If the sea power plant described in Problem 11.5 is to deliver power at $8/106 Btu, estimate the maximum permissible cost of the condenser and evaporator heat-exchanger surface in dollars per square foot, assuming a 20-year life, 10% discount rate, and 7% yearly fuel inflation. The next two problems are open-ended with no solutions:
Problem 11.5
A 100 MW ocean thermal gradient power plant is to be designed for a location where the ocean surface temperature is 300 K (80°F) and water at a lower depth is available at 278 K (40°F). If the heat exchangers are sized to operate a power plant using R-22 as the working fluid between 294 and 284 K (70°F and 50°F), calculate the flow rates of R-22 and water required, assuming that the condenser heat exchangers have an overall conductance of 1000 W/m2·K (176 Btu/h·ft2 °F) and an effectiveness of 100%. Also calculate the plant efficiency and the surface area of the condenser. The saturation pressure of R-22 at 294 K is 9.38 × 105 N·m2 (136.1 psia), the enthalpy is 256.8 kJ/kg (110.4 Btu/lbm), and the entropy is 0.900 kJ/kg·K (0.215 Btu/lbm°R). The enthalpy of the saturated liquid at 284 K is 56.45 kJ/kg (24.27 Btu/lb) and the heat of vaporization is 197.0 kJ/kg (85.68 Btu/lbm). The saturation pressure at 284 K is 6.81 × 105 N·m2 (98.73 psia), while the entropy at 284 K of the saturated liquid is 0.217 kJ/kg K (0.0519 Btu/lbm°R).
Assume efficiencies for the pump and the turbine are 80% and 90%, respectively. The specific volume of the saturated R-22 liquid at 284 K is 0.000799 m3 /kg (0.0128 ft3 /lb). A schematic diagram of the system is shown as follows:
