Computing the lifetime of granular activated carbon filters by means of travelling waves solutions

The aim of this paper is to propose a very simple way of computing the quantities relevant to the lifetime of a granular active carbon (GAC) filter. Our analysis is based on a sorption law, which, being linear separately in the adsorbed and non-adsorbed pollutant concentrations, allows the explicit computation of solutions in the form of a travelling wave. It is then easy to realize that, if the wave speed is much smaller than the advection velocity in the filter (as it happens in usual cases), then the travelling wave is an excellent approximation of the real profile of the pollutant concentration. The model is calibrated using laboratory experiments on a reduced scale. A linear stability analysis of the travelling waves is performed. Phenomena of diffusion–dispersion are neglected, however their effects are considered in the last sections, showing when they are really negligible and how they may influence the wave shape. The case of more pollutant species competing for the same adsorption sites on the GAC is also considered.