Chapter 8
Power and Refrigeration Cycles
8-177E
A geothermal power plant operating on the simple Rankine cycle using an organic fluid as the
working fluid is considered. The exit temperature of the geothermal water from the vaporizer, the rate
of heat rejection from the working fluid in the condenser, the mass flow rate of geothermal water at the
preheater, and the thermal efficiency of the Level I cycle of this plant are to be determined.
Assumptions
1
Steady operating conditions exist.
2
Kinetic and potential energy changes are negligible.
Analysis
(
a
)
The exit temperature of geothermal water from the vaporizer is determined from the
steady-flow energy balance on the geothermal water (brine),
F
267.4
2
2
1
2
brine
brine
F
325
F
Btu/lbm
1.03
lbm/h
384,286
Btu/h
000
790
22
T
T
,
,
T
T
C
m
Q
p
(
b
)
The rate of heat rejection from the working fluid to the air in the
condenser is determined from the steady-flow energy balance on air,
MBtu/h
29.7
F
55
5
84
F
Btu/lbm
0.24
lbm/h
4,195,100
8
9
air
air
.
T
T
C
m
Q
p
(
c
)
The mass flow rate of geothermal water at the preheater is
determined from the steady-flow energy balance on the geothermal
water,
lbm/h
187,120
geo
geo
in
out
geo
geo
F
8
221
0
154
F
Btu/lbm
1.03
Btu/h
000
140
11
m
.
.
m
,
,
T
T
C
m
Q
p
(
d
)
The rate of heat input is
and
,
,
,
,
,
,
Q
Q
Q
W
in
vaporizer
reheater
net
Btu /h
kW
22 790 000
11140 000
33 930 000
1271
200
1071
Then,
10.8%
kWh
1
Btu
3412.14
Btu/h
33,930,000
kW
1071
in
net
Q
W
th
8-165