4.15b. Stripping chloroform from water by sparging with air.
Repeat Example 4.5, but using an air flow rate that is twice the minimum required.

Solution
Initial estimate of the column height, Z
Initial estimate of gas holdup
Calculate power required
4.16b. Stripping chloroform from water by sparging with air.
Repeat Example 4.5, but using the same air flow rate used in Problem 4.15, and specifying a chloroform removal efficiency of 99%.
Solution
For 99% removal efficiency, xin/xout = 100
Z = 1.30 m
WT(Z) = 5.0 kW
4.17b. Stripping chlorine from water by sparging with air.
A vessel 2.0 m in diameter and 2.0 m deep (measured from the gas sparger at the bottom to liquid overflow at the top) is to be used for stripping chlorine from water by sparging with air. The water will flow continuously downward at the rate of 7.5 kg/s with an initial chlorine concentration of 5 mg/L. Airflow will be 0.22 kg/s at 298 K. The sparger is in the form of a ring, 25 cm in diameter, containing 200 orifices, each 3.0 mm in diameter. Henry's law constant for chlorine in water at this temperature is 0.11 kPa-m3/mole (Perry and Chilton, 1973). The diffusivity of chlorine at infinite dilution in water at 298 K is 1.25 ´ 10Ð5 cm2/s (Cussler, 1997).
(a) Assuming that all the resistance to mass transfer resides in the liquid phase, estimate the chlorine removal efficiency achieved.
Solution
Initial estimate of gas holdup
Iterating until Z = 2.0 m:
(b) Calculate power required
4.18c,d. Batch wastewater aeration using spargers.
In the treatment of wastewater, undesirable gases are frequently stripped or desorbed from the water, and oxygen is adsorbed into the water when bubbles of air are dispersed near the bottom of aeration tanks or ponds. As the bubbles rise, solute can be transferred from the gas to the liquid or from the liquid to the gas depending upon the concentration driving force.
For batch aeration in a constant volume tank, an oxygen mass-balance can be written as
where cA* is the oxygen saturation concentration. Integrating between the time limits zero and t and the corresponding dissolved oxygen concentration limits cA,0 and cA,t; assuming that cA* remains essentially constant, and that all the resistance to mass transfer resides in the liquid phase:
In aeration tanks, where air is released at an increased liquid depth, the solubility of oxygen is influenced both by the increasing pressure of the air entering the aeration tank and by the decreasing oxygen partial pressure in the air bubble as oxygen is absorbed. For these cases, the use of a mean saturation value corresponding to the aeration tank middepth is suggested (Eckenfelder, W. W. Jr., Industrial Water Pollution Control, 3rd ed., McGraw-Hill, Boston, Ma, 2000):
where
cs = saturation dissolved oxygen concentration in fresh water exposed
to atmospheric air at 101.3 kPa containing 20.9% oxygen,
Po = absolute pressure at the depth of air release,
Ps = atmospheric pressure,
Ot = molar oxygen percent in the air leaving the aeration tank.
The molar oxygen percent in the air leaving the aeration tank is related to the oxygen transfer efficiency, Oeff, through
where
Consider a 567 m3 aeration pond aerated with 15 spargers, each using compressed air at a rate of 0.01 kg/s. Each sparger is in the form of a ring, 100 cm in diameter, containing 20 orifices, each 3.0 mm in diameter. The spargers will be located 5 m below the surface of the pond. The water temperature is 298 K; atmospheric conditions are 298 K and 101.3 kPa. Under these conditions, cs = 8.38 mg/L (Davis and Cornwell, 1998).
(a) Estimate the volumetric mass-transfer coefficient for these conditions from equations (4-23) and (4-25).
(b) Estimate the time required to raise the dissolved oxygen concentration from 0.5 mg/L to 6.0 mg/L, and calculate the resulting oxygen transfer efficiency.
(c) Estimate the power required to operate the 15 spargers, if the mechanical efficiency of the compressor is 60%.

Solution
Initial estimate of gas holdup
Initial estimate of transfer efficiency
(b) Calculate power required