Activated carbon filters have a limited lifetime. After long-term use, their surfaces are saturated with adsorbed pollutants and no further purification occurs. The filter material therefore has to be replaced at regular intervals, according to manufacturer's instructions.The lifetime of a granular active carbon (GAC) filter. 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 speeds 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.