In a biofuels plant, a shell-and-tube heat exchanger is used to cool a hot stream of 100% carbon dioxide off-gas from a beer column from 77°C to 27°C (350 to 300 K) at 1.2 atm total system pressure. The total molar flow rate of CO₂ gas is 360 kgmol/hr. Liquid water will be used as the cooling fluid. The available cooling water temperature is 20°C (293 K). The CO₂ gas flows in the shell side, water in the tube side.
a. What is the predicted outlet temperature of the water at a water mass flow rate of 0.5 kg/s? Will the heat exchanger work? If not, calculate a new water flow rate to provide a “temperature of approach” of no less than 17°C on the tube outlet side. The heat capacity of water may be taken as 4200 J/kg · K.
b. A heat exchanger is available that consists of 0.5-inch nominal diameter, schedule 40 copper tubes. To ensure turbulent flow Reynolds number of 10,000 is desired inside the tubes. What is the overall heat-transfer coefficient, assuming a shell-side heat-transfer coefficient of 300 W/m² · K?
c. What is the required area of the heat exchanger?
d. How many tubes are needed to achieve the desired value of Reynolds number? What would the desired tube length be? If that length is not realistic for a single-pass heat exchanger, what would you do next?