A process is being developed to produce carbonated beverages. As part of this process, a packed-bed absorption tower will be used to dissolve carbon dioxide, CO₂, gas into water. Pure mountain spring water, containing no dissolved CO₂ enters the top of the column at a molar flow rate of 5.0 kgmole/min. Pure CO₂ gas at 2.0 atm is also fed to the top of the tower at a flow rate of 1.0 kgmole/min. As the liquid flows down the tower, CO₂ gas absorbs into the water, and the dissolved CO₂ concentration increases down the length of the bed. The carbonated water and the unused CO₂ gas exit the bottom of the tower. The absorption process is liquid–film controlling because only pure CO₂ is present in the gas phase.

The tower is packed with 1.0 in ceramic rings, and the inner tower diameter is 0.25 m. The temperature is maintained at 20°C. At this temperature, the Henry’s law constant for the dissolution of CO₂ gas in water is 25.4 atm m³/kgmole, the molar density of liquid water is 55.5 kgmole/m³, the mass density of liquid water is 998 kg/m³, and the viscosity of liquid water is 993 10 6 kg/m s.
a. What is the liquid-phase mass-transfer coefficient, kLa, for CO₂ in water flowing through the packed bed?
b. Estimate the depth of packing if the desired concentration of dissolved CO₂ in the outlet liquid is 95% of the saturation value for dissolved CO₂ in water under CO₂ partial pressure of 2.0 atm and 20 C.