67878 the influence of non-condensable gases on the net work produced by the geothermal steam power...

7/23/2019 67878 The Influence of Non-condensable Gases on the Net Work Produced by the Geothermal Steam Power Plants

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Geothermics, Vol. I1, No. 3, pp. 163- 174, 1982.

Printed in Great Britain.

0375 - 6505/82/030163 - 12 03.00/0

Pergamon Press Ltd.

© 1982 CNR.

T H E I N F L U E N C E O F N O N - C O N D E N S A B L E G A S E S O N T H E N E T W O R K

P R O D U C E D B Y T H E G E O T H E R M A L S T E A M P O W E R P L A N T S

E. E . MICHAELIDES

Department of Mechanical and Aerospace Engineering, University of Delaware, Newark, DE 19711, U.S.A.

Received 7 September 1981,accepted or publication 23 December 1981)

A b s t r a c t - - T h e

majority of geothermal reservoirs contain a fraction of non-condensable gases (mainly

C02) which are released and form a mixture with the steam entering the turbine of the power-producing

installation. This paper examines the effect of non-condensable gases on the turbine work, the turbine

efficiency and the extraction work. The theory developed determines the net work obtained by a

geothermal power plant and shows where atmospheric turbines should be preferred to condensing

turbines.

N O M E N CL A T U RE

co, specific heat W, work g, gas

E, exergy x, dryness fraction m a x , maximum

f, fraction of CO2 y, wetness fraction mix, mixture

H, enthalpy y, ratio of specific heats n, net

m, mass Ah, latent heat o, ambient

M, molecular weight q, efficiency s, steam

P, pressure la, ratio of molecular weights t, turbine

Pt, total pressure v, mole fraction w, water (liquid)

Q, volumetric rate

R, gas constant Subscripts Superscripts

S, entropy c, co mp re ss or ., flow rate

T, temperature D, dry - , average

V, volume e, exit 0, reversible

I N T RO D U CT I O N

The majority of geothermal plants are either of the f lashed or dry-steam type. The common

characteristic o f both is the presence of non- con den sab le gases in the workin g fluid of the

turbine and the necessity to extract them from the condenser. The gases are dissolved in the

water of the reservoir and are released when the pressure is reduced. Typi cal species of gases are

carbon dioxide (CO2), hydrogen sulfide (H2S), ammonia (NH3), methane (CH,), nitrogen (Nz)

and et hane (C,H6). The am oun t and composit ion of these gases depends greatly on the location

and the time of opera tion of the well. Carb on dioxide is the main c onstituent and its

comp osi tio n ranges from 85 to 96°70 of the gases (Wahl, 1977). For that matte r, the presence of

the other gases is often neglected and the geothermal vapor is treated as a mixture of steam and

CO,. The am ou nt of no n-c ond ens abl es varies from 10070 in some dry steam wells to alm ost zero

in others; this amount is also higher in the early stages of the operation of the well and drops

after some time. Liqui d brine resources c ont ai n a percentage of CO, of less than 2o70, which is

released when the pressure of the system is lowered in the well or in the flashing chamber.

Therefore, the steam effluent always contains a certain amount of gases before it enters the

turbine. This paper will examine the influence of the no n-co ndens able gases on the power

produced by the geot hermal i nstallation. I t includes the work recovered by the turbine and the

work required by the gas-extraction equipment. Based on the work balances, the point will be

determined at which atmospheri c turbi nes are preferable to c ondensin g ones (break-even

point) . The study will not address the effect of no n-cond ensab les on the heat transfer

163



164 E . E . M i c h a e l i d e s

c o e f f i c i e n t s i n t h e c o n d e n s e r , s i n c e t h i s s u b j e c t h a s a l r e a d y b e e n a d e q u a t e l y c o v e r e d

( H e n d e r s o n a n d M a r c e l i o , 1 9 6 9 ) .

B A S IC A S S U M P T I O N S

C a r b o n d i o x i d e c o n s ti t u t e s th e m a j o r f r a c t i o n o f t h e n o n - c o n d e n s a b l e g a s e s . S in c e it s

p r o p o r t i o n is a l w a y s m o r e t h a n 8 5 % , t h e m a s s o f n o n - c o n d e n s a b l e s o f g a se s m a y b e r ep l a c e d

b y a n e q u i v a l e n t m a s s - f r a c t i o n o f C O ~ . T h e r e f o r e , i t w i ll b e a s s u m e d t h a t a n i d e a l g a s e o u s

m i x t u r e o f C O 2 a n d s t e a m e n t e r s t h e t u rb i n e . T h e s t u d y w i ll c o n c e n t r a t e o n t h e

t u r b i n e - c o n d e n s e r s y s t e m a n d w i l l n o t c o n s i d er w h e t h e r t h e s t e a m is p r o d u c e d i n a f l a sh i n g

t a n k o r w h e t h e r i t c o m e s d i r e c t l y f r o m t h e w e l l. W h e n e v e r l i q u id w a t e r c o - e x i s ts w i t h t h e

m i x t u r e , t h e r m o d y n a m i c e q u i l i b r i u m w il l b e a s su m e d f o r th e t w o p h a s e s ; h e n c e th e p a r t ia l

p r e s s u r e o f t h e s t e a m w i l l b e t h e s a t u r a t i o n p r e s s u r e a t t h e g i v e n t e m p e r a t u r e . T h e s e

a s s u m p t i o n s w il l b e s u p p l e m e n t e d w i t h o t h e rs r e g a r d i n g e f f ic i e n ci e s o f t u r b o m a c h i n e r y a n d t h e

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

I t m a y s e e m t h a t t h e a s s u m p t i o n o f i d ea l -g a s b e h a v i o r f o r t h e C O 2 is n o t a p p r o p r i a t e a n d

t h a t a n e q u a t i o n o f s t a t e f o r r ea l g a s e s s h o u l d b e e m p l o y e d , g i v e n th a t s u c h e q u a t i o n s a r e

a b u n d a n t in t he l i te r a tu r e . A m o m e n t ' s r e f l ec t i o n , t h o u g h , w i ll p r o v e t h a t u n d e r t h e c o n d i t io n s

d e s c r i b e d i n th i s p a p e r , C O 2 i n d e e d b e h a v e s a s a n i d e a l g a s . T h e h i g h e s t p r e s s u r e c o n t e m p l a t e d

i n t h i s p a p e r i s l e ss t h a n 2 0 °7 0 o f t h e c r i t i c a l p r e s s u r e f o r t h e C O 2 ( P , = 7 . 3 9 M P a ) , w h i l e a ll t h e

t e m p e r a t u r e s m e n t i o n e d a r e a b o v e t h e c ri ti c a l t e m p e r a t u r e o f C O , (T c~ = 3 1 .0 5 ° C ) . A g l a n c e a t

a g e n e r a l i z e d c o m p r e s s i b i l i t y c h a r t s h o w s t h a t t h e c o m p r e s s i b i l i t y o f a n y r e a l g a s i s v e r y c lo s e t o

u n i t y f o r t h e s e c o n d i t i o n s . F o r C O 2 e s p e c i a ll y , t h e v a l u e s o f t h e c o m p r e s s i b i l i t y c o e f f i c i e n t Z

w e r e c o m p u t e d f o r t he c o n di t io n s o f g e o t h e r m a l s y s te m s f r o m t he B e a t t i e - B r i d g e m a n

e q u a t i o n o f s ta t e (V a n - W y l e n a n d S o n t a g , 1 9 78 ). T h e s e c o e f f i c i e n t s a r e s h o w n i n T a b l e 1 . I t

m a y b e s e e n t h a t Z i s v e r y c lo s e t o u n i t y a n d , h e n c e , t h e i d e a l g a s a s s u m p t i o n f o r C O , i s f u l ly

j u s t i f ie d a n d a l l c o n c l u s i o n s b a s e d o n t h i s a s s u m p t i o n a r e v a l i d f o r e n g i n e e r i n g c a l c u l a t i o n s .

T a b l e 1

P r e s s u r e / b a r T e m p . - 3 5 ° C T e m p . = 1 0 0 ° C T e m p . = 2 0 0 ° C

Z Z Z

0 .1 0 . 9 9 9 7 0 . 9 9 9 7 0 . 9 9 9 8

1 . 0 0 . 9 9 7 0 0 . 9 9 7 2 0 . 9 9 7 5

5 . 0 0 . 9 8 4 3 0 . 9 8 5 5 0 . 9 8 8 1

1 0 . 0 0 . 9 6 9 9 0 . 9 7 2 0 0 . 9 7 5 6

T U R B I N E W O R K

I d e a l a v a i l a b l e w o r k

T h e m i x t u r e o f C O 2 a n d s t e a m e x p a n d s a d i a b a t i c a l l y i n th e t u r b i n e f r o m a s ta t e 1 ,

c h a r a c t e r i z e d b y p r e s su r e P , a n d t e m p e r a t u r e T , , to s t a te 2 ( P2 , T 2 ) . T h e m a x i m u m w o r k t h a t

m a y b e r e c o v e r e d i n s u c h a p r o c e s s is e q u a l t o t h e c h a n g e o f e x e r g y :

W m a ~ = E , - E ~ = H , - H 2 - T o ( S , - $ 2 ) . (1)

I f th e m o l e f r a c t i o n o f C O ~ in t h e m i x t u r e i s v , t h e s p e c if i c e n t h a l p y a n d e n t r o p y p e r m o l e o f t h e

m i x t u r e a r e g i v e n b y t h e f o l l o w i n g e q u a t i o n s :

(1 v)h~ + h (2)

-- V g ,

k

s = (1 - v)~, + vs~ - M [v ln v + (1 - v)ln(1 - v)] . (3)



I n f l u e n c e o f N o n - c o n d e n s a b le G a s e s o n N e t W o r k 165

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

f r a c t i o n i s g i v e n in t e rm s o f t h e m a s s f r a c t i o n f a s f o l l o w s :

v , = f M s = f ( 4 )

(1 - J ) M S + f M g (1 - 001a + f '

w h e r e M e a n d M s a r e t h e m o l e c u l a r w e i g h t s f o r c a r b o n d i o x i d e a n d s t e a m , a n d Ix i s t h e r a t i o

M / M , .

T h e p r e s s u r e a n d t e m p e r a t u r e o f th e m i x t u r e f a l l s u p o n e x p a n s i o n . S o m e o f th e s te a m

c o n d e n s e s t o l i q u id w a t e r a n d t h e m o l e f r a c t i o n s o f t h e g a s e o u s m i x t u r e c h a n g e . I f y k g o f

s t e a m c o n d e n s e , t h e a m o u n t o f s t e a m p r e s e n t i s (1 - f - y ) p e r k g o f o r i g i n a l m i x t u r e . T h e n e w

m o l e f r a c t i o n o f t h e g a s is

f

v 2 = ( 1 - f - y ) ~ t + f ( 5 )

I t i s o b v i o u s t h a t v 2 > v , .

T h e p a r t i a l p r e s s u r e o f C O 2 i s g i v e n a s f o l l o w s :

P g = v P , , ( 6 )

w h e r e P t i s t h e t o t a l p r e s s u r e . T h e p a r t i a l p r e s s u r e o f s t e a m is t h e s a t u r a t i o n p r e s s u r e P ~(T )

w h e n i t i s i n e q u i l i b r i u m w i t h l i q u i d w a t e r . T h e r e f o r e , e q u a t i o n ( 1) f o r th e a v a i l a b l e w o r k c a n

b e w r i t t e n f o r t h e i d e a l m i x t u r e a s

W m a x = ( 1 - - v l ) h s l J r - V l h g I - ( 1 - v 2 ) ~ T s 2 - V l h g 2 - ( v 2 - v l ) h w 2 - To [(l - v,)J '~,

r l

1 - v2) ln(1 - v2) ] . (7 )

T h e a p p a r e n t m o l e c u l a r w e i gh t o f t h e g a s eo u s m i x t u r e i s

l Ms

M = - . (8 )

1 - f f 1 - f + t x f

A 4 M e

T h e m a g n i t u d e o f t h e e n t r o p y o f m i x i n g i s v e r y s m a l l a n d t h e d i f f e r e n c e o f t h i s q u a n t i t y a s

e x p r e s s e d b y t h e la s t t w o t e r m s o f e q u a t i o n ( 7) c a n b e n e g l e c te d w h e n c o m p a r e d t o t h e o t h e r

t e r m s o f t h e e q u a t i o n . W e m a y a l s o a s s u m e i d e a l - g a s b e h a v i o r f o r CO ~ a n d e x p r e s s t h e

e n t h a l p y a n d e n t r o p y d i f f e r e n c e s i n t e r m s o f a n a v e r a g e s p e c if i c h e a t a n d t h e p a r t i a l p r e s s u r es .

W e c a n t h e n w r i t e t h e e x p r e s s i o n f o r t h e s p e c if i c a v a i l a b l e w o r k i n t e r m s o f m a s s e s a s f o l l o w s :

w ° = (1 -

f , ) h s , -

(1 - f~ -

y )h~2 - yh ~: + f , cog(T , - T2 ) -

T0[(1 -

f , ) s ~ ,

- (1 - f , - y ) s ~ 2 - Y S w 2 + c o in ~ ] . ( 9 )

P g

T h e s p e c i f i c a v a i l a b l e w o r k i s d e p i c t e d i n F i g . 1 a s a f u n c t i o n o f t h e i n i t i a l g a s c o n t e n t f o r

v a r i o u s i n i t ia l t e m p e r a t u r e s T , . T h e f i n a l t e m p e r a t u r e T2 i s t a k e n a s 2 5 ° C ( e q u a l t o t h e a m b i e n t

T o) a n d t h e p r e s s u r e P , , 1 a t m . T h e w o r k i s n o r m a l i z e d w i t h r e s p e c t t o i ts v a l u e a t f

= 0 ( g a s - fr e e s t e a m ) . T h i s i d e a l a m o u n t o f w o r k m a y b e r e c o v e r e d i n a re v e r s ib l e s y s t e m s u c h a s

t h e o n e s h o w n i n F i g . 2. T h e s y s t e m i s a n i d e a l o n e a n d c o n s i s ts o f a n i s e n t r o p i c t u r b i n e , a n

i s o t h e r m a l c o n d e n s e r a t t e m p e r a t u r e To a n d a n i s o t h e r m a l c o m p r e s s o r . I t m a y b e se e n f r o m



166 E. E. Michaelides

F i g . 1 t h a t t h e C O 2 r e d u c e s t h e a m o u n t o f a v a i l a b l e w o r k i n t h e m i x t u r e ; t h e d e c r e a s e is r o u g h l y

e q u a l t o 1 % o f a v a il a b l e w o r k p e r 1 % o f g a s c o n t e n t .

1 . 0

~ : 0 . 9

t~

o

0 . 8

.J

<

LtJ

a

a

h i

N

..J

< 0 . 7

o

z

P o = I a t

TO = 2 5 C

0 . 6 I z I

0 0 .1 0 . 2 0 . 3

M A S S F R A C T I O N O F C 0 a , f

F i g . 1 . N o r m a l i z e d i d e a l a v a i l a b l e w o r k .

T ~ / * C

2 0 0

1 7 5

1 5 0

1 2 5

W 0

S = S l

ID E A ~ W ~ <~ W o

C O N D E N S E R ~ Po,T o

To

Fig . 2 . Idea l system for the recovery of ava i lable work.

Real turbine work

T h e f ul l a m o u n t o f r e v e rs i b le w o r k i s n o t r e c o v e r e d c o m p l e t e l y f r o m a r e al s y s te m , w h i ch

i n c lu d e s i r re v e r s ib l e e q u i p m e n t s u c h a s n o n - i s e n t r o p i c t u r b i n e a n d c o m p r e s s o r , a n d a c o n d e n s e r

a t a t e m p e r a t u r e h i g h e r t h a n t h e a m b i e n t . T h e r e i s a l w a y s e n t r o p y p r o d u c t i o n i n t h is s y s te m a n d

s o m e f r a c t i o n o f t h e a v a i l a b l e w o r k i s d i s s i p a t e d . H e r e w e w il l e x a m i n e s e p a r a t e l y t h e r e a l

e x p a n s i o n , c o n d e n s a t i o n a n d g a s e x t ra c t i o n p r o c e s s.

T h e g a s m i x t u r e e x p a n d s i n t h e tu r b i n e f r o m t h e i ni ti a l p r e s s u r e P , t o t h e t u r b i n e b a c k

p r e s s u r e P2 . T h e t e m p e r a t u r e T2 a n d t h e w e t n e ss a t t h e e x it o f t he t u r b i n e a r e i m p o r t a n t

v a r i a b le s . F o r t h i s d e t e r m i n a t i o n w e m a y u s e t h e i s e n tr o p i c c o n d i t i o n ( K h a l i f a et al., 1979)

S~m,i~ = °mid'e(2' (10 )



Inf luence of Non-condensable Gases on Net Work

167

t o g e t h e r w i th a n i s e n tr o p i c t u r b i n e e f f i c ie n c y g i ve n b y t h e m o d i f i e d B a u m a n ' s r u l e ( M o o r e a n d

S i e l v e r d i n g , 1 9 7 6 ) a s f o l l o w s :

q , = lID(1 - 1 . 2 y ) , ( 1 1 )

where ' r iD

=

0 . 8 5 is t h e e x p a n s i o n e f f i c i e n c y o f a d r y m i x t u r e . F o r t h e c a l c u l a t i o n o f t h e e x it

t e m p e r a t u r e T2 w e a l so n e e d a n e x p r e s s i o n f o r t h e v a p o r p r e s s u re o f w a t e r i n te r m s o f

t e m p e r a t u r e . T h i s w a s o b t a i n e d b y i n t eg r a t in g t h e C l a u s i u s - C l a p e y r o n e q u a t i o n w i t h a l in e a r

e x p r e s s i o n f o r t h e s p e c i f i c h e a t ( K e s t i n , 1 96 8)

298 .15 ) T

Ps = 2 3 .1 0 6 1 - - 5 .3 6 2 I n - - (12 )

I n 3 . 1 6 9 k P a T 2 9 8 . 1 5 '

w h e r e T is i n ° K . T h e c l o s u r e e q u a t i o n s a r e f o r t h e to t a l p r e s s u r e P , a n d t h e e x p r e s s i o n o f th e

p a r t i a l p r e s s u r e o f C O 2 i n t e r m s o f i t s m o l e f r a c t i o n :

P ' = Ps2 + P~2, (13)

Pg2 = v2 P2. (14 )

T h e s e t o f e q u a t i o n s ( 1 0 - 1 4 ) f o r t h e i s e n t r o p i c e x p a n s i o n r e d u c e s t o t h e f o l l o w i n g t w o

e q u a t i o n s :

A h

1 - f , ) s , , - s,2 + y ~ = f , sg , - s , 2 ) 1 5 )

a n d

P, = Ps T2)/ 1 - v2), (16)

w h i c h c a n b e s o l v e d s im u l t a n e o u s l y t o y i e l d y a n d T 2. T h e a c t u a l s p e c i f ic w o r k p r o d u c e d b y t h e

t u r b i n e i s t h e n

w, = rl ,(h, - h2). (17 )

T h e p r e s e n c e o f t h e n o n - c o n d e n s a b l e g a s e s r e d u c e s t h e w e t n e s s f r a c t i o n i n t h e la s t st a g e s o f t h e

t u r b i n e a n d , t h e r e f o r e , i n c r e a s e s s l i g h t l y t h e t u r b i n e e f f i c i e n c y . F i g u r e 3 s h o w s t h i s c h a n g e o f

I .O 6 , , T , / o c

~ 200

, , ~ 1 . 0 5

r , - 1 7 5

O 1 . 0 4

< 1 5 0

ta_

t n I D 3

t n 1 2 5

~ 1.02

1.01

1.00

0 0 .1 0 . 2 0 . 3

M A S S F R A C T I O N O F C 0 2 , f

F iB . 3 . I n cr e a s e d t u r b i n e e f f i c i e n c y f a c t o r , d u e t o r e d u c e d w e t n e s s .



168 E . E . M i c h a e l i d e s

the turbine efficiency normalized with respect to the efficiency at f = 0. Howeve r, the

isentropic change of enthalpy (h, - h2) is considerably lower in the presence of gases and their

overall effect is a net decrease of the turbine work. The drop of the turbine work is depicted in

Fig. 4 for two initial temperatures T,. It is seen that for every 1°7o of CO2 the real turbine work

is decreased by app roxi mate ly 0.5°70. The total work pro duc ed by the turbine wt may be

determined if w, is multiplied by the mass of mixture passing through the turbine.

n r

0

~ 0 . 9

m

F -

a

b J

S

~ 0 , 8

~ 0

w

0

Z

(50oc) -~

- - I t = 0 . 7 5

. . . . - q t = ' r / ( f )

,.

0 I 0 . 2 O . 3

M A S S F R A C T I O N O F C O ~ , f

F i g . 4 . T u r b i n e w o r k w i t h c o n s t a n t a n d a d j u s t e d e f f i c i e n c y .

T~I°C

2 O O

125

125

2 O O

CONDENSATION AND GAS EXTRACTION

In practice, the following devices are in use for the extraction of non-condensable gases:

(i) steam ejectors; (ii) hot water ejectors; (iii) rotary compressors; (iv) reciprocating pumps;

and (v) combination of steam ejectors and radial blowers (ERR systems).

The ejectors are simple, inexpensive devices and require little maintenance. However, they

are inefficient and consume a great deal of available work. Compressors and pumps, although

more efficient, are expensive and require frequent maintenance. In general, ejectors are used

where the gas fraction is relatively low and compressors are used where the gas content is high.

The non -conden sable gases and a small fraction o f steam form an ideal gas mixture under the

total pressure of the condenser. The condensation does not proceed isothermally, but is

governed by the condition that the partial pressure of steam is equal to the saturation pressure

at any temperature. The mixture of steam and gases must be extracted by one of the above

devices at the expense of work. The mass of steam which must be extracted per unit time with

the gases is

# r ,

i 'n = t~ (P¢ _ P , )M~v~ (18)

The volumetric capacity of the gas extraction equipment in this case is determined by the

equation

m3RT3

O - - rhgV~. (19)

( P , - P , )M

The capacity of such an equipment per unit mass of CO2 is depicted in Fig. 5. The mass of

steam carried per unit mass CO2 is shown in Fig. 6. It is seen that both the mass of steam and



Influence of Non-condensable Gases on Net Work 169

I 0 0

80

,T

E

6O

° 1 - ~ 4 o

w

I---

'~ 2O

ne

0

J

u_ I0

. 6

0

> 4

22

i I I I I

BO 40 50 6 0

TEMPERATUR E T s , °c

Fig. 5. Volumetric capacity of gas extraction equipment.

I0

8

6

4

d . ~ 2

u.i

(,o

. 8

LI..

0 .6

< .4

.2

, / /

J

. I I [ I

50 40 50 60

TEMP ERAT URE T s °C

Fig. 6. Mass of steam carried with CO.,.

t h e v o l u m e t r i c c a p a c i t y o f t h e e x t r a c t i o n e q u i p m e n t d e c r e a s e s w h e n t h e u n d e r c o o l i n g a t t h e

c o n d e n s e r

Ts P) - T3)

i s h i g h . I t is a d v a n t a g e o u s t o i n c r e a s e t h e u n d e r c o o l i n g b y i n c r e a s i n g

t h e s u p p l y o f c o o l i n g w a t e r t o t h e c o n d e n s e r . M o r e s t e a m c o n d e n s e s i n th i s c as e a n d ,

t h e r e f o r e , w e n e e d t o e x t r a c t l es s o f i t. T h u s t h e a m o u n t o f w o r k s p e n t f o r t h e e x t r a c t io n o f t he



170

E . E . M i c h a e l i d e s

g a s e o u s m a s s e s is r e d u c e d c o n s i d e r a b l y . H o w e v e r , t h e c o n d e n s e r t e m p e r a t u r e m u s t b e h i g h er

t h a n t h e t e m p e r a t u r e o f t h e c o o l in g w a t e r , a n d t h i s f a c t im p o s e s a li m i t t o t he u n d e r c o o l i n g . I t

m a y a l s o b e d e d u c e d f r o m F i g s . 5 a n d 6 t h a t t h e r e a r e d im i n i s h i n g r e t u r n s w h e n t h e

u n d e r c o o l i n g e x c e e d s 1 0 ° C .

E q u i p m e n t f o r i d ea l g a s e x t r a c t i o n o p e r a te s i se n t r o p ic a l l y , a n d th e sa t u r a t e d C O , - H 2 0

m i x t u r e i 's c o m p r e s s e d f r o m 100 °7 0 r e l a t iv e h u m i d i t y t o a p o i n t o f l o w e r h u m i d i t y . D u r i n g t h is

p r o c e s s th e c o m p o s i t i o n o f t h e g a s e o u s m i x t u r e w il l b e c o n s t a n t a s g i v e n b y e q u a t i o n ( 18 ), a n d

t h e v a p o r w i ll b e c o m e s u p e r h e a t e d . A t t h e l o w p r e s s u r e s p r e v a i l i n g d u r i n g t h e g a s e x t r a c t i o n

p r o c e s s, w e m a y a s s u m e t h a t t h e s t e a m a n d C O 2 a lw a y s f o r m a n i d e al g a s m i x t u r e w i th s p e c if ic

h e a t

m

Cp = fecp~ + (l - f e ) c p s , (20)

w h e r e Cpg a n d Cps a r e t h e s p e c i f ic h e a t s a t c o n s t a n t p r e s s u r e o f C O 2 a n d s t e a m , a n d / e i s t h e m a s s

f r a c t i o n o f C O 2 in t h e m i x t u r e . T h e m i x t u r e g a s c o n s t a n t i s d e f i n e d i n a s i m i l a r m a n n e r :

= f e R g + ( 1 - f e ) R S. (21 )

T h e r e f o r e , t h e i s e n t ro p i c e x p o n e n t f o r t h e m i x t u r e i s g i v e n b y th e e q u a t i o n

t = c p / ( C p - R ) , (22)

a n d t h e s p e c i fi c w o r k r e q u i r e d f o r t h e e x t r a c t i o n o f t h e m i x t u r e o f g a s e s f r o m P , t o P0 is

e x p r e s s e d a s

wc = b-°r3 L \ ~ / - l / t ic , (23)

w h e r e tic i s t h e i s e n t r o p i c e f f i c i e n c y o f t h e g a s - e x t r a c t i o n e q u i p m e n t a n d T3 i s t h e t e m p e r a t u r e

o f t h e g a se s a t th e e x i t o f t h e c o n d e n s e r . T h e t o t a l e x t r a c t i o n w o r k W i s g i v e n w h e n w~ is

m u l t i p l ie d b y t h e m a s s o f t h e m i x t u r e .

T h e n e t w o r k p r o d u c e d i s g i v e n b y t h e d i f fe r e n c e o f t h e t u r b in e m i n u s t h e e x t r a c t i o n w o r k :

W o = W , - W ~. ( 2 4 )

T h e n e t w o r k p r o d u c e d b y a g e o t h e r m a l p l a n t a s a f u n c t i o n o f t h e tu r b i n e b a c k p r e s s u re

( w h i c h i s e q u a l t o t h e c o n d e n s e r t o t a l p r e s s u r e ) i s d e p i c t e d i n F i g. 7 . T h e a m o u n t o f C O 2

i n i ti a l ly p r e s e n t i s t h e p a r a m e t e r f i n t h e g r a p h . F o r c a l c u l a t i o n s o f t h is f i g u r e i t w a s a s s u m e d

t h a t t h e c o n d e n s e r m i x t u r e i s e x t r a c t e d a t 3 5 ° C , t h e in i ti al t e m p e r a t u r e o f t h e g e o t h e r m a l s t e a m

i s 2 0 0 ° C a n d c o n s t a n t e f f i c i e n c i e s f o r t h e t u r b i n e a n d t h e c o m p r e s s o r a r e 0. 7 5 a n d 0 . 7 0

r e s p e c t i v e l y . T h e r e a s o n f o r t h e d r a s t i c d e c l in e o f W o n e a r 5 . 6 k P a p r e s s u r e ( c o r r e s p o n d i n g t o

s a t u r a t i o n t e m p e r a t u r e 3 5 ° C ) i s t h a t t h e r e i s a l m o s t n o u n d e r c o o l i n g i n t h e c o n d e n s e r a n d a

h i g h f r a c t i o n o f s t e a m m u s t b e e x t r a c t e d w i t h t h e g a s a t t h e e x p e n s e o f w o r k . T h e e f f e c t o f

i n c r e a s e d t u r b i n e e f f i c i e n c y a c c o r d i n g t o e q u a t i o n ( 1 1 ) i s s h o w n i n F ig . 8 f o r f = 0 . 2 , T , =

2 0 0 ° C a n d ti~ = 0 . 7 . T h e n e t w o r k o u t p u t i s p l o t t e d t o g e t h e r w i t h t h e v a l u e o f t h e t u r b i n e

e f f i c i e n c y . T h e m a x i m u m e f f e c t o f in c r e a s e d t i, i s d e r i v e d w h e n t h e t u r b i n e o p e r a t e s a t n e a r -

a t m o s p h e r i c b a c k p r e s s u re a n d t h e e x h a u s t m i x t u r e i s d r y . I t m a y b e d e d u c e d f r o m t h is f i g u re

t h a t t h e v a l u e o f th e m a x i m u m w o r k i s a l m o s t u n c h a n g e d w h e n v a r i a b l e 11, is u s e d . O n l y t h e

p o s it io n o f th e m a x i m u m c h a n g e s.

W h e n t h e c o n d e n s e r t e m p e r a t u r e is fi x ed ( th i s is i m p o s e d b y t he t e m p e r a t u r e a n d a v a i l a b i l it y

o f c o o l i n g w a t e r ) , t h e w n c u r v e s a l w a y s e x h i b i t a m a x i m u m p o i n t . T h i s i s d u e t o t h e f a c t t h a t t h e



I n f l u e n c e o f N o n - c o n d en s a b l e G a s es on N e t W o r k

7 0 0 , ,

wt(o),

o , 6 0 0

i

5 0 0

x - 4 0 0

0

I - -

uJ

Z

3O0

I I I I I I I I I

T I = 2 0 0 C

r / t = 0 . 7 5

r / e - - 0 . 7 0

f = O . O

~ , 4

171

200 ' ~ ~

0 . 0 0 . 01 0 . 0 2 0. 0: 5 0 . 0 4 0 . 0 5 0 . 0 6 0 . 0 7 0 . 0 8 0 . 0 9 0 . 10

O . O 05 E ( 3 5 e C ) ( ~ l o t m )

B A C K P R E S S U R E , P 2 / M P 0

F i g . 7. N e t w o r k p r o d u c e d b y th e g e o t h e r m a l p l a n t .

.=¢

¢

EL

I - -

: 3

0

n -

O

I - -

5 0 0

4 0 0

3 0 0

2 0 0

O 0

T t = 2 0 0 C , f = 0 . 2 , ' r / e = 0 . 7

r = C O N S T A N T = 0 . 75

. . . . . V A R I A B L E r /t

/

..__..- -

_ . _ . . . - - -

0 . 8 5

0 . 8 0

0 . 7 5

I I

0 0 , 0 1 0 2 0 1 0 0 1 0 4 0 0 5 0 1 0 6 0 1 0 7 0 1 0 8 0 1 0 9 0 0 ° 7 °

B A C K P R E S S U R E , P z / M P o

Fig. 8. Effect o f adjusted turbine efficiency on net w ork .

gt

t u r b i n e w o r k i n c r e as e s w i t h d e c r e a si n g b a c k p r e ss u r e a n d t h e e x t ra c t io n w o r k i n c r ea s es w i t h

d e c r e a s in g b a c k p r e ss u r e (b e c a u s e o f l o w e r u n d e r c o o l i n g ) . T h e r e is a p o i n t (e n c i r cl e d i n F i g . 7 )

w h e r e t h e m a r g i n a l in c r ea se s o f w o r k b e c o m e eq u a l , a n d th i s y i e ld s th e m a x i m u m a m o u n t o f

w o r k t h a t is e x tr a ct ed f r o m t h e g e o t h e r m a l s y s te m . T h i s m a x i m u m w o r k b e c o m e s h ig h e r a s t h e

a m o u n t o f n o n - c o n d e n s a b l e g a s e s i s d e c r e a s e d , a n d r e a c h e s it s h i g h e s t va l u e w h e n t h e s e g a s e s



172 E. E. Michaelides

are absent. This value is shown as IF* (0) in Fig. 7. When the initial gas contentfbecomes high,

the curve for the net work is flat, an indication that the gas extraction work is dominant in the

case. The value of the maximum work obtained from a given installation is depicted in Fig. 9 as

a function off. For two initial steam temperatures T,, the figure shows the total effect of the

non-conde nsa ble gases on the work out put of the plant. A 10070 initial CO2 cont ent may cause

20 - 25070 reduc tion of the net work obtained. Whe n this fi gure is com par ed to Fig. 4 it becomes

obvious that the extraction work is a very important item in the net work balance. The two

figures demonstrate the influence of non-condensable gases on the total turbine and gas

extraction work in a geothermal power plant.

o 1.0

O.9

$ c

0 . 8

n -

O

0.7

~- 0.6

,~ 0.5

Ld

N

J 0.4

n~

o 0.5

z 0

I I

~

r/t =0.75 , 'r / e=O. 7

1 5 0 ° C ~

I I I

0 .1 0 . 2 0 . 5

M A S S F R A C T I O N O F CO 2 , f

F i g . 9 . M a x i m u m n e t w o r k v s C O . , f r a c t i o n .

0 . 4

CONDENSING VS ATMO SPHE RIC TURBINES

It can be seen in Fig. 9 that the work for the extraction of non-condensable gases is a

significant proportion of the net work obtained in a geothermal installation. In addition, the

cost of the condenser, cooling system and gas extraction eq uipment may add up to 40 - 50°70 of

the total cost for the plant (Moore, 1976). For that matter, it was thought that it may be

advantageous to use atmospheric turbines in the plants where the gas content is significantly

high. The atmospheric turbine exhausts the geothermal fluid at atmospheric pressure and does

not recover the work done at sub-atmospheric pressures. The magnitude of this work is of the

same order as the work recovered from the atmospheric expansion (Kestin and Michaelides,

1979). The sacrifice of this type of work, though, simplifies considerably the design of the

plant. Because of this, a great deal of geothermal installations (especially the older ones)

exhaust to the atmosphere. As a general rule, the geothermal power plants employ condensing

turbines if the initial gas con tent is less than 407o. Otherwise, atmo spheric turbines are used

wherever this is environmentally acceptable. A review of the thermodynamic and economic

advantages of the atmospheric and condensing turbines for geothermal installations is given in

Kestin and Michaelides (1979) and Michaelides (1979). In these studies the break-even point for

the employment of a condensing turbine is equal to the work produced by an atmospheric

turbine. At gas contents above this point there is no advantage in using a condensing cycle.



I n f lu e n c e o f N o n - c o n d e n s a b l e G a s es o n N e t W o r k 173

S E P A R A T I O N O F N O N - C O N D E N S A B L E G A S E S

B e c a u s e o f th e a d v e r s e e f f e c t s o f t h e n o n - c o n d e n s a b l e g a s e s o n t h e p o w e r e x t r a c t e d a n d t h e

d r a s t ic r e d u c t i o n o f th e h e a t t r a n s f e r c o e f f i c i e n t i n t h e c o n d e n s e r ( H e n d e r s o n a n d M a r c e l lo ,

1 96 9) , e f fo r t s h a v e b e e n m a d e t o s e p a r a t e t h e n o n - c o n d e n s a b l e s b e f o r e t h e e n t r a n c e t o t h e

c o n d e n s e r . T h i s i s p o s s i b le o n l y i f t h e w e ll p r o d u c e d l iq u i d b r i n e , b y m e a n s o f p r i m a r y f l a sh i n g

( M i c h a e l i d e s , 1 9 80 ). A s c h e m a t i c o f s u c h a n i n s t a l l a t i o n is s h o w n i n F ig . 1 0, t o g e t h e r w i t h t h e

T - s d i a g r a m f o r t h e p l a n t . T h e l i q u id b r i n e i s s u p p l ie d t o a p r i m a r y f l a s h i n g c h a m b e r F , , w h e r e

a s li g ht r e d u c t i o n o f p r e s s u r e r e l ea s e s m o s t o f t h e C O2 a n d s o m e s t e a m . T h i s m i x t u r e p a s s e s

t h r o u g h a n a t m o s p h e r i c t u r b i n e T , a n d is t h e n v e n t e d t o th e s u r ro u n d i n g s . T h e r e m a i n i n g b r i ne ,

f r e e o f t h e m a j o r f r a c t i o n o f C O 2 , is f l a s h e d a n d s u p p l i e s a c o n d e n s i n g t u r b i n e T , w it h s t e a m

( a n d o n l y s m a l l a m o u n t o f C O 2 ). T h e a m o u n t o f C O 2 re l e a se d a t th e f i rs t fl a s h in g c h a m b e r i s

s h o w n i n F ig . 11 a s a f u n c t i o n o f th e f l a s h i n g t e m p e r a t u r e f o r a n i n s t a l l a t i o n r e c e i v i n g b r i n e a t

2 0 0 ° C ; f i s t h e m a s s f r a c t i o n o f C O 2 i n i ti a l ly p r e s e n t i n t h e b r i n e a n d m i s t h e m o l a l i t y o f t h e

b r i n e . T h i s s y s t e m re q u i r e s a v e ry sm a l l a m o u n t o f w o r k f o r t h e e x t r a c t i o n o f t h e C O2 f r o m t h e

c o n d e n s e r a n d is v e r y m u c h f a v o r e d o v e r a si m p l e f l a s h i n g s y s t e m , e s p e c i a l ly a t f i e ld s w i t h a

h i g h p e r c e n t a g e o f n o n - c o n d e n s a b l e s . A t f = 0 . 2 % i t g iv e s 5 0 % m o r e w o r k t h a n a c o n v e n t i o n a l

d u a l - f l a s h s y s t e m .

2

2'

3 '

3

,. 4

C

I o ~

~S

Fig. 10. Primary flashing installation for the separation of the non-condensables.

T h e a b o v e s y s t e m c a n o n l y b e a p p l i e d w h e n t h e g e o t h e r m a l r e s o u r c e y i e ld s li q u id b r i n e . I n

t h e c as e o f d r y - s t e a m w e l l s, t h e n o n - c o n d e n s a b l e g a s es f o r m a h o m o g e n e o u s m i x t u r e w i th t h e

s t e a m a n d s e p a r a t i o n i s p r a c t i c a l l y u n f e a s i b l e .

C O N C L U S I O N S

T h e p r e s e n c e o f n o n - c o n d e n s a b l e g a s e s i n t h e g e o t h e r m a l s t e a m p o w e r p l a n t s h a s an a d v e r s e

e f f e c t o n t h e n e t w o r k r e c o v e r e d . T h i s is d u e t o t h e d e c r e a s e o f th e t u r b i n e w o r k a n d t o t h e



174

E . E . M i c h a e l i d e s

o

12-

>

Z

Z

W

W

n~

o_

0 . 0 0 8

O . 0 1 0 . . . . . . . . . . . . . . . . . . . ~ - -

0 . 0 0 6

0 . 0 0 4

0 . 0 0 2

0 . 0 0 0

f = 0 . 0 1

f = 0 . 0 0 5

. .

2 0 0 1 9 0 1 8 0 1 7 0 1 6 0 1 5 0 1 40

F L A S H T E M P E R A T U R E , T 2 , o c

F i g . 1 1. A m o u n t o f C 0 2 r e l e a s e d u p o n p r i m a r y f l a s h i n g .

p o w e r s u p p l i e d t o t h e g a s - ex t r ac t io n e q u i p m e n t . T h e o n l y p o s i t i v e e ff e c t o f t h e g a s e s is t h e

s li g h t i n c r e a s e o f th e t u r b i n e e f f i c i e n c y , w h i c h i s n o t e n o u g h t o c o u n t e r a c t t h e ad v e r s e e ff e c t .

S t e a m m u s t b e e x tr a c te d f r o m t h e c o n d e n s e r w i t h t h e g a s b e c a u s e th e t w o f o r m a n i d e a l g a s

m i x tu r e . T h e w o r k s p e n t o n t h e g a s - e xt r a ct i o n e q u i p m e n t a n d i t s v o l u m e t r i c c a p a c i ty d e p e n d o n

t he u n d e r c o o l i n g i n th e c o n d e n s e r . T h e f u n c t i o n o f t he n e t w o r k r e co v e r ed e xh i bi ts a m a x i m u m

a t a ce r ta i n t u r b i n e b a c k p r e s su r e ; t hi s m u s t b e t h e d e s i g n p o i n t f o r t h e p l a n t . W h e n t h e a m o u n t

o f n o n - c o n d e n s a b l e s i s h i g h , a t m o s p h e r i c t u r b in e s o r p r i m a r y f la s h in g m a y b e u se d i n o r d e r to

r e d u c e t h e w o r k s p e n t o n t h e e x t ra c t io n o f g a s es .

REFERENCES

H e n d e r s o n , C . L . a n d M a r c e l l o , J . M . ( 19 69 ) F i l m c o n d e n s a t i o n i n t h e p r e s e n c e o f a n o n - c o n d e n s a b l e g a s . J. Heat

Transfer 9 1 , 4 4 7 .

Kest in , J . (1968)

A Course in Thermodynamics,

V o l . I I . B l a i se l , W al th am ( r ep r in t ed : M cG raw -H i l l , 1 9 7 8 ) .

K e s t i n , J . a n d M i c h a e l i d e s , E . E . ( 1 97 9) W a s t e r e j e c t i o n i n g e o t h e r m a l p o w e r p l a n t s . Brown University Report

No. GEOFLO/I, DOE/ET/27225-1.

K h a l i f a , H . E . , M i c h a e l i d e s , E . E . a n d K e s t i n , J . (1 97 9) E f f e c t o f n o n - c o n d e n s a b l e g a s e s o n t h e p e r f o r m a n c e o f t h e

g e o t h e r m a l s t e a m p o w e r p l a n t s .

Proc. 14th Intersociety Energy Conversion Engin. Conf., Paper AC S

No. 799221.

M i c h a e l i d e s , E . E . ( 19 79 ) W a s t e h e a t r e j e c t i o n i n g e o t h e r m a l p o w e r p l a n t s . M . S . T h e s i s , B r o w n U n i v e r s i t y .

M i c h a e l i d e s , E . E . ( 19 80 ) S e p a r a t i o n o f n o n - c o n d e n s a b l e s in g e o t h e r m a l i n s t a l l a t io n s b y m e a n s o f p r i m a r y f l a s h i n g .

Geothermal Resources Council Trans. 4.

M o o r e , F . K . ( 1 9 7 6 ) D r y c o o l i n g t o w e r s . Adv. Heat Transfer 12.

M o o re , M . J . an d S i e lv e rd in g , C . H . (1 9 7 6 )

Two Phase Steam Flow in Turbines and Separators.

H e m i s p h e r e ,

W a s h i n g t o n .

V an -W y len , G . I . an d S o n tag , R . E . (1 9 7 8 ) Fundamentals of Classical Thermodynamics. W i l e y , N e w Y o r k .

W ah l , E . F . (1 9 7 7 ) Geothermal Energy Utilization. W i l e y , N e w Y o r k .

67878 the influence of non-condensable gases on the net work produced by the geothermal steam power...

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