Adsorption with activated carbon, made from bituminous coal of soluble organic compounds (SOCs), to purify surface and groundwater is a proven technology, as discussed by Stenzel [Chem. Eng. Prog., 89 (4), 36–43 (1993)]. The less-soluble organic compounds, such as chlorinated organic solvents and aromatic solvents, are the more strongly adsorbed. Water containing 3.3 mg/L of trichloroethylene (TCE) is to be treated with activated carbon to obtain an effluent with only 0.01 mg TCE/L. At 25C, adsorption-equilibrium data for TCE on activated carbon are correlated with the Freundlich equation:

where q = mg TCE/g carbon and c = mg TCE/L solution. TCE is to be removed by slurry adsorption using powdered activated carbon with an average d_p of 1.5 mm. In the absence of any laboratory data on mass-transfer rates, assume the small-particle absorption rate is controlled by externalmass transfer with a Sherwood number of 30. Particle surface area is 5 m²/kg. The molecular diffusivity of TCE in low concentrations in water at 25°C may be obtained from the Wilke–Chang equation. 

(a) Determine the minimum amount of adsorbent needed. 

(b) For operation in the batch mode with twice the minimum amount of adsorbent, determine the time to reduce TCE content to the desired value. 

(c) For operation in the continuous mode using twice the minimum amount of adsorbent, obtain the required residence time. 

(d) For operation in the semicontinuous mode at a feed rate of 50 gpm and for a liquid residence time equal to 1.5 times that computed in part (c), determine the amount of activated carbon to give a reasonable vol% solids in the tank and a run time of not less than 10 times the liquid residence time.

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