10-19
10-27 A single-flash geothermal power plant uses hot geothermal water at 230ºC as the heat source. The mass flow rate of
steam through the turbine, the isentropic efficiency of the turbine, the power output from the turbine, and the thermal
efficiency of the plant are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential energy changes are negligible.
Analysis (a) We use properties of water for geothermal water (Tables A-4 through A-6)
T1  230C
 h1  990.14 kJ/kg
x1  0

h2  h f
P2  500 kPa

990.14  640.09

 0.1661
x2 
h2  h1  990.14 kJ/kg 
h fg
2108
3
steam
turbine
4
separator
The mass flow rate of steam through the turbine is
m 3  x 2 m 1  (0.1661)(230 kg/s)  38.20 kg/s
2
condenser
(b) Turbine:
6
P3  500 kPa  h3  2748.1 kJ/kg

x3  1
 s 3  6.8207 kJ/kg  K
P4  10 kPa 
h4 s  2160.3 kJ/kg
s 4  s3

Flash
chamber
production
well
1
5
reinjection
well
P4  10 kPa 
h4  h f  x 4 h fg  191.81  (0.90)(2392.1)  2344.7 kJ/kg
x 4  0.90 
T 
h3  h4
2748.1  2344.7

 0.686
h3  h4 s 2748.1  2160.3
(c) The power output from the turbine is
W T,out  m 3 (h3  h4 )  (38.20 kJ/kg)(2748.1  2344.7)kJ/kg  15,410 kW
(d) We use saturated liquid state at the standard temperature for dead state enthalpy
T0  25C
 h0  104.83 kJ/kg
x0  0

E in  m 1 (h1  h0 )  (230 kJ/kg)(990.14  104.83)kJ/kg  203,622 kW
 th 
W T, out
15,410

 0.0757  7.6%

203,622
E in
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