Thermodynamics

Cogeneration plants have proved to be economically very attractive. Consequently,more and more such plants have been installed in recent years,and more are being installed.Chapter 10 | 581EXAMPLE 10–8An Ideal Cogeneration PlantConsider the cogeneration plant shown in Fig. 10–23. Steam enters the turbineat 7 MPa and 500°C. Some steam is extracted from the turbine at 500 kPa forprocess heating. The remaining steam continues to expand to 5 kPa. Steam isthen condensed at constant pressure and pumped to the boiler pressure of7 MPa. At times of high demand for process heat, some steam leaving theboiler is throttled to 500 kPa and is routed to the process heater. The extractionfractions are adjusted so that steam leaves the process heater as a saturatedliquid at 500 kPa. It is subsequently pumped to 7 MPa. The mass flowrate of steam through the boiler is 15 kg/s. Disregarding any pressure dropsand heat losses in the piping and assuming the turbine and the pump to beisentropic, determine (a) the maximum rate at which process heat can besupplied, (b) the power produced and the utilization factor when no processheat is supplied, and (c) the rate of process heat supply when 10 percent ofthe steam is extracted before it enters the turbine and 70 percent of thesteam is extracted from the turbine at 500 kPa for process heating.Solution A cogeneration plant is considered. The maximum rate of processheat supply, the power produced and the utilization factor when no processheat is supplied, and the rate of process heat supply when steam is extractedfrom the steam line and turbine at specified ratios are to be determined.Assumptions 1 Steady operating conditions exist. 2 Pressure drops and heatlosses in piping are negligible. 3 Kinetic and potential energy changes arenegligible.Analysis The schematic of the cogeneration plant and the T-s diagram ofthe cycle are shown in Fig. 10–23. The power plant operates on an ideal7 MPa500°CT1, 2, 3123Mixingchamber119Boiler107 MPaExpansionvalve4500 kPaPump IIProcessheaterPump I57Turbine500 kPa65 kPaCondenser85 kPa1011 798564sFIGURE 10–23Schematic and T-s diagram for Example 10–8.