Exergy Analysis - DiPippo 1984

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Geothermal Resources Council, TRANSACTIONS, Vol. 8, August 1984

EXERGY ANALYSIS OF GEOTHERMAL POWER PLANTS

by

Ronald DiPippo(l) and David F. Marci l le (2)

Mechanical Engineering Department Southeastern Massachusetts Univers i ty

North Dartmouth, MA 02747

ABSTRACT

The thermodynamic b a s i s f o r t h e use of exergy is presented. Exergy is shown. t o be a powerful t o o l i n the assessment of t h e performance of geothermal power p l a n t s r e g a r d l e s s of t h e type of energy conversion system employed. A methodology is presented t o permit t h e use of exergy a n a l y s i s i n a sys temat ic fashion. The method is i l l u s t r a t e d wi th t h r e e d e t a i l e d exam- p l e s using a dry-steam, a double-flash, and a b inary p lan t . Overal l Second Law e f f i c i e n c i e s are ca lcu la ted f o r s e v e r a l a c t u a l geothermal p l a n t s i n var ious count r ies .

INTRODUCTION

The concept of a v a i l a b l e work o r exergy was proposed long ago as a means of a s s e s s i n g t h e performance of thermal power p l a n t s [l-41. I n recent years t h e idea h a s been used t o c a l c u l a t e so-cal led “Second Law e f f i c i e n c i e s , ‘’ and has been appl ied i n p r i n c i p l e t o a wide assortment of engineer ing and s c i e n t i f i c systems [ 5-71. Despi te r igorous thermodynamic advantages over ana lyses based s o l e l y on F i r s t Law p r i n c i p l e s , exergy ana lyses have not achieved wide usage and acceptance wi th in t h e t e c h n i c a l community. Whereas t h e a p p l i c a t i o n of Second Law ana lyses is c e r t a i n l y b e n e f i c i a l , a l b e i t o p t i o n a l , i n t h e case of conventional power p l a n t s such as coal-, o i l - , gas-, o r nuclear-fueled p l a n t s , i t s use i n t h e c a s e of geothermal p l a n t s is e s s e n t i a l i f one wishes t o gauge t h e performance i n a thermo- dynamically r igorous fashion. Futhermore, i t a l lows v a l i d d i r e c t comparisons wi th conven- t i o n a l , o r non-conventional a l t e r n a t e energy systems. Several a u t h o r s have r e c e n t l y w r i t t e n on t h e a p p l i c a t i o n of exergy a n a l y s i s t o geothermal systems [8-111.

OBJECTIVES

The purpose of our paper is: (1) To o f f e r a s i m p l i f i e d thermodynamic basis f o r t h e use of exergy as a proper measure of geothermal power p l a n t performance r e g a r d l e s s of t h e type of energy conversion system employed; ( 2 ) To des-

( l )Also , Div. of Engrg., Brown U., Providence.,

(*)Current address: M.E. Dept. , Georgia I n s t . R. I.

of Tech., Atlanta , GA

c r i b e a methodology f o r a sys temat ic exergy a n a l y s i s of a geothermal power system; (3) To i l l u s t r a t e t h e method wi th d e t a i l e d sample cal- c u l a t i o n s f o r t h r e e a c t u a l p l a n t s - a dry-steam plan t , a double-flash p l a n t , and a binary p l a n t ; and l a s t l y , (4) To g i v e a summary of o v e r a l l Second Law p l a n t e f f i c i e n c i e s f o r many geothermal p l a n t s now i n opera t ion o r under con- s t r u c t i o n .

EXERGY AS A MEASURE OF PLANT PERFORMANCE

Regardless of t h e s p e c i f i c des ign f e a t u r e s of a geothermal power p l a n t , i.e., dry-steam, s ing le- f lash , double-flash, binary, etc., i n a l l c a s e s a stream of geof lu id (steam, b r i n e , two-phase mixture) is brought t o t h e s u r f a c e of t h e e a r t h from a deep r e s e r v o i r by some means ( a r t e s i a n flow, pumped, etc.). Once a t t h e sur- f a c e t h e f l u i d has a pressure and a temperature t h a t exceed those of the . atmosphere, and thus has a p o t e n t i a l t o perform u s e f u l work. The f l u i d passes through a series of processes de- signed t o e x t r a c t a s much u s e f u l work from t h e f l u i d a s is f e a s i b l e , given t e c h n i c a l and eco- nomic c o n s t r a i n t s . During t h e series of processes undergone by t h e f l u i d , h e a t may be t r a n s f e r r e d between the f l u i d and t h e surroundings. I n t h e end, t h e f l u i d is discharged t o the surroundings i n a s t a t e t h a t is inf luenced by t h e p r e v a i l i n g ambient condi t ions.

The e s s e n t i a l po in t is t h a t t h e geof lu id does not experience a cyc le , but r a t h e r a series of processes from some i n i t i a l set of c o n d i t i o n s ( i n i t i a l s t a t e ) t o some f i n a l set of c o n d i t i o n s ( f i n a l s t a t e ) . This i s t r u e even i n t h e case where a n i n t e r n a l c y c l e is p a r t of t h e energy conversion process as i n t h e c a s e of b inary p lan ts . . _

A genera l ized , but somewhat s i m p l i f i e d re- presenta t ion of a system opera t ing as descr ibed above is shown i n Fig. 1. Only one i n l e t and one o u t l e t f o r mass f lows a r e included, but more could be assumed without d i f f i c u l t y . An impor- t a n t condi t ion f o r our a n a l y s i s is t h a t t h e sys- t e m must opera te i n a s teady-s ta te manner.

The F i r s t Law of thermodynamics f o r t h e system can be w r i t t e n a s

47

DiPippo and Marcille The a c t u a l power developed by a system can

now be compared with t h e maximum p o s s i b l e power and a Seco?d,Law e f f i c i e n c y may be def ined as

rl(I1) = W/El (12)

I f t h e k i n e t i c energy o r t h e p o t e n t i a l en- e rgy is important, one must augment t h e enthalpy of t h e geof lu id with these terms; i.e., r e p l a c e

( h i ) with (hl +yV1 + gzl). SURROUNDINGS ( TEMPERATURE * 1.1 make a cont r ibu t ion i f state 1 is a t t h e bottom

of a very deep geothermal w e l l and t h e p l a n t is

2 1 2 The (gz)-term may

Fig. 1. Open system i n s teady-s ta te operat ion. on t h e sur face .

I f we ignore, f o r t h e moment, t h e kinetic-energy and potential-energy d i f f e r e n c e terms r e l a t i v e t o t h e enthalpy d i f f e r e n c e , we can s i m p l i f y t h i s t o

6-fi = m(h2-hl)- (2)

The Second Law f o r t h e system and t h e surroundings can be expressed a s

Q .

TO

. . 8 = m(s2-sl) - - (3)

The entropy product ion w i l l be reduced t o zero i n t h e i d e a l limit of r e v e r s i b l e opera t ion , and r e p r e s e n t s t h e upper l i m i t on t h e performance of the p l a n t f o r a given i n i t i a l and f i n a l s ta te of t h e geof lu id . For t h i s s p e c i a l case , eqn. (3) becomes

6 = To(S2-S1). (4 1

imaX = A[ (h 1 -h 2 ) - T 0 ( s 1 - s 2 ~ l *

By combining eqns. ( 2 ) and (4), we w i l l ob ta in an expression f o r t h e maximum thermodynamic work

(5)

I f we so design t h e system t h a t t h e f i n a l s t a t e of t h e geof lu id is i d e n t i c a l i n every way wi th the ambient surroundings, then t h e maximum p o s s i b l e work w i l l be e x t r a c t e d from t h e geo- f l u i d , f o r a given i n i t i a l s tate. This u l t imate work?s c a l l e d the exergy and i s given by

The s p e c i f i c exergy is defined a s e -- E/&, o r simply

E = h[hl-ho - To(S1-So)]. (6 1 . el = hl-ho - To(s - s ). 1 0 (7 )

Values f o r the enthalpy and entropy a r e r e a d i l y obtained from property t a b l e s .

For the c a s e of binary p l a n t s , o r i n cases where the geof lu id is u t i l i z e d s o l e l y a s a l i q - u id , eqn. ( 7 ) may be s implied s i n c e

(8 1 (9 1

Thus, t h e exergy of a l i q u i d having a constant s p e c i f i c hea t , c , may be expressed as

sl-so = c Iln(T1/To),

and hl-ho = c(T1-To).

e l ( l i q u i d ) = c[T1-To-To 2n(T1/To)l. (10)

It fol lows t h a t t h e maximum power t h a t can be obtained from a l i q u i d being cooled from a tem- pera ture T 1 t o a temperature T2 is given by

Gmax ( l i q u i d ) = k[T1-T2-To kn(Tl/T2)]. (11)

EXERGY METHODOLOGY FOR GEOTHERMAL PLANTS

A geothermal power p l a n t may be represented by t h e func t iona l schematic given in Fig. 2. The phases of opera t ion are broken down as: Production (of t h e geof lu id) , t ransmiss ion , pre- p a r a t i o n , u t i l i z a t i o n , and d isposa l . Within each catagory t h e r e may be a v a r i e t y of compo- nents and processes. The bas ic i d e a of a Second Law a n a l y s i s is t o compute the exergy of the geof lu id (and any o t h e r f l u i d used i n t h e p l a n t ) a t a l l Important s t a t e s , and t o examine each ma- j o r component t o determine t h e change i n exergy.

I - - -

I ;I; RESERVOIR

Fig. 2. Block diagram of geothermal power p lan t .

Unlike energy, exergy is not a conserved quant i ty . Exergy is destroyed by d i s s i p a t i v e processes such a s f r i c t i o n , tu rbulence , mixing and hea t t r a n s f e r . Any process t h a t is thermo- dynamically i r r e v e r s i b l e robs t h e f l u i d of exergy and diminishes i ts p o t e n t i a l t o produce use- f u l work.

Any p l a n t component may be eva lua ted on a Second Law b a s i s by applying the fo l lowing equa- t i o n : (exergy i n ) - (exergy o u t ) = (exergy l o s t ) . (13) The f i r s t term c o n s i s t s of exergy c a r r i e d i n t o t h e component by means of mass f low and hea t flow (See Fig. 1 ) ; t h e second term is found from exergy c a r r i e d out with mass flow and produced as work. The exergy assoc ia ted wi th work is p r e c i s e l y equal t o t h e work; t h e exergy associ- ated with hea t is equal t o the product of the hea t times t h e Carnot e f f i c i e n c y w r i t t e n f o r the temperature of the system a t the p o i n t where t h e hea t is received and t h e temperature of t h e surroundings ( t h e dead-state temperature) . Thus,

48

eqn. (13) may be w r i t t e n as .. m LL I

2 - T I Q ~ 0 ' - i= 1 i i n

+ C kjej -o:tQk = AE. (14 )

DiPippo and Marcille C. Mechancial power developed by

0 Turbine i n t e r n a l Second Law

0 Turbine absolu te Second Law

turbines... . .................... 123.02 MW

ef f ic iency . ..................... 79.23

The exergy l o s t , AE, must always be p o s i t i v e . e f f i c i e n c y ...... i......,........ 62.1%

With regard t o t h e assessment of t h e performance of t h e power p l a n t a s a whole, t h e ne t power de l ivered by t h e p l a n t s.hould be compared with t h e r a t e of exergy ex t rac ted from t h e re- s e r v o i r , i n preference t o the r a t e a t which exergy i s de l ivered t o t h e p lan t . With re ference t o Fig. 2, some exergy w i l l be expended dur ing the geof lu id product ion phase, t h e exergy of t h e geof lu id a t the wellhead being less than t h a t i n t h e r e s e r v o i r f o r a self-f lowing w e l l . Not a l l of t h i s d e c l i n e i n exergy can be taken as a l o s s , however, because some of t h i s exergy sup- p l i e s t h e work needed t o l i f t t h e geof lu id t o the sur face .

D. Exergy r a t e i n e j e c t o r steam...... 15.99 MW

steam........................... 0.26 MW

steam........................... 0.23 MW

steam........................... 16.48 MW

Exergy r a t e i n H2S a u x i l i a r y

Exergy rate i n t u r b i n e gland -

0 Tota l exergy rate in a u x i l i a r y

E. N e t power de l ivered t o busbar . . . . . 1 13.43 MW 0 N e t p lan t Second Law e f f ic iency:

Based on r e s e r v o i r exergy....... 43.2% Based on exergy received a t

p l a n t boundary............. ... 52.8%

It might be argued t h a t basing t h e e f f i c i e n - cy of a geothermal p l a n t on t h e r e s e r v o i r exergy puts such p l a n t s a t a disadvantage when being compared t o convent ional power p l a n t s which are evaluated on t h e b a s i s of t h e exergy of t h e f u e l burned a t the p lan t . Thus, the convent ional p l a n t s a r e not burdened wi th t h e pena l ty of t h e work required t o br ing t h e f u e l t o s u r f a c e and t ransmit i t t o t h e p l a n t . The geof lu id wellhead exergy would i n f a c t be a b e t t e r b a s i s f o r such inter-technology comparisons. Within t h e realm of geothermal p l a n t s , however, the most meaning- f u l comparisons ought t o be based on r e s e r v o i r exergy t o account f o r d i f f e r e n c e s among p l a n t s i n methods of producing t h e geofluid.

SAMPLE CALCULATIONS Fin. 3. Simplif ied schematic of PGLE Geysers

To i l l u s t r a t e t h e method we have chosen Units Nos'. 16-18. W = wells; T/G = t u r b i n e / t h r e e d i f f e r e n t types of p lan t : (1) PGLE Units genera tor ; C 1 = condenser; E = steam je t ejec- 16, 17, and 18 a t The Geysers, Cal i forn ia ; (2) t o r s , i n t e r - and af ter-condensers ; C2 = a f t e r - Kraf la Unit 1, Iceland; and ( 3 ) Nigorikawa p i l o t condenser d r a i n cooler ; S = H2S abatement sys- binary p l a n t , Hokkaido, Japan. tem; C3 = var ious coolers ; CT = cool ing tower.

1. PGLE Geysers Uni t s 1'6, 1 7 , 18

These u n i t s a r e e s s e n t i a l l y i d e n t i c a l and may be considered a "standard" PGLE Geysers u n i t . A s impl i f ied schematic i s shown i n Fig. 3. Table 1 conta ins a summary of s ta te -poin t values f o r "100% Guaranteed Flow" condi t ions [12]. The dead s t a t e was taken a t t h e des ign wet bulb temperature, i.e., To 65OF = 524.67OR. Based on t h e s e c a l c u l a t i o n s , w e may summarize t h e a n a l y s i s i n the fol lowing way:

A. Exergy e x t r a c t i o n rate from reservoir.......................262.75 MW

bounda ry........................ 214.75 MW wells and pipelines., 48.00 MW

Exergy rate received a t p l a n t

0 Exergy drop:

B . Exergy rate e n t e r i n g turbines.....198.26 MW Exergy r a t e leav ing turbines . . . . . . 42.99 MW

0 Exergy drop through turbines....,.155.27 MW

S t a t e p o i n t

R 1 2

3

4

5

6

7

8

9

1 0

0

Table 1 . Summary of s t a t e - p o i n t data and exergy v a l u e s for PG&E Geysers Uni t s 16, 1 7 and 1 8 . See F i g . 3 for l o c a t i o n s of s t a t e p o i n t s .

- - o: Dtuylbm

460 1 2 0 5 . 3

337 1190.0 337 1190.0

337 1190.0

135 103 .0 337 1190.0

113 9 7 2 . 1

113 8 1 . 0 103 7 1 . 0

7 9 . 5 4 8 . 1

7 9 . 5 4 8 . 1

6 5 3 3 . 1

B t uy lbm°F

1 . 4 7 1 2

1 . 5 9 3 3

1 .5933 1 .5933

0 . 1 9 0 2

1 . 5 9 3 3

1 .7083

0 . 1 5 2 5

0 . 1 3 5 0

0 .0924

0 .0924

0 . 0 6 5 1

e Btu/lbm

434.5

3 5 5 . 1

3 5 5 . 1 3 5 5 . 1

4 . 2 9

3 5 5 . 1

.76 .9

2 .07

1 .26

0 . 7 1

0 . 7 1

0

1 0 3 1 L / h

2 0 6 3 . 9 2 0 6 3 . 9

1905.6 1 5 3 . 7

1 9 2 . 8

2 . 5

1907.7

2053.2

8 4 3 6 4 . 2

82314 - 0 6 9 8 7 5 . 0

--

E . Mw

262.75

214.75

1 9 8 . 2 6 1 5 . 9 9

0 .24

0 . 2 6

42 .99

1 . 2 5

31 .06

1 7 . 1 9

14 .59 --

49

DiPippo and M a r c i l l e One w i l l observe t h a t these u n i t s are very

e f f i c i e n t . The e f f i c i e n c y based on r e s e r v o i r exergy is s i g n i f i c a n t l y g r e a t e r than t h a t ob- ta ined on s ta te-of- the-ar t f o s s i l and nuc lear p l a n t s , and t h e e f f i c i e n c y based on exergy received a t t h e p l a n t fa r exceeds even that claimed f o r t h e la tes t combined steam and g a s t u r b i n e p lan ts . This is achieved i n s p i t e of r e l a t i v e l y low t u r b i n e e f f i c i e n c i e s ; on ly 62% of t h e exergy i n t h e incoming steam is converted i n t o u s e f u l output . The Second Law e f f i c i e n c y va lues may be compared d i r e c t l y with t h e usua l thermal ( o r F i r s t Law) e f f i c i e n c i e s f o r t h e convent iona l p l a n t s [13]. From t h e PGdE Heat Bal- ance Diagram [12], a t o t a l of 6.52 MW of elec- t r ic power i s used f o r p a r a s i t i c s ; t o t h i s we should add t h e 16.48 MW of exergy represented by a u x i l i a r y steam, making a t o t a l of 23 MW f o r s t a t i o n power. It should a l s o be not iced t h a t 48 MW go i n t o steam production and t ransmission.

2. Kraf la Unit 1, Iceland

This p l a n t is a double-flash p l a n t r a t e d a t 30 MW. The a n a l y s i s i s based on t h e des ign s p e c i f i c a t i o n s [14] , a l though t h e p l a n t has ye t t o achieve f u l l output due t o l a c k of steam. Figure 4 shows t h e p l a n t schematic and Table 2 l i s ts t h e s ta te -poin t da ta . The Second Law

A.

0

B.

0

C.

0

D.

0

E.

0

0

F. 0

a n a l y s i s may be summarized as follows:

Exergy e x t r a c t i o n rate from reservoir....................... 86.42 MW

Exergy rate received a t separa tor . 78.52 MW Exergy drop: wells and 2-phase

pipel ines . . ..................... 7.90 MW

Exergy rate i n steam leaving separator....................... 49.93 MW

Exergy ra te received a t t u r b i n e inlet........................... 45.64 MW

Exergy rate i n a u x i l i a r y steam.... 2.38 MW Exergy l o s s : main steam pipe l ine . 1 .91 MW

Exergy rate i n hot water from

Exergy rate i n secondary steam a t

Exergy rate i n h o t water from

Exergy l o s s :

separator....................... 28.63 MW

turbine......................... 13.30 MW

flasher......................... 13.15 MW

p i p e l i n e ........................ 2.18 MW f l a s h e r and LP steam

Exergy rate e n t e r i n g turbine...... 58.94 MW Exergy r a t e leav ing turbine....... 18.99 MW Exergy drop through turbine....... 39.95 MW

Mechanical power developed by

Turbine i n t e r n a l Second Law

Turbine a b s o l u t e Second Law

Net power de l ivered t o busbar..... 28.5 MW N e t p l a n t Second Law ef f ic iency:

Based on r e s e r v o i r exergy....... 33.0% Based on exergy received a t

separator..................... 36.3%

turbine......................... 31.11 MW

efficiency........... ........... 77.9%

eff ic iency. . . . .................. 52.8%

50

Fig. 4. Simplif ied schematic of Kraf la double- f l a s h p lan t . W = wells; S1, S2 = separa tor , f lasher / separa tor ; T/G = turbine/generator ; C 3 condenser; E = steam j e t e j e c t o r s and inter-condensers ; CT = cool ing tower.

Tablc 2. Summary of statc-point data and cxcrqy valucs for Kratla doublc-tlash ?lant. SCC Fig. 4 for locations OP state points.

state point

R 1 2 3 4 5 6 7 8

9 10 11 0

t 0 - 518 344 344 253 344 329 247 329 121 72 91 113 52

h Btullbm

509.6 509.6 315.3 221.8 1191.7 1188.2 1163.3 1188.2 998.8 39.6 59.3 81.4 20.1

B t u lbm°F

0.7109 0.7371 0.1953 0.3723 1.5859 1.6019 1.7037 1.6019 1.7342 0.0776 0.1138 0.1532 0.0400

e Dtu/lbm

146.2 132.9 62.3 31.8

380. G 368.9 292.0 368.9 111.9 0.27 1.43 3.35 0

1 0 3 1 % 1 h

2017.2 2017.2 1569.5 1413.2 447 * 8 422.2 155.4 22.0 579.2

12259.9 877.4

13715.0 --

i blw

86.42 78.52 28.63 13.15 49.93 45.64 13.30 2.38 18.99 0.98 0.37 13.48 --

One w i l l n o t i c e t h a t 57.8% of t h e exergy ex- t r a c t e d from t h e r e s e r v o i r is c a r r i e d i n t h e main steam a s it leaves t h e separa tor , and that 15.4% of t h e r e s e r v o i r exergy i s c a r r i e d i n t h e f lashed o r low-pressure steam. Thus, t h e steam production, t ransmission and prepara t ion phases may be viewed a s 73.2% e f f i c i e n t . Over 1.9 MW of a v a i l a b l e work is l o s t dur ing t h e t ransmission of t h e high-pressure steam from t h e separa tor t o t h e t u r b i n e along t h e 1640 f t of piping

3. " This p l a n t was b u i l t , t e s t e d , and even-

t u a l l y dismantled i n t h e l a t e 1970's under Ja- pan's Sunshine P r o j e c t [15] . The power c y c l e working f l u i d was dichlorotetrafluoroethane (R-114). The p l a n t schematic i s given i n Fig. 5; t h e s ta te -poin t d a t a i n Table 3. The r a t i n g of t h e p lan t was 1.0 MW ; i t achieved s l i g h t l y more than t h i s dur ing some test runs. The ana l - y s i s i s summarized below:

A. Exergy rate i n b r i n e received a t

Exergy r a t e l e a v i n g evaporator.. . . 3.02 MW

0 Exergy drop through evaporator.. . . 1.85 MW 0 Exergy drop through preheater.. . . . 1.06 MW

p l a n t ........................... 4.87 MW

Exergy r a t e leav ing prehea ter . .... 1.96 MW

B. Exergy rate i n R-114 e n t e r i n g preheater................ ........ 0.026 MW

Exergy r a t e i n R-114 leaving

Exergy r a t e i n R-114 leaving preheater;......; ............... 0.562 MW

evaporator...................... 2.27 MW 0.536 MW 1.708 MW

0 Exergy rise through preheater.. . .. 0 Exergy rise through evaporator....

C. Prehea ter Second Law e f f ic lency . . . 92.3%

D. Evaporator Second Law e f f ic iency . . 50.6%

E. Exergy rate e n t e r i n g turbine... . . . 2.21 MW 0.642 MW 1.568 MW

Exergy rate leaving turbine....... 0 Exergy drop through turbine.......

F. Mechanical power developed by

0 Turbine i n t e r n a l Second Law

0 Turbine absolu te Second Law

turbine......................... 1.00 MW

e f f i c i e n c y ...................... 63.8%

efficiency...................... 45.3%

G. N e t electrical power de l ivered t o

0 Net p l a n t Second Law e f f ic iency: busbar.......................... 0.975 MW

Based on i n l e t b r i n e exergy..... Based on br ine exergy drop ...... 20.0%

33.5X

0 T/G

FROM CT

Fig. 5. Simplif ied schematic of Nigorikawa pi- l o t binary p l a n t . PW, IW = production, i n j e c - t i o n w e l l s ; PH = preheater ; E = evaporator ; T/G = tu rb ine /genera tor ; MC, AC = main, a u x i l i a r y condensers; CP = condensate pump; CT = cool ing tower.

State point

1 2 3 4 5 6 7 8 9 10 11 * O

0

Table 3. Summary of state-point data and exergy values for Nigorikawa pilot binary plant. See Fig. 5' for locations of state points.

- 05

284 230 198 77 178 212 209 139 59 64 72 50 50

h Btu/lbm

253.3 198.3 166.1 96.4

121.1 167.0 166.7 160.3 27.1 32.1 40.1 18.1 90.1

B t u? 1 bm°F

0.4154 0.3388 0.2910 0.2591 0.3008 0.3693 0.3695 0.3767 0.0536 0.0632 0.0794 0.0361 0.2471

e Btu/lbm I - -

41.90 25.95 18.10 0.164 3.61 14.60 14.20 4.13 0.075 0.187 0.461 0 0

n L 0 lbm/ h

396.8 396.8 396.8 531.3 531.3 531.3 531.3 531.3

2431.7 2431.7 2431.7 -- --

E Mw

4.87 3.02 1.96 0.026 0.562 2.27 .2.21 0.642 0.054 0.134 0.328 -- --

Note: @ applies to R-114 at dead-state temperature; we ignore the chemical availability of R-114 relative to the atmosphere.

DiPippo and Marcille The o v e r a l l e f f i c i e n c y i s r e l a t i v e l y low f o r

a geothermal p lan t . It should be noted t h a t on ly 2.91 MW of exergy are taken from t h e geo- f l u i d , a t h i r d of which ends up as u s e f u l output . The R-114 picked up 2.24 MW while passing through the two h e a t exchangers making t h e process 77.1% e f f i c i e n t on t h e whole.

OVERALL PLANT EFFICIENCIES

I n Table 4 we l ist t h e o v e r a l l Second Law e f f i c i e n c y f o r s e v e r a l geothermal p lan ts . The va lues are based on r e s e r v o i r condi t ions, e i t h e r taken d i r e c t l y from the l i t e r a t u r e o r c a l c u l a t e d us ing d a t a on sur face condi t ions and assuming i s e n t h a l p i c w e l l flow. '

Table 4. Overall plant second law efficiency based on reservoir conditions.

. . CountryfPlant Name Plant Type '(I1) =

El Salvador Ahuachapan:

33.1% 1-Elash Units 1 E, 2 combined Units 1, 2 & 3 combined I-, 2-flash 38.2

Iceland Krafla Unit 1 Z-flash 33.0

Italy Lagoni Rossi:

Unit 1 dry steam 39.7

Unit 3 dry steam 48.4 Unit 2 dry steam 24.7

Larderello Cycle 3 dry steam 52.1 Molinetto dry steam 24.2

Japan Hatchobaru Kakkonda Matsukawa Nigorikawa Otake

2-f lash 41.6 1-flash 26.5 dry-steam 43.1

1-flash 29.0 binary 20.0

Kenya Oklaria Unit 1 1-flash 50.6

Mexico Cerro Prieto I

Philippines Mak-Ban Unit 1 Tiwi Unit 1

1-, 2-Elash 33.2

2-Elash") 43.5 2-flash"' 32.3

United States Geysers, PGSE Unit 5 dry steam 55.7 Geysers, PGSE Unit 13 dry steam 39.9

dry steam 43.2 Geysers, SMUDGE0 No. 1 dry steam 51.7 iieber Demonstration binary 29.7

Geysers, PGSE Unit 16-18

Magmamax binary 34.9

("Original design: currently running as 1-flash.

CONCLUSIONS

The method out l ined i n t h i s paper can be e a s i l y appl ied t o geothermal power p l a n t s t o g a i n a sharper understanding of t h e real l o s s e s involved i n var ious energy conversion systems. The Second Law e f f i c i e n c i e s of some geothermal p l a n t s f a r exceed those of convent ional p l a n t s . S i g n i f i c a n t expendi ture of exergy occurs i n producing, t ransmi t t ing , and preparing g e o f l u i d s p r i o r t o t h e i r in t roduct ion i n t o t h e power gen- e r a t i n g equipment. I n binary p l a n t s , a consid- e r a b l e l o s s of exergy can occur i n t h e h e a t exchangers owing t o l a r g e temperature d i f f e r e n c e s between t h e b r i n e and t h e c y c l e working f l u i d , l ead ing t o r e l a t i v e l y low o v e r a l l p l a n t e f f i - c i e n c i e s .

51

DiPippo and Marcille

ACKNOWLEDGEMENTS

The a u t h o r s thank C.J . Weinberg and S.G. Sharp of PG&E f o r providing us with h e a t balance diagrams f o r s e v e r a l Geysers u n i t s .

REFERENCES

Darr ieus . G.J .M. "The Rational d e f i n i t i o n of Steam Turbine Eff ic ienc ies" , Engineer- %, 1930, pp. 283-285.

Keenan. J.H. "A Steam Chart f o r Second Law Analysis", Mech. Engineering, v. 54, 1932, pp. 195-204.

Bosnjakovic, F., Technische Thermodynamik, v. 1, Ste inkopff , Dresden, 1935. *

Keenan, J .H. , Thermodynamics, John Wiley & Sons, I n c . , New York, 1941.

Bruges, E.A. , Available Energy and t h e Second Law Analysis, Butterworths Sc ien t i - f i c Pub., London, 1959.

Haywood, R.W., "A Crit ical Review of t h e Theorems of Thermodynamic A v a i l a b i l i t y , with Concise Formulations", J. Mech. Engr. Sci., V. 16, 1974, pp. 160-173 amd pp. 258-267. -

Moran, M.J., A v a i l a b i l i t y Analysis: A Guide t o E f f i c i e n t Energy Use, Prent ice- Hal l , Englewood C l i f f s , N J , 1982.

Milora , S.L. and Tester, J . W . , Geothermal Energy as a Source of Electric Power, MIT Press , Cambridge, MA, 1976.

Kes t in , J., "Available Work i n Geothermal Energy'' , i n Sourcebook on t h e Production of Geothermal Energy, J.Kestin, edi tor- in- c h i e f , R.DiPippo, H.E. Khalifa , and D.J.

DiPippo, R., Geothermal Energy a s a Source of E l e c t r i c i t y , U.S. Dept. of Energy, Washington

B i l i c k i , Z., DiPippo, R. , Kest in , J. , Maeder, P.F. , and Michaelides, E.E. , "Available Work Analysis i n t h e Design of Geothermal Wells", Proc. I n t ' l . C s Geoth. Energy, BHRA Flu id Engineering,

1982, pp. 227-248.

PG&E, "Mechanical Heat Balance Diagram, Uni t s No. 16, 17, 18, The Geysers Power Plant" , Rev. 2, March 10, 1982, San Fran- c i s c o , CA.

Khal i fa , H.E., "Hybrid Fossil-Geothermal Systems", i n Sourcebook on t h e Production of E l e c t r i c i t y from Geothermal Energy, J. Kest in , edi tor- in-chief , R.DiPippo, H.E. Khal i fa , and D.J. Ryley, e d i t o r s , U.S. Dept. of Energy, Washington, DC, 1980.

Gudmundsson, J.S., Thorhallsson, S., and Ragnars. K.. "Sta tus of Geothermal Elec- t r i c Power i n Iceland 1980", Proc. F i f t h Annual Geoth. Con€. and Workshop, Electric Power Research I n s t . . Rep. No. EPRI AP-2098, P.alo Alto, CA, 1981, pp. 7.52-7.65.

"Development of S p e c i f i c Hot Water Type Binary Cycle Test Plant" , Annual Report, Sunshine P r o j e c t , M.I .T.I . , Tokyo, Japan, June 1977, pp. 104-108.

Ryley, e d i t o r s , U.S. Dept. of Energy, Washington, DC, 1980.

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Exergy Analysis - DiPippo 1984