10-21
10-29 A combined flash-binary geothermal power plant uses hot geothermal water at 230ºC as the heat source. The mass
flow rate of isobutane in the binary cycle, the net power outputs from the steam turbine and the binary cycle, and the
thermal efficiencies for the binary cycle and the combined 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

P2  500 kPa

 x 2  0.1661
h2  h1  990.14 kJ/kg 
m 3  x2 m 1  (0.1661)(230 kg/s)  38.20 kg/s
m 6  m 1  m 3  230  38.20  191.80 kg/s
P3  500 kPa 
 h3  2748.1 kJ/kg
x3  1

3
separator
steam
turbine
P4  10 kPa 
h4  2344.7 kJ/kg
x 4  0.90 
P6  500 kPa 
 h6  640.09 kJ/kg
x6  0

T7  90C 
 h7  377.04 kJ/kg
x7  0

condenser
4
9
1
isobutane
turbine
2
BINARY
CYCLE
8
The isobutane properties are obtained
from EES:
P8  3250 kPa 
 h8  755.05 kJ/kg
T8  145C

P9  400 kPa 
 h9  691.01 kJ/kg
T9  80C

5
air-cooled
condenser
6
pump
heat exchanger
flash
chamber
1
1
7
production
well
reinjection
well
P10  400 kPa  h10  270.83 kJ/kg

3
x10  0
 v 10  0.001839 m /kg
w p ,in  v10 P11  P10  /  p


 1 kJ 
 / 0.90
 0.001819 m 3/kg 3250  400  kPa 
1 kPa  m3 

 5.82 kJ/kg.
h11  h10  w p ,in  270.83  5.82  276.65 kJ/kg
An energy balance on the heat exchanger gives
m 6 (h6  h7 )  m iso (h8  h11 )
(191.81 kg/s)(640.09 - 377.04)kJ/kg  m iso (755.05 - 276.65)kJ/kg 
 m iso  105.46 kg/s
(b) The power outputs from the steam turbine and the binary cycle are
WT,steam  m 3 (h3  h4 )  (38.19 kJ/kg)(2748.1  2344.7)kJ/kg  15,410 kW
W T,iso  m iso (h8  h9 )  (105.46 kJ/kg)(755.05  691.01)kJ/kg  6753 kW
W net,binary  W T,iso  m iso w p ,in  6753  (105.46 kg/s)(5.82 kJ/kg )  6139 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.
10-22
(c) The thermal efficiencies of the binary cycle and the combined plant are
Q in,binary  m iso (h8  h11 )  (105.46 kJ/kg)(755.05  276.65)kJ/kg  50,454 kW
 th,binary 
W net, binary
6139

 0.122  12.2%

50
,454
Qin, binary
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,plant 
W T,steam  W net,binary 15,410  6139

 0.106  10.6%
203,622
E
in
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.