A power plants boilers produce steam at 600 psig 42 MPa and

A power plant\'s boilers produce steam at 600 psig (~4.2 MPa) and

825 F (~440°C). After partial expansion through the turbine generator, steam at 15 psig (~205

kPa) and 350 F (~175°C) and at 125 psig (~960 kPa) and 530 F (~275°C) is bled off and routed to campus for heating and processing.

Assume that one of the boilers feeds one of the turbines 120,000 lb/hr of steam. This is about 15 kg/s. Also assume that 15% of the ~4 MPa/440°C flow is bled off to the ~1000 kPa/~280°C line and an additional 10% is bled off to the ~200 kPa/~160°C line. The remaining 75% exits the turbine at a pressure of 0.1 bar and a quality of 90%.

What is the turbine power rate? Report your answer in MW.

Solution

Solution:

State 1 : Inlet to the turbine

Pressure = 40 bar, Temperature = 440 Deg.C , h₁ = 3308.04 kJ/kg , Mass flow rate = 15 kg/s

State 2 : First bled from turbine

Pressure = 10 bar, Temperature = 280 Deg.C , h₂ = 3008.61 kJ/kg, Mass flow rate = 15% of 15 kg/s =2.25 kg/s

State 3 : Second bled from turbine

Pressure = 2 bar, Temperature = 160 Deg.C , h₃ = 2789.66 kJ/kg, Mass flow rate = 10% of 15 kg/s =1.5 kg/s

State 4 : Exit of turbine

Pressure = 0.1 bar, Temperature = Saturated , Dryness Fraction = 0.9, h₄ = 2344.65 kJ/kg, Mass flow rate = (15 - 2.25 - 1.5 )=11.25 kg/s

Turbine Powe Rate = 15 x (3308.04 - 3008.61) + (15 - 2.25) X (3008.61 - 2789.66) + (15 - 2.25 - 1.5) X (2789.66 -2344.65) = 12289.425 kW = 12.29 MW