A mathematical model is developed to describe column adsorption when the contaminant constitutes a significant amount of the fluid. This requires modelling the variation of pressure and velocity, in addition to the usual advection-diffusion-adsorption and kinetic equations describing concentration and adsorption rates. The model builds on previous work based on a linear kinetic equation, to include both physical and chemical adsorption. A semi-analytical solution is developed and validated against a numerical solution. The model is tested against experimental data for the adsorption of large quantities of CO$_2$ from a helium mixture, with a CO$_2$ volume fraction ranging from 14% to 69%, and a N$_2$ mixture with 16% to 33% CO$_2$ volume fraction. Our results show a significant improvement with respect to models for the removal of trace amounts of contaminant.

30 pages, 9 figures, 6 tables. Contains Supplementary Material (8 pages,2 figures, 2 tables)