Calculating Number of Stages in Counter-Current Absorption: An industrial operation results in releasing air containing chloroform into the environment. A counter current tray absorber column is desired to reduce the concentration of chloroform in air from 200 ppm (YN+1) to a permissible value of 10 ppm (Y1) before release by scrubbing it with pure water (X0 = 0). Air stream enters the absorption column at 1000 kmol/hour (V’) at 1.5 atm (P) and 25 °C (T). The carrier gas may be considered insoluble in the solvent and the solvent may be considered nonvolatile. Assume dilute species with constant flow rates. Assume mole ratios (Y, X) are equal to mole fractions (y, x). Assume Henry’s law for equilibrium with Henry’s constant for chloroform in air as 211.2 atm.
(a) Calculate minimum water flow rate (L’min) to perform the operation. If a multistage/multitray absorber column was used for the above process, how many trays/stages (N) will be required to perform the required operation? Calculate and show the concentrations after each stage.
(b) If the actual liquid rate is 1.4 times the minimum value, what is the outlet liquid composition (XN)? (Hint: Do not calculate the number of trays/stages and concentrations for each stage. Try to infer from mass balances/operating line equation.)
(c) If the actual liquid rate is 1.4 times the minimum value, solve for the actual number of trays using graphical methods/EXCEL/MATLAB/MATHCAD etc. Calculate and show the concentrations after each stage.
(d) If the actual liquid rate is 1.4 times the minimum value, solve for the actual number of trays using the Kremser relationship.