In this paper a detailed mathematical formulation is developed for the numerical modelling of the behaviour of a channel of a hygroscopic compact matrix. A comparison between the detailed version and a simplified one is performed considering a two-dimensional airflow between desiccant parallel plates. The distinct heat and mass transfer phenomena are strongly coupled, and some properties of the airflow and of the desiccant medium exhibit important changes during the sorption processes. Both physical models take into account the gas side and solid side resistances to heat and mass transfer. The wall domain is treated similarly in both models, by taking into account the simultaneous heat and mass transfer together with the water adsorption/desorption process. Two phases co-exist in equilibrium inside the desiccant porous medium, the equilibrium being characterized by sorption isotherms without hysteresis. The detailed model is based on the solution of the differential equations for the conservation of mass, energy and momentum, assuming that no momentum transport exists in the porous wall domain. In the simplified model, the airflow is treated as a bulk flow, the interaction with the wall being evaluated by using appropriated convective coefficients. Both models are compared in the simulation of a parallel plate channel during an adsorption process. The results show a good agreement for channel lengths greater than 0. 1 m. In part 11 of the paper, the simplified model is adapted to the simulation of the three-dimensional problem in the channel of a hygroscopic rotor, and it is used to perform parametric studies. (c) 2007 Elsevier Ltd. All rights reserved.