In this paper the numerical modelling of the behaviour of a channel of a hygroscopic compact matrix is presented. The heat and mass transfer phenomena occurring in the porous medium and within the airflow are strongly coupled, and some properties of the airflow and of the desiccant medium exhibit important changes during the sorption/desorption processes. The adopted physical modelling takes into account the gas side and solid side resistances to heat and mass transfer, as well as the simultaneous heat and mass transfer together with the water adsorption/desorption process in the wall domain. Two phases co-exist in equilibrium inside the desiccant porous medium, the equilibrium being characterized by sorption isotherms. The airflow is treated as a bulk flow, the interaction with the wall being evaluated by using appropriated convective coefficients. The model is used to perform simulations considering two distinct values of the channel wall thickness and different lengths of the channel. The results of the modelling lead to a good understanding of the relationship between the characteristics of the sorption processes and the behaviour of hygroscopic matrices, and provide guidelines for the wheel optimization, namely of the duration of the adsorption and desorption periods occurring in each hygroscopic channel.