Renewable energy sources will play a key role in meeting future energy demand. One major criticism of those sources stands in their intermittency requiring both a more effective management of demand and efficient storage systems. We focus on thermo-chemical storage by adsorption-desorption mechanism. Eco friendly, economically viable and suitable with solar energy temperature range made the zeolite 13X - water pair ideal for buildings applications. We built an energy storage model in a cylindrical adsorber which contains the mentioned zeolite13X - water pair. Energy storage has been modeled to present coupled heat and mass transfers thanks to a bi-dimensional model. The numerical simulations lead to the time-space evolution of the heating fluid and adsorbent temperatures and pressure. These knowledge models include typically a great amount of coupled differential equations to solve and strong non linearities. The originality of this study is to build a knowledge model of coupled heat and mass transfer in an adsorber and use the Proper Orthogonal Decomposition (POD) and Galerkin projection to build a minimal model of lower dimension without significant loose of accuracy.