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 CO2gas 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 20°C. At this temperature, the Henry's law constant for the dissolution of CO2 gas in water is 25:4 atm/ (kg mol/m3). At 20°C, 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 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 atm and 20°C.