Thermodynamics

592 | Thermodynamics410 kPa. Isobutane is condensed in an air-cooled condenserand pumped to the heat exchanger pressure. Assuming thepump to have an isentropic efficiency of 90 percent, determine(a) the isentropic efficiency of the turbine, (b) the net poweroutput of the plant, and (c) the thermal efficiency of the cycle.10–26 The schematic of a single-flash geothermal powerplant with state numbers is given in Fig. P10–26. Geothermalresource exists as saturated liquid at 230°C. The geothermalliquid is withdrawn from the production well at a rate of 230kg/s, and is flashed to a pressure of 500 kPa by an essentiallyisenthalpic flashing process where the resulting vapor is separatedfrom the liquid in a separator and directed to the turbine.The steam leaves the turbine at 10 kPa with a moisturecontent of 10 percent and enters the condenser where it iscondensed and routed to a reinjection well along with the liquidcoming off the separator. Determine (a) the mass flowrate of steam through the turbine, (b) the isentropic efficiencyof the turbine, (c) the power output of the turbine, and (d) thethermal efficiency of the plant (the ratio of the turbine workoutput to the energy of the geothermal fluid relative to standardambient conditions). Answers: (a) 38.2 kg/s, (b) 0.686,(c) 15.4 MW, (d) 7.6 percent2FlashchamberSeparator63Steamturbine4Condenser526Flashchamber1ProductionwellSeparatorI7FlashchamberSeparatorIISteamturbineCondenserReinjectionwell10–28 Reconsider Prob. 10–26. Now, it is proposed that theliquid water coming out of the separator be used as the heatsource in a binary cycle with isobutane as the working fluid.Geothermal liquid water leaves the heat exchanger at 90°Cwhile isobutane enters the turbine at 3.25 MPa and 145°Cand leaves at 80°C and 400 kPa. Isobutane is condensed in anair-cooled condenser and then pumped to the heat exchangerpressure. Assuming an isentropic efficiency of 90 percent forthe pump, determine (a) the mass flow rate of isobutane inthe binary cycle, (b) the net power outputs of both the flashingand the binary sections of the plant, and (c) the thermalefficiencies of the binary cycle and the combined plant.Answers: (a) 105.5 kg/s, (b) 15.4 MW, 6.14 MW, (c) 12.2 percent,10.6 percent38FIGURE P10–279451ProductionwellFIGURE P10–26Reinjectionwell10–27 Reconsider Prob. 10–26. Now, it is proposed that theliquid water coming out of the separator be routed throughanother flash chamber maintained at 150 kPa, and the steamproduced be directed to a lower stage of the same turbine.Both streams of steam leave the turbine at the same state of10 kPa and 90 percent quality. Determine (a) the temperatureof steam at the outlet of the second flash chamber, (b) thepower produced by the lower stage of the turbine, and (c) thethermal efficiency of the plant.2ProductionwellFlashchamber1Separator63Isobutaneturbine8Heat exchangerSteamturbine794Air-cooledcondenserBINARYCYCLE11FIGURE P10–28CondenserPump510Reinjectionwell