Natural gas sweetening is an essential process within hydrocarbon processing operations, enabling compliance with product quality specifications, avoiding corrosion problems, and enabling environmental care. This process aims to remove hydrogen sulfide (H2S), carbon dioxide, or both contaminants. It can be carried out in fixed-bed adsorption towers, where iron oxide-based solid sorbent reacts with the H2S to produce iron sulfides. This study is set out to develop a fluid-dynamic model that allows calculating the pressure drop in the H2S adsorption towers with the novelty to integrate reactivity aspects, through an iron sulfide layer formation on the solid particles’ external skin. As a result of the layer formation, changes in the particle diameter and the bed void fraction of the solid sorbent tend to increase the pressure drop. The shrinking-core model and the H2S adsorption front variation in time support the model development. Experimental data on pressure drop at the laboratory scale and industrial scale allowed validating the proposed model. Moreover, the model estimates the bed replacement frequency, i.e., the time required to saturate the fixed bed, requiring its replacement or regeneration. The model can be used to design and formulate new solid sorbents, analyze adsorption towers already installed, and help maintenance-planning operations.