Thermodynamics

580 | Thermodynamics3BoilerExpansionvalvePump II245Pump IProcessheaterTurbine7CondenserFIGURE 10–22A cogeneration plant with adjustableloads.861when the utilization factor is defined on the basis of the heating value of thefuel. The utilization factor of the ideal steam-turbine cogeneration plant isobviously 100 percent. Actual cogeneration plants have utilization factors ashigh as 80 percent. Some recent cogeneration plants have even higher utilizationfactors.Notice that without the turbine, we would need to supply heat to thesteam in the boiler at a rate of only 100 kW instead of at 120 kW. The additional20 kW of heat supplied is converted to work. Therefore, a cogenerationpower plant is equivalent to a process-heating plant combined with apower plant that has a thermal efficiency of 100 percent.The ideal steam-turbine cogeneration plant described above is not practicalbecause it cannot adjust to the variations in power and process-heatloads. The schematic of a more practical (but more complex) cogenerationplant is shown in Fig. 10–22. Under normal operation, some steam isextracted from the turbine at some predetermined intermediate pressure P 6 .The rest of the steam expands to the condenser pressure P 7 and is thencooled at constant pressure. The heat rejected from the condenser representsthe waste heat for the cycle.At times of high demand for process heat, all the steam is routed to theprocess-heating units and none to the condenser (ṁ 7 0). The waste heat iszero in this mode. If this is not sufficient, some steam leaving the boiler isthrottled by an expansion or pressure-reducing valve (PRV) to the extractionpressure P 6 and is directed to the process-heating unit. Maximum processheating is realized when all the steam leaving the boiler passes through thePRV (ṁ 5 ṁ 4 ). No power is produced in this mode. When there is nodemand for process heat, all the steam passes through the turbine and thecondenser (ṁ 5 ṁ 6 0), and the cogeneration plant operates as an ordinarysteam power plant. The rates of heat input, heat rejected, and processheat supply as well as the power produced for this cogeneration plant can beexpressed as follows:Q # in m # 3 1h 4 h 3 2Q # out m # 7 1h 7 h 1 2(10–25)(10–26)Q # (10–27)W # p m # 5h 5 m # 6h 6 m # 8h 8turb 1m # 4 m # 521h 4 h 6 2 m # 7 1h 6 h 7 2(10–28)Under optimum conditions, a cogeneration plant simulates the idealcogeneration plant discussed earlier. That is, all the steam expands in theturbine to the extraction pressure and continues to the process-heating unit.No steam passes through the PRV or the condenser; thus, no waste heat isrejected (ṁ 4 ṁ 6 and ṁ 5 ṁ 7 0). This condition may be difficult toachieve in practice because of the constant variations in the process-heatand power loads. But the plant should be designed so that the optimumoperating conditions are approximated most of the time.The use of cogeneration dates to the beginning of this century whenpower plants were integrated to a community to provide district heating,that is, space, hot water, and process heating for residential and commercialbuildings. The district heating systems lost their popularity in the 1940sowing to low fuel prices. However, the rapid rise in fuel prices in the 1970sbrought about renewed interest in district heating.