Advanced energy analysis of high temperature fuel cell systems

ADVANCED EXERGY ANALYSIS

OF

HIGH TEMPERATURE

FUEL CELL SYSTEMS

ADVANCED EXERGY ANALYSIS

OF

HIGH TEMPERATURE FUEL CELL SYSTEMS

Proefscbrift

ter verkrijging van de graad van doctor aan de Technische U.niversiteit Delft,

op gezag van de Rector Magnificus prof. dr.ir. J.T. Fokkema voorzitter van het College voor Promoties,

in het openbaar te verdedigen op rnaandag 12 januari 2004 om 15:30 uur

door A.rend DE GRO()T werktuigkundig ingenieur

Dit proelschrift is goedgekeurd door de promotoren: Prof. ir. R.W.J. Kouffeld

Prof. dr. ir. H.J. Veringa

~ enstelling promotiecolnrnissie: Rector Magnificus.

D~ç~fir. R.W.J. Kouffeld, Prof. dr. ir. H.J. Veringa. Prof. ir. J. Grievink, Prof. dr. 0.0. Hirs, Prof. dr. ir. J.R. Selman. Prof. dr. ir. J.H. de Wit, Dr. SB. van der Molen,

voor.’itter

Tcchnische Univcrsiteit I)elft, pron~otor Universiteit l’wente, prolw)tOr

‘l’cchnische Universiteit DelIt Universitcit ‘1 wcnte

Illinos Institute of Technology. VS. Technische Universitcit 1)elft

Pnergieonderioek Centrurn Nederland (E( N), Pctten ir. N. Woudstra hccft als bcgclcidcr in helangrijke mate aan de totstandkorning van het proefschri ft hijgcdragen.

Pu/ills hed

us.

the Energy research (en re of the Netherlands (LCN) Petten, the Netherlands

ECN R—03 002 Key words:

voor nuja ouders:

The research presented in this thesis was partly funded by the Stichting Technische Wetenschappen (STW).

The financial and academic support from the Energy Research Center of the Netherlands (ECN) has been instrumental in producing this thesis,

SUMMARY

Ii tI is thesis the performance of high temperature fuel cell systems is studied using a new method of exergy analysis. I he thesis consists of three parts:

In the first part a new analysis method is deve oped, which iot only considers the total exergy losses in a ut it operation hut which distinguishes between differen types of exergy losses:

The seconu part describes the nevetopment of a fuel cell model.Adetailed model is used to determine the relev’ nt aspects of the performance of the fue cell. Using this knowledge,

a sinspler model for the off design performance of a fuel cell is designed fur the system c’ilcu ttions.

Irs the last part the adva iced exergy analysis method ‘s used o comps re different high temperature f tel cell system configurations. ‘I’he focus is on understanding he effect of changes in the conceptual design on the pet fri i’uce of the system. The value of the exergy analysis iiethod is discussed td se n ad factors i iflueneing the systet effic’ency are ‘dentified,

The fuel cell is a single component in a complex sys ens. As this study. and earlier studies o fuel cell sys e ss show, th d ‘sign of the fuel cell syst‘tolargely determi ses the ef ‘icieney(if

the system. ~“o cnieve a bigteffic’ency a hign regree ot integration ‘s necessary. t3ut a nigti degree of it egration gcnerally tends sss ketp i siis’itio of sys etiis diff cult. ftc focus of

this thes’ s 1, 01 theref ire0 i:

Identi 3’it g Ii iw tIreitit‘ract on hetw o~ns rhsystems in tI e te ~l1systeti ‘Gets st ‘ai~h forward opti not iom

denti ‘yi ig how ex~rg~ alysi. or s he u e t Is op s isat~ ocess. Lzergs’ airal ‘sit

In the lu cell syste is e ergy lo s it ‘ intpo ie 0’ unt 0 ie not s zy lie I e resuto one or tsio ‘e process‘s with th“tspeci ic driv’ g lbrces. Its the netho developed in tb’s

Ii sis 5 such drivi ig )rces ~re disti iguisl ed it the fuel cell syste is

ctttpesat tie diffuteuce ‘ teat r’trts~’er:

pressure difl’ere ice siass flow:

difl’erence its eoncetstra io s siix’tig (isotls ‘r ssal): ~ differenc its else ssical po citial clseniical re~tctione • difference it electrical po e stal dec neal cit ‘retst.

If inly one drivi sg force ilays ‘n rol is ‘s tnt operation, c’ilculatitsg tI e ot’rl ‘xergy loss s sufficietst. Howcvcr if the proccsses in a ut it operat on are deter ssined by tssor’ than iiw drivirsg forcc, it is secessary to detcri iiise which part ol the otal cx ‘rgy I iss can be attr’h tted to cads of thin separate causes Its this thesis, nsetlsods are deve sped to calcula e these losses separatel . I he l’irs tssetltsd is ‘sequntitial a odellusg’, where a cottiplex process is cotssdered

s a series of process occutTing s ‘quntitially. or exattiple the combustiots p ‘ocess caih cotsodered~ aproc~~whsere o thefior step fuc~atid oxidant ac tiii~cd u ts the sc i3 step reac ioti takes place. Iti other cases processes caisnot be separated in tlsis way atsd ati50te detailed rstodel is required. Iti the fuel cell systens this is the case lor thse refornser and tl foe cell itself.

1 he system analysis shows that the losses as a result of heat transfer and the losses as nt result of chiciiiical reactions are of particitlar interestiti the hitch cell system. Different graphical niethitids to analyse these losses are discussed. Diagrams which can he used to analyse tIte losses as a result of heat tratisfer are the value and pitichi-value diagrani. Chetisical reactions are more difficult to analyse. because they getierally occitr simiittltamseoutsly with other processes as heat transfer, h’nictiomi atid miiixiisg. I lie coticept of tlse equihihiniittss tetsiperatutre is introduced to chnsnify exergy losses ittchemical reactions. Usimig the equtihib ‘irtin tenspenatutre. niakes it possible to visualize the chemical reaction~iint‘vahite diagram’ as well. However.

this tnethiod is useful omily bin a hunted class of reactions and atiothier tiiore getierntl method is developed to isuahize the losses in (electi o )chieniical reactions its those cases where no cheiiiical equilibrium tetsiperatutre can lie deterntitsed. ‘1 his method cotisidens separately tlse change iiiexergy of the process flows atid the exergy supplied to the process its the harm of

heat or power. For both (luamitities a separate getierahized Cartiot factor ( exergy/energy ratio) is calculated. Using these Canti(it factors, complex processes itivolvimig chemical reactions atid heat transfer can he represetsted in a ( ‘trnot factor enthialpy diagram. ‘I’hese diagnosis play an important roleititlse analysis of the losses in the fuel cell systetsiitithe systcmss atsalysis of the fitel cell systems.

/nd

cell

ioo~lelluig

A detailed model for the fuel cell is developed.‘ lie model calcitlates the curretit (letisity (distnihtttiois) along the fuel cell. Other phetitsmemia which ann included its tIne model are the heat transfer in the hardwareandfromss the hardware to the p ‘ocess flow amsd cheniicntl reacttotis occurntng in the fitch cell. 1 tie hilt conce itration amid temperat cc profiles are calculated by the tiiodel. ‘lIme most uiipontnttit oittpitt panatiietens for tIm system calculations are tine comiipositiot s aind teisipe atitnes at tine outlet(if tIne fitch cell (cathion e and ‘usode). ‘I lie detailed futel cell timodel is utsed to aisahyse several fitch celldOt figurations atsd types:

MCI’C atid SOh’C. co atsd courster-liow, extenmsal and intenmial refininsing. I lie objective s itndenstand which characteristic hintrntttneters have a Loge influence on tim futef cell perfiiisiatice. This kmiowledge can he used to simplify the fitch cell mntodeh for use in syst ‘tin calcul’ttiotis. Specihically two essential paraisseters are idemit fied wIne s cbanactense lie temperatutne (histnihution its the fumel cell:

• TIne effective temperature is a tsneasure Ion the ‘tvenage tetnipenatutne at which the eheetnochietinical reactioti takes place. Atialysis of the cahcuhatiotn nesuthts of the detailed tsiodel shows thi~ the comisbitiatioms of tetsiperatune amid current demisity distnihuttiori is itsipo ‘tant. ‘I Isis leads to tIme defimsitiomi of the ‘effective emsipenatutre’.

• ‘I’he temsipenatumne approach is the diffenemice between the tmsaxiiniutss temsipenat m e its the fitch cell amid tim ou let temssperatutne of thin cathode flow. Because the fitch cell is cooled by the cathode flow, the outtlet tetsipenatitre of the cathode flow dctenmstines how much heat ‘an he retnioved from the fitch cell. The calcutlati(itss shio~that, ifnt sintxitstutiii tenspenatutre is ntssuttiie(l for tite hardware, the outlet tentperature (i.e. the temperature approach) depemtds

omi tIne operating chtaractenistics (e.g. fuel uttihisation, cell voltage).

‘1 lie teitipernttttre approach amid the ef’fdctive tetispennttutre are essemitial pntnatstete s beca se both have a large i iipact oti the systemsi calcuthations. ‘I bse tetsiperatutne approacht deter snits s how mttch ‘tin is tieeded to cool the cell stack. 1 Inc effective tetssperatutre is a tiieasutne Ii’ tIne perh’ontnamice of tIne fitch cell stack.

A simplified model of tim fitch cell is developed for the systetil calcuthatioiss. ‘I he tiiaimi simphificatitsts in tIne tnsodel is that the processesiiithe fuel cell (electrochsemical amid chein ical reactiomis) are calculated at a cottstant tetnsperatutre. ‘Ihierefore the sitsmphified nnodel ((in isothernsal nsodeh) does tiot require iterative pr(icedures to solve for the tentsperatttre ‘ttmd

(‘tineit(leissity distnibiutions, Using tine detailed mould, the performamice of the fuel cell at diffenctit (sf1 design conditions (dih’ferent values of the cell voltage and fuel uttihisation) is st utdied. Stnhsequtently it is showmi that using simple correlatiotis him the tetiiperatutne approach an( tIme effective teniperatutre. the performnmnce predicted with the siniphified of’f desigmn isnouhel, oi respomids well with tIme perfontmmatsce predicted usitsg the detailed mimodel. S’s5/COtS iitiitl~,si,s

Its the last part tIne calcuthatiots results for a large miutmher of SOh’C ntmid MCI’C system cotsfigttratiotms are amialyseul. ‘I he miiethsod of detailed exergy amialysis. which distimmguishnes diffdne nt cntutses of exergy losses, is used to khemitify the miiaiti txmechiatiistsms of Itisses imi the f’utel cell systetni. I lie most imssptirtaiit coitchutsion is that heat traissfer is the doisiinant cause(if

exergy losses. ‘h’hie hitch cell getserates electrical power and heat. ‘i’hie heat nepresemits a smibstaist intl part of tIne total exergy (powcm’+heat) ‘generatcul’. More iienmt is gcnernmhly timutchm available than the ntmontnt of heat requmired in the system (e.g. bin refiintiier steam hiroduictoti on p ‘eheatitng tine amiode amid catlioule gas). I here is thienef tire a ‘heat surplus’ its the systemmi. lit hiotlm the SOh’C atid the MCb’( systems exergy h(nsses nts a resumit of heat tnattsf’er ntre

nespnmmssihhe for approximiiatehy half of tine exergy losses. fo i improve the systemsi efficiency. reducing time losses its a result tmf heat trntmssfer is mtecessntny.

I lie key comiipomments in the fitch cell systeisare the compotieimts in which the fuel s comiverted: tIme fuel cell tIne nefonmiienntii( the cotsihuiston. lIme exergy losses its thin se coistponeimts are smsiahh, hut chiatiges in lie process withitis these coitipomiemmts hiave l’mnge cotisequtetices 1dm time systemsi perf)nnmiiatice, ms the cotmmpanisomi mm large miummhen of systemsi c(itsfigutrat i(itis shows. Rcdutcimsg time exergy losses as a result of heat tratisfen requires optimisitig the proc sses its these coisipotnemits.

‘I lie dets ihed attn hysis of the systemnm cahem latio is imi I us thesis also leads to ntdistimictiiii hetweems the imiteimihed on pnimisntny effect of a clint i~emn the process desigms atid the secomidany ef’fiicts. Coisipmnnisoms(iftim d I lenetnt conf’ignsnatiomss cica ‘l~imidicates that eveiii suple changes

iiiprocess desgion changes ‘is prtieess hiannt mieters geisenahly result imi a imummiihen of sec(>ti(lmtny effects, In m satsy eases the secomidary effects largely off se the pninsany effect.

It is in idetmtifyitig the secondary effects that exengy amialysis plays au impontaist role, Becaumse the caicu hated efficietscies imme oftems tIme citmuthative result of a msutnnher of different effects, t is (lifticuit ho idemitih’y what ehnainges oecutr by comisidet’ tsp time emiengy inputs mmnd outputs. Butt by detcrniii i ig the exengy Itisses ntmsd cotispmt ‘imng the exergy lossesiiidiffdnemit cotsfigunmttioiis. it is possible to determrnine where th‘ehntmiges in the system occur mtnd to quatntif’y themtt, ‘lie tiucthiod of splitting exengy losses into difle cmnt types of losses, as ititnouhutcediti this thesis is ‘t

uanticuilm ny powerfuth msncthod, I nstly hecmtutse it tinnmkesitp(issihhe to detect clmmmnges mn tIme process which mtneti oredifficult to necogmsi/e by cotisidening time totnth exeng~l(isses.

Secuiimdl~.by identibyiisg time entuse uif the losses, it is emtsier to tnmtce the ummidenhyiiy’ chnamtges imn the process which cmtutse tine ‘xcrgy losses. titnderstmm idimig how eltamig‘5 ~ilone pmtnt of lie system affec lie systems as mt wlnole is thin key to optimmmisimig time systetmm. l)e a’ led exengy anmtiysis offCns a systetnmatic ntppn(mmtdhn to identil’yi sg these cIiammges.

TABLE

OF CONTENTS

S mtmnary

I

Samisemivatting

(;etseral iimtroductiois ,.,,.,,,..,.,,..,,,,..,,.,.,,.,..,,.,,,,,,,,,,.,,,,. PART I: EXERGY ANALYSIS

I stroductioim I ...6

fable of Contetmts I .,,,,,,...,.,,.,..,,,,,...,.,,,,...,,,,,....,.7

2. Calculating exergy losses amid exergy flows 2 Introdurction ,,,,,,,...,,,,.,.,,.,,,..,,,,,,,.,,,,..,,,,,...,.9

2,2 Energy mtiid exergy ...,...,,....,.,.,....,..,...,...lO 2.3 Chatige imu exergy in chemical remtctionss ... 17

2,4 Calcuibnttiing time ems ‘rgy of process flows ... 22

2.5 Calcuilnttiing the exergy(ifprocess flows ... 26

3. Causes of exergy losses 3.1 In roduction ,,,,,,...,,..,,,.,,,..,,,,,,..,,,,,.,.,,,,.,,...3 1 3.2 Analysis(if the causes of exengy losses ...,. 32

3.3 Cmtlculmttioti of diffenemit types of exergy losses, ... ... 39

3.4 Chemical equihibriuns mmnd exergy bosses....,,,,,,.,,,,,...,, ,,,.,.,., 47

3.5 Graphicmth rnscthods to represemit excngy losses ..,,,,...,..,,,....,,,...53

Discussion I ,,,,,...,,...,,,...,....,,,,,,...,.,....,..,,,,...,.67

PART II. FUEL CELL MODEL Introductiomm II ... .70

Table of’ C asteimts II ,,,,,,,,,,,,,,,,,,,7 I 4 A detailed model for th fuel cell 4. 1 Itutroduction ,,,,,,,.,..,,,..,..,,,,,,.,,.,.,.,..,,,..,,.,,,,,,,73

4.2. Scope of tIme foe cell mmdcl ... ‘ ‘.74

4.3 Single cell iuodel... 17

4.4. Equatiomus for the sutheehl imnodel ... 89

4.5 Integrated tuiodeh of he foci cell ... 101

5. Analysis of tlme calcutlatiomn results for the detai ed fuel cell mode 5. 1 Introductions ...~.. 107

5.2 Stmnrtimug points amid i spot dnttmt fo’ the cmtlcula io i ... 108

5.3 External rcformiiig fund cehls,,.,,,,,,,,,,.,,., ... 1 3 5.4 Internal reforming fuel cells. .... ... ... 126

6. Development of a simplified fuel cell mode for system calctmlatio is 6.1 lntroditction ,,,,,,,,,,,,,,,.,,,,.,,.,,,,,,,,,,,,,,...,,,,.,,,. 135

6.2 Aim isotlncrnuumti fuel cell mnodel for systens caheulmttiotns ... 136

6.3 Off desigtm cahcuhmmtiomis wit s the detmtiled fuel ccli tnodel... 142

6.4 Perfonnuamuce at off desigis for extcnimmtl refoniniisg cc is 144 6.5 Penformaiuce at off-desigmi for imstennal reforming ceils..,,,,..,,...,,., 152

6.6 Comparison of the isotheniuual aIid the detailed m(idel ... 159

I)iscussion II ~ 75

JAR’ III: SYS’I’EMS ANALYSIS

Ii trocluctioms III .178

Tn he f (‘oimtents III I 79

7. A taiysis of SOFC and MOPE’ base cnmse systeisis

7, 1 lntnodumction 181

/.2 Stmtrting poittts for the systenm cntlcuihnttioiss 181

/.3 Bntse cmnse systenus 186

7.4 Lisengy atid exengy mmmsmtlysis of the humtse cmtse systeisms 191

7.5 Anmnlysis of hemtt tnmttisfdn in the fitch cell systemms 202

7.6 Ixergy losses its the fitch comivension 208

8. Analysis of SOFC commfigurations

8. I ntrodutction 223

8.2 SOl ( systetsms utsing mt cnttliode (ilf-gmns recycle 223

8.3 ltuf’hnmemice of the pressure 233

8.4 Imnflumcnce of time fumel uttilismttksmi 244

8.5 Anmmhysis of mtmi mmtennntl nefiinmiuiitg systetmn 52

8,6 Influetsce of the pressure on the imitem intl nefonmsiiiug systemsn ~6 I 9. Analysis of MCF( configtmrationms

9. 1 Imutnodutetiomu 269

9.2 Systeiin witim hemmt recovery in the aimode (ml f-gnts recycle 27 1

9.3 Using mmin prehemttiiig to nedutce Iucmtt tnansfdr losses 274

9.4 Lxte ‘mial cfontsning MC ( systeni with stemtmin injedtomm 283

9.5 Systenu v~ithn direct ecycle of at od off tots ~87

9.6 IrA uteince of tIne systetsi pnessutne 0mm time extenmmmtl nefinnmis mg systett 293

9.7 Atsmtlysis of atm imitennntl neflmnisuimig MC C systeisu 10()

9.8 In0nemice of the lime I01Ii smttiomt 109

Discussio m III 117

10, (‘am c unsi is I

Refereitc’s

Appendices 1 7

Samnet Vitiiif

l)ank~soord

I

Acki owiedgeme its (‘um’ric iluni vitae

CHAPTER

1

GENERAL INTRODUCTION

I)esigmm and amsalysis of fuel cell systems

In this thesis the perfoniuimtntce of high teanperature fuel cell systems is studied usingitmiew inmethiod of exergy analysis. The thesis consists of three pmsrts:

• lit the first part a new anmtlysis tsuethod is (bevelOped. which not otihy considers the totmtl excngy losses in a ummit operation. hut which distimiguishes between cli fferemmt types (if exengy losses (part I: Exergy rnnalysis):

• The secoiud part describes the development of a fuel cell nuodel. A detailed isiodel is used to detenimuine the relevant aspects of the performmtnce of the fuel cell. Using this knowledge,

a simuipler model for the off-desigmi perfornnuance of a furel cell is designed for the system calculations (pa ‘t II: Fuel Cell Model).

• In the imtst part time advmnnced exergy anmnlysis niethod is used to compare differcist high tempermnture fuel cell system comifigutnatiotis. The focums is on identifyiimg the effecttif

changes in the conceptual desigis omi the performance of the system. I he value of the exergy anmmlysis method is discussed and the mmtin fmnetors influencing the syste is efficiency mire ide utified (part III: Systems Analysis).

‘I wo types of high temuuperature fuel cells are considered. The trtoltcii cmunhotiate fuel cell (MCIiC) atud tine solid oxide fitch cell (SOFC). The operating principle of a fuel cell is simple. ‘h’he process flows. fitch mind air, are supplied sepnu’ately to time f’uel eehl. In the fitch cell

iuydnuigen ntnd oxygen fromsi these flows react directly to produce electricity amid heat. However, eveii if tine operating principle of time fuel cell is simple. to ipermtte the fuel cell requiresntcomuip cx systemmi. Feed flows have to he pre-hemited to hip s temperatures (600 C on even 850 C). Conmipotietits which are hmtnmuuftmi for time fuel cell, fo‘exmtmssple sulphur

components, hmtve to be reduced to low levels, On the other hamid he remmc ants, iiydnogemu mtnd oxygemu (aiid its thedmt5eof time MCPC CO, as well), s sould he present in lugh coimcetutrmst’ to s to increase tine perfor nmance of the fuel cell, ~ressunismttioiuitsereases the performance (if the fuel cell as well. Tine fuel cell systcni should he desigmmed to conditiomi the feed flows in au efficient manmuen. At time sante time achieving mt high eft’iciemicy for the total systeni renhuires effective recovery (if energy flows ide (Hoot 1998]. Ion example the hemtt f’nom th-’ outlet flows is use to heat time feed flows the power generated by expanding tim off-gntsses ~tia pressurized systenr is used to cotispress time incoming gmms flows amid of’f gmns front tIme fuel cell cmnnn be used to provide hemnt to the reformer. Asitresult, tine fitch cell hecomnes part of mt complex system of heat exchiamsges, comuipresso ‘s, reactors moud other utnit (iperations.

As this stutdy mind earlier stumdies 0mm fitch cell systems (e.g. ]Patel, 1983], [Dicks, 1)90]) show, tIme design of the balance—of phmnnt Imurgely detenusu’nes the efficiency of time systenn. How ‘ye’ mt highs degree of imutegr’ttion gemnermmlhy makes optiisuisatiott of systenis chaile sging. I he focus(if this thesis is ott therefore(iii identifying how the hight degree of iiutegratio s affects stmaiglm forward optinnisnmtiomu mitid how exengy analysis cmtn he used is opt ins up the systens. How should the fuel cell systenu hr designed’? The strong immteractioui hetweems compomsents its the systenu due to time high degree of ititegration, muiakes it difficult to deternmine on forehand what the (mptimumui cotsf’iguration of tine systeisu will he. ‘1 he ‘sinsple’ appromtch to optimumisatioms is to carry (mitt a hmnrge number of system cmticuimntions, iiiorder to determimie Isow each of the relevant parmnuneters and different systetui coiufigumrations will effect tine perfonimsance of the system. But there are iusmportmtnt limnitmttiotis to this mtppromtch in the case of highly integnm ted

sysems. I lie mmnsouunt of pinrmtnmeters which can or sisoutid hr vmunicd is getsenmully large. whsich tmmmnkcs it immuhmossihie to optimmn/e lie systemum fully. h’unthiertsiore, iuupuut hmttmu o‘connelmttions utsed

ms the systeums calciuhatitimu chmnmuge (for exmonmphe itSa nesumlt of devehopimug t‘cimunology or insights umto the technology). ‘I lie ‘emnpinic’th mupproacis’(iflens ittie kisowledge(iti how tine outtconme (if time Optitsutsatioti cmmum chmnnge mtmsrl will ofiemi ‘qutire redoimmg the evmulu mttiott with thin mmew dmttmt. it is thmenefore tmeccssmiry to commmplemnemnt thin type of stu dies indicmtted above, witim stutdes wInch fiicus moore fimmmrlmnmsseuutmtlly oms utmmdenst’tmudiumg time mnechmmuusismmns v hin’h underlie the

iptinmismttiois of tIne systemsus. Its this thesis sumchn a dctmniled mtunmtiysis is msmmtde of high teumnpe ‘mttntre fitch cell syste mis utsimng exergy ammmnhysis. Rat men thin tnyiumg to detcnmmsimse tIme optmmnmtl

dOtfigunrmttioms. the ohjectiw of thus stumuly is to idetitify whim t phenomssemnmt iunfluemsce time optimmnismmtiomm process.

Tine n ole of exergy a salysis (I)

lime commcept of exergy ammmmlysis is hmtsed 0mm tIme secotsd Ltw of theninodyiittiiids. Althnoutghm time comscept of exengy linus h e i stnodutced mnuteh ~a’ icr mu (hits “connect” ‘tpplcmu io s hmts heems a source(iflmemnted dehmt e. u terest its the use of exergy ‘tummtlysis hiss heemu boosted is tIme 90’s sy tIme developmsmemit(If flow slmeetimmg pnognmmmmss. which tssmtk’ it possible todit coimute time exergy flows mosd losses imu mi syste mm ittitfmtinly n ohmic mmsmu m ncr. I lown yen mthtfmoutgh thur dahduthati( m (if

exergy flows a nd hIsses mnay hr comusidened stmomdmtrd procedutre, it is tmot‘lwmuys clemir Imowiii exergy ‘nnmnlysis cm mm c omtnihnmte to optinnsim g ‘ p ‘ocess. hum this thesis thuc use of exengy mtuualysis mis a tool Ibm p ‘ocess optimnnismntiom is takeum m ste forth ‘n h5 develo imme itumsetlmod which milso iulentifies 0 which type of in’ ‘vensihihityon irnevensihihities cmtcl loss c’nms lie muttnihm, ted. By clmuitymm p Ime cmtuuses of lie losses h‘doties siunplnn 0 ass ‘ssthin wmiy mms whmich tIme losse emit lie ‘‘duictol mi sd lie e eit Ii vIne n hne~cmii lie neduic ‘d. Its P Isa Her 2 time Iitdmomscmitals of e ‘tgy ummilys’ s mine m n’ukd a sul tl eonnelmtt4 os mime dcv ‘It ie( lot emulco a imtp the exengy losses mind vmiloes. is h’mpter lmt mew siethod is rfiscutsscd whni ‘Is

(histiimpntislmds dif’fitncust cmiumsesof e engy Ia sses. forth cnn one miethods of rep ese stimsg Is’

exergy losses its (imitnmtmnns ‘inc dscuusscd.

TIme Pu 0 ccl s ale (II)

Ahthoutgh the utel cell is on y (its (if t s‘cotnn~os‘ ts ims ti e fir I c II syst ‘m. me penfo tm mime of the fitch ccliii fluiemme s tIm’ perfon imi ne of the to mul systens s nommgly. I-lowe ‘n mmonl ‘1 imp tine fume cell is cotupl ‘x. A l~rae usuouhe’(ifdif’f’enemi pm‘s msmeun’i )ccumn s he fitch ‘cli: ehmeussic’d mond elcetnochemssical ‘diet ons, Inemit tnminsfen, tmi’t. s tnmim slen et .‘him ‘n is mi stro ig iumteraetion hetwecu ‘ill pnoeesses. [tin exmit spin, mill of tI es mnoeesses m ne ‘m flute mc ~n stnisghy by the temmnpenm time ‘imsd os tI e temsmpen itumne r st “hnutiom i tIne cc is mi result, the nmi e o ‘ti processes occuurning imi time lute cell is geusenmilly distnihot ‘d iso m-utunifb u nhy. A d ‘tmniled mu rIch

(ifthe fuel cell thmenefone iso ommly niescnihes time hocmnh phcmmommie ia us tIne fuel c II hot m iso cmulculmttes the distnib itioms of tIme imin’tm setcns: te ntpeumttonc mrofiles, comuceunt a ioms i‘ofiles e n. Solvinsg the mtsatiieummmitical umiorlel mtusmthytic’tIly is msot possible if lie local pnoeessrs mine descnilmeul its somise d ‘tail mis in tine mnmode d‘veloped Imene. hi order to solve time fuel ccl mm ode a msutnmmcnicmul nmetlsod is nerhuoned. Sumchs ii smodeh is umot well sumtc for cmtnrymmg ottsys ntis caicumlatiomis. Systemss cm Icuilmitiouss itsvoive highly itcnmm iv proc ‘dunes to cmthcu mite mmhl th process flows its the systeii.C on ‘espomsdimmgly its tIne coumnse of ot c system emilcu Imi oms. I fuel cell muuodei is cmtllcd mmmmiusy timsscs. Use(ifa (ictamled mmuodcl as rlescnihed shove its a syst in cmtheulmutioms will therefore reqonc cxtncmmsc cmticulmmtioms times. More f’uuumdmtnumeuutmtliy.

convergeusce of systemum cmulcuulmttiouss is mtlways i0i issute. esp~cimuiIyfOr systetuss with a high degree of immtegrmttiomn mis fuel cell systemums. I hmenefore a rohuust usmorlch is nequmireni for these type (if emuleulmitiomus wh’le time detailed nsodeh is very scmssitive to vmtniatioums imi input pmtnm msuetens.

mm systcmum cmtlculmutiotss timereftire mt highly simsuphb’ied fuel cell umsodel is required. In Chapter 4 tIme nievchoptsmcmmt of a detmniled mmmonlcl is described, which can lie used to calcuil’t e huotlm the ouutput pmnnmnussetcrs (e.g. (muutlct commcemutnmntiouss) mis the distnibutiomm(ifrelevaust hmmtnmummsctem s oven the cell (e.g.it cuirremut deussity distnibotiomu (in temsspcrmttumne profile). Imu

‘hap er 5 the cmmlcumimttious results for this miodel mnu’e discumsscd for diffenemut stmick

commf”putmatiomms: SOIT mimmd M( 1 (,cxtcr smil mnmmrl imutenummul ref’orunmimng. co-flow mtmnd coummster flow. Bmiscd (inn the results of dctmuihcd musorlel, iui Chaptem’ 6 suteh ‘u siumuplified mmmdci is devehoperl. which ciii he usediiitime systcmsm emilculatiomus,

Systems

I

nnalysis (III)

‘I Inc mitutml icmttion selected for moumtiysis is mm to ‘mnh gmis fuelled utmmits fist imsdustnimtl c munhmiused hemut mimud power. Nmttuurmnl gmus is tIme most I mgicmtl fute ton high tcmmupcnmiturr fitch cell systemmms heemiuse i is widely mtvailmnhuie pnimisminy fuel mnmmd emmus lie used ins time fitch cell systenmm ‘ehmut’vehy simple. Nmitmmm mih gmus emits he used either directly (immtcn mal ncfonmsmimug) (in imy uusinmg iirefo ‘men to commvcnt the rim tuun m 1 gmts to Isydrogc n rich sy mthmcsis gmts (cxtenmmmil ‘cfonmnumsg). h’umntimenmusorc, tIme cumnreust ehectnicit~ geumenmntioms cmipmicity its time Nethenimoids ‘s based imirgely oti mmmntuurmui gas

I loweve‘, wh ‘e hmc ceousinmisy ~mfsemile dictmttes very Imoge scale produictiomu for the cunneust stmnte—of he an techmus miogy (ton exmnussplc gmns fined comunhinsed stemumum mtumd pits turhitme cycles aund comil past ficmitiotm). the c~ots~iniyof scale is usot mIs stromug for the fuel cc I systemus.‘ he

efficiencies which nrc expected fm’ Imoge scmmlc sys eusms (> 00 MW) mi ‘c usot ummuch higher thmun the efficicumeics imu time I ...2 MW nmnumge ‘~I enefonr (mime of the nost interesti sg m pphcmttioums is is tine latter rmi ge. wit ‘r’ tlse sys ems cmii he umsed tOn coutubitmed hemit a md p iw’en. I lemm (leuuumtumdiii time imuduistry comssists p ‘i iiinily of prode. s stni in, ‘I hscrcftnne time stant’mi.~poiu ts selected bin the systems s corns de ml ‘mm timis Inesis ‘nrc:

• msmiturmil gas fiteiled:

• uomninmil electnicmnb power: I MV

• cousdit’omms pro ‘ess stcmimss. 180 C/l 0 hon

Systemim ealculmutioums Immtve hecum con’ ‘d out us’ung the fl w she ‘tim g pn mgn’ tim CYCLE-’ EM N), develohmed‘itDeift Utuiversity of ‘I ech mof igy. wo hmnse cm se eom’figonmtt’o is ( ‘01 C a muh

MCI-C) an’ discussed i m Unapt’ 7. h’ deta’led ‘xcmgy am’ ysis rlev ‘hof cr1iiithe first pant of time thesis ‘s oserl to idemmti ‘y ~ loch hOc ons insult tI e systeims eff”cicuscy. Its the ciulcumlatio is the detmui led firci cell nmmodel noveloped it seco d pm nt of tIm’ times’s is umsed o cakolmite the performuua ice for these hmmtse emis comsfuguur’ntion s.

Rmmthmen thans carry out a Imirge mmumusmhen of micumlm ti muss Ion a w’dc nmtmtgn ml app icatiomms (lie

‘cuuupinicnI mnp~romichu’).itdctmtihed mtm ahysis of mi hind ed mmomnhcn of co mfigurmttiomus is cau’nied ou Diffenems conmfigturmm iomss for 801 ( systenms mire coumsid ‘red its haptem’ 8. Severmi

configunatiomis are evahumated to de cnmmmimmc how time tnmtyon exergy losses idcmutif’ied its he hmise cmuse cmticumlmntiomus e’uu he nedumeed: cmitlmode(iff-gmus uecycliusg. pressum ‘isimug the systeu s

iuscremusiumg the fitch utihismitious mmd ‘ttcn mif rel’ontmuinmg mtre mimmalysed. A si suilmir series o

calcuthatioums of MCI’C systcmnms is discuusscdiiiChapter 9. ‘I’he (ibjective of these calcuhmitio is mtmmd time suuhsnniunemut mtmmmnhysis is to detenmuuimme how the mummujor exengy losses Iahcumtified ins the hmusc case systemums cmiii he reduuccd.

PART I:

INTRODUCTION

I:

THE ROLE OF EXERGY ANALYSIS

‘lime et’f’iciemucy of mm systcmsm is the rmitio hetweems time osefiml eusengy outpmut ~mftIn system imiumuh the e sengy iuuputt to the systeums (fOr exmonpheiii hue fOrum (if fiuch). I lie ‘hmthmnmmcc’ of the emsengy

(‘umpot mmsiumuts inseftmh ootputt) lemives the systemss itm a Iomnu whmicls cmmtmothe necovencrl, for

ext splc mis semmsihhc hemmt ‘mm the coohimmg wmttcr (In semssihm c mimudImit ‘mit hsemit imu tine flue gmts stmncP I h xc mn ‘c time emsengy losses(if thc syxtemis. ‘line object ye of optimsusimsg tIme system m is is ~ct e el to fi d time systeiss comsfigumnmttiou which (tmukiusp into mtceou mit ‘‘s mm imsts with respect o

dOS mind tech micmtl hinmitmitiomus) tniuuimssizcs the cmmcngy loss s.

ne fins law ~ mcmmmiody tansies fOr siemtdy s’ate cmmergy sysmein(energs’ in =energs ole) ta n he umsed to detennsimsc which osses(Iddumnits lie systemmm: how msmuuchm hemit is klst with time coohii p wmiten. 1 ow msmuch emmergy does the flue g’is comit’Iim .‘I his type of emse ‘gy miummilyxis coumsiders otily tIme em ergy I Ia ws go’ mg in mimsd ouut of the svst( mm: time sys etsu is t‘emited mis bluehihox. ‘herefone emuergymmmmnlysis 15 of hinsi ed vmuiute winemu it comicst idemu ifying amid qumtmmt’fyimug thmr )nocesses withi u Inc systems which I mid to these losses ‘lo le’o n mutore ft the

proc us within his hulmtck- iox, 1 is imuspontaitto takejill ‘iddlutist hi “r u mulity” of msentry.‘ Inc seco mc law of thenmsmorlytmmtmmnics stmites limit i cmtchm ems ‘ngy c immve ‘sio s mis a resui t if tIme tirev rsihihity of ftc proc ‘ss es), the rhummth y or tIme vi I e of th’ m e ‘gy (Iccnc’ ses (ill oogl quumnmst y ne5‘iiis coumstmtit ittmiccondmtumce to hr f’ins Imnw),‘ lie closer mi proc ‘ss‘5 t I

reversihil’ty ti e sun nilem he losses w’ll he. ‘1 lie se ‘oma lmtw tine clOne offers m c nmin ohject’ve

iOi ftoi tin p the syxocul. i iii it ting th oss S itS resol on’ immeses ml’’ my,

It tunas ot o he ver utsefol, i mum lys’ A seco d m v losses in te ‘1 mn’c’d sys eusms t se th commcep if em rgv to o imit tify h vmdu e I eti ‘cy. line cx ‘ngy(If ~t0 ‘‘ss flow (in mcu’gy flow ix def’immeda~the ‘0iOu t (ifpo en w ‘elmdOOd lie mnodtmced f’ immu time flow its mi m idnmii techmmi ‘mnh pro ess. Usii p the ‘xengy ~omscc~mimu I e mit hy is ofth i ch ‘‘I system . pu’ovidcs powe -f ul ool. n the ( I’ apter 2 sonic of lie basic pi”mmeiphes0 ‘tim com dept of exer~ymund connehat isis On emuiculm tium3 exengy v’n umes ‘numd cx ‘rgy osses will me rex icwcd sinortly. Jsit

e

these o ‘elmi 3 m , the x ‘ngy loss sii all the process st ‘ps‘i In’ On r I sy. teums ca lie detenmso med.

Its tIme id ‘mml eusengy systems m o deg ‘midm tiou of em c ‘gy ecors, ‘.e. 1 ‘systeuss ohmcnm es reversibly However ins momy rem I c nengy commvensiomm syst ‘mum, mi dm ivummg fOrce is tnccess’’ . on cAitlnpie,1i‘at t‘iO’Si ( iiy ulceutuui ncxuim mu’tmmmi cra ore dftf’encmicc mnnl a mm ss wil IC y flow fromu (sine point to a mother if thmene is a dif’fcne ice iuu pressure. I hese dnivi sg forces mnc umeccss’mny for the process to oceuu’ its a 1” site tiuusc immtenv’nl amid geoumsetny. mutt milso iumtnod c irreversibility ims o ti e syst n .hi ximmgbe process step dif’ferenmt types of dniximmp forces um y cause time exengy losses o kusow how tine cx ‘ngy losses cmii me mcdi ced, it is esse m imth to kumow to whmnt citeite’nch(iftie sepmimate (lnivmumg fOrces do nt ‘ihumt~sto time to mti exergy loss. Chapter 3 diffeneumt ypes of it reversible processes which plmiyiiroleiiithe fuel cell sys us mtre idem tified. Sulssequmeumthy usmethods mire developed to mthtnihutc tite loss in em chd0tt5~0teust of the finch cell systenu to diffeneust types of inrcvensihmihtics, Ge Ienmitiusg th’sititOrtimmttiomm is uusefuul to foe us the exergy mmusmihysis usore specifically(Ii idetnt’l’yitsp how the process cats he

inmproved. as will he shown un part III.

In the des~pnof au energy systeumlrhe si/c of these dnisjump forces is subject to omptiisnisami(Ims. A langr uhnivinmg force will jun pemmeral icaul to conmpmict commspomiemsts mttmd i’euhumccd invcstnsetmt cost. But milance

hrhvimimp h’om’ce wilt also lead to Imunge losses in ihuc comsshiommcmsts of ihme emiengy systemms mimidd(iiiSd~U(iily tower cfficictmcies,

TABLE OF (‘ONTENTS I

m t oductioms I .6

2 ( alcu Imntimsg cx‘ gy losses amid exergy flows

.1 lustrodoctiomu 9

2.2 ‘mscngymtmmd excmgy 10

22 l’imefistImiw of therm sodynmt sues: ‘msengy h’tlmtmmees for closed ‘imud ompeus systcmsms 2.2,2 Cotivensioti (IfI emut Ito v (Ink

2.2.3 Lost w(mrk mnumd exengy losses 2.2,4 ‘lIme cxcney hmtlmiumce of a process

2.3 Ciumimige is exengy in chsemssicmml ‘emidtiouns 17

2.3. (‘mnlcumhmitimug the chmomgc iii comsspositiomm ‘is mi nesutit ~ chemssic’uh u’cmte iomms 2.3.2 ( milcudmit’ tsp time dhumtmsge us exenpyas a resol (If ci cumuicmmh nemictions

2,4 (mile thmttitmg time em ergy of process flows . .

~.4. I Rcqumircmsscumts for a ‘efenrmuce stmite Ion tlse cmtlcoimttiomu of time emsthsmtlpy 2,4,2 Different ncfc ‘dice stmttes for system is w’thi ehnemmuiemi nemictiomss

2.4.3’’imenmsso mmmechsmtmuicmml mntsd cimcumsieaIemienpy

2.5 Cmilcrmlmttimmg time exerpy of tmnocess flows ... 26 2,5.1 A nefCrcmsce stmtte IOn the calcuibatut t i‘exerpy

2.5.2 C mu mositiomi of time em vinoimnm’

2.5.3 ‘Use’ s o-mncchnmnnic’ti as I cli oniic’t ‘engy 3. ( anuses of ezergy osses

3.1 hmntro loctiomi

..,.,.,,.,,,....,,,,....,.,,..,..,,,..,.,,...,.3

3.2 Ausmilysis of ti emooses of c cn3y 055 ‘s .,,,,,,,,,,,,,,,,,,,,,,,,,,,,,37

3.2.1 rle m i ‘icmit’oo of hue typ s(if cxc A 1 sses imm I e fite c I sys 5 3.2.2 iamsses s m resumlt of seat tnmtuisfCn

3.2.3 Lossesmi a nesunht of fnicti us

3.2.4 osses mis nes ult of is 10 c ‘mn’n n’xi ~ 3.2.5 I osses as a result(if elm mmsicmI nc’ic i miss 3.2.6 11 ‘etu”c’d loss’s

3,1

(‘mile dm ion o ‘diffeneit yp 0 xc 4y 055 5

3.3.1 Scpmomtti mg time exr ‘gy Ia ss ‘sm5 m nesu t oftI e d’ff’eu ‘mt driving 0 ces 3.3.2 8cr ucmutinl unm id ‘is mom sepmtrate tIn off’’ nt myp 5 (if exengyI- sscs 3.3.3 h)etmiil ‘d smod ‘is tot spmtnate lie dif’fe es ty mrs of cx gy ho s

3.4 (lmetsuicmth cqoihih ‘louis mond exengy losses . ...~ 7

3.4, 1 Chcmuuicmd en ollibniummn

3.4.2 hmmfluiem cc if time eqoiliht”uitu om thm x ‘my foss ‘s‘0 ‘di dtio 3.4 .3’llsc equihihniuimms tenmpermituiue

3.5 Gnaphmicmth mssctisods to reprcscmmt exen2y Osses .5. 3.5. 1 ‘I’hme vahume rhimtgnatsn fOr Inemit tmmiuusfeu

3.5.2 ‘I lie v’iloc d’agrmiusi Ot che iiicm 1 ne’ictiouss 3.5.3 he Cminusot f’mictom en thmmtl~uy (t’, ) Gmignmt n

Disciussi tntI (7

CHAPTER 2

CALCULATING EXERGY LOSSES AND

EXERGY FLOWS

2.1 lNi ROl)UCTION

Amsmtiysis of emsergy systemsus is hazed on tlsenmsuodymmmnusuics mus time study of eumergy

tnmimssfonmnmntiouss, the comiversioms of muse lOrmn of energy imuto mumnmther f’orns, ‘I hmernsodymsmonics u ses two a xiouuis whucim mire kmuowmn mis the first mtmud secomsul lm’w of timenunody muamusics. “he first imiw, comuumm’nommiy kumswms mts the lruui’of r’o,m.seri’atio,m of emiergv. postuuimttes tismut the cimminpe of time (iumtenmmah) energy of mu systens, is erlumnl to time mmcl eusergy stupphu’d to the systeusm. On for a stemudy state systesuu (him which the iustenmsmul emuergy does umot cInmtmige), thumut totmtl energy sumpphierl to the sys ciun is erlumui to tmtmnl emuerpy delivered imy time systemuu. Optiuuiisitig the system therefore focuusses omi msumtxiussisiisg tIme eusergy which cmuus umsed mtuud mm muuituusmisimmg time etserpy ‘‘losses’’ of the systemmn: emsergy flows wimicim cmtunusot he m’ccovered utsel’utlly. First imtw mumumulysis cams idemmtify where in a systemmu these emuengy losses occur mum) how they rlcpcnrl (1mm tlne desipim of tlsc systens. however, where the losses mire cmuused mnmsd how time losses camm he reduced does riot fisilow fromnum the mnuumtlysis. ‘1(1 heminus usmore muhoutt the process withmimm the systeuss. tine ammalysis should he hmtsed on tIme secomsd lmtw ~mfthenummmdymmmiunics mis well.

‘fhe 2”~imtw 0r ~hmer.smudyttminncsstmttes. that aithmuughs time mnsmouuumt of euso’gy stmtys thc smi~umeds mimsy comuversious step. inreversihmihity omf processes mtiwmtys lemids to degrmtdmutioum of eumergy. Omuc of time wmtys i u which the sccouud hmiw cmiii beets l’onmnmtlmitcd‘5: ‘it’orkranhe o’onmpleied

trrnmsfdrincrl into1mm!, lint! heril ow oimlt’he trait sJorntr’rl prnrtiallv

ui/a

ui’orlm‘. I hmrooghu time introductioum of tine couscept of emitropy it is possible o quimumitify how Imunpe lie irreversibility is in mi specific process step. For techmuicmnh systeusms time loss mis mi result (if inrevensihihty cmos he trmnmmshaterl (ma tsiore hmr’tcticmml couscept of exergy. The excngy of ats emmergy on process flow is (lefined as time timeoneticmih mousoummut of work which cmiii h’ produced by hringimsg the flow imi equnihhuniuumus with time sutrroumsdiusg eusvinoumnseustiiim reversible process. ‘l’his reflects very well the ‘vmuhue’ wiulcis the eumergy or process fhmw rehuneseusts. By calcuulmttimmg the exergy losses it is poissihie to detenuinimme Itow reversible mi process step Is..~8tuidy’migthe exenpy hmsses in the foci cell systemim muuakcs it possibletadeteruiiiiue not uly tha size of timese losses. but also ~~,tme~’etIn’

osses occur. In thus chimipten lime hmnsir’ pnimsciples mind conrelmutdmuss will he tremited. ii Sectioin 2.2 tine first mnnd seconud law of therunodymummn sics are unsed to

define two concepts: host work and exengy. Sulmser~uemstlythe caicobation of differemices ium exer~ybetween two thermorlymnmtnmic slates is treated.

Becmmuse of’ Its inutmorlammec 1mm time fund cell systems the exerpy losses misci result of (electi o )chemsuicmnh remuctions mire tremnted sepminately in Sectio u 2.3, Both enthaipyitsd exergy are relative variables,ietinily time differenmceiii

emstimmmlpy or exerpy hetweemu two stmmtes Is dclused. ‘10 he muhbe to define the

entlmalpy (energy) or exengy of mi process flow, it is nseccssary to defuse mi refe ‘etude stmtte at which nbc entllmihimy u’especti’ ely the excrgy is equtmil to zaro. ‘l’he selection ‘if a materemuca s at” muimd time nmethod for cmdcun mitimmg mthsmlutc vmtlumes for tire entlsmulpy mure tremited inn Section 2.4, hue correspondiumg uhefimutious of a neferemice stmtte fOr the emulcutiatiomu mf exergy vmnhuucs mind thu calculation mf those values is the subject mf Section 2,5.

2.2 ENERGY AND EXERGY

2.2.1 The first law of thermodynamics: energy balances for closed amid opeus systemmis closed systemsu is mt system where mmm minmiss is exchmtmuged mucrmss the system hoummdmury to on fronum the surrounditmps: omuly energy flows micross the hoituudary r’mtut occur. lime first lmnw omf ther m’sodynamics or the law of ‘couiservmition mf emsengy’ applied to mm closed system, states the relmition between the emmerpy fhmws to the system amid the cinanspe (if stmite mf thmtt systemum. A ckmsed system is schemnaticaily nepreseusted iiifigure 2. h-mn. Energy is alwmnys trmmnsferred to mtumri fronu mu systenn ins the hiirmn of hemnt

(Q)

on ‘mu the fmrmni of work (W). ‘l’he first lmtw of

the ‘mi’si,mdynaisiics fom itcloserb system, stmttes thmtt the Iota mtmsumunt of eumergy does not change its he pnmcess hat is, the total eumerpy transferred Pm mi system is equal to tine immcremtse mf the internal eumerpy mf the systenn. ‘I he iustcnnah eumergy mf the system in the imuitimul state is imsdicmmted with U1 ammd in the final stmnte with U,. I he first law on the emuerpy hmmiaumce fOr the trmtuusitiomm froun state I Pm state 2, can thaum he wni teus mis:

Q

W U2 Ut (2.1)

Here

Q

- W is the total eumergy sunpphied to the system mmmd II U1 the chamuge of euuerpy in the systenum. ‘I he sign comsve mtkmn which has beets used imu the equatiomm amid ii figure 2.1 is that hmeat

Q

is considererl positive if tnmu msf erred to a systenuu mmd work W is coumsidered positive if perfbruned by the systeuss°.This sign comivenition will hue used coums’stetmtly ‘n this thesis. In a fuel ccli system the componnemuts (imeat exchangers, pumps, reactors) mire usot choserh systensus hint opens systemnms, in which unmtss is tra ssf ‘med Pm mmtsd tiomus line systeur.‘ he sclme ummitic representation of suds a systenm is giveniiifigur’ 2.1 h.

it ckmsed system : h ope system m:

[~~j

II~ H,

I Q=H, 91+W

Figure 2.1. Energy balances ,fhr a closed sv.s teem and an open 51.5! on

Only stemidy-state systeuns moredo ssidcmed. I e first law mtpphied tm mtmm mpen stem dy stmute syste mm does nmot c m isides the cha spe its enmerpy hetweemu twtm ummomnents in tiune (t1 t,), itS iii time cltmsed system. hut the chauuge ins emserpy (if the process flows hetweemu iuslet (1) amid mimtlet (2). ‘1 mc eusergy mf time prmcess flows cmmnsists of the ‘mnteruum I energy U. Other types of cumerpy msmay he relevaust ‘ts well, e.g. th‘kimuetic emmengy of time process flow on the poteistimd eumenpy if th e differences in height are signit’icatut. However, for the type mf systeunm whichu will he considered tIme kinetic anrl potential energy can he umeglected. The change its energy of hi

‘I’his Opus comsvemstiomm is lopicmul four cycles uliichu use hsemtt tom pnomduucc power (power p amits, gas turhittes). As txmwer gemsermitiolnn is the mmuaius aim of a fitch cell systcmss this cousventmoms is umscd.

l—hmweven, oilmen sigmm cousvemstiouss mmmc utsed jim tither miremus,

w

Q

+w

p ‘ocess flows is tiseref’tmre U - U1.

line work which is supplied tom time prmcess iiifigure 2.1-hi consists of two parts. l’he \V iusrhicmiteni imu time l’igure is the ‘tecimmncmtl work’ which is genermuted by the process flow mnuud tnmimnst’emresl to or froutus time systeusu. In time figumu’e this is represented by time shmtft of a~it5 tunrhimuc.

lie sunrtauummdinp atnumsphucre milso perfmmnms w’onk (mum tIme process flmw. At the inlet time process flow wills vomiumne V istrminsfcnred to) the systeun umnsder a pressure p. ‘~his pressumne ‘displmices’ time wmiumune V1 mtnrh therefmrc work p1V is work which is perftmrnned mm time syste is. Siunihmirly p~Vis time wmrk which is perf’onmmsed hmy time systeun. I Inc wmrk pV whicim is perfimnmedOiiomr by time process fltmws is immdicmtted its tIme vmhuuunetnic work. I he totmnh energy fmr ti e mpcmm systemuu is:

Q

(W p,V, p1V1) U LI1

1mm usnost cases tIme immterest is ommulyiiitIme tecismmicmnl work. Tom ehiinummmnte the vmhuuusme nc wmrk fioums time emmergy lumuimince, time stmmte vminimuhle “eusthsmnlpy’ hits heemu defused with the synshmh H:

H U pV

Sumhstitumti imp time iumtenmsal eumergy U by the enthmnhpy H ehimsninmitcs the vohuunnnetr’c wmrk lioun the energy hmn lmtnce. pivimug the smost comunmoum forums for the emiergy hmnhmtumcc four mimi opemu stemidy—stmnte systeums:

Q

H H1 W

2.2.2 Conversious of heat into work

It is impossible to cousvcnt Iucmtt fully iumtom xvonk. ‘1 his ‘s (mmmc 0 ‘mmsohmmtio s mf time secousd law of thenunorlyismtusuics. / very imnportmims qunestioms ‘s thereftmre, winch frmnctitm m(iftine hsemut cmiii he comuverted ituto wounk. Cmmssidcr a stemtdy-stmntc prmcess which uses heat to promduce work (mt huemit

euugiimc). 1 s figunne 2.2 such mt heat emugimme is simowus. o huroduucc tue work, huemut01 is used by the hmcmnt eungiume mit ems p ‘rmntuoc ‘I’. ‘fhe hnemi is umsed to p amduucc wo ‘kW, winch mtccorrhimmg to the secomud imiw is sussmnlicn thm m time hemit (W<Q). h (mrder to smut’sf’y he eusengy hahmnmsce oven time imemut emugimuec, a secomumd flow of lmemmt is mueccssmnny. This fltuw, imsdicmtted as

Q,

in figure 2.2. fkmws fnomnm time system mit teunmhmenmttumre ‘I~‘ h shumided rect’tmiplcs ‘l’l mmumrl ‘I, repuesemml hsemit

ro’seryo ins

‘1 he msuaximnmunsm mimnoumut omf work whs’chu cams he huroduced uusiumg the m moottomf I emit

Q~

dep minis

tmumthe temmupermuture mit which the hnemut is mivaihable (‘I ) and tine tempermuture mit wimichs it duOhe removed t’rommns the systennu (13. Accordiimp to the Cmirumot pniuuciphe. tine unmixi nnuumu amomutust of womrk which cmtn he Imnoduced frmnmu01 is cuhumal tom:

W,nic QI (i II) (2,1

‘fhme lenin hetweemu hrmncI-cts is time fimictkmus (if time hsemtt01 which cmos hue co uvented imutom york uusiusg the wo he’tt ‘es ‘rvomins its figure 2.2. auud is indicmited mis tIme ( anmmot efficiemucy:

Becmuuuse the sysmeuss is stemahy sImile, misc imsierunmil dumpy of thne systeumu tItles usout dlimimmgc amid ilict lISP

emmem’gy sm,mplmlied Rutime systeusi must he/dm’O.

l-lemtt reservoirs are idealized somumrces moid sinksloInhueai whuenc hmcmit cmou he supplied tom tin ext ‘mictcth Irons wimhmuumi clmmingiump the temsspermttuum’e of the m’cscns’oin.

‘1

(2.4)

Note hiatt four time work penhimnitnerl by time systemmniiil’igumre2.2to he ptmsitivc, time temmupcnmitumrc

mf hue hmemtt suupphicd (‘1

3

must hue lnghcn humus lime siusl\ temsspcnmmttmure (‘F,). As tIme nmttio hmccomsues

ekisertom umumily, i.e. time temumpenmitumne dihleremncc hetwecuntheimout (I) munrl cold (2) m’esenvoirs hmedllmmmcs smsmmdlen, time (‘mirmuot efficiemmcy decremises.

‘i’hme ruumtxiiumuuusi ansoont(Ifwork dmes usmut dcpcmmd oistime puoldess iiiwhich tIme hiemit is lmmintimihiy

ctmuuverteh iustm wurk, However.itcmin lie simowus thsmit mimsy pnuccss which reummlers time nmmuxiumuummmm mtmmsouummut wmrk, nsumst he mt reversible process’1

I

Summithu & vmuus Ness.Inmi simsuilmin mmmmimsuucr it emun

he A owus thimit mull reversible paicesses usiutst has c time smiu’me ef’b’icim’mtcy, i.e. the (‘min’umt cf’l’icicuscy.

I ‘igit, c’ 2.2.’ A Iteat en gitme u’orkirug bet o’e nilmc’ lit(11 ,‘e,s ei’t ‘01cm I’~and I’ to produc ii’orh H

~sImiw~~

~~H1

+wJ

H1 5,

J”igmmii 2.3’ lii’s!and second lan’ oftit r’omods’natoies

.5/riPopen sn,5!(/n

2.2,3 Iwst work amid exergy losses

for a rei’t ,‘,siblr proc s,s in ri siectd

Amsy meal mm tier ss ‘s ‘n ‘evens’ ble u sri co iseqocuitly has a lower ef f’ic’emscy thin s lie meyers’ be pntmcess wimicin heutrls to) lie smimsse ehumimmge iiistmite. I kmu innesensihmiy mm a ‘luau p ‘ocess Iddo’

cmiii he rhctn ‘misused by comsipanimug time neutl pm’occss with thur mcvnrsihlc pnoie ‘s .Its figmumes ~ I

mind 2.4 a m’cvcnsihhc mtmnd mimi inneversihule p ‘ocess mire shmowmn. lime dlmmtusge its stmtte hctw e s iuuhet (1) a url oummhct (2) is the s’musme its hmotlu l~~o~cesse~.‘ lie neycnsihulc process tmu’onloces uiiiu

utnsoLmmtt o~fwmnk W,, .which is referred tomis the reversible vcork.‘ lie mictumud pamcess pnomd ices

A proucess is i’cvcmsihmlc if a ~inomccmsis possibleiiiwhmichu mill momiss mmmiii cm mgy tImel’IlImss(11aunt fruit

mhic sysmcni ,im’ciii lime oppo~sic tImed ioumi. A ncmnl sysmcusm is imcvr,r comitplc(cly i’cynrsifilc,

01

w

12 secommsd law: ‘I 2 (ic(T)

w ImP a sm muller mtimnuuuut of wmmrk which will he denoterlitSW. loin time chmnuuge of state fnmni (I)

tom (2), theeusergy imucremise of time pno~cessfkmws is eqummnl to(H~ H1). ‘~lie work which is produced huy time prmcess is eqummul to time hscmmt sumphuhied Ru time sy steusm usuimmos time imucremiseiii

umergy(If the proeess fluws. Rewnitimug eqummitiomun (~.2):

Vi 1) (II, Ill)

lime m imixi uuuumsu miussoumunt ouf work ~amnhe geuse ‘mmterl if the pnomcess is reversible, ‘l’buis mimumoumit oil is w(mnk iii (hiemited mis the m’cversihmle workW,,. umusd tIme connespomudimug amuuoummmt of I cut mis time nevensihule hucmtt

0~,,

lo cmtlcuhmmte time mmsumxiunmumusu moumoummt tuf hemit which ditOhe srmpphicd tom time process.

Q,,,.

it is uuccessmury to immtrorhumce mtusomther property(Ifstmile: time “emutropy” xx ith time symbol “5”. ‘I’hc emitnopy (if the prucessuitIv~ii~figuures2.3 mmmurl 2.4 chum’umges l”o,’u~l tom S~.As

miuty stmmunrhunnd timer smodyumummmucs texh will immdicmmtc, tIme miusntmummmt ~ufhmcmmt mthmsmnhucd by time reversible ~mroccssis mietemnuniuserl by tIme chummusge ins emitnopy. ‘lime reversible hucunt cuts he emilcumluitemi f’noun:

Q,c, (2.6)

1-loweven, IOu mimsy nemml, irreversible promeess which nesudtsiii tIme sit tue dhsmmmsgc if stunte (1 2) tIme work mumud Iuemnt smmpplied to time systeuss will lie rhif’f’eremmt fuxmmsu the wok ummud hscmmt

ui

time reversible systeusu. Flue imrevers’hle imromcess is immdicumtcmh imm f’igumne2,4

W=W-, W

I I,S ~ H ,S

S

- I Q(’h)=Q.,, ~

l’igtm,’e 2,4.’ I”irst rtnd.sr mid lao’oftltci’onool~’narnicsfor rtrm opert. sieadi sum> sn’s/eatin a

irrener,sible5y5tent

hue work pror ocerl by time irneve ‘sible Ii xmccss is smsmmmller humus W ,. I hue difle eusce will I e

dcmnmtcd as the “kmst wmrk” AW. hlecause the ehsutmuge mf state is time saunc fun time reversib Ic

process in figure 2.3 u mmdtime irreversible process ins f’igune 2.4. time chumiusge ims ‘ustiuuulpy (II, H,) is the smimmue iiiboth cumses. ‘I luenefimne

Q

ims time inreversihie prmcess is sinu 11 ‘n tlnmnms

Q,,

. ‘Ih first hum (equmumtious ~.5) imudiemmles thmmmt tIm differemuce Imetweens time imemit sumimphich to time

‘eversible ummsd the im’m’evensihle process will he eqummil to tIme hifferensce huetween time work sumpplied i n t mc m’eversihie mmmiii time inTeversible prttcess (mnlthutluughm oilopposite s’~n). inn ottisr wounds, AW its figumne 2.4 Iseriummil toAQ.

Lqummitiouu 2.6us miotxcmhid for tIne irreversihmlc pro‘ess. ‘ho gemncr’mlizc tIme erhumumlomu filmbomtl

reversible mumunl mmcv rsihle proccsscs.thr in ‘eversihml eusiropy imieneumse iS , is introduced. his qimusuutity is mthwmiys positive (>0).

first lumw:

Q

=H~ H1 +W

I simu~the concept of the umreversuhic emmlropy imucremise. tIne cimummuge in entropy iii lime mcmii process cans he written mus:

s

~

AS,,,

(2.7)

‘Ii e irn ‘versible em tropy immenemuse caum he umsed ttm cmulcumluttc AQ:

AQ 1 AS,,, (2.8)

/ mmd the differcumcc iii wurk perftmrusm ‘d by thu reversible pn cess mind th’ irreversible process. previously defimued mis the host wt.unk, cmimm he cutlcolmi d (‘ma n time irreversible emutnopy imsereunse as well:

EW ‘f AS,,, (2.9)

AS, ‘s Ia ‘per ths’umm zero fOr mu nemil inrevrnsihle process mumid qu ‘il tom/ ‘notim ra’eversuhmlr hmrodess As time host work

us

prtmportkuuummh to) AS,,,, time i ‘reversible emitropy umscrcutse (on emstrtm uy genenatiomu) is mm mmmcm sure I/mr thc irreversibility of time pro cess. ftmwevcr, lo’ techmuical systeusus

a mssore unsefuni nscumsorc for time inreversuhuh y cmiii he ‘m trodunced thumns time tmst worl’. The host work indicates htmw umsuch mmmre womrk cmumld I umvc he ‘nu prmdumccd its u process

resiubti mg its time suimmue chummumpe ouf slate firumn 1 tm ~ indicmtted iiifupure 2. I. On if the womrk is sumpplied othe process (ep. ‘f f”gumre 2.4 represcmsts mm c mum mrcssomr). wills [ow mmsumci less work the sausme chaumpe tmf state comuk h’nve hmccn muchmieved, ‘I Iuem’eliuu’c ti e kmst work is m m e’uso‘d (If tine ‘cost’ of time imrevensihihuty omf ‘u prmeess Hmwcveu, he dit’ffreuncc h twe ‘in the meversihl maid lb irreversible pnoccss‘. sot (mmuhy the ml’ ‘‘ rem e ‘ wo k ou putt W. If is‘r ‘uml pnmc ss mroduuces less wmr ‘tin som ctunsmmm s less I cut Amid mis amsamumu t of neum AQ represem Isiii mmmsmtm mutt(If v’ho ‘as well. ‘l’o qumimutify the“ ‘I” losses u s‘ r suit omf inn ‘vensiii i y hmt 1 ost womrk u sd tim lower h at neuuoreusucmmt Em t e Pu id ‘55 hut c to me ‘m en in m accoummt tim I cu ‘lod( mmspmun t me vunlue of time h em AQ to the (is So ‘k the u s outt of wurk wInch co d he

produced from n thus hmc’ut shtmunlr lie detc ‘mmsiuued, Is go enal, m’ wmnk wh’chm cc ihe promdumc n fro n ~uuumu immunm of hemut depru ds on time te npcmcmtuu ‘eml which time he’mt is uuvuuih mhle. ‘time v ink

equ ivutlenu of AQ c umu he cmtlcolmmted fix mu lie (‘a usu rffieucm cy (s ‘e qumu loin 2.4). V liii lb e teusmpenunture

ft 3

at which h’ hmeunt is mtv’u’l’mhle is detenusmim er by ti e process. tI Ic np ‘n’ u ‘c omf time ‘mvmu’lahlc siusk ftmr heumt is mso mu churn’ dtrnistie (if the prmcess. hfowev ‘r, he ‘aleumlu iom omf time uummmmu. nit (if work which dit he produced di n \ req m’rcs th’ t time tcmnnpenatumne If thin ‘uvaihahie heunt siusk (1’ ) f/mn time rejected meunt ‘s deter mmmcd ‘is we

For tech m’cal systeuns inc nato ‘al sunk f’on he’tt ‘s fri ‘mmcd my e cmvi ‘tim n ‘mi (u i’. w’ t r). ‘I heref’omre a logicunl start’msp p nut 10’ time cunlc mlunt’oum if thc a nouunst rmf work w mich c’miu lie produ ned tiomus mm q immustity o ‘hea for tee nnicah sys cuss, is limit tie t ‘msmper’ tune if I ‘h ‘it sinmk (‘I,) fur the i ummmg’msu my hcmmt cmmgim eiiiI’ipunne 2.2 ‘s ‘qouul to tIne te ipcnumtumre tml the c uvirommu seust (1,,). ‘3 Inc nnsaximsm mmii wmrk winici cumin he pnoduuce f ‘(mmmi he [e’mt umsimp he eunvino mmmi mit

is ~m

simuk h’or hmeat, is knomwn mis thin ‘x ‘rgy E1~omf hr scmmt

I

Ru mill ‘mmmi is cmilcumlmmted fromsu:

EQ 0(1 ~‘

)

.

I lie ins. itS ~tresult of inneyc‘s’hility in II e neu 1 pntmccss cuts he ci uuu tIed so ‘r emme ly ums’msg tlue exerpy Os ‘tbne hemmt ‘I he muctounl promcess pntmdmiees \W 1 ‘ss work thimumu inc u eversuhi’ p ocess

wuth

tIme st ne chmnnge oil sImile I .2. Al the samne timmne, time ‘evensihle prtmcess coussumusses AQ less hemut. ‘I isis luemi ,usiumg the eumviro mmciii as mi hsemmt siusk. comoid he umserl to hunodu cc mm ‘ xxii mm

i ‘reve ‘sible turtmccss is therehiure eqummui to lime ltmst wrurk AW usuimsos time exerpy of AQ. ‘l’his ‘mmcl Fist womrk’ is cmtilerl time exerpy buss AE~mf time mmcv ‘rsihlc process:

\E AW AQ(l

~)

Btm Is AW amid

\Q

mire eqoumi tom tIne I AS,,, (see equummtiomus 2.8 mind 2.9). ‘1 Isis heunds ttm the fomhlowimmg expressious I/mr the exergy loss in mmii Irreversible pmnmcess imm mimi open. steuudy—stmnte systeums:

AE1 ‘l,,AS,,, (2.11)

‘I’his erlomutiomu

us

mm geumermil ulefiumitkmus uf tIme exergy kiss AIi~

mrs

mm process. It shtmws the funmsdmumumeuu tmmh rcimutinmnshsip between exergy loss mmmmd emulnopy pcnermntuons However, to cmmlculunte time exerpy Fuss time exergy hmtlmiuuce discumssed helomw will he used.

2.2,4 ‘fise exergy balance of a process

fom unumy process imu au mpemm stemmdy-state systemus. eumergy is supplied In the (turin mf heat

0

utmmd/oniii the form mf work W. The energy supplied to time systemmu crunrespnmnds lou mm certaimu muussounl of’ exerpy. The exergy of time eunergy which is supplied to mm prmcess in the mpemu system is:

Ii F0 E~

‘I he exergy mf tIme hsemtt

Q

is defim ed mis the ummsmoummul nmf work which cmuuhd he prmdumccd frtmumm this hemit usiumg the euuviroumnncumt mis mu heat r servomir. More its pemuenmil. time exerpy nmf miusy emsergy fhnmw cats he del”tied ‘is the umunnmumst of work‘ represeumts, umsi up time emmvurtmuu muemit as mm huemit siusk. ‘Ihe exergy tmf time hcumt is deli sed by eqummitiomu (2.10). The exerpy tuf the work prtmduccd by tue pnnuccss is (by definutit.uru) equmml Ru tIme wourk itself (E55=W).‘hercfomre the‘ ergy of lIme eume ‘gy

flows to prtucess‘ii the ompemu systeusm is cqummml tom:

E Q~l

~‘J

w

(2.12)

Suhstituti’mg cddc titium~(2.5) f’m,mT I ework W ummurl (2.7) 1/tn m’mc imeumt, she cxcrpysipplieniInI tim’ prtmccss us equmni tm:

I ‘i”) W H, H1 ‘l,,(S, S~) h,,AS,,,

‘Ihe last tenmn tins the m”glmt ha md side ‘s the exergy loss imu the imneversihule process. ‘lime equatinmmm eamu tbseneftmrc he rewrutteum tom:

I 10) W (II, ‘h,,S,) (H1 i,,S~) AE~ (2.13)

‘~lieahomve equmituor shows thu” tIme exergy wimch is supplied to the urrcvc1suhhe promces’ vysi~ energy flouws depeusds omumly tutu the exerpy homss in tIne pmnucess amid on the change tuf the shmmir oil time process flomws. This leads ttm the introrbuctiouuu mf mm umew vuuniahlc ouf siumte ftmr the process

flow, the “exergy” with syimihtmi “E”:

E II ‘i,,S (2.14)

‘lime exergy chsmmumge I/mr time proicess flow its lIme ompemu system in l’igumrc 2.4 timerefore hecmmsues:

E, F1 H, H1 ‘i,,(S, ~ (2.15)

‘I he exergy omf hemnt huts hucemu defiumedmis usumuxiusuoun mmmssomumnl ofwork tismit cumum he prtmduccrl fm’omss tIme Iuemmt osimug the eisvirommmcmst mis mm hucunt sumuk. (‘nlmrespomurhimugly time exergy Ii ouf mu process flouw cmiii he rlefimued mis time muummximnumnu umumuomumit o~fwturk thuml cmmn he proudumeed f’romun tIme flomw, usimsg the enyiromnnmemml mis a sink tOn both mnmiss mmuud hemit. ‘ho detenmumimme the umsmmxumsummusm mmnsouuusl ouf wuirk for the pnmuco’s’. the pruucess fliuw in time f’imu:nl snumle of mimE pruuces’. (H, miusrh 8,,) ummust have iernm womrk ptmteustumtl with respect P.m the eumvurommuunemst, i.e. he us equihibniumun with the

ensvurommmsucnt. A definitiomum tmf the exergy of a prmacess flomw

us

the fOllowuuug:

The exergv of’aum ermer,gs’ cttrrier indicate.s lion uniicln work carm he prodnrr’eolirua rem’er,sihle

proc’e.s.s nx’/mich/ake.splace in an operu armds’teads’ state s’v.s’/enmmt.s’irmg only the e,mi’ironmotenmta.s tt

Jmetmt .sirukand sm’heretIme eumergs’ carrierat tIn eiud of/he process is’ in c’onmpleie equilihritnn

mu’ith the cutt’ironmrmenm/.”

I

Lien, 19771.

Using the exergy mf the promcess Amw E.dOhimmliommm (2. 13) sumnplil’ies tom:

i

h)

W E F1 AE1 (2.16)

‘I’hsis equmu litmus cam he comnsidcrcdit5ftc “e ergy halmuusce” I/mr umum im’rcversihle pruccss imu mmmi ompe s stcmndy-stmmtc systemmu:

exergy supplied to tine process = exergy increase of the process flows cxci gy hss inn figure 2.5 the exergy humlutusce is ‘ehuneseumled scimemsummticm Ily. If time exergy halutunce is umsed tom cunlculmmte tIme exerpy lossiii the process us mmii tmpems stemmriy-stmmtc sysle is. erhuatiomu (2. 16) cutus lie rewnilteus tom’

AE~ Q(l l~) W (E, F,)

l”igure 2.5: ‘Ezerg:’ halctnce’ fur rum operm. .stetmds’ .5/cm/c si’s/cnn

2.3 ( HANGE IN ENERGY IN CHEMICAL REACTIONS

2,3, ( aiculating the change in connpositioms as a result of chemical reactioius Although time usummuuher omf comsspouncmsts ~ii itfitch ccii sysleims in which cimemnicmui nun

elcclntmcheusuicmmi rcmmdtiomus occur ussm’ctil (time cmnuhumstomr, tIme refnmmnuer mumud time fuel cell), tIme iuuflnmcmmc‘rmf lime losses iii these domnsptuiieuuls ommu the nesl nuf time systeun

us

very Immrge. i’hsere(nure

ime chum sgeiii exergy(Ifmm prtmcess fltmw mis mu resull of cisemsuicmih remmctuons will he umuvestigutted ims musore detumil in tisis sedluon. ‘i’iue resuults will be umseni in cimmnpler 3 to cahcuulutle the exergy Fusses in mm specuf’ie chucu’nmucmmi remuctuomn hum systems with usuture tiummnn omme remnctitmuu, Tine exergy misses ums mu result ot’ mm cheuuuicmml remmemiomi mmmc ccmuusinlered its the opeun. slemidy-stmmte systenm. i’urliueruuuoreiii this sedliomu the chuennemmi remudliolmu is considered mt5 mmii isothenmnunl process (muom chumusge

mis

tcmnpenmmtumrc mmusd a cnmumstmmm’mt pressure is mmssumusmed). Its mnny chsemmmicmmh remictinums there mmmc cheunicmml species w uch mmmd etumusumuneni (reumdtumuuts) mmmmd chemicunh species which mire fomnmncd fnmun time rcmmdtmmuuts (lumomolumets). (‘Iumurmmctenistuc fmr lime ciucusnemml remmdl’ous is thmmt time remmelmimuts mire

cuuusuummmed uomnl the products mire cremnted in fixeb nmmtuous.’I’Ise msummsshens which neprescust Ihe fixed natitms between the proudumcts mmusrl readlmnusts mmmc cunlled time stomicimiommsnetnic coefficiemits mind imudicated mis v,. The stoichunnmmsmetnic comefficuents I/mr prmducl species arc defineni pousitive toni time stnuiclmiomusuetnic cmefficucmnts f/mn nemmdlummmls usegmilive. Usimig v1 tom unducuste the stomichiommimetnic etuefficiemuts of coumupnmumemst X mm peusermil uunmtmmtioum fmn mm cheusmicuth reuuctksmms is:

~v1

J

X1 + v, X, + ... ‘

Iv,

N,+

Iv,

tIX, +

In a cimeuniemu nemmetioms mill species. produmc umund remmdlmmumt, huive zero) chumrpc. hum ~musclectrom chemical rcactkuuu chummrged species (uomss) arc ummvomlvenl atm lIme loutal charge mf lime remnelammts amid products is mmml unecessmmniiy cniouml’ f/mr every usmomle remucted mm fixed nmuunnhen nmf dec rouss cmmn he cuther pnnuchumccd on coumsonuerl its lime memuctiommi. [his stouiclnnmmsmetnie umnummuher f/mr lime electromns is indicutted hyi. ‘i’hmc munutuitiomum I/in chuemssicmml neumetinmuss cmiii he expmmumdeol om inchumde

electromchscmsuicmml remmdliommus:

IvmIX1+IvIY,+..’IvIX+Iv,IX,]+..±/e

A coumuyemutiommmal wumy omf rep ‘csemmtimmg lime comumpomsutiommu ouf mm guts fhuw, is by uusimsg mmxxuic fiu dliomus. I’omr the cmuhcuiuitiouns umuvomlviump cinmouges in dounpolsitioum mis mm ‘esuli omf cbmeummicuml mcumctiomuss it is nuoure ctunveusiemst omf use the mole vector us, which umses time mutmusuhen of moles I/mn cmmchm etmuumptimmems rmmthmen timummu time l’numdtiol us. ‘I lie chum sge its usumunhen ouf umsoles I/mr cmmciu omf time commuspommemlts as mm nesumit omf mm cheumncmmi neactiomum is propnlrlioummmh to lime stouchmiomu metric cmr I Iic’eus of time commmpomumcmst. If n is the uuuuunshen of ussomles mf cousupommemut i. timeus A s is the chmummupe its lIme

miumumuher ouf mnuomles misitresult omf lIme chuenuiemul rcmmdtiomuss. mu mum ‘s time muumumsher nuf chscmuuicmmh species in the systeums, Ihemu the nmmtios ins the chmmngcs iii time umomsuher nmf usuomles ouf time sepmmruule

cnmnsuponeuuls mire determimienh by the sRmichntmuusetnic coefficiemuls:

Am1 Aim, Aum,,,

“I ~S ‘

‘I lbs rumtio imudicumles Imoxx mmsousy muoles ,ifeumchm cclmmmpnmmemul

us

c’umssu’smcnl “r prcmd~c’ent,i.e. 1’,’xx l’mmr mu remidtiomus promeccobs. ‘lime vumniumble is defiuned mus time dismumuge of the remuctimlum coomrdinmum c c:

Ac An, (tIn mmumy i—hums (2.18)

‘l’hue ehamuge nuf the commmpolsmtuomm mis mu result of time chmeummicuil nemudtiomu is lhem’ef/mu’c f’ixenl by 17

sinsgh e punramumeter (Ac) insstemid tmf by the ctmmmcemmtruutitmns nun mule t’nmnctiomus nlf time species iusvnm ved If moire reuictitmuus tuccuriiitime systens. severumi meumctinmms cmtmrdimumnles (0usd (nun every che nicmml remidtioms) ennui he defimmed. If the muuuuuhcr of rcmmdtitmuus is eqouml tm (. time chmmmmge in time

mum usher omf msunmles nmf commnspommmeuut i

us

givems by:

Am, ~ v0, Ac~ fiuni=t us

‘line ehmunmuge in the blush numumuher omf mmutulcs mis un result ouf is givemu by:

An ~ Av1’ Ark (2.20)

whcm’e Av0 is the chsauupe ims time ttitmtl umumusuher omf nxxmles, i.e.:

Ay0 ~ v,0

In figure 2.6 the schematic rcprescmmtatioum omf a cheunicah remnethumu is giveus.

Differemst cheunucal ctmunprmnemmts ((nun exunmuuple comsupommemuts A, B) cuter time system. l’hse nummiuher nmf mtmlcs (or these enmunptmmne its mmmc mu1,~mind um1~0respectively. As a result mf the cheusuicuml

reactiomum the umumunher nuf unnuies oif time counpommeusts change. In the exunmnphc giveum ii figure 2.6 the f’olhowing neadlinmum tmccurs:

which learhs to the tkmws mm,~ u ~ mmumd u, leavimug 1 e syste mm.

Note limit lime prtmcess bmw tom the reactor is mmme sunsplc flow unmud time pun tium pmessumres which moe comns’dered mmmc the punrl’al pressures mf he pre— nixed neumetamuls mmusd tIne muoxtumne nuf prt.udumc s ‘~herd/methe losses mu the systeun unre surely the kisses omf time chc uuicumh readtiom mm ud muoml the itmssesiii lime mumixin p promcess (see Section 3 2).

p~‘I’

Ac

L~>~

10

Fzgmor’2.6: Ma sctnmcl e,mo’rg:’jlosm’.s01cr tIme .mv.s/enm hotirtdars’(- -) of cm mi’s/cnnin wlmiclt t

c’henrmic’ctl recmc’/ion oc’c’mirs

‘lime chumm ge

mi

cx rgy Rim the mm dlions cuin lie caic miumled umsiump tIme p ‘mmcm m 1 cnlu’mliol hm’mse om the exergy n’hnmmumge (on un steady-stale ompeum prtucess (equmutioms 2.15):

AE AH T,,4S

‘los cumlcumImmte lime chaumpe omf I me exergy its Inc mm cheunicmmh promccss mis ims figure 2.6, the Oh mum lilies AH mind AS humve to he cmilcuiatenl.

2,3.2 Calculating the change in exergy as a result of chemical reactiomus Eum //mrmlps’ of rear/iou

Becutumse mm wm.mrk is dehuvereri by time gemuermil ciueunicmml remudtitlmu in fipunre 2.6, mmccourdimup to time

fmrst

lmmw f/In time stemndy sImile ompemu systemsu (enlumutioums 2.2) Ihe hemmt which is transs(emreol froumn the systeun

(Q)

is equmuml to time chmmmsge imu emutimumlpy:

Q

LI~ H,

‘I he emulhumilpy chmnumge mis ut result ruf Ihe remmdliolmu in mimi isnmtiuenmsmmnh remndlinlns

us

lhere(omre erhummi tom the imemul promnhutced iii time nemudtioms mutud inmdicmmled mus the heunt omf reutdlion. To cmmlcunhmntc the eustlualpy chmmuuge, umse is mssmmde tuf the remmdtitmmu emmthmnhpy A,h. This Is the heust nmf reactitmmu if I

motile omf the “charuictenistic” comnpomnemmt nemmdts. Four exmumnple. the hemut or reaction fmr the counhustiomu reutctmnmmm omf hydropeum 1H~+ ~(), .11,01 will he given per unole II,, the heat tmf reundliomu f/mn time rcfmnmninp neadtiommm ICH +11,0 ‘ 3H, +GO! per motile CH1. etc. Jsimup the remidlioum cnmomnuliimmtte imutrouduced in the previomums sedtinmuu, the remictitums enthmnhpy per nxxule cmiii he defined by lSmsuith&Van Nessj:

A Is ±~i!. (2.22)

dc t~.l

wisene time imuduces p unmud T imuducate thmmt the denivumtmve is taken al coumstmnumt pressunre and temperature. Usimmg the remictionu cumthmnhpy lime heat whucim

us

gemmenmutedfcnmmusun ned imu the rcmndtinmmu is erhumud tom:

AH A,lm Ac (2.23)

If more linnmms omsue remmctiounm omccurs, the ttmtuih emutimunlpy ci anugc for line ismtiucnmmumm remmetiomums is the sunmn of the enhimmulpy chummuges omf line sepmurmmte readtiomus momd can hue wnitteus mis:

AH ~ ( \,Is)0 Ac~ (2.24)

If the reuudtitmms enthmuipy A,im is mepumlive. imeal is produced by the system munol Ihe remmdtkmnm is cumlied mm “exmthenmnuml” remudtimmmm. ‘lime nepmttive AH imudicates a decremmsc om( the cheusmucumi emuergy of the flow(s), i’ise ch7usslr’al emuergy us cmummv 2nled multi hemmn, If tine rcundlittn cnthmmlpy is positive imemit is used tom immcnemmse time cheismical energy om( the flow(s) mmumd time rcmmctiomm is imnolicunted mis “enndtmthermnunl”.

‘~lieenthalpy h, is the cmslhumhpy omf tIne pure species ‘mit lemmuperutture ‘I’ (Appeumdix I). L)uuc to the sehectioms omf the refereusce fomr the calcumlmmtmmn of the etutlualpies h, (Section 2.4), the nemudtious enthaipy (fOr houmnopeneomus gums phumse reundtiomus) cmiii he emulculmuted simply fromusu the euulimmmhpy tmf the pure species:

Aim ~v, h, (2.25)

Enutrops’ of rear’tiorm

Annaitmgosus lou time “eundtion cull uulpy, the reumc i’umu entropy camu he dcf1muen by’

As dS (2.26)

dc