A \(100 \mathrm{MW}\) ocean thermal gradient power plant is to be designed for a location where the ocean surface temperature is \(300 \mathrm{~K}\left(80^{\circ} \mathrm{F}\right)\) and water at a lower depth is available at \(278 \mathrm{~K}\left(40^{\circ} \mathrm{F}\right)\). If the heat exchangers are sized to operate a power plant using R-22 as the working fluid between 294 and \(284 \mathrm{~K}\left(70^{\circ} \mathrm{F}\right.\) and \(\left.50^{\circ} \mathrm{F}\right)\), calculate the flow rates of \(\mathrm{R}-22\) and water required, assuming that the condenser heat exchangers have an overall conductance of \(1000 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\left(176 \mathrm{Btu} / \mathrm{h} \cdot \mathrm{ft}^{2}{ }^{\circ} \mathrm{F}\right)\) and an effectiveness of \(100 \%\). Also calculate the plant efficiency and the surface area of the condenser. The saturation pressure of R-22 at \(294 \mathrm{~K}\) is \(9.38 \times 105 \mathrm{~N} \cdot \mathrm{m}^{2}\) ( \(136.1 \mathrm{psia}\) ), the enthalpy is \(256.8 \mathrm{~kJ} / \mathrm{kg}\) ( 110.4 \(\left.\mathrm{Btu} / \mathrm{lb}_{\mathrm{m}}\right)\), and the entropy is \(0.900 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\left(0.215 \mathrm{Btu} / \mathrm{lb}_{\mathrm{m}}{ }^{\circ} \mathrm{R}\right)\). The enthalpy of the saturated liquid at \(284 \mathrm{~K}\) is \(56.45 \mathrm{~kJ} / \mathrm{kg}\) (24.27 Btu/lb) and the heat of vaporization is 197.0 \(\mathrm{kJ} / \mathrm{kg}\left(85.68 \mathrm{Btu} / \mathrm{lb}_{\mathrm{m}}\right)\). The saturation pressure at \(284 \mathrm{~K}\) is \(6.81 \times 105 \mathrm{~N} \cdot \mathrm{m}^{2}(98.73 \mathrm{psia})\), while the entropy at \(284 \mathrm{~K}\) of the saturated liquid is \(0.217 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}\left(0.0519 \mathrm{Btu} / \mathrm{lb}_{\mathrm{m}}{ }^{\circ} \mathrm{R}\right)\).

Assume efficiencies for the pump and the turbine are \(80 \%\) and \(90 \%\), respectively. The specific volume of the saturated R-22 liquid at \(284 \mathrm{~K}\) is \(0.000799 \mathrm{~m}^{3} / \mathrm{kg}\left(0.0128 \mathrm{ft}^{3} / \mathrm{lb}\right)\). A schematic diagram of the system is shown as follows:

Transcribed Image Text:

Seawater in at 300 K 2 Pump 1 Saturated liquid Cold seawater in at 278 K Boiler Condenser 3 Saturated vapor Seawater out Turbine R-22 at 284 K Discharge at 284 K + Generator Power out