10-67
10-69 A single-flash geothermal power plant uses hot geothermal water at 230ºC as the heat source. The power output from
the turbine, the thermal efficiency of the plant, the exergy of the geothermal liquid at the exit of the flash chamber, and the
exergy destructions and exergy efficiencies for the flash chamber, the turbine, and the entire 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, A-5, and A-6)
T1  230C h1  990.14 kJ/kg

x1  0
 s1  2.6100 kJ/kg.K
P2  500 kPa
 x 2  0.1661

h2  h1  990.14 kJ/kg  s 2  2.6841 kJ/kg.K
3
steam
turbine
m 3  x 2 m 1
 (0.1661)(230 kg/s)
 38.19 kg/s
P3  500 kPa  h3  2748.1 kJ/kg

x3  1
 s 3  6.8207 kJ/kg  K
P4  10 kPa  h4  2464.3 kJ/kg

x 4  0.95  s 4  7.7739 kJ/kg  K
P6  500 kPa  h6  640.09 kJ/kg

x6  0
 s 6  1.8604 kJ/kg  K
separator
4
2
condenser
6
Flash
chamber
1
production
well
5
reinjection
well
m 6  m 1  m 3  230  38.19  191.81 kg/s
The power output from the turbine is
W T  m 3 (h3  h4 )  (38.19 kJ/kg)(2748.1  2464.3)kJ/kg  10,842 kW
We use saturated liquid state at the standard temperature for dead state properties
T0  25C h0  104.83 kJ/kg

x0  0
 s 0  0.3672 kJ/kg
E in  m 1 (h1  h0 )  (230 kJ/kg)(990.14  104.83)kJ/kg  203,622 kW
 th 
W T, out
10,842

 0.0532  5.3%

203
,622
E in
(b) The specific exergies at various states are
 1  h1  h0  T0 ( s1  s 0 )  (990.14  104.83)kJ/kg  (298 K)(2.6100  0.3672)kJ/kg.K  216.53 kJ/kg
 2  h2  h0  T0 ( s 2  s 0 )  (990.14  104.83)kJ/kg  (298 K)(2.6841  0.3672)kJ/kg.K  194.44 kJ/kg
 3  h3  h0  T0 ( s 3  s 0 )  (2748.1  104.83)kJ/kg  (298 K)(6.8207  0.3672)kJ/kg.K  719.10 kJ/kg
 4  h4  h0  T0 ( s 4  s 0 )  (2464.3  104.83)kJ/kg  (298 K)(7.7739  0.3672)kJ/kg.K  151.05 kJ/kg
 6  h6  h0  T0 ( s 6  s 0 )  (640.09  104.83)kJ/kg  (298 K)(1.8604  0.3672)kJ/kg.K  89.97 kJ/kg
The exergy of geothermal water at state 6 is
X 6  m 6 6  (191.81 kg/s)(89.97 kJ/kg)  17,257 kW
PROPRIETARY MATERIAL. © 2011 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course
preparation. If you are a student using this Manual, you are using it without permission.
10-68
(c) Flash chamber:
X dest, FC  m 1 ( 1  2 )  (230 kg/s)(216.53  194.44)kJ/kg  5080 kW
 II,FC 
 2 194.44

 0.898  89.8%
 1 216.53
(d) Turbine:
X dest,T  m 3 ( 3  4 )  W T  (38.19 kg/s)(719.10  151.05)kJ/kg - 10,842 kW  10,854 kW
 II,T 
W T
10,842 kW

 0.500  50.0%
m 3 ( 3  4 ) (38.19 kg/s)(719.10  151.05)kJ/kg
(e) Plant:
X in, Plant  m 1 1  (230 kg/s)(216.53 kJ/kg)  49,802 kW
X dest,Plant  X in, Plant  W T  49,802  10,842  38,960 kW
 II,Plant 
W T
X in, Plant

10,842 kW
 0.2177  21.8%
49,802 kW
PROPRIETARY MATERIAL. © 2011 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course
preparation. If you are a student using this Manual, you are using it without permission.