10-73
10-77 A cogeneration plant modified with regeneration is to generate power and process heat. The mass flow rate of steam
through the boiler for a net power output of 25 MW is 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),
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 /kg 1600  10 kPa 
 1 kPa  m 3

 1.61 kJ/kg
3
Turbine
Boiler
7
8




Process
heater
5
h3  h4  h9  h f
v4 v f
 858.44 kJ/kg
4
@ 1.6 MPa
 0.001159 m /kg
3
PII
3
wpII,in  v 4 P5  P4 

@ 1.6 MPa
Condense
r
9
h2  h1  wpI,in  191.81  1.61  193.41 kJ/kg
1
PI
fwh
2
T

 1 kJ
 0.001159 m 3 /kg 9000  400 kPa 
 1 kPa  m 3

 8.57 kJ/kg




6
5
h5  h4  wpII,in  858.44  8.57  867.02 kJ/kg
P6  9 MPa  h6  3118.8 kJ/kg

T6  400C  s 6  6.2876 kJ/kg  K
3,4,9
2
s7  s f
6.2876  2.3435
1

 0.9675
P7  1.6 MPa  x 7 
s fg
4.0765

s7  s6
 h  h  x h  858.44  0.96751934.4  2730.0 kJ/kg
f
7
7 fg
9 MPa
1.6 MPa
7
10 kPa
8
s
s8  s f 6.2876  0.6492

 0.7518
P8  10 kPa  x8 
s fg
7.4996

s8  s 6
 h  h  x h  191.81  0.75182392.1  1990.2 kJ/kg
8
f
8 fg
Then, per kg of steam flowing through the boiler, we have
wT,out  h6  h7   (1  y )h7  h8 
 3118.8  2730.0  kJ/kg  1  0.352730.0  1990.2 kJ/kg
 869.7 kJ/kg
wp,in  (1  y ) wpI,in  wpII,in
 1  0.351.61 kJ/kg   8.57 kJ/kg 
 9.62 kJ/kg
wnet  wT,out  wp,in  869.7  9.62  860.1 kJ/kg
Thus,
m 
W net 25,000 kJ/s

 29.1 kg/s
wnet 860.1 kJ/kg
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