Modelling large mass removal in adsorption columns

Abstract

A novel mathematical model is developed to describe column adsorption when the contaminant constitutes a significant amount of the fluid. This requires tracking the variation of pressure and velocity, in addition to the usual advection–diffusion–adsorption and kinetic equations describing concentration and adsorption rates. The model goes beyond previous work, based on a simple linear kinetic equation, to include both physical and chemical adsorption. Using rigorous mathematical techniques we are able to simplify the governing equations to obtain an approximate analytical solution. The advantage of such analytical solutions is that the effect of system parameters on the behaviour is clearly defined and, in this case, only a single unknown needs to be fitted to the data. The simplicity of the solution is advantageous when testing new configurations and optimising operating conditions. Fitting a single unknown from an explicit expression is significantly more efficient than fitting multiple parameters to the base system of equations. The analytical solution shows excellent agreement with breakthrough data for multiple experiments. For the most extreme case of 69% CO${}_2$ our model had a Sum of Squares Error of 0.01 and an R${}^2$ = 0.99, compared to values 4.8, 0.94 for the standard constant velocity model.