Thermal storage devices are becoming crucial for the exploitation of solar energy. From the point of view of seasonal energy storage, the most promising technology is represented by adsorption thermal batteries, which allow storing energy without heat loss with time. The improvement of thermal batteries design is related to a better understating of transport phenomena occurring in the adsorption/desorption phases. In this work, we discuss an efficient computational protocol to characterize adsorbent materials, in terms of both heat and mass transfer proprieties. To this purpose, a hybrid Molecular Dynamics and Monte Carlo method is developed. The proposed model is then tested on two types of 13X zeolite, with 76 and 88 Na cations. The results obtained, such as adsorbate diffusivity, adsorption curves, and heat of adsorption are validated with the literature. Finally, in the view of a multiscale analysis of sorption thermal storage devices, the possible use of the simulation outputs as inputs of thermal fluid dynamics models of adsorbent beds is discussed.