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, CO 2 , gas into water. Pure mountain...

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 flow rate of 5 kg mol/min. Pure CO₂
gas at 2 atm is also fed to the top of the tower at a flow rate of 1 kg mol/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 in. ceramic rings and the inner tower diameter is 0.25 m. The temperature is maintained at 20C. At this temperature, the Henry’s law constant for the dissolution of CO₂
gas in water is 25:4 atm/ (kg mol/m³). At 20C, the molar density of liquid water is 55.5 kg mol/m³, the mass density of liquid water is 998.2 kg/m³, and the viscosity of liquid water is 993kg/ms.

a. What is the liquid phase mass transfer coefficient, k_La, 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 atm and 20C.