5 Thermodynamic Analysis of Gas Turbine Cycles with Chemical Reactions H. B. VAKIL Corporate Research and Development, General Electric Company, Schenectady, NY 12301
Thermodynamic exergy analyses of gas-turbine c y c l e s show t h a t t h e major l o s s e s occur n e i t h e r duri n g t h e compression o fairnor d u r i n g t h e expansion of hot combustion p r o d u c t s , but r a t h e r d u r i n g t h e combustion r e a c t i o n s . Main reasonsforthese l o s s e s stem from t h e peak temperature limitations imposed by t h e m a t e r i a l s o f c o n s t r u c t i o n , coupled w i t h t h e very high thermodynamic quality o f t h e f u e l source. T h i s paper i n v e s t i g a t e s t h e p o t e n t i a l for reducing exergy l o s s e s d u r i n g combustion by l o w e r i n g the thermodynamic quality o f the fuel through endothermic chemical r e a c t i o n s , utilizing t h e lowgrade heat from t h e t u r b i n e exhaust gases. Using methanol as an example, it is shown t h a t steam r e f o r m i n g o r methanol c r a c k i n g r e a c t i o n s c o u l d yield higher energy products o f lower thermodynamic quality, w i t h a subsequent r e d u c t i o n o f entropy production d u r i n g combustion. Using t h e "second law" a n a l y s e s , it is shown t h a t t h e use o f low-grade exhaust heatforthechemical c o n v e r s i o n o f h i g h - q u a l i t y f u e l i n t o medium quality gaseous products offers a h i g h e r o v e r a l l efficiency than even a reversible c o n v e r s i o n o f t h e exhaust thermal energy t o mechanical work. T h i s apparent violation o f thermodynamic laws can o n l y be e x p l a i n e d by t a k i n g into c o n s i d e r a t i o n t h e entropy p r o d u c t i o n d u r i n g t h e combustion s t e p . These results suggest t h e possibility that lowering the exergy ratio o f fuels through chemical r e a c t i o n s u s i n g low-grade heat c o u l d p r o v i d e an e a s i e r t e c h n i c a l r o u t e t o higher efficiencies than t h e search for higher temperature materials. 0097-6156/ 83/ 0235-0105S06.00/ 0 © 1983 American Chemical Society
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Clean f o s s i l f u e l s i n e i t h e r l i q u i d o r gaseous form have p l a y e d , and w i l l c o n t i n u e t o p l a y , a major r o l e i n s u p p l y i n g our energy needs. The f a c t t h a t t h e p r i m a r y energy i n t h e f o s s i l f u e l s can be c o n v e r t e d e a s i l y t o e i t h e r mechanical o r e l e c t r i c a l energy has l e d t o t h e i r widespread use i n t h e I n d u s t r i a l and T r a n s p o r t a t i o n s e c t o r s . W h i l e t h e r e are many d i f f e r e n t r o u t e s f o r c o n v e r t i n g t h e chemical energy o f f o s s i l f u e l s i n t o u s e f u l work, almost a l l o f them i n v o l v e an i n i t i a l c o n v e r s i o n o f t h e f u e l energy i n t o thermal energy through combustion; t h e thermal energy i s then used i n comb i n a t i o n w i t h a thermodynamic c y c l e t o produce u s e f u l work. The gas t u r b i n e i n an e x c e l l e n t example o f such systems f o r power gene r a t i o n , i n t h a t i t i s s i m p l e , e f f i c i e n t , and r e l a t i v e l y inexpens i v e . The b a s i c g a s - t u r b i n e c y c l e F i g u r e 1 c o n s i s t s o f t h r e e steps: 1.
Ambient a i r i s compressed ( u s u a l l y , a d i a b a t i c a l l y ) t o a p r e s s u r e o f r o u g h l y 10-12 bars i n a compressor.
2.
The compressed a i r i s used t o c a r r y o u t combustion o f the f o s s i l f u e l i n a h i g h temperature combustor t o gene r a t e p r e s s u r i z e d hot gases.
3.
The hot combustion p r o d u c t s a r e expanded i n a t u r b i n e t o generate power, a p a r t o f which i s made a v a i l a b l e t o t h e compressor.
The e f f i c i e n c y o f a gas t u r b i n e i s u s u a l l y d e f i n e d as t h e f r a c t i o n o f f u e l combustion e n t h a l p y change t h a t i s d e l i v e r e d as net mechanical ( o r e l e c t r i c a l ) energy a f t e r s u b t r a c t i n g t h e energy requirements o f t h e compressor. The c o n t i n u i n g push f o r h i g h e r e f f i c i e n c i e s has r e s u l t e d i n s e v e r a l m o d i f i c a t i o n s o f t h e b a s i c c y c l e d e s c r i b e d e a r l i e r ; most o f these i n v o l v e t h e use o f r e c u p e r a t i v e heat-exchange w i t h t h e t u r b i n e exhaust. F o r example, t h e s e n s i b l e heat o f t h e hot exhaust gases can be used e i t h e r t o preheat t h e compressed a i r p r i o r t o combustion, o r t o generate steam i n a b o i l e r f o r a d d i t i o n a l power g e n e r a t i o n . More r e c e n t l y , a d i f f e r e n t use o f t h e r e c u p e r a t e d heat has been proposed — one where t h e heat i s s u p p l i e d t o c a r r y o u t an endothermic chemical r e a c t i o n w i t h t h e f u e l (.1,1). The net r e s u l t i s t h e g e n e r a t i o n o f a d i f f e r e n t , secondary f u e l f o r combustion. An example o f such chemical r e c u p e r a t i o n w i t h methanol as t h e p r i m a r y f o s s i l f u e l i s the use o f exhaust heat t o c a r r y o u t e i t h e r t h e steam-methanol r e f o r m i n g r e a c t i o n o r t h e methanol c r a c k i n g r e a c t i o n . I t i s t h e aim o f t h i s paper t o p r e s e n t a comparison o f t h e r mal and chemical r e c u p e r a t i o n o p t i o n s i n a thermodynamic framework. The paper w i l l begin by i d e n t i f y i n g t h e major i r r e v e r s i b i l i t i e s i n a s i m p l e g a s - t u r b i n e c y c l e w i t h l i q u i d methanol f u e l ; c o n t i n u e w i t h a comparison o f thermodynamic l o s s e s and o v e r a l l e f f i c i e n c i e s among v a r i o u s o p t i o n s u t i l i z i n g thermal and/or
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chemical r e c u p e r a t i o n ; and conclude w i t h an examination of the thermodynamic " q u a l i t y " o f the primary and secondary f u e l s t o understand the i m p l i c a t i o n s of f u e l m o d i f i c a t i o n . I t i s not the purpose of t h i s paper t o e v a l u a t e the s u i t a b i l i t y of methanol as a f u e l f o r gas t u r b i n e s . Consequently, no a t t e n t i o n w i l l be given t o such f a c t o r s as the c o s t o f methanol f u e l , s a f e t y c o n s i d e r a t i o n s of exchanging heat between hot exhaust gases and f u e l , and the dynamics of the complex c y c l e w i t h r e c u p e r a t i v e chemical r e a c t i o n s . The purpose of t h i s paper i s to outl i n e the thermodynamic i m p l i c a t i o n s o f chemical r e c u p e r a t i o n using methanol f u e l as an example. CYCLE CALCULATIONS
In order t o s i m p l i f y and s t a n d a r d i z e the c y c l e c a l c u l a t i o n s , the f o l l o w i n g c o n d i t i o n s were assumed: I n l e t a i r t o compressor Compressor o u t l e t a i r Combustor o u t l e t / t u r b i n e i n l e t Turbine exhaust Regenerator o u t l e t / s t a c k gases
1 atm; 12 atm; 12 atm; 1 atm; 1 atm;
77F 650F 2000F 1000F 200F
The c a l c u l a t i o n s of the energy f l o w s are r e l a t i v e l y s t r a i g h t forward once these c o n d i t i o n s are s p e c i f i e d ; t h e same i s t r u e f o r the c a l c u l a t i o n s of entropy p r o d u c t i o n and the a s s o c i a t e d exergy d e s t r u c t i o n . The o n l y area of c o m p l i c a t i o n i s the need f o r a "dead-state" d e f i n i t i o n i n o r d e r t o c a l c u l a t e the e n t h a l p y and exergy l o s s e s a s s o c i a t e d w i t h the stack exhaust. The d i f f i c u l t i e s a s s o c i a t e d w i t h the c h o i c e of an a p p r o p r i a t e "dead-state" have been d i s c u s s e d e x t e n s i v e l y i n the l i t e r a t u r e [3). In the present c o n t e x t , however, the exact d e f i n i t i o n of the "dead-state" i n gene r a l , and the chemical p o t e n t i a l o f C 0 and FLO i n p a r t i c u l a r i s important o n l y f o r determining the exergy content o f the s t a c k exhaust. As w i l l become apparent l a t e r , t h i s i s not a major f a c t o r i n the o v e r a l l e f f i c i e n c y . Consequently, i t i s not necessary t o have a d e t a i l e d and s o p h i s t i c a t e d d e s c r i p t i o n of the "deads t a t e " ; any reasonable c h o i c e of r e f e r e n c e s t a t e i s adequate f o r the purpose of t h i s paper. The r e s u l t a n t ambiguity i n the exergy l o s s e s i n the stack exhaust i s a consequence of the e f f e c t o f "dead-state" c o m p o s i t i o n on the expansion work of C 0 and H^O — a phenomenon of l i t t l e i n t e r e s t here. Thermodynamic p r o p e r t i e s were c a l c u l a t e d u s i n g i d e a l gas mixt u r e assumption and the standard r e f e r e n c e s t a t e s of 77F (298.15K) and 1 atm f o r a i r (molar composition - 80% N , 20% Og*), f o r C 0 (pure gas at 1 atm), and f o r H 0 (pure l i q u i d at T. atm). I t 2
2
2
9
* Molar r a t i o of 4:1 was assumed i n o r d e r t o s i m p l i f y the s t o i c h i o m e t r y and thermodynamic c a l c u l a t i o n s .
2
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should be noted t h a t i n view of the assumed combustor o u t l e t temp e r a t u r e of 2000F, the a i r / f u e l r a t i o i s determined d i r e c t l y from a i r and f u e l c o n d i t i o n s a t the i n l e t o f the combustor assuming complete combustion under a d i a b a t i c c o n d i t i o n s . I R R E V E R S I B I L I T I E S I N A SIMPLE GAS-TURBINE CYCLE
The s i m p l e s t example o f a g a s - t u r b i n e c y c l e i s one i n which no heat r e g e n e r a t i o n t a k e s p l a c e ; t h e compressor o u t l e t a i r i s sent d i r e c t l y t o t h e combustor a t a temperature o f 650F and l i q u i d methanol a t ambient temperature i s combusted t o produce hot gases at a temperature o f 2000F. Thermodynamic p r o p e r t i e s of t h e f l o w streams at v a r i o u s l o c a t i o n s as w e l l as the thermal and mechanical energy f l o w s f o r the c y c l e are shown i n F i g u r e 2 u s i n g 1 g-mole o f l i q u i d methanol as the b a s i s . A l s o shown i n the f i g u r e are the magnitudes o f e n t r o p y p r o d u c t i o n and exergy d e s t r u c t i o n i n each of the process s t e p s . The o v e r a l l c y c l e produces net t u r b i n e work ( a f t e r a c c o u n t i n g f o r the compressor work) o f 253.5 K j per g-mole o f l i q u i d methanol. Without any heat r e c o v e r y from the t u r b i n e exhaust, the major energy l o s s (based on t h e f i r s t - l a w o f thermodynamics) appears to be due t o the hot s t a c k gases. However, c a l c u l a t i o n s o f e n t r o p y p r o d u c t i o n c l e a r l y show t h a t the i r r e v e r s i b i l i t i e s i n t h e combustor g i v e r i s e t o t h e l a r g e s t exergy l o s s i n the e n t i r e c y c l e — a n amount exceeding e i t h e r t h e t o t a l net t u r b i n e work or the exergy l o s s r e s u l t i n g from throwing away t h e hot t u r b i n e exhaust gases. By comparison, the l o s s e s a s s o c i a t e d w i t h compression/expansion i n e f f i c i e n c i e s are almost i n s i g n i f i c a n t . The combustion exergy l o s s i s even more prominent i f a t h e r mal r e g e n e r a t o r i s used f o r e x t r a c t i n g heat from the t u r b i n e exhaust i n o r d e r t o generate steam t o form a combined gas t u r b i n e / s t e a m c y c l e . The r e g e n e r a t o r i s capable o f e x t r a c t i n g 336 K j of thermal energy from the exhaust gases w i t h an exergy c o n t e n t o f 154 K j . P r e v i o u s s t u d i e s of steam c y c l e thermodynamic e f f i c i e n c y (4) have shown t h a t r o u g h l y 80% o f i n p u t exergy t o the steam c y c l e can u s u a l l y be made a v a i l a b l e as steam t u r b i n e work o u t p u t . Thus, the net exergy l o s s a s s o c i a t e d w i t h the exhaust gases i s reduced t o 30.8 K j i n the steam c y c l e and 9.5 K j as unrecovered exergy* i n the s t a c k gases a t 200F (366.5K) from the regenerator. The main reason f o r the s u b s t a n t i a l i r r e v e r s i b i l i t y i n t h e combustion process i s the peak temperature l i m i t a t i o n imposed by the m a t e r i a l s o f c o n s t r u c t i o n i n t h e f i r s t stage of the gast u r b i n e , coupled w i t h the high thermodynamic " q u a l i t y " o f the f u e l combustion energy. One way t o reduce t h i s i r r e v e r s i b i l i t y i s t o develop t u r b i n e s t h a t can w i t h s t a n d h i g h e r i n l e t t e m p e r a t u r e s — a * T h i s amount w i l l v a r y depending on the p a r t i c u l a r d e f i n i t i o n o f the " d e a d - s t a t e " as d i s c u s s e d e a r l i e r .
5.
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Gas Turbine Cycles with Chemical Reactions
AIR NET TURBINE OUTPUT
COMPRESSION WORK COMPRESSOR |
^1
=)TURBINE
TURBINE EXHAUST FUEL REGENERATOR
STACK GASSESl
THERMAL OUTPUT
F i g u r e 1. Schematic o f gas t u r b i n e c y c l e .
AIR 22 435 g-moles HO S4450 NET TURBINE OUTPUT 253.5KJ H-492 S5547 H-239, i — L I T S 127 nCH 0H(l) 1 g-mole
REGENERATOR OUTPUT
3
LEGEND I H2I3 ENTHALPY(Kj) *S4469 ENTROPY (j/K) 266 (892)
EXERGY DESTRUCTION (Kj) ENTROPY PRODUCTION (j/K)
F i g u r e 2.
* HEAT 335 7Kj EXERGY I53.9KJ H-828 S4937
STACK LOSSES —••HEAT 137 4 Kj EXERGY 9.5KJ
Thermodynamics o f the Base Case.
109
110
SECOND LAW ANALYSIS OF PROCESSES
s u b j e c t of c o n s i d e r a b l e r e s e a r c h i n t e r e s t t o m a t e r i a l s s c i e n t i s t s and t u r b i n e d e s i g n e r s . A t o t a l l y d i f f e r e n t approach would be t o manipulate the f u e l i t s e l f i n order t o lower i t s " q u a l i t y " and thereby make i t more s u i t a b l e thermodynamically t o existing materials. The use of thermal and/or chemical r e c u p e r a t i o n are examples of the l a t t e r approach of reducing the " q u a l i t y " o f the f u e l t o be burned. I t should be emphasized, however, t h a t a l o w e r i n g of the thermodynamic " q u a l i t y " of the f u e l i s d e s i r a b l e o n l y i f the t o t a l amount o f i r r e v e r s i b i l i t i e s — t h o s e i n t h e combustor as w e l l as those i n h e r e n t i n the f u e l p r o c e s s i n g s t e p i s reduced. In order t o c l a r i f y these i d e a s , we need t o compare the i r r e v e r s i b l e entropy p r o d u c t i o n s ( o r the exergy d e s t r u c t i o n ) i n c y c l e s t h a t u t i l i z e r e g e n e r a t i v e h e a t i n g of compressed a i r , t h e r mal r e c u p e r a t i o n i n the form of e v a p o r a t i o n and superheating of the methanol f u e l , and chemical r e c u p e r a t i o n through e i t h e r r e f o r m i n g or c r a c k i n g r e a c t i o n w i t h methanol. The next s e c t i o n presents such a comparison i n a s i m p l i f i e d form t o i l l u s t r a t e the u t i l i t y of thermodynamic analyses. ANALYSES AND COMPARISON OF CASES
In a d d i t i o n t o the simple c y c l e without any form of r e c u p e r a t i o n (Base Case) t h a t was analyzed i n the previous s e c t i o n , we w i l l c o n s i d e r f i v e separate cases w i t h thermal and/or chemical r e c u peration. I n the i n t e r e s t o f m a i n t a i n i n g u n i f o r m i t y , we w i l l assume a constant temperature of 800F as the e x i t temperature of any stream undergoing such r e c u p e r a t i o n . A d e s c r i p t i o n of the f i v e cases i s as f o l l o w s : Case 1
Regenerative h e a t i n g of compressed a i r from 650F t o 800F w i t h l i q u i d methanol a t 77F as the f u e l .
Case 2
P r e h e a t i n g of compressed a i r as i n Case 1, combined w i t h the e v a p o r a t i o n and p r e h e a t i n g of methanol t o g i v e methanol vapor at 800F as the f u e l .
Case 3
P r e h e a t i n g of compressed a i r , combined w i t h evap o r a t i o n and p r e h e a t i n g of an equimolar m i x t u r e of methanol and water t o g i v e CrLOH + H 0 vapor mixt u r e at 800F as the f u e l . ?
6
Case 4
Thermal r e c u p e r a t i o n as i n Case 3 w i t h the a d d i t i o n o f c a t a l y t i c reforming of methanol/steam m i x t u r e t o g i v e C 0 + 3H a t 800F as the f u e l . 2
Case 5
c
2
Thermal r e c u p e r a t i o n as i n Case 2, w i t h the a d d i t i o n of c a t a l y t i c c r a c k i n g of methanol to g i v e CO + 2H at 800F as the f u e l . 9
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111
The c a l c u l a t i o n procedure c o n s i s t s of a d e t e r m i n a t i o n of the a i r / f u e l molar r a t i o t h a t w i l l r e s u l t i n a combustor o u t l e t temp e r a t u r e of 2000F, f o l l o w e d by the c a l c u l a t i o n of e n t h a l p y and entropy of f l o w streams at the v a r i o u s s t a t e p o i n t s i n the c y c l e . The net work output from the t u r b i n e i s c a l c u l a t e d by s u b t r a c t i n g the compressor work requirements from the t o t a l t u r b i n e expansion work determined from the e n t h a l p y balance. I r r e v e r s i b l e entropy p r o d u c t i o n s are c a l c u l a t e d by a r o u t i n e entropy balance around each process s t e p . The t o t a l amount of regenerated heat f o r each of the cases i s broken down i n t o t h r e e separate thermal energy f l o w s ; the amount needed t o preheat the compressed a i r (Q ), the amount absorbed by the f u e l d u r i n g thermal or chemical r e c u p e r a t i o n (Q*), and the s u r p l u s made a v a i l a b l e t o the steam c y c l e ( Q ) . The work output from the steam c y c l e i s c a l c u l a t e d from the net exergy f l o w t o the steam c y c l e , a f t e r s u p p l y i n g the r e q u i r e d exergy f l o w s a s s o c i a t e d w i t h Q and Q w i t h an e x e r g y - d e l i v e r y e f f i c i e n c y of 80%. E a r l i e r s t u d i e s (5) have shown such 'second law methods f o r e s t i m a t i n g steam-cycle outputs to be more v a l i d and u s e f u l than an assumption of a constant ' f i s t - l a w c o n v e r s i o n e f f i c i e n c y * . T h i s i s espec i a l l y so when the steam c y c l e i s coupled to d i f f e r e n t processes r e q u i r i n g heat at d i f f e r e n t temperature l e v e l s , as i n t h i s analysis. The magnitudes of the mechanical and thermal energy f l o w s f o r each of the cases are given i n Table 1. A l s o shown i n Table 1 are the values of the o v e r a l l c o n v e r s i o n e f f i c i e n c y , which i s d e f i n e d as the r a t i o of t o t a l work output (w + w ) t o the molar heat of combustion of l i q u i d methanol (727 K j ) . The r e s u l t s i n d i c a t e very c l e a r l y the p r o g r e s s i v e i n c r e a s e s i n e f f i c i e n c y w i t h i n c r e a s i n g degree of r e c u p e r a t i o n e x e m p l i f i e d by the sequence: Base Case ^ Case 1 -> Case 2 Case 5. The most important p o i n t t o note i s t h a t even w i t h a r e v e r s i b l e c o n v e r s i o n o f Q , the t o t a l work i s lower w i t h o n l y thermal r e c u p e r a t i o n than t h a t w i t h chemical r e c u p e r a t i o n . For example, a comparison of Case 5 w i t h Case 2 (the o n l y d i f f e r e n c e being the presence or absence of the decomposition r e a c t i o n ) shows an i n c r e a s e i n the net t u r b i n e output by 42.2 K j — a n amount n e a r l y t w i c e as l a r g e as the corresponding decrease i n the steam c y c l e output. Even i n the r e v e r s i b l e l i m i t , the decrease i n steam c y c l e output would equal o n l y 24 K j . An analogous r e s u l t i s obtained by comparing Cases 3 and 4, thereby showing a s i m i l a r behavior w i t h the steam-reforming r e a c t i o n . The f a c t t h a t one can improve the o v e r a l l e f f i c i e n c y by withdrawing some exergy from a r e v e r s i b l e steam-cycle and c a r r y i n g out i r r e v e r s i b l e f u e l t r a n s f o r m a t i o n w i t h i t appears, at a f i r s t g l a n c e , t o be i n v i o l a t i o n of the second law. However, a more d e t a i l e d look at the combustion i r r e v e r s i b i l i t i e s shows t h a t t h i s s t
f
1
1
T
t
t
* T h i s e f f i c i e n c y i s g e n e r a l l y r e f e r r e d t o as the ' f i r s t law' efficiency.
22.44
25.04
27.83
26.58
29.47
32.44
Base Case
Case 1
Case 2
Case 3
Case 4
Case 5
3
Moles A i r per Mole CH 0H
-
83.5
75.9
68.4
71.7
163.8
184.1
120.0
61.8
-
224.3
187.5
219.8
275.7
306.8
335.9
"st
Qex
157.5
197.9
192.1
148.3
142.7
137.4
Thermal Flows (Kj) C
307.6
279.5
252.0
263.9
237.5
T
345.2
341.6
315.1
303.0
277.5
253.7
W
st
72.5
71.4
80.3
91.7
101.5
123.2
W
Work Flows (Kj)
212.8
W
Mechanical and Thermal Energy Flows
64.5
Table 1.
57.45
56.80
54.38
54.29
52.13
51.83
Efficiency %
C/5
O *n T5 70 O n m CO m
>
>
I
r
ia
m
C/3
So
5.
VAKIL
Gas
113
Turbine Cycles with Chemical Reactions
i s not so, and t h a t the e f f i c i e n c y g a i n s r e s u l t from l a r g e reduct i o n s i n the e n t r o p y p r o d u c t i o n d u r i n g combustion o f the d e r i v e d fuels. The magnitudes of e n t r o p y p r o d u c t i o n d u r i n g combustion and the a s s o c i a t e d exergy l o s s e s f o r the v a r i o u s cases are shown i n T a b l e 2 w i t h two d i f f e r e n t n o r m a l i z a t i o n s : one based on 1 g-mole of methanol, and the o t h e r based on 100 K j of t o t a l net work (w + st) P * p r o g r e s s i v e r e d u c t i o n i n combustor i r r e v e r i i b f i i t i e s w i t h i n c r e a s i n g amount o f r e c u p e r a t i o n i s e v i d e n t from the r e s u l t s . The decrease i s even more prominent on the b a s i s of equal t o t a l work produced, which i s the more r e a l i s t i c b a s i s of the two. The chemical r e c u p e r a t i o n u s i n g methanol c r a c k i n g r e a c t i o n appears t o reduce combustor i r r e v e r s i b i l i t i e s by n e a r l y onet h i r d of t h a t w i t h no r e c u p e r a t i o n . In o r d e r t o understand why t h i s should be so, we need a q u a n t i t a t i v e measure o f the thermodynamic " q u a l i t y " o f f u e l s and o f the r e q u i r e d t a s k o f h e a t i n g compressed a i r from 800F t o 2000F. In second law a n a l y s e s of s y s tems w i t h t h e r m a l , m e c h a n i c a l , and chemical changes, we have found the concept of exergy r a t i o - a r a t i o of exergy change t o e n t h a l p y change of a g i v e n process - t o be a p a r t i c u l a r l y u s e f u l measure o f thermodynamic q u a l i t y ( 4 , 5 ) . F o r a process w i t h an e n t h a l p y change of H and an e n t r o p y change S, T
w
r o d u c e c l
T h e
Exergy R a t i o (a ) £
= 1 - T (AS/AH) Q
where T i s the ambient temperature (298.16K). I t may be noted t h a t the exergy r a t i o o f mechanical work i s equal t o u n i t y , and t h a t of thermal energy a t a temperature T i s equal t o the Carnot f a c t o r (1-T / T ) . For chemical r e a c t i o n s such as the combustion of methanol, trie exergy r a t i o depends on the r e l a t i v e magnitudes of e n t h a l p y and e n t r o p y changes; f o r exothermic r e a c t i o n s i t i s usua l l y - but not always - i n t h e range from z e r o t o u n i t y . The key energy t r a n s f e r s t e p s f o r which we need t h e exergy r a t i o s are: t Compressed a i r h e a t i n g from 650F t o 800F • B o o s t i n g the temperature of a i r from 800F t o 2000F* t Recovery o f heat from t u r b i n e exhaust (1000F t o 200F) t Thermal and/or chemical r e c u p e r a t i o n f o r the f u e l • I d e a l i z e d combustion of methanol and d e r i v e d f u e l s . * T h i s i s an approximation r e p r e s e n t i n g the i d e a l i z e d t a s k o f the combustor.
114
SECOND LAW ANALYSIS OF PROCESSES
Table 2.
Entropy Production During Combustion
and A s s o c i a t e d Exergy Losses
' Base Case Basis:
1
2
Example Cases 3 4
5
1 g-mole Methanol
Entropy Production (j/k)
892.5
864.1
788.4
768.3
686.2
672.6
Exergy Loss (kj)
266.1
257.6
235.1
229.1
204.6
200.6
236.9
228.0
199.8
194.4
166.2
161.1
70.6
68.0
59.6
58.0
49.6
48.0
Basis:
100 K j Total Network
Entropy Production (j/k) Exergy Loss (Kj)
5.
VAKIL
Gas
Turbine Cycles with Chemical Reactions
115
Exergy r a t i o s f o r these s t e p s are shown i n T a b l e 3. The average " q u a l i t y " o f the thermal exergy needed i n the combustor i s i n d i cated by an exergy r a t i o o f ^0.7 ( c o r r e s p o n d i n g t o a temperature l e v e l o f r o u g h l y 1350F). By c o n t r a s t , t h e " q u a l i t y " o f energy r e l e a s e d by methanol combustion i s e x t r e m e l y h i g h as shown by an exergy r a t i o of 0.96 ( i . e . , e q u i v a l e n t t o a temperature
