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Pergamon PII: S0360-5442 96)00119-3EnergyVol. 22, No. 4, pp. 403-412, 1997 1997 Elsevier Science LtdPrinted in Great B ritain. All rights reserved0360-5442/97 17.00 + 0.00

E X E R G Y A N A L Y S I S O F S O L I D - O X I D E F U E L - C E L L ( S O F C )S Y S T E M S

K A I W . B E D R I N G A S , t I V A R S . E R T ES V A G ,* S T A L E B Y G G S T O Y L ~ A N DB J O R N F . M A G N U S S E N

D e p a r t m e n t o f A p p l i e d M e c h a n i c s , T h e r m o d y n a m i c s a n d F l u i d D y n a m i c s , N o r w e g i a n U n i v e r s i t y o f S c i e n c ea n d T e c h n o l o g y , T r o n d h e i m , N o r w a yReceived 8 January 1996)

A bs tra ct -- T he exerg y concept has been used to analyze two methane-fueled SOFC systems. Thesystem s include preheat ing o f fuel and air, reforming of methane to hydrogen, and com bustion ofthe remaining fuel in an afterburner. An iterative computer program using a sequential-modularapproach was developed and used for the analyses. Simulation of an SOFC system with externalreforming yielded first-law and second-law efficiencies of 58 and 56%, respectively, with 600%theoretical air. Heat released from the afterburner was used to reform methane, vaporize water,and preheat air and fuel. When these heat requirements were satisfied, the exhaust-gas temperaturewas so low that i t could only be used for heat ing rooms or water. Because of heat requirementsin the system, fuel utilization (FU) in the FC was limited to 75%. The remaining fuel was usedfor preheating and reforming. Reduced excess air led to reduced heat requirements and the possi-bility of a higher FU in the FC. Irreversibilities were also reduced and efficiencies increased.Recycling fuel and water va por from the FC resul ted in frst-law and second-law efficiencies of75.5 and 73%, respectively, with 600% theoretical air, vaporization of water was avoided and theFU was greater. 1997 Elsevier Science L td. All rights reserved.

1 . I N T R O D U C T I O NM o r e e f f i c i e n t a n d l e s s p o l l u ti n g p o w e r - g e n e r a t i o n s y s t e m s t h a n a r e n o w a v a i l a b l e a re n e e d e d . F o r t h isp u r p o s e , F C s m a y b e u s e f u l . A n F C c o n s i s ts o f a fu e l e le c t r o d e ( a n o d e ) a n d a n o x i d a n t e le c t r o d e( c a t h o d e ) , s e p a r a t e d b y a n i o n - c o n d u c t i n g e l e c t r o ly t e . T h e e l e c t r o d e s a r e c o n n e c t e d t h r o u g h a l o a d ( e . g .an e l ec t r i c m o t o r ) i n a c i r cu i t. Ion s a re t r ans po r t ed i n t he e l ec t ro l y t e , and e l ec t rons a re t r ans po r t ed i n thec i rc u i t. I n a s o l i d - o x i d e e l e c t r o ly t e , o x i d e i o n s ( 0 2 - ) a r e t r a n s p o rt e d b e t w e e n e l e c t ro d e s ; a t e m p e r a t u r e o fapp ox i m at e l y 1200 K i s r equ i red . The fue l is u s ua l l y gas e ous hyd roge n H2 . Ox yge n i n a ir is the m o s tc o m m o n l y u s e d o x i d i z e r . T h e r e a c t i o n p r o d u c e s e l e c t r i c e n e r g y a n d w a t e r . W h e n m e t h a n e i s u s e d a sfue l , i t i s f i r s t r e fo rm ed t o H2 and C O2 i n an endo t he rm i c p roces s wh i ch r equ i res wa t e r vapo r . ' . 2 F o ra n S O F C s y s t e m t o b e e f f i c i e n t , t h e e x h a u s t g a s e x i t i n g f r o m t h e F C m u s t h e a t t h e i n c o m i n g f u e l a n da i r ) T h e r e m a i n i n g f u e l , w h i c h e x i t s f r o m t h e F C , i s b u r n t , a n d t h e h e a t r e l e a s e d m a y b e e m p l o y e d t or e f o r m m e t h a n e a n d p r o d u c e w a t e r v a p o r f o r t h e r e f o r m i n g p r o c e s s ( s e e , e . g. A p p l e b y a n d F o u l k e s , 'p . 208 ) .

I m m e d i a t e l y f o l l o w i n g o r d i n a r y c o m b u s t i o n , t h e k in e t ic e n e r g y o f th e r e a c t io n p r o d u c t s i s m u c hh i g h e r t h a n t h e s t a ti s it ic a l a v e r a g e k in e t i c e n e r g y o f n e i g h b o r i n g m o l e c u l e s . A t r a n s f e r o f m o m e n t u mw i l l t h e r e f o r e t a k e p l a c e , t h e p r o d u c t s w i l l b e s l o w e d d o w n a n d c o o l e d b y t h e s u r r o u n d i n g s p e c i e s .D u n b a r a n d L i o c a l l e d t h is p r o c e s s a n internal thermal energy exchange T h e y s h o w e d t h a t t h i sp r o c e s s w a s r e s p o n s i b l e f o r a p p r o x i m a t e l y 7 0 % o f th e e n t r o p y g e n e r a t io n i n a c o m b u s t i o n c h a m b e r .

In t he F C , t he chem i ca l po t en t i a l o f 02 a t t he anode , where ox i da t i on occu r s , i s l ower t han i n o rd i na ryc o m b u s t i o n . T h e n u m b e r o f s u r ro u n d i n g s p e c i e s , w h i c h c a n s l o w d o w n p r o d u c t m o l e c u l e s , is th e r e f o r el o w e r . A s a r e s u l t , e n t r o p y g e n e r a t i o n d u e t o i n t e r n a l t h e r m a l e n e r g y e x c h a n g e i s m u c h l o w e r i n a nF C t h a n i n a c o m b u s t i o n c h a m b e r . T h e F C r e q u i r e s b o t h a h i g h t e m p e r a t u r e a n d c o o l i n g a i r . T h et e m p e r a t u r e g r a d i e n ts h a v e t o b e s m a l l . 5 T h e r e f o r e , c o o l i n g a i r h a s t o b e h e a t e d b e f o r e e n t e r i n g t h e

~ P r e s e n t a d d r e s s : K a t h m a n d u U n i v e r s i t y , S c h o o l o f E n g i n e e r i n g , K a t h m a n d u , N e p a l .* A u t h o r f o r c o r r e s p o n d e n c e . F a x : + 4 7 7 3 5 9 3 5 8 0 , e - m a i l : I v a r . S . E r t e s v a g @ s i n t e f . e n e r g y . n o~Deceased 11 Februa ry 1993 .4 0 3


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404 K .W . Bedring~ts et alF C . I n h i s l i te r a tu r e s u r v e y , B o s s e l 6 f o u n d r e p o r t s o f t h e o r e ti c a l a i r r a n g i n g f r o m 3 0 0 t o 1 0 0 0 . D u n b a re t a l 3 s i m u l a t e d a n S O F C s y s t e m w h i c h u t il i z e d a b o u t 2 0 o f th e f u e l i n t h e F C a n d p r o d u c e d v a p o rf o r a b o t t o m i n g s t e a m c y c l e . T h e y r e p o r t e d a s e c o n d - l a w e f f i c i e n c y o f a b o u t 6 2 . T h e f u e l w a s H 2and 200 t heo re t i ca l a i r wa s app l i ed .

S i ng l e S O F C un i t s can be s t ud i ed 7 s epa ra t e l y , w i t h a h i gh ex t en t o f C H4 re fo rm at i on and H2 u ti l iz -a t i o n . H o w e v e r , a c o m p l e t e F C s y s t e m c o n s i s t s o f s e v e r a l h e a t e x c h a n g e r s i n a d d i t i o n t o t h e F C u n i ta n d , t o o b t a i n h i g h e f f i c i e n c y , t h e t o t a l s y s t e m m u s t b e o p t i m i z e d . E x e r g y a n a l y s i s i s u s e d t o p i n p o in tt h e t h e r m o d y n a m i c l o s s e s i n e a c h u n i t a n d t o a s s e s s t h e w o r k p o t e n t i a l s o f t h e s t r e a m s o f m a t t e r a n do f h e a t i n t e r a c ti o n s . T h u s , t h e p o s s i b il i ti e s f o r i m p r o v e m e n t s i n t h e s y s t e m s a r e m a d e c l e a r . I n t h isp a p e r , w e p r e s e n t r e s u lt s f r o m s i m u l a t io n s o f t w o m e t h a n e - f u e l e d S O F C s y s t e m s .

2. THE EXERG Y CONCEPT2.1 . nergy and exergy

E n e r g y i s a c o n s e r v e d q u a n t i ty . H o w e v e r , w h e n e n e r g y i s c o n v e r t e d f r o m o n e f o r m t o a n o t h er , t h eab i l i ty to p roduc e w ork i s i r r eve r s ib ly lo s t. F u r the r , no t eve ry ene rg y fo rm has the s ame va lue o r ab i l i tyt o b e t r a n s f o r m e d t o o t h e r f o r m s . T h e e x e r g y c o n c e p t a l lo w s c a l c u l a t i o n o f th e r m o d y n a m i c lo s s es a n dc las s i f ica t ion to the t rue t r ans fo rm ab i l i ty o f d i f f e r en t ene rgy fo rm s . Ran t 8 g rouped ene rg y in tw o ca tego r -i es : T r a n s f o rm a b l e e n e r g y e x e r g y ) t h at c a n b e c o n v e r t e d fu l l y to w o r k a n d n o n - t r a n s f o r m a b l e e n e r g ya n e r g y ) t h a t c a n n o t b e c o n v e r t e d t o a n y o t h e r f o rm . E x e r g y c a n b e def in ed 9 '1 as t h e m a x i m u m o b t a i n -

ab le w ork a s ubs tance can y ie ld w hen i t i s b rough t r eve r s ib ly to equ i l ib r ium w i th the env i ronmen t .T h e a b i li t y t o h e a t o r t o p r o d u c e w o r k h a s t o s o m e e x t e n t b e e n a c c o u n t e d f o r i n t h e t ra d i ti o n a l e n e r g yf i rs t -l a w ) a n a ly s is . O n e e x a m p l e is t h a t h e a t a n d w o r k o u t p u t w h a t y o u w a n t ) h a v e b e e n c o m p a r e d

t o i n p u t f u e l e n e r g y w h a t y o u p a y f o r ) , i . e. f u e l c h e m i c a l e n e r g y i s m o r e v a l u a b l e th a n h e a t t r a n sf e r re df r o m t h e s y s t e m . A n o t h e r e x a m p l e i s t h e c o m m o n k n o w l e d g e t h a t o n e c a n n o t h e a t w a r m w a t e r w i t hc o l d e r w a t e r . T h e s e t w o e x a m p l e s a r e a c t u a l l y c o n s e q u e n c e s o f t h e s e c o n d l a w o f t h e r m o d y n a m i c s .Th e exe rg y m e thod i s a s upp leme n t , no t an a l te rna t ive , to ene rgy ana lys i s and p rov ides a means toquan t i fy and ana lyze the ab i l i ty fo r hea t ing and pow er p roduc t ion .2 .2 . The exergy balance for open systems

T h e e x e r g y c o n c e p t f o r o p e n s y s t e m s w i t h c h e m i c a l r e a c ti o n s m a y b e d e s c r ib e d a s f o l l o w s . ~ I np o w e r - p r o d u c i n g s y s t e m s , t h e g o a l i s m a x i m i z i n g n e t w o r k a n d e f f i c i e n c y . A p o w e r p l a n t o p e r a t e sa c c o r d i n g t o t h e f i r s t a n d s e c o n d l a w s o f t h e r m o d y n a m i c s . T o c a l c u l a t e t h e m a x i m u m w o r k t h a t c a nbe p roduced , w e cons ide r the s ys tem in F ig . 1 . We s uppos e tha t the hea t - t r ans fe r in te r ac t ions Q ~ . . . Q p

i n l e ti

I

L _ _ _

T o

_ Q:n v i r o n m e n t

Po Toi = i , . . , n

T / I l = 1 , . . . , p )Fig. 1. An open thermodynamic system.

o u t l e t

W


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Exergy analysis of solid-oxide fuel-cell SOFC ) systems 405and p roper t i e s en tha lpy , en t ro py ) a t t he in l e t and ou t l e t a r e f ixed . The s t r eams in and ou t o f the s ys temcons is t of n species wi th m olar f lowrates /~/~ ,i,, -/~ .o~t, i = 1 . . . . n ) . Th e f i r s t and seco nd laws for th es ys tem s how n in F ig. 1 a r e r e s pec t ive ly ,

p n

O o + E ~ t - W + E - h t . i - o . i ) i , , Ni.i, - 2 ( h t . i - h o , ,) o . t N ~ . o .t= d E / d t , ( 1 )I= i=l i=l~ 3 g ~ . : d S / d t ) - O o / T o ) - 2 Q , / T , ) - s , - s o . , ) , . [V , . , .+ ( S i - - S o . ' ) o u t ~ f i . o u ' ( 2 )

1=1 i=1 i= l

H e r e , h, .~ = h + V + gz)~ i s t he to t a l s pec i f ic en tha lpy and V and g z a r e , r e s pec t ive ly , the ve loc i tyand po ten t i a l ene rg y o f the mas s f low . We neg lec t the s ma l l k ine t ic and po ten t i a l ene rg ies o f the mas sflow so that ht,~ h i E i s t he s um o f the in t e rna l, k ine t i c and po ten t i a l ene rg ies o f the s ys tem , and Si s the s ys tem en t ropy . S teady s t a t e i s a s s umed s o tha t t ime de r iva t ives a r e ze ro . I f 0o i s e l imina tedbe tw een Eqs . 1 ) and 2 ) , t he exe rgy ba lance is ob ta ined . W i th ze ro expans ion ,

( 1 - T o / T , ) Q , + ~ [ ( f i ; - T o ; ; ) , . - ~ o . ; ] ~ ; . , ,, = ~ . ,I= i=l

i ) i i ) i i i )

+ 2 [ ( h i - T ~ i ) o u t - / o , i 1 / V i . . . + T o S g ~ . ,i = l ( 3 )i v ) v )w here Ew = I;V i s the ava i l ab le w o rk o r ex e rgy fo r s y s tem s w h ich do no t ex pand aga ins t the a tmos ph ere .A s u s ua l , en t ropy genera t ion r educes the ava i l ab le w ork . The exe rgy ba lance fo r an open s ys tem inEq . 3 ) s how s tha t the exe rg ies in hea t f low s i ) and mas s f low s ~ i) s upp l i ed to the s ys tem a re equa lto the w ork p roduc ed i i i ) , exe rgy in the ou t l e t mas s f low iv ) , and exe r gy des t roy ed th rough i r r eve r s ib lep roces s es v ) . Th e ene rgy inpu t equa l s the ene rgy ou tpu t fo r a s teady - s t a t e , s t eady - f low s ystem. Theou t l e t exe rg y is a lw ays l e s s than the in t ake exe rgy becau s e o f i r r eve r s ib le p roces s es . Ex ergy des t ruc t ioni s incu r r ed w hen i r r eve r s ib le chemica l and phys ica l p roces s es t ake p lace .

I r r e v e r s i b i l i t y fo r a s y s tem i s de f ined as the d i f f e r ence be tw een the r eve r s ib le w ork and the ac tua lwork : ) = Ew) ,ev - ~ :w = ToSg~,. Th e i r revers ib i l i ty can be ca lcula ted f rom the ex erg y acco unt by us ingEq . 3 ) . Th e f i r st - law e f f i c i ency i s de f ined as ~ = W,e t/Q H , w he re W. t i s the ne t w ork p rodu ced andQ H t h e l o w e r h e a t i n g v a l u e L H V ) . F o r m e t h a n e , L H V i s 5 0 , 0 0 9 k J / k g o r 8 0 2 , 3 0 0 J / t o o l. T h e s e c o n d -law e f f i c i ency is de f ined as the r a t io o f the ava i l ab le w ork to the r eve r s ib le w ork , i . e . ~ [ = F .w / F . w ) . ..H ere , Ew ) ,~ v i s the che mica l e xe rg y o f the fue l s ee S ec . 2 .3 ) . I n the f i rs t -l aw e f f i c i ency , the ou tpu ti s comp ared to the inpu t . I n the s econ d- law e f f i c i ency , the ou tpu t is com pared to the hypo the t i ca lm a x i m u m o u t p u t .2 .3 . T h e r m o c h e m i c a l p r o p e r t ie s

P h y s i c a l f lo w e x e r g y i s t h e w o r k p r o d u c e d w h e n a s t re a m o f m a t t e r i s b r o u g h t re v e r s i b ly t o t h er es t r i c t ed dead s t a t e w h i l e o n ly excha ng ing h ea t w i th the the rm al r e s e rvo i r o f the env ironment .~ 2 Thusex = h - h* - To s - s*) , w he re the s upe r s c r ip t * deno tes p roper t i e s eva lua ted a t the r e s t r i c t ed dead s t at e .In th i s s ta t e , t he t emp era tu re i s To and the p r es s u re P o , bu t the chem ica l po ten t i a l s o f the comp onen t sa r e d i f f e r e n t f r o m t h e c h e m i c a l p o t e n ti a l s o f t h e c o r r e s p o n d in g c o m p o n e n t s i n t h e e n v i r o n m e n t . C h e m i -ca l exe rg y t i s the m ax im um ob ta inab le w ork w hen the s t r eam o f ma t t e r is b rough t f rom the r e s t ri c t eddea d s ta te to th e to ta l de ad s ta te To, Po, I- to , /-Lo.2 . . . . p~ . , ) as the resul t of heat t rans fer and exc han geo f s ubs tances on ly w i th the env i ronmen t . Th i s cons t r a in t i s exp res s ed as ech = ~ . ~z = I I d , 7 - - [ d , O , i ) X i . T h echem ica l exe rg y o f me thane t~ w as s e t equa l to 51 ,748 kJ /kg 830 ,20 0 J / too l ) .2.4. T h e e n v i r o n m e n t

Exergy ana lys i s r equ i r es tha t the env i ronmen t i s de f ined . Th i s may d i f f e r f rom p lace to p lace andf rom t ime to t ime . H ere , t empera tu re and p res s u re o f the env i ronmen t w ere s e t equa l to the r e f e r enceEGY Z2 4 C


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406 K .W . Bedring~is et alt e m p e r a t u r e a n d p r e s s u r e ( 2 5 C , 1 a t m ) . T h e a t m o s p h e r e w a s m o d e l e d ~3 a s a n i d e a l g a s m i x t u r e w i t ht h e c o m p o s i t i o n s h o w n i n T a b l e 1 .

3. SIMULATIONOF SOFC SYSTEMS3 1 Simulation program for power systems

A g e n e r a l t h e r m o d y n a m i c s y s t e m c a n b e r e p r e s e n t e d b y a f l o w s h e e t , w h i c h i s a s y s t e m o f u n i ts a n di n t e rc o n n e c t i n g s t re a m s . T o s o l v e a f l o w s h e e t m e a n s t o d e t e r m i n e a l l v a r i a b le s i n th e s y s t e m . A g e n e r a ls i m u l a t io n p r o g r a m ~4 f o r p o w e r s y s t e m s w a s u s e d i n t h is s t ud y . T h e f l o w s h e e t w a s s o l v e d i t e r a ti v e l yb y a s e q u e n t i a l m o d u l a r a p p r o a c h . 1~ T h e s y s t e m u n i ts w e r e R e a c t o r , M i x e r , S p l i tt e r, a n d H e a tE x c h a n g e r . A l l u n i t m o d e l s a p p l y t h e i d e a l - g a s l aw . I n t h e s e q u e n t i a l m e t h o d , o u t l e t st r e a m v a l u e s a r ec o m p u t e d f r o m i n l e t s t r e a m s a n d p a r a m e t e r s o f t h e u n i t ( e . g . h e a t - t r a n s f e r a r e a ) . I t e r a t i o n o f t h e l o o pw a s t e r m i n a t e d w h e n t h e r e l a t i v e d i f f e r e n c e i n t h e e n t h a l p y o f t h e t e a r s t r e a m w a s l e s s t h a n 0 . 0 1 .T h e r m o d y n a m i c p r o p e r t i e s w e r e c a l c u l a t e d b y u s i n g t h e d a t a b a s e C H E M K IN . 63.2. Chemical reactions

D i r e c t o x i d a t io n o f m e t h a n e h a s n o t b e e n s u c c e s s f u l s o f a r. A t t e m p e r a t u r e s a b o v e 8 0 0 C , m e t h a n eb r e a k s u p a n d c a r b o n d e p o s i t s w i l l p l u g t h e p o r o u s a n o d e . A r e m e d y f o r c a r b o n i z a t i o n i s t o m i x w a t e rv a p o r a n d m e t h a n e a t a p p r o x i m a t e l y 1 0 0 0 C . H 2 i s f o r m e d f r o m CH 4 i n a r e f o r m i n g r e a c t io n . T h ee n d o t h e r m i c o v e r a l l r e a c t i o n i n t h e r e f o r m e r i s L7

C H 4 + 2 H 2 0 -~ CO 2 + 4H 2 . ( 4 )S u f f i c i e n t w a t e r m u s t b e s u p p l i e d s o t h a t c a r b o n i z a t i o n i s a v o i d e d . W a t e r - m e t h a n e m o l e r a t i o s e q u a lt o 3 .0 and 2 .2 ha ve b een s ugges t ed . 2'7.~7 Th e l a t t e r va l ue w as u s ed i n t h i s s t udy . Th e o ve ra l l r eac t i onfo r t he ce l l i s

H2 + 02 -* H2 0 . (5 )T h e d e g r e e o f f u e l u ti l iz a t io n ( i n t h e F C u n i t ) h a s a s t r o n g e f f e c t o n t h e e f f i c ie n c y o f t h e s y s t e m .C o m p l e t e f u e l u t i l iz a t io n i s i m p o s s i b l e b e c a u s e t h e c e l l v o l t a g e a d j u s ts t o t h e l o w e s t c h e m i c a l p o t e n t i a l sf o r t h e g a s m i x t u r e a t t h e e x i t o f t h e a n o d e a n d c a t h o d e c h a m b e r s . ,8 T h e r e f o r e , t o m a i n t a i n th e c h e m i c a lr e a c t io n s , t h e r e m u s t b e f u e l a t t h e e x i t o f th e a n o d e . I n t h e a f t e r b u r n e r, u n r e f o r m e d C H 4 a n d s u r p lu sH 2 a r e b u r n t , a n d c o m p l e t e r e a c t i o n i s a s s u m e d .3.3. Simulation of an SOFC system with external reformer

T h e F C s y s t e m s h o w n i n F ig . 2 c o n s i s t s o f a n S O F C , a r e f o r m e r , a n a f t e rb u r n e r , t w o p r e h e a t e r s , av a p o r i z e r , a n d a m i x e r . M e t h a n e a n d w a t e r v a p o r a t t h e r e s t r i c t e d d e a d s t a t e e n t e r t h e m i x e r a n d a r eh e a t e d i n p r e h e a t e r 2 b e f o r e e n t e r i n g t h e r e f o r m e r . T h e r e f o r m e r a n d t h e v a p o r i z e r a r e h e a t e d b y t h ea f t e r b u r n e r . S o m e h e a t i s l o s t f r o m t h e a f t e r b u r n e r w h i l e t h e o t h e r u n i t s a r e a s s u m e d t o b e a d i a b a t i c .T h e w a t e r - m e t h a n e m o l e r a t i o w a s e q u a l t o 2 . 2 a n d t h e t h e o r e t i c a l a i r w a s 6 0 0 % . O n e s i m u l a t i o n c a s ew a s s t o i c h io m e t r i c ( F i g . 3 ). T h e e x t e n t o f r e a c t io n o f C H 4 i n t he r e f o r m e r w a s s e t e q u a l t o 0 .9 . T h i sva l ue s eem s t o b e a c ons e rva t i ve f i gu re . 7,~7 Th e e x t en t o f r ea c t i on o f H i n t he F C was s e t equa l t o0 .75 . Wi t h a h i ghe r va l ue , t he re was no t s u f f i c i en t fue l l e f t t o s a t i s fy t he hea t i ng r equ i r em en t s i n t hev a p o r i z e r a n d r e f o r m e r .

T h e r e f o r m i n g r e a c t i o n d e p e n d s o n t h e t e m p e r a t u r e . T h e r e f o r m e r o u t l e t t e m p e r a t u r e a n d t h u s a l s o

Table 1. M ole fractions and ch emical exergy (J/mol) of the reference components in atm ospheric air.Component, i N2 02 H20 CO2 Ar

M ole fractio n, Xo.i 0.7567 0.2035 0.0303 0.0003 0.0092Chem ical ex erg y, ech.i (J/ m ol) 691.1 3946.7 8667.9 20108.5 11622.6


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E x e r g y a n a l y s i s o f s o li d - o x i d e f u el - c e ll ( S O F C ) s y s t e m s

2 5 .9

A i r @ z - @0 .0 1 8 1 .30 . 0 9 1 . 62 0 7 1

M e t h a n e 1 ~ : 0 l @1 0 0 . 0 ~ ) r - - - 7 r ~ - 7 ~ -1 00 .0 ~ - j M i x e r ~ _ P r e P a r e r 2 ~======;===i~ e f o m@ (2 7~'

W a t e r

58.1

; ~ 1 ~ 3 5 . i ~ 1 ( 4 .9 ) ~/ ~ 0 I

2 5 8 .7 I

~ ~ 9

F i g . 2 . T h e S O F C s y s t e m w i t h p r e h e a t i n g a n d e x t e r n a l r e f o r m i n g . R e s u l ts a r e s h o w n t o r 6 0 0 % t h e o r e t i ca l a i r( C a s e 1 ) . E n e r g i e s ( u p p e r n u m b e r ) a n d e x e r g i e s ( l o w e r n u m b e r ) a r e g i v e n f o r e a c h s t r e a m o f m a t t e r a n d h e a tf l o w , a s w e l l a s i r r e v e r s i b i l i ti e s f o r e a c h s y s t e m u n i t . T h e e n e r g y i s in % o f t h e L H V o f t h e s u p p l i e d f u e l ;e x e r g y a n d i r r e v e r s i b i l i t y a r e in % o f c h e m i c a l e x e r g y o f t h e s u p p l i e d f u e l .

4 0 7

M e t h a n e100.0100.0

1 6 . 6 '9 . 5

0.0 I 30 . 0 3 7 . 0 '2 1 . 6

@

5 ) I

@ . . . . 1 0 17 ~ ~ - ~ 1 09 loo ~ ~1 ~:~2 3 3 1 6 [

IVa~o rizerl ~ 12.16 .5W a t e r

@2 0 . 48 . 6 6 6 . 8

~-~ 135. i ' ' III 89.11l i n e r I ~

~ ~ ~ . 5

F i g . 3 . T h e S O F C s y s t e m w i t h p r e h e a t in g a n d e x t e r n a l r e f o r m i n g . R e s u l t s a r e g i v e n f o r s t o i c h io m e t r i c c o n -d i t i o n s ( C a s e 2 ) . E n e r g i e s , e x e r g i e s a n d i r r e v e r s i b i l i t i e s r e f e r t o t h e s a m e c o n d i t i o n s a s i n F i g . 2 .

t h e F C f u e l i n l e t t e m p e r a t u r e w a s s e t e q u a l t o 1 1 0 0 K . T h e S O F C r e q u i r e s a h i g h t e m p e r a t u r e , w h i l et h e t e m p e r a t u r e g r a d i e n t s h a v e t o b e s m a l l . 5 A c c o r d i n g l y , th e F C o u t l e t t e m p e r a t u r e w a s s e t a t 1 2 0 0 K .T h e F C a i r - i n l e t a n d r e f o m e r - i n l e t t e m p e r a t u r e s w e r e c a l c u l a t e d b y u s i n g t h e i te r a t iv e s i m u l a t i o n p r o -g r a m . T h e a f t e r b u r n e r w a s a s s u m e d t o b e i s o t h e r m a l , i . e. it s in l e t a n d o u t l e t te m p e r a t u r e s w e r e s e t e q u a lt o th e F C o u t l e t te m p e r a t u r e o f 1 2 0 0 K .

T h e t o t a l h e a t - tr a n s f e r c o e f f i c i e n t s w e r e s e t e q u a l t o 0 . 0 5 k W / m z K f o r t h e c o u n t e r f l o w h e a te x c h a n g e r s . T h e h e a t - t r a n s f e r a r e a s w e r e a d j u s t e d s u c h th a t t h e m i n i m u m t e m p e r a t u r e d i f f e r e n c e s w e r eg r e a t e r t h a n 2 0 K . W i t h 6 0 0 % t h e o r e t i c a l ai r , t h e h e a t - t r a n s f e r a r e a w a s 2 5 , 0 0 0 m 2 i n p r e h e a t e r 1 a n d5 0 0 m 2 i n p r e h e a t e r 2 . W i t h 1 0 0 % t h e o r e t i c a l a ir , t h e a r e a o f p r e h e a t e r 1 w a s 1 0 0 0 m z. W a t e r w a sa s s u m e d t o b e a n i d e a l g a s at t h e e n t ra n c e ( s t r e a m 3 ) . T h e n e g l e c t e d c h e m i c a l e x e r g y o f l i q u id w a t e r


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408 K.W . Bedring/ts et alw as 0 .8 o f the fue l chem ica l exe rgy . I n the s imu la t ions , the p r es s u re w as s e t equa l to 101 ,325 P a(1 a tm) . P res s u re lo s s es and as s oc ia t ed lo s s es o f ene rgy and exe rgy in the s ys tem w ere neg lec ted .3 .4 . S im u la t ion o f an SO F C s ys tem wi th ex te r na l r e fo rm ing an d r ecyc l ing

Th e F C s ys tem s how n in F ig . 4 i s s imi la r to the s ys tem de s c r ibed in S ec . 3 .3 , exce p t tha t exhaus tg a s e s a r e r e c y c l e d a n d a n e x t e r n a l w a t e r s u p p l y i s n o t n e e d e d . T h e o b j e c t i v e o f re c y c l i n g e x h a u s t g a se st o t h e r e f o r m e r is t o u s e t h e w a t e r v a p o r i n t h e e x h a u s t f o r t h e r e f o r m i n g o f m e t h a n e . T h e r e f o r e , th i ss ys tem r equ i r es l e s s hea t than the s ys tem w i thou t r ecyc l ing . The F C anode ( i . e . f ue l s ide ) ou t l e t s t r eamis s p l it . A s in the p r ev iou s s ys tem, th i s cas e w as s imu la ted w i th 600 o f theo re t i ca l a i r, 90 r eac t iono f C H4 in t h e r e f o r m e r , a w a t e r - m e t h a n e m o l e r a ti o e q u a l to 2 . 2, 7 5 r e a c t io n o f H 2 i n th e F C , a n dcomple te ox ida t ion in the a f t e rbu rne r . The s p l i t f r ac t ion fo r the anode ou t l e t s t r eam w as s pec i f i ed tog i v e t h e d e s i re d w a t e r - m e t h a n e m o l e ra t i o f o r th e r e fo r m e r . In t h is c as e , 0 . 4 4 o f th e a n o d e s tr e a mw a s r e c i r c u l a t e d . T h e r e a c t o r a n d s p l i t t e r m o d e l s w e r e c o m b i n e d t o s i m u l a t e t h e F C . T h i s c o m b i n e dreac to r - and - s p l i t t e r m ode l w as r ega rde d as a one -un i t F C in the s imu la t ion . U n l ike the s ys tem o fS ec . 3 .3 , f ue l and a i r a r e no t comple te ly mixed in o r a f t e r the F C . F u r the rmore , the to t a l hea t t r ans f e rcoe f f i c i en t s w ere s e t equa l to 0 .05 kW /m2 K fo r the coun te r f low hea t exchan ger s . The he a t - t r ans f e r a r easo f p r ehe a te r s 1 and 2 w ere 25 ,000 m 2 and 150 m 2, r e s pec t ive ly . Th e p res s u re w as 1 a tm.

4. RESULTS4.1 . a l a n c e o f e n e rg y a n d e x e r g y

F i g u r e s 2 - 4 p r e s e n t d a t a f o r e n e r g y a n d e x e r g y f r o m t h e s i m u l a t io n s f o r t h r e e ca s e s. H e r e , e n e r g yi s t h e s u m o f t h e r m a l e n t h a lp y a n d f u e l e n t h a l p y , e x p r e s s e d i n o f th e L H V f o r s tr e a m 1 . I n t h ep res en ta t ions , the en tha lp ies o f fo rma t ion o f the r eac tan t s a r e exp res s ed in t e rms o f an en tha lpy o fr eac t ion o r hea t ing va lue , w h ich i s a s s oc ia t ed w i th fue l . F low exe rg ies and i r r eve r s ib i l i ti e s a r e in o ft h e c h e m i c a l e x e r g y o f s t r e a m 1 . A t t h e e n v i r o n m e n t a l p r e s s u r e a n d t e m p e r a t u r e , t h e f u e l e x e r g y i se q u a l t o t h e c h e m i c a l e x e r g y o f t h e f u e l. T a b l e 2 s h o w s c o m p a r i s o n s o f i n p u t a n d o u t p u t d a t a f o r th eth ree cas es. Te mp era tu res and mas s f low s a r e l i st ed in Tab le 3.

Air 185.994.9 [

206.9 l @ 161.1109.9 144.9Methane Q I: Preheater2 [ @ =100.0 (1.1) I0 5.6 F ~ ~ 34.9100.0 103.0 29.8

2 12 .5 l @113.9 236.7135.5

.3 r - - F ue l _Cell . . . . . . . . . . . . . . . .~ Prehea ter ~ _ _ _ ~ ,

0.0 (10.7) : II . . . . . . . ~ 'I 5~ [ ~v ..... [,,0 .0 . . . . . . . . . . . . . ~__._ _~ . . . . . . . i _ _ _

Fig. 4. The SOFC system is shown with preheating, external reforming, and recycling. Results are given for600 theoreticalair (C ase 3). Energies, exerg ies and irreversibilities e fer to the sam e conditions as in Fig. 2.


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410 K.W . Bedringis et ale r s . I t was t he re fo re pos s i b l e t o i nc reas e t he u t i l i za t i on o f a i n t h e F C f r o m 7 5 t o 8 0 ( r e s u lt s n o ts h o w n ) , w h i c h r a i s e d t h e s e c o n d - l a w e f f i c i e n c y f r o m 6 4 .6 t o 7 0 . 0 . T h e s t r ik i n g f e a tu r e o f th e s t o ic h i o -m e t r i c c a s e w a s t h e i n c r e a s e o f e f f i c i e n c y a n d t h e l o w i r r e v e rs i b il i ty r a t e in p r e h e a t e r 1 c o m p a r e d t oC as e 1 wi t h 600 t heo re t i ca l a i r .

4 .4 . C a s e 3 : S O F C s y s t e m w i t h e x t e r n a l r e fo r m i n g a n d r e c y c l i n g a n d a l a r g e e x c e s s o f a irT h i s i s t h e s e c o n d s y s t e m ( F ig . 4 ) s i m u l a t e d w i t h 6 0 0 t h e o r e ti c a l ai r. T h e o b v i o u s a d v a n t a g e o ft h is s y s t e m w a s t h a t n o h e a t w a s r e q u i r e d t o v a p o r i z e w a t e r a n d , b e c a u s e o f r e c y c l i n g , m o r e H 2 en t e r e dt he F C i n C as e 3 t han i n C as e 1 . Th i s i nc reas ed t he fue l u t i l i za t i on i n t he F C . As i n C as e 1 , p rehea t e r1 t r ans fe r red a g rea t dea l o f hea t , equa l l i ng abo u t 2 . 5 t i m es t he e l ec t r ic ou t pu t o f t he F C . H ere , t hei r r eve r s i b i l i t y wi l l be a l i t tl e l owe r i n the F C t han t he r e s u l t s i n F i g . 4 i nd i ca t e a nd co r res po nd i ng l yh i g h e r i n t h e a f t e r b u r n e r . H o w e v e r , b e c a u s e t h e r e c i r c u l a t e d m a t t e r w a s n o t m i x e d w i t h e x c e s s a i r , t h ei r r e v e rs i b i li t y o f t h e F C w a s l o w e r t h a n i n C a s e 1 . T h e s e c o n d - l a w e f f i c ie n c y in C a s e 3 w i t h r e c y c l i n gw a s l a r g e r t h a n t h e c o m p a r a b l e C a s e 1 w i t h o u t r e c y c l i n g . T h i s i n c r e a s e r e s u l t e d m a i n l y b e c a u s e n ohea t was needed t o vapo r i ze wa t e r . I r r eve r s i b i l i t i e s i n a l l un i t s excep t p rehea t e r 2 were a l i t t l e l owerand fue l u t i l i za t i on was h i ghe r .

5. DISCUSSION5 . 1. B a l a n c e o f e n e r g y a n d e x e r g y

T h e b a l a n c e s s h o w n i n T a b l e 2 e m p h a s i z e t h e im p o r t a n c e o f a n a l y z i n g b o t h e x e r g y a n d e n e r g y f l o w s .T h e e x e r g y i n p u t i s r e la t i v e l y c l o s e t o t h e e n e r g y i n p u t , a n d t h u s t h e s e c o n d - l a w e f f i c ie n c y i s c lo s e t ot h e f i r st - la w e f f i c i e n c y . T h e p r i m a r y d i f f e r e n c e b e t w e e n t h e e n e r g y a n d e x e r g y b a l a n c e s i s id e n t if i c a ti o no f l o s s e s . E n e r g y w a s m a i n l y l o s t i n t h e e x h a u s t g a s , w h i l e e x e r g y w a s m a i n l y l o s t b y i r r e v e r s i b i l i t i e si n t he s y s t em un i t s . In a r ea l s y s t em , t he hea t l o s s es and i r r eve r s i b i l i t i e s w i l l be s om ewha t l a rge r . Thee x h a u s t - g a s t e m p e r a t u r e s w e r e 4 1 0 K ( 1 3 7 C ) a n d 3 9 2 K ( 1 1 9 C ) f o r C a s e s 1 a n d 3 , r e s p e c ti v e l y .T h e s e t e m p e r a t u r e s m a y b e u t i l i z e d f o r l o w - t e m p e r a t u r e h e a t in g , e . g . r o o m a n d w a t e r h e a ti n g . I n c o n v e n -t i o n a l p o w e r p l a n t s , c o o l i n g o f e x h a u s t g a s e s t o a t e m p e r a t u r e a p p r o a c h i n g t h e d e w p o i n t i s u s u a l l ya v o i d e d , p r i m a r i l y t o p r e v e n t d e p o s i t i o n o f s u l f u r i c a n d n i t r i c a c i d s b u t a l s o t o p r o v i d e s t a c k d r a u g h tt o m a i n t a i n t h e g a s f l o w . I n a m e t h a n e - f u e l e d s y s t e m , t h e s u l f u r c o n t e n t i s u s u a l l y n e g l i g i b l e . T h e r em a y , h o w e v e r , b e s o m e n i tr i c o x i d e s f r o m t h e a f t e r b u rn e r . F u r t h e r c o o l i n g o f t h e e x h a u s t g a s e s h a s t ob e e v a l u a t e d a g a i n s t t h e r e d u c e d s t a c k d r a u g h t a n d p o s s i b l e n e e d f o r m e c h a n i c a l l y f o r c e d v e n t i n g o ft h e s y s t e m .5.2. C h e m i c a l e x e r g y i n e x h a u s t g a s r e s ta t in g t h e r e f e re n c e ?

T h e e x e r g y i n t h e e x h a u s t g a s c a n b e s p l i t i n t o t w o c o m p o n e n t s , c h e m i c a l a n d t h e r m a l e x e r g i e s( T a b l e 4 ) . T h e r e i s , h o w e v e r , n o p r a c t i c a l d e v i c e t h a t c a n u t i li z e t h e c h e m i c a l e x e r g y o f t h e e x h a u s tgas . The ques t i on i s t hen whe t he r i t i s co r rec t t o i nc l ude t h i s work i n t he ava i l ab l e ene rgy . The f i r s tf a c t t o n o t e i s t h a t t h e c h e m i c a l e x e r g i e s o f e x h a u s t - g a s c o m p o n e n t s h a v e t o b e i n c l u d e d i n t h e c a l c u -l a ti o n s. H o w e v e r , a f t e r p e r f o r m i n g t h e s y s t e m c a l c u la t i o n s, i t i s p o s s i b le t o s u b t r a c t t h e r e l e a s e d c h e m i -

Table 4. M ole fractions in the exhaust gas. Chemical and therma l compo-nents of the exerg y released in the e x h a u s t g a s in of the fuel chemicalexergy.C a s e 1 C a s e 2 C a s e 3

xH2 0.0975 0.345 i 0.0636xo2 0.1601 0.0001 0.1661xN 0.7170 0.5709 0.7441Xco2 0.0167 0.0770 0.0172XAr 0.0087 0.0069 0.0090Chem ical exe rgy 1.89 4.29 1.24Thermal exergy 4.06 5.23 3.06S u m 5 9 5 9 5 2 4.30


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Exergy analysis of solid-oxide fuel-cell SOFC) systems 411

c a l e x e r g y f r o m t h e s u p p l i e d e x e r g y a n d f r o m a l l o t h e r e x e r g y f l o w s . T h i s a p p r o a c h y i e l d s a l o w e rm a x i m u m w o r k a n d t h u s a h i g h e r s e c o n d - l a w e f f i c i e n c y . I t i s s o m e w h a t s i m i l a r t o u s i n g t h e l o w e rhea t i ng va l ue an d t hus no t inc l ud i ng t he non -u t i l i zab l e hea t o f condens a t i on . B u t s uch an ope ra t i onra i s es s eve ra l new ques t i ons . One ques t i on i s whe t he r we s hou l d , e . g . s ub t r ac t t he r e l eas ed chem i ca le x e r g y o f t h e a c t u a l p r o c e s s o r , a l te r n a t iv e l y , u s e a q u a n t i t y b a s e d o n a c o r r e s p o n d i n g s t o ic h i o m e t r i cp r o c e s s o r s o m e o t h e r r e f e r e n c e p r o c e s s . T h e c h e m i c a l e x e r g y o f t h e e x h a u s t g a s e s i s n o t o n l y a c h a r a c -t e r i s ti c o f t he fue l bu t a l s o a func t i on o f t he a i r - fu e l r a t i o and o t he r f ea t u res o f t he ac t ua l p roces s . I ts e e m s t o u s t h a t k e e p i n g t h e c h e m i c a l e x e r g y o f t h e e x h a u s t g a s i n c l u d e d i n th e e x e r g y b a l a n c e i s th eo n l y p r e c i s e a n d u n a m b i g u o u s p r o c e d u r e i n e x e r g y a n a l y s e s .5.3. Operational parameters

T h e c o m p u t a t i o n a l r e s u lt s d e p e n d o n a l a r g e n u m b e r o f p a r a m e t e r s i n th e s y s t e m s a n d a l so o n t h ec o n f i g u r a t io n o f t h e s y s t e m . T h e c h o s e n a n d c a l c u l a t e d v a l u e s a r e w i t h i n r e a li s ti c r a n g e s f o r a c t u a ls y s t e m s . H o w e v e r , i n a n a c t u a l o p e r a t i n g s y s t e m , t h e v a l u e s w i ll p r o b a b l y d i f f e r so m e w h a t . T h e s i m u l a -t io n s s e r v e a s i n d i c a t i o n s o f w h a t m a y b e e x p e c t e d f r o m r e a l s y s t e m s w i t h a s i m i l a r c o n f i g u ra t io n .S o m e o f t h e o p e r a t i o n a l p a r a m e t e r s a r e d e t e r m i n e d b y t h e a v a i l a b l e e q u i p m e n t , e . g . h e a t e x c h a n g e r s .W h e n t h e a c tu a l s y s t e m u n i t s a r e k n o w n , a m o r e d e t a i le d c a l c u l a ti o n m a y b e p e r f o r m e d a n d t h e n as e n s i t i v i t y a n a l y s i s o n i m p o r t a n t p a r a m e t e r s m a y b e p e r f o r m e d .

Excess air C a l c u l a t io n s w e r e p e r f o r m e d f o r t h e t w o c o n f i g u r a ti o n s w i t h 6 0 0 t h e o r e ti c a l a i r. T h i sa m o u n t o f e x c e s s a i r i s c o n s i d e r a b l y h i g h e r t h a n i s u s e d i n c o n v e n t i o n a l p o w e r p l a n t s . A g a s b u r n e rt yp i ca l l y ope ra t e s a t 105 t heo re t i ca l a i r . A gas t u rb i ne t yp i ca l l y ope ra t e s a t 300 t heo re t i ca l a i r. TheF C r e q u i r e s a h i g h a i r - f u e l r a t io f o r t w o r e a s o n s : t o m a i n t a i n a r e la t i v e ly h i g h 0 2 c o n c e n t r a t io n a t t h ec a t h o d e a n d f o r c o o l i n g w i t h o u t l a r g e t e m p e r a t u r e g r a d i e n t s . W e h a v e s e e n t h a t t h e l a r g e a m o u n t o fexces s a i r i nc reas ed t he i r r eve r s i b i l i t y cons i de rab l y .

Extent of reaction of 1 12 in FC In t he ca l cu l a t i ons , t he ex t en t o f r eac t i on was l i m i t ed t o 75 byt h e h e a t r e q u i r e d f o r t h e r e f o r m i n g r e a c t i o n . T h i s p e r c e n t a g e m a y b e r a i s e d b y u s i n g a n a l t e r n a t i v ec o n f i g u r a ti o n o f t h e s y s t e m ( s e e t h e f o l l o w i n g d i s c u s si o n ) .

Water methane mole ratio and extent of reaction of methane in the reformer C o m p l e t e r e f o r m i n gi s n o t r e a li s ti c . R e a c t i o n s o f 9 0 o f t h e C H 4 i s c o n s i d e r e d t o b e a c o n s e r v a t i v e v a l u e . F r o m t y p i c a lda t a g i v en by R i d l e r and T w i gg t7 (p . 260 ) , i t s eem s t ha t a h i ghe r va l ue i s pos s i b l e . An ex t en t o f r eac t i onas h i gh as pos s i b l e i s des i r ed i n o rde r t o m i n i m i ze i r r eve r s i b i l i t i e s . F o r a s pec i f i c dev i ce , t he ex t en t o fr e a c t i o n c a n b e i n c r e a s e d b y i m p r o v i n g l o c a l m o l e c u l a r m i x i n g i n t h e r e a c t o r . I n t h e c a l c u l a t i o n s , aw a t e r - m e t h a n e m o l e r a t i o o f 2 . 2 w a s u s e d , i . e . 2 . 2 m o l e s w a t e r v a p o r w e r e s u p p l i e d i n s t r e a m 3 f o re a c h m o l e o f m e t h a n e s u p p l i e d in s t r e a m 1 . T h e m i n i m u m v a l u e f r o m E q . ( 4 ) i s 2 . T h u s , w i th r e a c t io no f 9 0 o f CH 4 i n t h e s im u l a t i o n , 2 . 4 4 m o l e s o f w a t e r v a p o r w e r e s u p p l ie d f o r e a c h m o l e o f r e a c t e dm e t h a n e . R i d l e r a n d T w i g g t7 s u g g e s t e d a s t e a m - c a r b o n r a t i o o f 2. 2 b u t u s e d a h i g h e r f r a c t io n a l c o n v e r -s i on fo r CH 4. E x c e s s w a t e r v a p o r i s r e q u ir e d t o a v o i d c a r b o n i z a t io n i n t h e r e f o r m e r . O n t h e o t h e r h a n d ,wa t e r vapo r i za t i on i nc reas ed t he i r r eve r s i b i l i t y .5.4. Combustion in the afterburner

C o m p l e t e c o m b u s t i o n w a s a s s u m e d i n t h e a f t e r b u r n e r . T h e m o l e f r a c t i o n s o f H 2 a n d C H 4 w e r e v e r yl o w . T h e b u r n e r t e m p e r a t u r e w a s m o d e r a t e l y h i g h a t 1 2 0 0 K . P r e m i x e d c o m b u s t i o n o f fu e l - l e a n m i x t u r e si s known t o be d i f f i cu l t t o i gn i t e and s t ab i l i ze . Thus , an i m por t an t ques t i on i s whe t he r t he m i x t u re wi l lbu rn . C o m bus t i on c a l cu l a t i ons o f a p e r fec t l y s t ir r ed r eac t o r w i t h t he P S R code 2'2~ bas ed o n C HEMKIN16i n d i c a t e d t h a t t h e a f t e r b u r n e r m i x t u r e w i l l b u r n a t t h e g i v e n t e m p e r a t u r e d u e t o t h e l o w e x t i n c t i o nt e m p e r a t u r e o f h y d r o g e n / a i r m i x t u re s . W i t h a r e s i d e n c e t i m e w i t h in a r e a l is t ic l i m i t ( > 1 0 m s ) , c o m b u s -t i on wi l l be v i r t ua l l y com pl e t e .5.5. System configuration

I n t h e s i m u l a t e d s y s t e m s , t h e h e a t f o r t h e r e f o r m i n g r e a c t i o n i s s u p p l i e d f r o m a n a f t e r b u r n e r w h e r ee x c e s s f u e l i s c o m b u s t e d . T h i s h e a t r e q u i r e m e n t l i m i ts t h e e x t e n t o f re a c t i o n i n th e F C . F u e l r e f o r m i n gi s e x p e n s i v e i n t e r m s o f e x e r g y , a n d c o m b u s t i o n o f r e f o r m e d f u e l s h o u ld b e r e d u c e d i f p o s s i b le . A na l t e rn a t i v e c o n f i g u r a ti o n m i g h t b e t o u s e s o m e o f t h e m e t h a n e d i r e c t l y t o h e a t t h e r e f o r m e r , i .e . b yus i ng a s ho r t cu t f rom t he fue l i n l e t t o t he a f t e rbu rne r o r t o a s epa ra t e bu rne r . In t he s i m u l a t ed s y s t em s ,t h e c o o l i n g a i r f o r th e F C w a s m i x e d w i t h e x c e s s f u e l a n d r e a c t i o n p r o d u c t s . T h i s m i x i n g i s ir r e v e r si b l e.


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412 K .W . Bedringhs et alI f s o m e c o o l i n g a i r i s k e p t s e p a r a t e f r o m t h e r e a c t i n g s t r e a m , i r r e v e r s i b i li t y d u e t o m i x i n g i s r e d u c e d .W h e n t h is i s d o n e , a d d i t i o n a l h e a t e x c h a n g e r s a r e n e e d e d t o u t i l iz e t h e th e r m a l e n e r g y o f t h e c o o l i n ga i r . T h e s e a l t e r n a t i v e c o n f i g u r a t i o n s w e r e n o t i n v e s t i g a t e d b u t s h o u l d b e c o n s i d e r e d i n f u t u r e s t u d i e s .

6 . CONCLUSIONSI n o u r s i m u l a ti o n s , t h e e x t e n t o f r e a c t io n i n t he F C w a s l im i t e d b y t h e a m o u n t o f h e a t re q u i r e d f o r

t h e re f o r m e r . T h i s r e s u l t d e m o n s t r a t e d t h a t th e s y s t e m h a s t o b e a n a l y z e d a s a w h o l e r a t h e r t h a n f o rs e p a r a t e u n i ts . T h e e x h a u s t - g a s t e m p e r a t u r e w a s l o w , a n d it w a s o n l y s u it a b l e f o r h e a t i n g r o o m s o rw a t e r. S i m u l a t i o n o f a n S O F C - s y s t e m w i t h e x t e r na l r e f o r m i n g r e s ul t e d i n f ir s t- l aw a n d s e c o n d - l a we f f i c i e n c i e s o f 5 8 a n d 5 6 , r e s p e c t i v e l y , w i t h 6 0 0 t h e o r e t i c a l ai r. W i t h s t o i c h i o m e t r i c ai r, t h e a i r -p r e h e a t e r a n d F C i r r e v e r s i b il i ti e s w e r e r e d u c e d a n d t h e e f f i c i e n c y in c r e a s e d . R e d u c e d a i r p r e h e a t i n ga l l o w e d i n c r e a s e d f u e l u t il i z a t io n i n t h e F C i ts e l f. R e c y c l i n g o f fu e l a n d w a t e r v a p o r i n c r e a s e d t h ee f f i c i e n c y s i g n i f i c a n t ly b e c a u s e w a t e r v a p o r i z a t i o n w a s a v o i d e d a n d f u e l u t il i z a ti o n w a s h i g h e r . S i m u l -a t io n o f a n S O F C - s y s t e m w i t h e x t e r n a l r e f o r m i n g a n d r e c y c l i n g r e s u lt e d i n f i rs t- a n d s e c o n d - l a w e f fi c i-e n c e s o f 7 5 . 5 a n d 7 3 , r e p e c t i v e l y , w i t h 6 0 0 t h e o r e t i c a l a i r.Acknowledgements--K. W. Bedring~s was partially funded by NT NF (Ro yal Norw egian Council for Scientific and IndustrialResearch) under the research program SPUNG . We are grateful to a colleague, N. I. Lilleheie, for performing the PSR combustioncalculations used in the discu ssion of c omb ustion in the afterburner.

REFERENCES1. Appleby, A. J . and Foulkes, F. R., Fuel Cell Handbook. Van Nostrand Reinhold, New York, 1989.2 . So l id ox ide fue l ce ll t ech no logy development . A nnual Repor t, 1 May 198 7-30 Apr il 1988, Wes t inghouseElec tric Corp., R& D Center, Pittsburgh, 1988.3 . Dunbar , W. R. , L io r , N. and Gagg io l i , R . A. , Energy--The International Journal 1991, 16, 1259.4 . Dunbar , W. R. and L io r , N. , Proceedings of the W orld Energy Conference Florence, Italy, 1990, p. 347.5. H. Karoliussen, Dr. Ing. thesis . Norw egian Inst itute of Tec hno logy, Trondh eim, 1993.6. Bossel, U. G., Facts & Figures. International Ene rgy Age ncy SO FC Tas k Report , Sw iss Federal Office ofEne rgy, Berne, A pri l 1992.7. Ratkje, S. K. and M011er-H olst, S., Electrochimica Acta 1993, 38, 447.8. Rant, Z., Gaswarme 1963, 12, 31.9. Fratzscher, W . and Gruhn, G ., Brennstoff-Wiirme-Kraft 1965, 17, 337.10. Kotas, T. J., The Exergy M ethod o f Thermal Plant Analysis . Butterworths, L ondo n, 1985.11. Bejan, A., Advanced Engineering Thermodynamics. John Wi ley & Sons , New York , 1988 .12. Keenan, J. H., Mechanical E ngineering: the journa l o f the American Society of Mechnical Engineers 1932,54, 195.13. Moran, M. J., Availability Analysis: a Guide to Efficient Energy Use. Corr . ed . ASME, New York , 1989 .14. Bedringhs, K . W ., Dr. Ing. Thesis , N orw egian Insti tute of Techno logy, Trondh eim, 1993.15. Forder, G. J . and Hutchinson, H. P. , Chemical Engineering Science 1969, 24, 771.

16. Ke e, R. J., Miller, J. A., and Jefferson, T. H., CH EM K IN : a general-purpose, problem-independent, transport-able, fortran chemic al kinetics co de package. Sa ndia Report SA ND 80-80 03, Sandia Laboratories , Albuquerque,NM and L ivermore , CA, 1980 .17. Ridler, D. E. , and Twigg, M. V., Catalyst Handbook 2nd edn, ed. M.V. Twigg. Wolfe Publishing, London,1989.18. Kinoshita, K., McLarnon, F.R., and Cairns, E.J., Fuel Cells--A Handbook. Lawrence Berkeley Lab., Berkeley,CA, 1988.19. E1-Masri, M. A., Transactions of the ASME Journal of Engineering for Gas Turbines and Power 1987,109, 228.20. Glarb org, P. , Kee, R., Grcar, J . F. , and Miller, J . A., PS R: a Fortran program for mod eling well-s t irred reactors .Sand ia Repor t SAN D86-82 09 , Sand ia Labora to r ies , Albuquerque , NM and L ivermore , CA.21. Lil leheie, N. I . , private comm unicat ion , 1995.

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