An absorption tower containing wooden grids is to be used for absorbing SO, in a sodium sulfite solution. A mixture of air and SO, will enter the tower at a rate of 70,000 ft3/min, temperature of 250°F, and pressure of 1.1 atm. The concentration of SO2, in the entering gas is specified, and a given fraction of the entering SO, must be removed in the absorption tower. The molecular weight of the entering gas mixture may be assumed to be 29.1. Under the specified design conditions, the number of transfer units necessary varies with the superficial gas velocity as follows:
where Gs is the entering gas velocity as lb/(h)(ft2) based on the cross-sectional area of the empty tower. The height of a transfer unit is constant at 15 ft. The cost for the installed tower is $1 per cubic foot of inside volume, and annual tied charges amount to 20 percent of the initial cost. Variable operating charges for the absorbent, blower power, and pumping power are represented by the following equation:
The unit is to operate 8000 h/year. Determine the height and diameter of the absorption tower at conditions of minimum annual cost.