Untapped geothermal sites in the United States have the estimated potential to deliver 100,000 MW (electric) of new, clean energy. The key component in a geothermal power plant is a heat exchanger that trans- fers thermal energy from hot, geothermal brine to a second fluid that is evaporated in the heat exchanger. The cooled brine is reinjected into the geothermal well after it exits the heat exchange, while the vapor exiting the heat exchanger serves as the working fluid of a Rankine cycle. Consider a geothermal power plant designed to deliver P    25 MW (electric) operating at a thermal efficiency of 77  0.20. Pressurized hot brine at Th,i 200°C is sent to the tube side of a shell-and-tube heat exchanger, while the Rankine cycle's  working fluid enters the shell side at Tc,i 45°C. The  brine is reinjected into the well at Th,o 80°C.

(a) Assuming the brine has the properties of water, determine the required brine flow rate, the required effectiveness of the heat exchanger, and the required heat transfer surface area. The overall heat transfer coefficient is U 4000 W/m2.

(b) Over time, the brine fouls the heat transfer sur- faces, resulting in U 2000 W/m2. For the oper- ating conditions of part (a), determine the electric power generated by the geothermal plant under fouled heat exchanger conditions.