Question

Consider the following combined cycle. The mass flow rate of air is 73 kg/s. Air enters the compressor at state 1 with Patm =1 atm and Tamb = 20°C. The compressor has a pressure ratio of 7.5 and an efficiency ?c = 0.85. Air enters the combustor and is heated to a temperature TH = 1250°C. The turbine has an efficiency of ?t,1 = 0.87. The air leaving the turbine enters the steam boiler where it transfers heat to the water in the Rankine cycle. The ratio of the mass flow rate of water in the Rankine cycle to air in the Brayton cycle is 0.1. The water leaving the boiler achieves temperature of 550°C. After boiling the water in the Rankine cycle, the remaining heat left in the Brayton cycle will be used to produce steam for industrial processes. The air enters the steam generator after leaving the boiler and is used to heat water from the inlet state of 5 atm, 20°C to saturated vapor. The temperature of the air leaving the steam generator is 180°C. In the Rankine cycle, the water enters the pump as saturated liquid at 55°C. The pump efficiency is ?p = 0.65 and the exit pressure of the pump is Pboiler = 8.0 MPa. The water enters the heat exchanger (boiler) where it is converted to steam by the heat transfer from the air. The steam turbine has an efficiency of ?t,2 = 0.84. The condenser transfers heat from the water to a river cooling water entering the condenser at Tamb = 20°C. Due to EPA regulations the temperature of the river water at the exit of the condenser cannot be more than 5°C higher than at the inlet.

a.) [20 points] Draw the T-S diagram and the line/component diagram for this combined cycle.

b.) [20 points] Determine all of the state points for this combined cycle. You may consider creating a table including all relevant points with at least the pressure, temperature, entropy and enthalpy.

c.) [10 points] Determine the mass flow rate of steam for industrial purposes produced in the steam generator.

d.) [10 points] Determine the efficiency of the Brayton cycle, the efficiency of the Rankine cycle, and the efficiency of the combined cycle (relative to producing power - do not include the value of the industrial steam that is produced).

e.) [10 points] What is the net power produced by the cycle?

f.) [10 points] If natural gas is used to energize the cycle and the cost of natural gas is NGc = 8$/million Btu determine the yearly fuel cost required to run the plant.

g.) [10 points] Determine the cost associated with producing the same amount of power using a conventional natural gas fired plant with efficiency ?conv = 0.34 and the same amount of steam using a natural gas fired boiler. What are the savings per year associated with using the combined cycle?

h.) [10 points] If natural gas produces 100 lbm of CO2 per million Btu, what is the environmental impact of using the combined cycle versus the conventional natural gas power plant (include power and industrial steam generated).

Answer 1