10-70
10-74 A cogeneration plant is to generate power and process heat. Part of the steam extracted from the turbine at a relatively
high pressure is used for process heating. The net power produced and the utilization factor of the plant are to be
determined.
Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential energy changes are negligible.
Analysis From the steam tables (Tables A-4, A-5, and A-6),
h1  h f @ 10 kPa  191.81 kJ/kg
v1  v f
@ 10 kPa
 0.00101 m 3 /kg
wpI,in  v 1 P2  P1 


 1 kJ
 0.00101 m 3 /kg 600  10 kPa 
 1 kPa  m 3

 0.60 kJ/kg
6




h2  h1  wpI,in  191.81  0.60  192.41 kJ/kg
h3  h f
Mixing chamber:
E  E
in
@ 0.6 MPa
7
8
Process
heater
5
 670.38 kJ/kg
Condenser
3
1
P II
out
i i
PI
 E system 0 (steady)  0 
 E in  E out
 m h   m h
or,
Turbine
Boiler
e e
4
2

 m 4 h4  m 2 h2  m 3 h3
m 2 h2  m 3h3 22.50 192.41  7.50 670.38

 311.90 kJ/kg
m 4
30
v 4  v f @ h f 311.90 kJ/kg  0.001026 m3/kg
T
w pII,in  v 4 P5  P4 
 1 kJ 

 0.001026 m3/kg 7000  600 kPa 
1 kPa  m3 

 6.57 kJ/kg
h5  h4  w pII,in  311.90  6.57  318.47 kJ/kg
h4 


P6  7 MPa  h6  3411.4 kJ/kg

T6  500C  s 6  6.8000 kJ/kg  K
6
7 MPa
·
Qin
0.6 MPa
4 3 ·
Qproces
5
2
P7  0.6 MPa 
 h7  2774.6 kJ/kg
s7  s6

1
s8  s f
6.8000  0.6492

 0.8201
P8  10 kPa  x8 
s fg
7.4996

s8  s6
 h  h  x h  191.81  0.82012392.1  2153.6 kJ/kg
8
f
8 fg
7
10 kPa
·
Qout
8
s
Then,
W T,out  m 6 h6  h7   m 8 h7  h8 
 30 kg/s 3411.4  2774.6 kJ/kg  22.5 kg/s 2774.6  2153.6kJ/kg  33,077 kW
W p,in  m 1 wpI,in  m 4 wpII,in  22.5 kg/s 0.60 kJ/kg   30 kg/s 6.57 kJ/kg   210.6 kW
W net  W T,out  W p,in  33,077  210.6  32,866 kW
Also,
Q process  m 7 h7  h3   7.5 kg/s 2774.6  670.38 kJ/kg  15,782 kW
Q in  m 5 h6  h5   30 kg/s 3411.4  318.47   92,788 kW
and
u 
W net  Q process 32,866  15,782

 52.4%
92,788
Q in
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