An open pond containing 200 m³ of wastewater is contaminated with a small concentration of trichloroethylene (TCE), a common industrial solvent. The pond is 2.0 meters deep and 10 meters on a side. Air is sparged into the bottom of the trench to “strip out” the dissolved TCE. The inlet air flow rate is 0.15 m3 air per 1.0 m³ of water per min. At this air flow rate, the gas holdup is calculated to be 0.015 m³ air per 1.0 m³ water. The air sparger provides an average bubble diameter of 5.0 mm. The temperatures of the air and water are 293 K. TCE is only sparingly soluble in water, and the Henry’s law constant for TCE in liquid water is 9.98 atm m³/kgmole, and the molecular weight of TCE is 131.4 g/gmole.
a. What the liquid-phase mass-transfer coefficient for TCE in water surrounding the bubble?
b. Assume there is no inflow or outflow of water to or from the trench. Determine the required time to reduce the dissolved TCE concentration from 50 g TCE/m³ to 0.005 g TCE/m³. You may assume that the air stream serves as an infinite sink for TCE transfer.
c. Now assume that there is a 1.0 m³/s inflow of wastewater containing 50 g TCE/m³, and a 1.0 m³/s outflow so that the total pond volume is still 200 m. What is the steady-state concentration of dissolved TCE?