcncy causs a sgnfcant mprovmnt n th total rrvrsblty of th cycl (hgh SB), t wll b ws to put much of th dsgn ffort n mprovng th ffcncy of ths componnt. Othrws (low SB), an mprovmnt of th ffcncy of th consdrd componnt s not worthwhl. Ths coffcnts can hlp us to dtrmn for on slctd componnt of th systm ts optmum ffcncy, for whch a mnmum total cost s achvd (Kotas, ). In th prsnt study, ths mthod wll b appld to th analyss of absorpton cycls. Th analysd cycls ar ammona-watr absorpton coolng cycls wth ncrasng ntrnal hat rcovry. smlar approach has bn appld by Sözn (00) for an ammona-watr rfrgraton cycl. Modllng starts wth th frst law analyss, followd by th xrgy analyss (Karakas t al., 0; tar t al., ; Bst t al., ). Onc th rrvrsblts of th componnts and th whol cycl ar valuatd, th coffcnts of structural bonds can b valuatd. ompard to a formr study (Bor t al., 00), hr th SB s ar not constant, but thr dpndnc on th ffcncs s shown and thr bhavour s quantfd and compard for dffrnt cycl confguratons. Ths SB s can b usd n th structural mthod of xrgoconomc optmsaton (Byr, 7). Th fnal purpos s th dsgn of mor cost-ffctv absorpton cycls. Th applcaton of th SB s s dscrbd n KzIlkan t al. (007) and wll b summarzd brfly. Mor dtals can b found n Kotas (). Th optmum ffcncy spcfcaton for a componnt wll b dtrmnd n ordr to obtan th mnmum annual Vol. (No. ) / 7

2 opratng cost. Ths opratng cost s composd manly of th ful and captal costs. n c c c ( x ) = t c ( x ) + a ( x ) + b () t op n n l = Th frst trm of th rght hand sd rprsnts th ful cost, th scond on th captal nvstmnt amortsaton and th thrd on othr cost factors that ar not affctd by th optmsaton, for xampl mantnanc costs. Th captal rcovry factor s gvn by n c ( + ) a = n () ( + ) t th optmum pont t c I k c k c SB k, = a () x x op n quaton () dpnds only on paramtrs of componnt k, whch s optmsd. Th ntracton wth th systm s takn nto account by th SB. I k / x dscrbs th ffct of th ffcncy paramtr x on th rrvrsblty of c th componnt. k / x taks nto account th dpndnc of th componnt cost on x. Both paramtrs dpnd on th ffcncy of th analysd componnt. From quaton () th ffcncy that rsults n th lowst opratng cost t can b obtand (KzIlkan t al., 007).. scrpton of th cycls For ths study an ammona-watr absorpton cycl has bn slctd (Fgur ). Basc componnts ar th absorbr (), th condnsr (), th gnrator (), and th vaporator (). Th cycl s compltd by th soluton hat xchangr (), th dphlgmator () and th rctfcaton plats (R). To obtan th ncssary prssur changs, th cycls nclud th soluton pump (), th rfrgrant xpanson valv () and soluton xpanson valv (). For cycl I, th soluton crculats btwn th absorbr, whr th rfrgrant s absorbd at low prssur, and th gnrator, whr th rfrgrant s dsorbd at hgh prssur (stat ponts to ). Th strong soluton lavs th absorbr (), s prhatd n th soluton hat xchangr (), and ntrs th rctfcaton column. Th column has thr thortcal stags, whch s suffcnt n coolng applcatons (Rorz t al., 00). Th fd ntrs n cntral plat two. Vapour and lqud n qulbrum lav plat two towards plats on and thr, rspctvly, whl saturatd lqud from plat thr and saturatd vapour from plat on ntr plat two. Tmpratur and concntraton of ammona n th vapour ncras from plat on to plat thr. Th gnrator acts as th rbolr of th rctfcaton column. Th wak soluton () lavs towards th absorbr. In th dphlgmator, th ncssary lqud rflux s obtand, whl th rst of th vapour () condnss compltly n th condnsr (0). Th condnsat xpands n th rfrgrant throttlng valv, causng partal vaporsaton (), and ntrs th vaporator. u to th watr contnt of th mxtur, th tmpratur ncrass durng th vaporsaton procss as th lqud contans lss and lss ammona, whch s th mor volatl componnt. Vaporsaton n th vaporator s only partal, as total vaporaton would l rqur too larg of a tmpratur gradnt. Th cycl s closd whn th vapour wth a small lqud fracton () ntrs th absorbr. Strams to ar th xtrnal hat transfr fluds (n all cass ths s watr), whch dlvr or xtract th hat to or from th cycl. 0 0 ycl I 0 0 RH ycl II 0 R 0 RH 7 7 ycl III R R Fgur. mmona-watr absorpton cycls wth ncrasng ntrnal hat rcovry. ycl II s smlar to ycl I xcpt for th rfrgrant hat xchangr (RH). In ycl II aftr lavng th condnsr th condnsat (0) s subcoold () n ordr to supply hat for th partal vaporsaton n th vaporator (). n addtonal fatur of ycl III s a hat xchang btwn th strong soluton aftr th soluton pump () and th dphlgmator (). rhatng th strong soluton (7) lmnats th us of coolng watr n th rctfr.. Mthodology of th smulaton computr cod for smulatng th cycl has bn stablshd usng th ngnrng quaton Solvr S program. roprts for ammona watr ar gvn by Tllnr-Roth and Frnd (8). Typcal coolng opraton condtons ar assumd as follows: vaporator coolng capacty 000 kw Tmpraturs: hlld watr nlt/outlt () /º oolng watr nlt/outlt (paralll flow through and ) 7º/º 8 8 / Vol. (No. ) Int. ntr for ppld Thrmodynamcs (IT)

3 Hot watr nlt () 0º Mnmum tmpratur dffrnc n th dphlgmator K Mnmum tmpratur dffrnc n th rst of hat xchangrs K Th hot watr outlt tmpratur n th gnrator s adjustd to mnms th msmatch of hat capacty rats (product of mass flow and spcfc hat) n th gnrator. Ths mans that th tmpratur dffrncs btwn th hot and cold strams ar th sam on th hot and th cold sds of th gnrator (Kotas, ). In th sam way th dgr of vaporaton n th vaporator s chosn to obtan th sam tmpratur dffrnc at th nlt and outlt of th vaporator. Th man assumptons ar: Stady stat. Hat losss ar not consdrd. rssur losss ar not consdrd. Th rfrgrant lavng th condnsrs s saturatd lqud. Th mass xchang ffcncs n absorbr and gnrator ar 0.. Th lqud and vapour lavng th adabatc rctfcaton plats ar n qulbrum. Th soluton and rfrgrant valvs ar adabatc. Th pump ffcncy s 0.. Modlng starts wth a frst law analyss. Stady stat mass and nrgy balancs for th componnts of th cycls ar stablshd as follows: lobal mass balanc: Σ = Σ () m Mass balanc for ammona: Σ z = Σ z () nrgy balanc: + = 0 Q W mh mh (7) For adabatc componnts th nrgy balanc s: Σ h = Σ h + W (8) Th mchancal powr only appars n th nrgy balanc of th pump. Th mass xchang ffcncy for absorbr and gnrator taks nto account that thrmodynamc qulbrum s not totally rachd at th outlt (tar t al., ) and s dfnd as: ε (z z ) ral m = () (z z ) qulbrum Th coffcnt of prformanc (O) s dfnd by th coolng output dvdd by th drvng hat nput. (h O = m (h 7 8 h h 7 ) ) (0) Th drvng hat s dlvrd by th hot watr. Th subscrpts n qns (0) and () corrspond to th numraton of stat ponts prsntd n Fgur. Th gnral xrgy balanc s gvn by Kotas (): = T0 0 ( )Q W + I () T onsdrng componnts as adabatc, th abov quaton can b smplfd as Σ = Σ + W + I () Spcfc xrgy (q. ) consdrs only th physcal xrgy (Jonsson t al., 000). Th chmcal xrgy of watr and ammona cancls out n th xrgy balancs as ntrng and lavng quantts ar th sam (Kotas, ). Mxng ntropy has alrady bn takn nto account n th calculaton of th ntropy of th mxtur = h-h - T (s-s ) () Th proprts ndcatd wth th subscrpt 0 rfr to th nvronmntal stat, whch s takn as º and bar. Usng xrgy flow rats = m () t follows Σ = Σ + W + I () Irrvrsblts ar obtand from th xrgy analyss. Th rsultng quatons for th dffrnt componnts ar gvn by Karakas t al. (0). Th xrgy ffcncy s dfnd as th usful xrgy output dvdd by th rqurd xrgy nput. For th cycl th xrgy nput s gvn by th rducton of th xrgy flow of th xtrnal hatng flud n th gnrator and th pump work. Th xrgy output producd n th vaporator s gvn by th ncras n th xrgy flow of th chlld watr. Ψ = ( 7 8 ( ) + 7 ) W pump () Th output data obtand ar: Th prssurs, tmpraturs, concntratons, mass flows, nthalps, ntrops and xrgs of ach stat pont of strams. Th thrmal or, n th cas of th soluton pump, mchancal powr and rrvrsblty rat of th man componnts. Th O and th xrgtc ffcncy. Onc th rrvrsblts of th componnts and th whol cycl hav bn dtrmnd, a paramtrc study can b achvd. Th U valus n Tabl corrspond to mnmum tmpratur dffrncs ΔT mn n th hat xchangrs for th bas cas takn as K, xcpt for th dphlgmator, whr t s K. U valus for all componnts ar mantand constant (Bor t al., 00), xcpt for th on whch s analysd. For ths slctd componnt, th mnmum tmpratur dffrnc s vard, whch rsults n a varaton of U. Th varaton of ΔT mn for any componnt s typcally btwn and 0 K, f opraton s fasbl, xcpt for th dphlgmator whr varatons wr achvd btwn and 0 K. Ths rang s lmtd by th opratng condtons n ordr to avod hgh soluton flow ratos of opraton wth low prformanc. s a rsult, th nflunc of th hat transfr ffcncy of ths componnt on ts own rrvrsblty and also on th rrvrsblty of th whol cycl s valuatd. Ths data can b usd to dtrmn th SB (qn. ) for a gvn st of Int. J. of Thrmodynamcs (IJoT) Vol. (No. ) /

4 Tabl : U Valus orrspondng to th Fxd ΔT mn n th Bas as. omponnt ycl I II III U [kw/k] RH opratng condtons, whch s th man objctv of ths analyss.. Rsults. Frst and scond law analyss Rsults of th nrgtc analyss for th dffrnt stat ponts ar prsntd n Tabl, and. Th corrspondng thrmal or mchancal powr of th componnts ar gvn n Tabl. Th xrgy balancs hav bn achvd for th dffrnt componnts n ordr to obtan th rrvrsblts (Tabl ). For all cycls, th hghst rrvrsblts wr found n th soluton hat xchangr () followd by th absorbr (), th vaporator () th condnsr () and th gnrator (). Th rrvrsblts of th soluton xpanson valv () and th dphlgmator () wr lss mportant. Th rrvrsblty of th rfrgrant xpanson valv () s consdrably rducd by th ntroducton of th rfrgrant hat xchangr (RH). Th rfrgrant hat xchangr (RH) and th rctfcaton (R) contrbut lss to th rrvrsblts. Irrvrsblts n th adabatc rctfcaton plats wr low and causd by mxng of strams wth dffrnt tmpraturs and concntratons. Tabl : Opratng ondtons for ycl I. Stat T z h s ont [] [bar] [kg kg - ] [kg s - ] [kj kg - ] [kj kg - K - ] [kj kg - ] [kw] Tabl : ondtons for ycl II. Stat T z H s ont [] [bar] [kg kg - ] [kg s - ] [kj kg - ] [kj kg - K - ] [kj kg - ] [kw] Tabl : Opratng ondtons for ycl III. Stat T p z h s pont [] [bar] [kg kg - ] [kg s - ] [kj kg - ] [kj kg - K - ] [kj kg - ] [kw] Tabl : Thrmal or Mchancal owr for a Fxd oolng apacty. omponnt ycl I II III owr [kw] RH / Vol. (No. ) Int. ntr for ppld Thrmodynamcs (IT)

5 omponnt Tabl : Irrvrsblts. ycl I II III Irrvrsblty [kw] RH R Th man sourc of rrvrsblts s th tmpratur btwn hot and cold strams. Irrvrsblts for ar hgh du to th low gnrator tmpratur. Th concntraton dffrnc btwn wak and strong soluton s small and soluton flow rats larg. Rsults agr wth Bst t al. (), xcpt n th gnrator. In our cas th gnrator shows lowr rrvrsblts, as th msmatch of th hat capacty rats has bn mnmzd. Hat ntgraton affctd th rrvrsblts n th followng way. Th man ffct of th rfrgrant hat xchangr (componnt RH n ycls II and III) was a strong rducton n th rrvrsblty of th rfrgrant xpanson valv du to th chang n workng condtons. Th rfrgrant valv nlt tmpratur (stat ponts 0 and for ycls I and II, rspctvly) dcrasd from 7º to about.8º, thus rducng th nthalpy h n th vaporator nlt from 8 kj/kg to about kj/kg. Ths ld to an ncras n th nthalpy dffrnc n th vaporator and, for a fxd coolng powr, th rfrgrant mass flow dcrasd from 0. kg/s to 0.87 kg/s. onsquntly, th soluton flow rat also dcrasd. Th rducton of th rrvrsblty n th rfrgrant valv s gratr than th rrvrsblty addd by th rfrgrant hat xchangr. Th rrvrsblty of absorbr () dcrasd bcaus th vapour () ntrd wth lss dffrnc n tmpratur wth rgard to th soluton () and th mxng took plac at a mor unform tmpratur. Bcaus of th rducton n th mass flows, all rrvrsblts wr gnrally smallr. Th combnd soluton prhatr and dphlgmator (componnt n ycl III) rrvrsblty n th soluton hat xchangr was also rducd by prhatng of th soluton. Th strong soluton ntrd th soluton hat xchangr at.º (T 7 ) compard to.º (T ) n ycl II. t th sam tm, howvr, T ncrasd from 7.º n ycl II to 0.º n ycl III, and thus ncrasd th absorbr rrvrsblty. Thus, th rducton of rrvrsblty n th dphlgmator and soluton hat xchangr s partally compnsatd for by th ncras n th absorbr. Ths rductons n rrvrsblts du to th bttr hat ntgraton mprovd th O and th xrgtc ffcncs Ψ of th cycls (Tabl 7). Th rfrgrant hat xchangr had a gratr ffct (+%) than th soluton prhatng (compard to ycl II lss than %). Tabl 7: nrgtc (O) and xrgtc ffcncs (Ψ). ycl I II III O Incras of O compard to ycl I (%) Ψ Incras of Ψ compard to ycl I (%) rassmann dagrams Th xrgy flows and rrvrsblts can b rprsntd n graphcal form. Th rassmann dagram (Szargut t al., 88; Kotas, ) can b usd to llustrat cyclc procsss and thr componnts wth thr corrspondng rrvrsblts, th xrgy flows and th rcrculaton of xrgy n th cycl. Th nlt xrgy flow s on on sd of ach componnt, and n th componnt tslf, part of ths xrgy flow s dgradd du to rrvrsblts. On th othr sd of th componnt xrgy flows ar lavng. ach componnt rprsnts a graphcal xrgy balanc and shows how part of th xrgy nput s lost n th succssv nrgy transformaton n th cycls. Th wdths of th lns ar proportonal to thr xrgy flow. Ths typ of dagram alrady has bn mployd for absorpton cycls (nand t al., 8; Szargut t al., 88; Jong t al., 00). Th thrmal xrgy flows Q corrspond to th chang n th xrgy flow rat of th xtrnal fluds. Fgur rprsnts th xrgy flows of ycl I. Th dscrpton starts wth th xtrnal hat and xrgy transfr. Th xrgy nput Q rprsnts th rducton n hot watr xrgy and th xrgy output Q rprsnts th ncras n chlld watr xrgy. Th xrgy flows Q, Q and Q ar dsspatd by th coolng watr. Q 0 W Q Q Q L - V - Q Fgur. rassmann dagrams of ycl I. Wth rgard to th cycl tslf, on th rght sd s stuatd th soluton crcut wth th strong soluton (ponts to ) and th wak soluton (ponts to ). Th xrgy nput to th cycl s gvn by th thrmal xrgy Q suppld to th gnrator and th pump work W. Ths xrgy s usd to ncras th xrgy of th soluton (ponts to ) and gnrat vapour flow V -. In th dphlgmator thrmal xrgy Q s dsspatd and a rflux L - s cratd. In Fgurs, and th xrgy dstructon n th rctfr s ncludd n th xrgy dstructon n th gnrator and th dphlgmator n ordr to smplfy th fgur. Th vapour (pont ) ntrs th condnsr, whr agan thrmal Int. J. of Thrmodynamcs (IJoT) Vol. (No. ) /

6 xrgy Q s dsspatd. Th rfrgrant passs through th rfrgrant xpanson valv and ntrs th vaporator, whr th usful thrmal xrgy output Q s producd. Th vapour (pont ) ntrs th absorbr, whr th rfrgrant jons th soluton crcut and th thrmal xrgy Q s dsspatd. Th strong soluton xrgy s ncrasd n th soluton hat xchangr (ponts to ) whl th wak soluton xrgy s rducd (ponts to ). It can also b obsrvd that th rrvrsblts n th soluton pump and soluton xpanson valv ar rlatvly small. In th rassmann dagram for ycl II (Fgur ), th rfrgrant hat xchangr has bn addd. nw loop for th rfrgrant flow s thrfor addd on th lft hand sd. Th lns rprsntng th xrgy flows ar slghtly narrowr than for ycl I du to th rducton n th mass flows. In th rassmann dagram for ycl III (Fgur ), th coolng of th dphlgmator by coolng watr s rplacd by a hat xchang, whch prhats th strong soluton. Th dsspaton of th thrmal xrgy flow Q s thrfor lmnatd. Th vapour flow V - and th strong soluton should ntr on th sam sd but n ordr to obtan a clarr prsntaton an xcpton has bn mad n ths cas. Q Q 0 RH Q Q W Q Q L - V - Q Fgur. rassmann dagrams of ycl II. 0 RH W Q L - 7 V - Q Fgur. rassmann dagrams of ycl III.. Structural analyss Onc th rrvrsblts ar obtand, t can b chckd how a chang of th rrvrsblty of on componnt affcts th rst of th cycl. In th componnt, whr th mnmum tmpratur dffrnc s modfd, th rrvrsblty ncrass wth a hghr mnmum tmpratur dffrnc. For th othr componnts th rrvrsblts can ncras or dcras dpndng on th ntractons among th componnts. Th analyss starts wth th absorbr. Th mnmum tmpratur dffrnc ΔT,mn btwn soluton and coolng watr s modfd. In Fgur can b obsrvd how th rrvrsblty of th absorbr and of th othr componnts ar affctd. s ΔT,mn ncrass, th concntraton dffrnc btwn wak and strong soluton dcrass. In ordr to mantan th coolng capacty, th soluton flow rat has to ncras. s a drct consqunc, th rrvrsblts n th soluton hat xchangr, th gnrator, th soluton valv and th pump ncras. Ths ffct s mor accntuatd at tmpratur dffrncs abov K, n whch cas as th absorbr ΔT,mn ncrass th rrvrsblty of all componnts ncrass. Fgur also shows that th rrvrsblts of th absorbr and soluton hat xchangr ar th man contrbutors to th total rrvrsblty, followd by th vaporator and condnsr. Irrvrsblts [kw] R ΔT,mn [K] Fgur : Irrvrsblts du to a varaton of absorbr mnmum tmpratur dffrnc for ycl I. Fgur prsnts th total rrvrsblty of th whol cycl vrsus th rrvrsblty of th absorbr du to th varatons of ΔT mn for th cycl confguratons consdrd. Th trnds for th dffrnt cycl confguratons ar smlar, although thr ar slght dffrncs among th valus and slops of th curvs. It [kw] ycl I ycl II ycl III I [kw] Fgur : Total rrvrsblty chang vrsus absorbr rrvrsblty for chang of absorbr mnmum tmpratur dffrnc. Ths obsrvatons wll b quantfd by th SB s as thy corrspond to th slop of th curvs rprsntng th / Vol. (No. ) Int. ntr for ppld Thrmodynamcs (IT)

7 total rrvrsblty vrsus th rrvrsblty of th absorbr. Thr valus ar dtrmnd by applcaton of qn.. For th absorbr cas, such an quaton can b rwrttn as: SB ; ΔT ΔI t = ΔI Δ T,mn = var, U( comp ) = const Valus of th SB for th absorbr for th thr confguratons cycls ar prsntd n Fgur 7. t hghr ΔT mn th SB s ar hghr. Ths mans that th bnft of ncrasng th ffcncy of a lss ffcnt hat xchang s hghr than for an alrady ffcnt hat xchangr wth a low ΔT mn. If th valu of th SB s lowr than on, th rducton of th rrvrsblty of th componnt undr consdraton s offst by an ncras n th rrvrsblty of th othr componnts. Ths mans that a furthr mprovmnt of ths componnt s not worthwhl. ycls I and II hav vry smlar valus of SB s, whl cycl III has lowr SB s for mnmum tmpratur dffrncs blow K. In th consdrd rang SB valus ar btwn.7 and.. Ths mans that n all cass a rducton n th rrvrsblty of th absorbr s accompand by a gratr rducton n th cycl s total rrvrsblty. Th chang n th slop at a ΔT mn of about. K corrsponds to th pont whr th ΔT mn shfts from th hot to th cold sd of th hat xchangr. Th sam phnomnon xplans also suddn shfts n th slops of th SB s for othr componnts. Onc th dpndnc of th SB s of th componnt ffcncs ar obtand, w can apply qn. to dtrmn th optmum ffcncy, whch rsults n th lowst opratng cost. SB [-],,, ycl I ycl II ycl III (), 7 8 ΔT,mn [K] Fgur 7: SB for th absorbr. Th sam procdur s appld to th othr man componnts of th dffrnt cycls n ordr to obtan th corrspondng SB s ( Fgur 8). omparng th dffrnt confguratons, vry smlar valus for cycls I and II ar found, whl valus for cycl III ar gnrally slghtly hghr. omparng th dffrnt componnts, th hghst SB rsults ar for th rfrgrant hat xchangr. vn at small tmpratur dffrncs valus ar stll much hghr than unty. Th condnsr and vaporator hav smlar SB s wth valus abov two. For th gnrator and soluton hat xchangr t sms lss ntrstng to mprov thr hat transfr ffcncs onc ΔT mn s blow K, as n ths rang SB s ar nar unty. Th dphlgmator shows a totally dffrnt bhavour wth a sngularty. Whl at mnmum tmpratur dffrncs abov K SB s ar ngatv, thy chang to postv valus for lowr ΔT mn. Ths mans that w should oprat at a ΔT mn btwn 0 to K. For lowr ΔT mn th SB approachs zro and furthr mprovmnt maks no sns. Ths dffrnt tndncs ar du to th strong ntractons of th dphlgmator wth th rst of th cycl. s th hat xchang ffcncy mprovs th lavng ammona bcoms mor pur, but thr s an ncras n othr paramtrs, namly th hat whch has to b dsspatd, th tmpratur dffrnc along th rctfcaton column, and th rflux. Th ntractons btwn th dffrnt componnts can b bttr undrstood obsrvng th changs n th rrvrsblts n dtal. Tabl 8 rprsnts th ffct of th mprovmnt of on componnt on th rrvrsblty of th othr componnts for th thr cycl confguratons. For ach componnt changs n rrvrsblts ar prsntd n two columns, th lft n kw and th rght n %. Th valus corrspond to th dffrncs of th rrvrsblty for ΔT mn of K and K, xcpt for th dphlgmator ( K and 0 K). postv numbr rprsnts an mprovmnt, whch s a rducton n rrvrsblty. Morovr, thr s also a postv ntracton f th rducton n th rrvrsblty of on componnt also causs a rducton n th rrvrsblty of othr componnts. gry background marks th ffct on th componnt tslf. bold numbr ndcats an mportant mprovmnt (>0%), whl an talc numbr corrsponds to strong losss (>0%). Th rducton of th ΔT mn of all man componnts (absorbr, gnrator, vaporator and condnsr) affcts th prssurs and concntratons and lads to a rducton n th soluton mass flow rato. s a consqunc, th rrvrsblty of th soluton hat xchangr s always rducd. Ths also bnfts othr componnts of th soluton crcut such as th pump and th soluton xpanson valv. n mprovmnt of th absorbr rducs th soluton flow rat and rrvrsblts of all componnts n th soluton crcut, ncludng th rctfcaton column and th gnrator. Th sam ffct occurs wth th condnsr. s ts ΔT mn dcrass, th hgh prssur of th cycl s rducd and th soluton lavng th gnrator s wakr n ammona. Th rrvrsblts n all componnts xcpt th absorbr ar rducd. Th rrvrsblty s gvn by th dffrnc btwn xrgy nput and xrgy output. For th absorbr w obtan (for ycl I): I [ + ] [ ] = (7) s th hat dsspaton ncrass, th amount of xrgy output [ ] through th coolng watr ncrass. s th soluton flow rat ncrass, hghr xrgy flow rats of th soluton crcut ar obtand. But th xrgy of th lavng strong soluton ncrass mor than th xrgy of th ntrng wak soluton. So, th xrgy nput [ + ] bcoms smallr. onsquntly th rrvrsblty of th absorbr dcrass. If n th gnrator ΔT mn dcrass th wak soluton outlt tmpratur ncrass for a fxd hot sourc tmpratur. lso, th tmpratur dffrnc along th rctfcaton column and ts rrvrsblty ncrass. On th othr hand, th componnt for whch a dcras n Int. J. of Thrmodynamcs (IJoT) Vol. (No. ) /

8 rrvrsblty rsults n a dcras n rrvrsblts n all wak soluton bcoms wakr n ammona and th soluton flow rat dcrass, whch n gnral dcrass th rrvrsblty of th othr componnts of th soluton crcut. In th vaporator cas, a rducton n th ΔT mn ncrass th rfrgrant tmpratur for gvn tmpraturs of th chlld watr. Th low prssur of th cycl and as a consqunc th strong soluton concntraton of ammona n th absorbr wll ncras. u to th hghr drvng forcs for th mass transfr th rrvrsblty of th absorbr ncrass. Th rrvrsblty of th rctfcaton column ncrass as th rrvrsblty on th frst plat abov th gnrator mxs lqud and vapour wth a hghr concntraton dffrnc. Th rrvrsblts for th othr componnts of th soluton crcut dcras as th soluton flow rat dcrass. SB [-] 8 7 ycl I ycl II ycl III SB [-] 7 ycl I ycl II ycl III 7 ΔT,mn [K] ondnsr ΔT,mn [K] nrator, 0 SB [-],,, ycl I ycl II ycl III SB RH [-] 0 0 ycl II ycl III 0, ΔT,mn [K] vaporator ΔT RH,mn [K] Rfrgrant hat xchangr, 0 SB [-], ycl I ycl II ycl III SB [-] ycl I ycl II ycl III -0-0, ΔT,mn [K] Soluton hat xchangr ΔT,mn [K] phlgmator Fgur 8: SB for th man componnts. / Vol. (No. ) Int. ntr for ppld Thrmodynamcs (IT)

9 Tabl 8: Intractons Btwn omponnts (Valus orrspond to th ffrncs of th Irrvrsblty for ΔT mn of K and K, xcpt th phlgmator (K nd 0K)). ycl I ycl II ycl III ffct of th mprovmnt of on th rrvrsblty of RH kw % kw % kw % kw % kw % kw % R RH ycl R RH ycl R RH ycl componnt for whch a dcras n rrvrsblty rsults n a dcras n rrvrsblts n all componnts s th rfrgrant hat xchangr. Not only s ths componnt s rrvrsblty rducd f ΔT mn s rducd, but also thr s a consdrabl rducton n th rrvrsblts of th rfrgrant valv and soluton hat xchangr. On way to xplan ths ffct s that for a fxd coolng dmand, f th rfrgrant hat xchangr s mor ffcnt, th nthalpy of th rfrgrant ntrng th vaporator bcoms lowr, whl th vaporator xt nthalpy rmans constant. Thrfor a lowr rfrgrant mass flow s ndd for a gvn coolng powr. Ths nducs a rducton n all mass flows n th cycl. s a consqunc, a strong rducton n th soluton hat xchangr rrvrsblty s found. Ths hgh valus of SB appar both for ycls II and III. s th thrmal powr of th rfrgrant hat xchangr s only small, ts ffct on th total rrvrsblty rmans lmtd to 7 to 8 %. Th mprovmnt of th soluton hat xchangr n ycl I and II has a small mpact on th othr componnts xcpt th gnrator and th rctfcaton column du to th ncras of th soluton tmpratur ntrng th rctfcaton plats. Ths s rflctd by lowr SB valus than n ycl III. In gnral strong ntractons btwn th componnts can b obsrvd, whch n gnral cannot b quantfd asly. Snc SB valus dpnd on th componnts, thr ntractons wth th rst of th cycl and th opratng condtons, thr us smplfs xrgy analyss as drct postv or ngatv ntractons can b found obsrvng th valu of th SB s. It can b concludd that th SB s ar hlpful paramtrs, whch nabl us to bttr undrstand th bhavour of absorpton cycls and offr a possblty to gan mor nsght n th thrmodynamcs of absorpton cycls. Furthrmor thy can b usd n conomc optmsaton.. onclusons nrgy, xrgy and structural analyss hav bn achvd for dffrnt confguratons of ammona-watr absorpton coolng cycls. Th xrgy analyss dtrmns th rrvrsblts of th dffrnt componnts and th whol cycl. But rrvrsblts alon do not ndcat how to mprov th cycl n ordr to obtan th largst bnft. Int. J. of Thrmodynamcs (IJoT) Vol. (No. ) /

10 To do so, th structural analyss usng th coffcnts of structural bonds (SB) s appld. Th SB s ndcat how th rrvrsblty chang n on componnt affcts th rst of th systm. Ths analyss ncluds a varaton of th mnmum tmpratur dffrnc ΔT mn or U-valu of on componnt, whl th U-valus of th othr componnts ar fxd. In ths way, th ffct on th rrvrsblty chang n all th consdrd componnts of th whol cycl can b quantfd by th SB s. Thy ar dffrnt for ach componnt and cycl confguraton and also vary wth th ΔT mn or U-valu. Rsults show, as xpctd, that t s mor bnfcal to mprov lss ffcnt componnts wth hgh ΔT mn or low U-valus rathr than componnts whch alrady oprat wth low ΔT mn. Th componnts wth th hghst mpact on th cycl as a whol ar dntfd, and th rfrgrant hat xchangr has th hghst SB valus. Valus whch ar n gnral sgnfcantly hghr than unty can b sn n th vaporator, th condnsr, th gnrator and th absorbr. Valus around unty ar found for th soluton hat xchangr. Th dphlgmator shows a dffrnt bhavor du to ts strong ntractons wth th rst of th cycl. ffrncs btwn th cycl confguratons ar gnrally small. In summary, onc th xrgy balancs for a cycl hav bn stablshd and th rrvrsblts hav bn obtand, th structural mthod prsnts a usful mthod for bttr undrstandng and quantfyng th ntractons n th cycl. Wth th SB, th most cost-ffctv cycl for a gvn st of opratng paramtrs can b obtand. Howvr, as s prsntd n qn. 8 th optmum ffcncy valus of ach componnt dpnd also on th nrgy cost and th captal nvstmnt and th annual opraton tm. cknowldgmnts Ths rsarch projct was fnancally supportd by th Mnstro d nca y Tcnología rccón gnral d nvstgacón of Span (I ). Nomnclatur a c aptal rcovry factor (-) b c art of th annual opraton cost whch s not affctd by th optmsaton ( ) c n l c k, Untary cost of nput xrgy ( /kwh) Unt cost of rrvrsblty ( /kwh) c l aptal cost of th componnt l ( ) t nnual opraton cost ( ) O offcnt of prformanc (-) SB offcnts of structural bonds (-) Spcfc xrgy (kj kg - ) xrgy flow (kw) n Input xrgy flow (kw) h Spcfc nthalpy (kj kg - ) Intrst rat (-) I Irrvrsblty (kw) Mass flow (kg s - ) n Yars of rpaymnt p rssur (bar) s Spcfc ntropy (kj kg - K - ) t op nnual opraton tm (h) T Tmpratur (º or K) U roduct of hat transfr coffcnt and hat transfr ara (kw/k) W ump powr (kw) pump x aramtr n th ffcncy varaton of th SB z Mass fracton of ammona (kg/kg) rk lttrs ΔT mn Mnmum tmpratur dffrnc n a hat xchangr (K) ξ k, aptal cost coffcnt ( /kw) Ψ xrgtc ffcncy of th cycl (-) Subscrpts nlt xt k componnt k t total 0 nvronmntal stat (º, bar) omponnts bsorbr ondnsr phlgmator vaporator nrator Soluton pump R dabatc rctfcaton plats RH Rfrgrant hat xchangr Rfrgrant xpanson valv Soluton hat xchangr Soluton xpanson valvs Rfrncs nand,. K., K. W. Lndlr, t al., 8. "Scond-Law nalyss of Solar-owrd bsorpton oolng cycls and systms,." J. Solar nrgy ng 0: -8. tar,. and Y. ögus,. "omparatv study of rrvrsblts n an aqua-ammona absorpton rfrgraton systm." Intrnatonal Journal of Rfrgraton (): 8-. Bjan,.,. Tsatsarons, t al.,. Thrmal sgn & Optmzaton. Nw York, John Wly & Sons Inc. Bst, R., J. Islas, t al.,. "xrgy ffcncy of an mmona-watr bsorpton Systm for Ic roducton." ppld nrgy : -. Byr, J., 70. Structural analyss- ncssary part of ffcncy analyss of thrmal systms [Strukturuntrsuchungn- notwndgr Bstandtl dr ffktvtätsanalys von Wärmvrbrauchrsystmn]. nrg-anwndung (): 8-. Byr, J., 7. "Structur of thrmal systms and conomcal optmsaton of systm paramtrs [Struktur wärmtchnschr Systm und ökonomsch Optmrung dr Systmparamtr]." nrganwndung (): 7-7. Bor,., M. Mdrano, t al., 00. "xrgy and structural analyss of an absorpton coolng cycl and th ffct of ffcncy paramtrs." Intrnatonal Journal of Thrmodynamcs 8(): -8. ntc d'ccada, M. and F. d Ross, 8. "Thrmoconomc optmzaton of a rfrgraton plant." Intrnatonal Journal of Rfrgraton (): -. / Vol. (No. ) Int. ntr for ppld Thrmodynamcs (IT)

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