Question

A cogeneration plant is similar to a power plant, but some of the thermal energy in the working fluid is used for process heat (for example heating buildings, steel making, or oil refining). An ideal reheat Rankine cycle with regeneration is modified to a cogeneration plant by adding a process heater as shown in the figure below. The process heater acts as a heat removal step where the enthalpy of the steam is reduced by the heat output (qprocess=h7-h3). The plant is designed to provide 5 MW of process heat and 3 MW of work from the turbines (not net work, just work of the turbines). The steam enters the high pressure turbine at 10 MPa and 500°C, and expands to 1.2 MPa, the pressure of the process heater and the mixing chamber. At the outlet of the low pressure turbine, the steam has a quality of 0.8974 and a pressure of 10 kPa. At the exit of both the process heater and the condenser, the water is a saturated liquid. Assume all turbines and pumps to be isentropic.

a. Show the cycle on a T-s diagram with the saturation lines.

b. Find the temperature at the inlet of the low-pressure turbine. (Hint: Can you find the entropy at state 9 ? How are states 8 and 9 related?)

c. Find the flow rate of steam through the process heater (Hint: perform an energy balance on the process heater).

d. Find the fraction of total steam that passes through the process heater (Hint: you know the work output of the turbines, perform an energy balance on the turbines, see if you can solve for the total mass flow after you find the enthalpy in and out of each, Answer: 0.689).

e. How would you find the heat input to the boiler? ( 3 bonus points: Calculate the heat input to the boiler.)

Answer 1