A Simple Method for Calculating the Overall Adsorption Rate Constant in the Wheeler–Jonas Equation

Abstract

Use of the Wheeler–Jonas (WJ) equation to predict adsorbate breakthrough for a packed bed of granular activated carbon requires the calculation of the overall adsorption rate constant (k ν ) and the amount adsorbed. These quantities can be calculated from the intercept (A) and slope (B) of a linear fit to the elapsed time as a function of the logarithm of the ratio of the adsorbate concentration (C 0 – C x )/C x based on the breakthrough curve. Because k ν varies with the flow rate (F), numerous measurements at different values of F were performed to find the appropriate value of k ν . One relatively simple method for calculating k ν directly from the WJ equation is presented and the physical meaning of A and B revealed. The key factors that lead to a simplified calculation of k ν are the ratio of the breakthrough time to the equilibrium time (t 0.05 /t 0.50 ) and the ratio of the equilibrium time to the saturation time (t 0.50 /t 0.95 ), both of which remain nearly constant for different values of F, concentration and temperature. Knowledge of k ν , A and B, and their relationships, are very helpful for predicting the breakthrough behaviour of packed bed adsorbents using the WJ equation.