A random-packed tower is to be used for contacting 3000 lb/h of air with 4000 lb/h of water. The tower will be packed with l-in. chemical porcelain Raschig rings. The operating pressure is 1 atm, and the temperature is 70°F. Assuming column operation is in the preloading range, estimate the optimum diameter per foot of packed height to give minimum annual cost for fixed charges and blower operating charges. The following additional data apply:
Annual fixed charges = 0.2 times cost of installed unit
Cost of installed unit, complete with distributor plates, supports, and all auxiliaries = 2.0 times purchased cost of shell and packing
Cost of delivered power = $0.08/kWh
Operating time = 8000 h/year
Purchased cost of shell = $40/ft3 of packed volume
Purchased cost of packing = $22.00/ft3