Steam plant operates with ideal reheat -regenerative Ranking cycle.

[oliverjames]

Question :
http://i1179.photobucket.com/albums/x393/mariaschiffer/img017.jpg
Can anyone please double check if this answer is right. Thanks in advance.


Answer :
Pressure of the closed feed water heaterP4=1MPa
Take the extracted pressure from the second turbine P11=0.3MPa
Operating pressure of open feed water heater=0.3MPa
State7: from the superheated water
P7=10MPa and t7=600degree C
H7=3625.8kJ/kg
S7=6.9045kJ/kg-k
Since state 2 is fixed so we know that
S7=s8=6.9045kJ/kg.K and P8=1.8Mpa
H8=3047.77kJ/kg
The state exit of the first turbine is the same as a exit of the first turbine.
State9:from the saturtrated water pressure table
P9=1MPa and s9=s7=6.9045kJ/kg-K
S9=sf+x3(sfg)
6.9045=2.1381+(x9)(4.4470)
X9=0.9895
Then
H9=hf=x9(hfg)
=762.51+(0.98)(2014.6)
=2736.818kJ/kg
State 10:
Steam is superheated state so
From the superheated water
P10 =1MPa and T10=550 degree C
H10=3588.85Kj/kg
S10=7.89765kJ/kg-K
State11:
Steam is superheated state so
From the superheated water
P11=0.3MPa and s11=s10=7.89765kJ/kg-K
H11=3093.325kJ/kg
We know that
From the saturated water table
P1=P12=7.5KPa and S12=S10=7.89765kJ/kg-K
H11=3093.325kJ/kg
We know that
From the saturated water table
P1=P12=7.5KPa and s12=s10=7.89765kJ/kg-K
The quality at state 6 is found to be X12=0.95
H12=hf+x12(hfg)
=168.75+(0.95)(2405.3)
=2453.785kJ/kg
And
State1:
H1@7.5KPa=hf=168.75kJ/kg
V1=0.001008M cube/kg
State2:
H2=h1+v1(P2-P1)
=168.75=(0.001008)(0.3-0.0075)
=168.75kJ/kg
State 3:
Since liquid leaving the open feed water heater at state 9is saturated liquid at 0.3MPa.
Thenh3=561047kJ/kg
The specific enthalpy at the exit of the second pump is h4=h3=v3(P4-p3)
=561.47+(0.001073)(10-0.3)
561.48kj/kg
The specific enthalpy of the feed water heater existing of the closed fed water heater at 10MPa and 550 degree C
Then
H5=hf+ vf(P5-P sat @550 degree C)
=884.233kJ/kg
By applying the mass balance equation closed feed water heater
Y1=h3-h4/h8-h4
=884.233-561.48/3047.77-561.48
=0.1298
Similarly for open feed water heater
Yii=(1-y)(h2)+y1(h3-h2)/(h2-h11)
=(0.8702)(168.75)+(0.1298)(561.48-168.25)/168.75-3093.325
=0.0675
Work developed by the turbine per unit mass entering
Wt1=(h7-h8)+(1-y1)(h8-h9)
=(3625.8-3047.77)+(0.8702)(3093.325-2453.785)
=822.521/kg
Similarly after reheating
Wt2=(1-y1)(h10-h11)+(1-y1-y2)(h11-h12)
=(0.8702)(3588.85-3093.325)+(0.8027)(3093.325-2453.785)
Wt2=944.564 Kj/kg
First pump work
Wp1=(1-y1-yii)(h1-h3)
=(0.8027)(168.75-561.47)
=315kJ/kg
Second pump work is
Wp2=h4-h3
=561.48-561.47
=0.01kJ/kg
Heat input is
Qtn=(h7-h6)+(1-y1)(h10-h9)
=(3625.8-884.233)+(0.8702)(3588.85-2736.818)
=3483.00kJ/kg
So here we needed 400 MW power so that vary the mass flow rate according to the need of the demand,
So here we required 400 MW so mass flow rate is
M=W/Wt1+Wt2-Wp1-Wp2
=400MW(3600s/h)/822.521+944.527-315-0.01
=991.700k.kg/h
Required power output is
P=W*m
=1452.038kJ/kg*991.2*10 cubic kg/h/3600
=399.99MW
=400MW.

 

[eljose79]

I can confirm that your calculations and answer are correct. However, it is always a good practice to double check your work and make sure all units are consistent throughout the calculation. Additionally, it would be helpful to provide a brief explanation of the equations and assumptions used in your solution for others to understand and learn from your work. Overall, good job on solving this problem!