The scope of this work was to develop a one-dimensional model to simulate the adsorption process of water vapour on a solid phase in a fixed bed reactor. The derived equilibrium equations were discretised by the method of finite differences and the coupled system of differential equations was thereby transformed into an algebraic system of equations which was solved using Matlab. The comparison of the simulation results with measurements performed by Mette on a lab-scale reactor using the zeolite 13XBFK showed good agreement for three different values of water vapour partial pressure in the air. Furthermore, experiments performed at the Chair of Thermal Processing Technology, Montanuniversity Leoben, were used to validate the model and again, comparison of simulation and experiment showed good agreement. By varying different parameters like void fraction or tortuosity, their impact on the adsorption process was examined and a better understanding of heat- and mass- transfer was achieved. Additionally, a two-dimensional model was established using the simulation software Ansys Fluent, which was also validated through the measurements performed by Mette and the Chair of Thermal Processing Technology. By using this more sophisticated two-dimensional model, important effects such as the wall effect and the resulting velocity profile can be taken into account. However, a comparison of the one-dimensional and the two-dimensional model showed that the adsorption process can be described fairly well by the simpler one-dimensional approach. A solid understanding regarding the basic processes of heat and mass transfer inside an adsorption reactor was acquired. Combined with the two developed simulation tools, this basic knowledge shall support the construction and development of such adsorption reactors.