An analytical model for column adsorption with two competing contaminants

We develop a mathematical model to describe an adsorption process where two contaminants are simultaneously removed from a fluid mixture as it flows through a packed column. Both species compete to occupy the available sites, including displacing previously attached molecules. The system of governing equations involves mass balances for the two species coupled to an attachment model. In the common situation, where one contaminant is more strongly adsorbed than the other, the analysis may be split between two distinct regions — one where competition dominates the adsorption process and all of the first contaminant is eventually captured and a second region, ahead of the first, where only the weaker contaminant remains and so is able to be adsorbed without being displaced. In both regions, it is possible to find travelling waves which may be used to construct an analytical expression for the breakthrough curves. To verify this, a numerical solution is developed and compared with the approximate analytical solutions. The model results are then verified against experimental data for the capture of siloxanes, toluene and n-decane on activated carbon, obtaining excellent agreement with R2> 0.98 in the cases examined.