1 Determine the mass flow rate of steam produced in the stea

1) Determine the mass flow rate of steam produced in the steam generator.

2) Check your solution by carrying out an overall energy balance on the entire cycle.

3) Determine the efficiency of the Brayton cycle, the eciency of the Rankine cycle, and the efficiency of the combined cycle (relative to producing power, do not include the value of the steam that is produced).

4) What is the net power produced by the cycle?

5) If in natural gas is used to energize the cycle and the cost of natural gas is NG_c = 8 $/ million Btu, then determine the yearly fuel cost required to run the plant.

6) Determine the cost associated with producing the same amount of power using a conventional natural gas red plant with efficiency N_conv = 34% and the same amount of steam using a natural gas red boiler. What is the savings per year associated with using the combined cycle.

Solution

solution: first four parts are as follows

1)here temperature at outlet of compressor is given by

(T2/T1)=(P2/P1)^(k-1/k)

T1=293 k,k=1.4,Rp=7.5

so we get that

T2=521.05 k

from efficiency for comprressor

nc=T2-t1/T2\'-T1

t2\'=561.3 k

T3=1523 k

where for turbine again

(T3/T4)=(Rp)^(k-1/k)

T4=856.41 K

for efficiency we get that

nt=T3-T4\'/T3-t4

T4\'=943.06 k

here turbine work is given by

Wt=mcp(T3-T4\')=42547.29 kw

Wc=mcp(T2\'-T1)=19683.82 kw

net work=W=Wt-Wc=22863.46 kw

heat supplied=Qs=mcp(T3-T2\')=70555.12 kw

hence efficirency is

nb=W/Qs=32.40%

3)for rankine cycle

P4=1.01325 bar.T4=943.06 k

where given that

T9=T4-15=928.06 k

where for pump work is given by

Wp=Mw*(Pb-Pc)/.65*10=

Mw=.1*73=7.3 kg/s

Pc=1.01325 bar,T7=373 kso we get that

Wp=88.8081 kw

T8=393 k for h8=507.708 kj/kg enthalpy and Pc=80 bar

hence from energy balance for boiler we get

ma*cp(T4-T5)=Mw*Cps(T9-T8)

Cps=2.894 for Tmean=660.53 k

we get that

T5=788.98 k

where for turbibe

T9=928.06 k and P=80 bar

h9=3774.12 kj/kg

where for condenser temperature is given by

T10=293+5=298 k at 1.01325 bar

h10=104.3 kj/kg,cv=1.9394,Cp=2.894

hence turbine work=mw*cv(T9-T10)*.84=7492.92 kw

pump work=88.7081 kw

net work=Wt-Wp=7404.21 klw

efficiency=W/Qs4

Qs4=mw*Cp(T9-T8)=11303.78 kw

n=7404.21/11303.78=.655=65.5%

5)for steam generator energy balance is

ma*Cp(T5-T6)=mw*Cp(T12-T11)

T11=293 k

T12=425.33 k for 5 atm saturation

T5=788.90k

T6=453 k

hence staem generation rate

cp=4.2 for Tmean=359.16 k

so we get that

ms=44.33 kg/s

6)here net power produced is

W=Wb+wr=22863.46+7404.21=30267.67 kw

net efficiency=Wn/Qs=30267.67/70555.12=42.89%A