The ''soil venting'' shown in the figure below is used to treat soil contaminated with volatile, toxic liquids. In the present situation, the porous soil particles are saturated with liquid TCE, a common industrial solvent. The contaminated soil is dug up at the waste site and loaded into a rectangular trough. The soil consists of coarse, porous mineral particles with an average diameter of 3 mm, loosely compacted into a packed bed with a void fraction 0.5.
Air is introduced at the bottom of the trough through a distributor and flows upward around the soil particles. Liquid TCE satiating the pores of the soil particle evaporate into the air stream. Consequently, the TCE concentration in the air stream increases from the bottom to the top of the trough. Usually, the rate of TCE evaporation is slow enough so that the liquid TCE within the soil particle is a constant source for mass transfer, at least until 80% of the volatile TCE soaked within the soil is removed. Under these conditions, the transfer of TCE from the soil particle to the air stream is limited by convective mass transfer across the gas film surrounding the soil particles.
The mass flow rate of air per unit cross section of the empty bedis 0:1 kg/m3.s. The process is carried out at 293 K. At this temperature, the vapor pressure of TCE is 58 mmHg. The molecular diffusion coefficient of TCE vapor in air is given in example 4 of this chapter.
a. What is the gas-film mass-transfer coefficient for TCE vapor in air?
b. At what position in the bed will the TCE vapor in the air stream reach 90% of its saturated vapor pressure? In your solution, you may want to consider a material balance on TCE in the gas phase within a differential volume element of the bed.
Assume the convective mass-transfer resistances associated with air flowing over the top surface of the bed are negligible and that there is no pressure drop of the gas stream through the bed so that the total system pressure remains constant at 1 atm.