We focus our attention on hydrogen sulphide (H2S), which originates from various sources and is one of the major air pollutants. Concentrations above 140 mg m–3 are immediately harmful for human health. Below that threshold, H2S is an odorous compound, which can be detected by human beings in concentration higher than 5 µg m–3. Its removal is conventionally performed through scrubbing with amine or NaOH aqueous solutions. Adsorption on activated carbons is an alternative technique, particularly suitable for application in the low H2S concentration range, being a typical example of odour removal technique. In this work, we propose a model of packed bed reactor (PBR) embedding impregnated activated carbons (IACs), where the H2S adsorption involves a catalytic partial oxidation step causing the deposition of elemental sulphur on the catalyst, with consequent gradual deactivation. The model equations are integrated numerically through the software COMSOL Multiphysics 5.3a. Simulation results are validated through comparison with literature experimental data. Furthermore, application to an industrial case study is presented and discussed.