In a geothermal system, water is pumped into the ground (several kilometers deep) where it is heated by geothermal energy and then returned to the surface to provide energy for a power plant. In 2005, the U.S. had 2851 MW of installed geothermal power production; most of this capacity is in California and Nevada. This problem examines the use of geothermal energy for power production with the Rankine cycle shown in Figure 8.A-6. The cycle employs both reheat and regeneration with two open feedwater heaters. water from geothermal well returned to well water from geothermal well returned to well 78-180C T 180C W1 W2 W 4 4 4 9 toluene m Pg=260 kPa OM ww boiler reheater (1-1)(1-12 1-1 turbine 2 turbine Pext.2 - 50 kPa turbine 3 Pext, 1-120 kPa (1-12 turbine 4 Per 3-20 kPa 9 pump! 8 condenser 11 pump3 12 pump2 10 open feed water heater2 (OFWH2) open feed water heater (OFWHI) Wp1 | c cond w "2.2 Figure 8.A-6. Schematic of the power plant cycle consisting of a Rankine cycle with reheat and regeneration using two open feedwater heaters. The Rankine cycle uses toluene as the working fluid due to the low temperature of the heat source. The boiler pressure is Pb = 260 kPa. The water from the geothermal well is at Tg =180. C. The plant rejects heat to a temperature reservoir at TC = 30 C. The fluid is extracted at state 3 from turbine 1 at Pext, 1 = 120 kPa and a fraction of the flow fl is fed to the open feedwater heater 1. The fluid is subsequently extracted at state 4 from turbine 2 at Pext, 2 = 50 kPa and reheated. The fluid is finally extracted at state 6 from turbine 3 at Pext, 3 = 20 kPa and the fraction of the flow f2 is fed to open feedwater heater 2. The remainder of the flow passes through turbine 4 to the condenser. The efficiencies of the four turbines are nt,1 = 0.85, nt,2 = 0.86, nt, 3 = 0.88, and nt,4 = 0.89. The flow leaving the condenser is pumped to Pext,3 with pump 1 having efficiency np, 1 = 0.65. Saturated liquid is pulled from open feedwater heater 1 and pumped to the first extraction pressure, Pext,1, with pump 2 having efficiency np,2 = 0.67. Saturated liquid is pulled from open feedwater heater 2 and pumped to the boiler pressure with pump 3 having efficiency np,3 = 0.69. The approach temperature differences associated with the boiler and the reheater are _Tb = 15 K and_Trh = 10 K, respectively. The pinch points for both of these heat exchangers occur at their warm end. Therefore, water leaves the boiler at T2 = Thf,in - _Tb and it leaves the reheater at T5 = Thf, in - _Trh. The approach temperature difference associated with the condenser is _Tcond = 5 K. Neglect pressure loss for all of the heat exchangers. C) Determine the efficiency of the cycle. ? In a geothermal system, water is pumped into the ground (several kilometers deep) where it is heated by geothermal energy and then returned to the surface to provide energy for a power plant. In 2005, the U.S. had 2851 MW of installed geothermal power production; most of this capacity is in California and Nevada. This problem examines the use of geothermal energy for power production with the Rankine cycle shown in Figure 8.A-6. The cycle employs both reheat and regeneration with two open feedwater heaters. water from geothermal well returned to well water from geothermal well returned to well 78-180C T 180C W1 W2 W 4 4 4 9 toluene m Pg=260 kPa OM ww boiler reheater (1-1)(1-12 1-1 turbine 2 turbine Pext.2 - 50 kPa turbine 3 Pext, 1-120 kPa (1-12 turbine 4 Per 3-20 kPa 9 pump! 8 condenser 11 pump3 12 pump2 10 open feed water heater2 (OFWH2) open feed water heater (OFWHI) Wp1 | c cond w "2.2 Figure 8.A-6. Schematic of the power plant cycle consisting of a Rankine cycle with reheat and regeneration using two open feedwater heaters. The Rankine cycle uses toluene as the working fluid due to the low temperature of the heat source. The boiler pressure is Pb = 260 kPa. The water from the geothermal well is at Tg =180. C. The plant rejects heat to a temperature reservoir at TC = 30 C. The fluid is extracted at state 3 from turbine 1 at Pext, 1 = 120 kPa and a fraction of the flow fl is fed to the open feedwater heater 1. The fluid is subsequently extracted at state 4 from turbine 2 at Pext, 2 = 50 kPa and reheated. The fluid is finally extracted at state 6 from turbine 3 at Pext, 3 = 20 kPa and the fraction of the flow f2 is fed to open feedwater heater 2. The remainder of the flow passes through turbine 4 to the condenser. The efficiencies of the four turbines are nt,1 = 0.85, nt,2 = 0.86, nt, 3 = 0.88, and nt,4 = 0.89. The flow leaving the condenser is pumped to Pext,3 with pump 1 having efficiency np, 1 = 0.65. Saturated liquid is pulled from open feedwater heater 1 and pumped to the first extraction pressure, Pext,1, with pump 2 having efficiency np,2 = 0.67. Saturated liquid is pulled from open feedwater heater 2 and pumped to the boiler pressure with pump 3 having efficiency np,3 = 0.69. The approach temperature differences associated with the boiler and the reheater are _Tb = 15 K and_Trh = 10 K, respectively. The pinch points for both of these heat exchangers occur at their warm end. Therefore, water leaves the boiler at T2 = Thf,in - _Tb and it leaves the reheater at T5 = Thf, in - _Trh. The approach temperature difference associated with the condenser is _Tcond = 5 K. Neglect pressure loss for all of the heat exchangers. C) Determine the efficiency of the cycle
