2.22b. Volumetric mass-transfer coefficients in industrial towers.
The interfacial surface area per unit volume, a, in many types of packing materials used in industrial towers is virtually impossible to measure. Both a and the mass-transfer coefficient depend on the physical geometry of the equipment and on the flow rates of the two contacting, inmiscible streams. Accordingly, they are normally correlated together as the volumetric mass-transfer coefficient, kca.
Empirical equations for the volumetric coefficients must be obtained experimentally for each type of mass-transfer operation. Sherwood and Holloway (Trans. AIChE, 36, 21, 39, 1940) obtained the following correlation for the liquid-film mass-transfer coefficient in packed absorption towers
The values of a and n to be used in equation (2-71) for various industrial packings are listed in the following table, when SI units are used exclusively.


a) Consider the absorption of SO2 with water at 294 K in a tower packed with 25-mm Raschig rings. If the liquid mass velocity is L' = 2.04 kg/m2-s, estimate the liquid-film mass-transfer coefficient. The diffusivity of SO2 in water at 294 K is 1.7 ´ 10Ð9 m2/s.

Solution
For dimensional consistency, add the constants:
b) Whitney and Vivian (Chem. Eng. Progr., 45, 323, 1949) measured rates of absorption of SO2 in water and found the following expression for 25-mm Raschig rings at 294 K
where kxa is in kmole/m2-s. For the conditions described in part a), estimate the liquid-film mass-transfer coefficient using equation (2-72). Compare the results.

Solution
2.23b. Mass transfer in fluidized beds.
Cavatorta, et al. (AIChE J., 45, 938, 1999) studied the electrochemical reduction of ferrycianide ions, {Fe(CN)6}Ð3, to ferrocyanide, {Fe(CN)6}Ð4, in aqueous alkaline solutions. They studied different arrangements of packed columns, including fluidized beds. The fluidized bed experiments were performed in a 5-cm-ID circular column, 75-cm high. The bed was packed with 0.534-mm spherical glass beads, with a particle density of 2.612 g/cm3. The properties of the aqueous solutions were: density = 1,083 kg/m3, viscosity = 1.30 cP, diffusivity = 5.90 ´ 10Ð10 m2/s. They found that the porosity of the fluidized bed, e, could be correlated with the superficial liquid velocity based on the empty tube, vs, through
where vs is in cm/s.
a) Using equation (2-56), estimate the mass-transfer coefficient, kL, if the porosity of the bed is 60%.

Solution
b) Cavatorta et al. proposed the following correlation to estimate the mass-transfer coefficient for their fluidized bed experimental runs:
where Re is based on the empty tube velocity. Using this correlation, estimate the mass-transfer coefficient, kL, if the porosity of the bed is 60%. Compare your result to that of part a).

Solution
2.24b. Mass transfer in a hollow-fiber boiler feedwater deaerator.
Consider the hollow-fiber BFW deaerator described in Example 2-13. If the water flow rate increases to 60,000 kg/hr while everything else remains constant, calculate the fraction of the entering dissolved oxygen that can be removed.

Solution
2.25b. Mass transfer in a hollow-fiber boiler feedwater deaerator.
a) Consider the hollow-fiber BFW deaerator described in Example 2-13. Assuming that only oxygen diffuses across the membrane, calculate the gas volume flow rate and composition at the lumen outlet. The water enters the shell side at 298 K saturated with atmospheric oxygen, which means a dissolved oxygen concentration of 8.38 mg/L.

Solution
b) Calculate the mass-transfer coefficient at the average conditions inside the lumen. Neglect the thickness of the fiber walls when estimating the gas velocity inside the lumen.

Solution
Calculate the average flow conditions inside the fibers
Calculate the average oxygen molar fraction in the gas
From Lucas method for pure N2
From the Wilke-Lee equation
(From Example 2.13)