There are different methods to store thermal energy. The thermochemical heat storage is one of the sufficient thermal energy storage. The energy storage density of the thermo-chemical material (TCM) is higher compared with sensible and latent heat storage method. This paper presents a mathematical simulation of thermochemical energy storage process by using COMSOL Multiphysics modeling Software. The TCM studied is magnesium chloride hexahydrate. The model result is validated with the experimental results, and the temperature distribution in the bed and material are investigated. Two reactor designs are considered; cylinder and truncated cone with different radiuses and heights. The comparison of the performance between them is investigated. The validation shows good agreement between the present work and the literature. The results indicate that the increase in entrance area reduces the charging time and increases the pressure drop at constant volume and height of the bed. Cylinder reactor and truncated cone with small and large diameters of 15.5 cm and 18.4 cm are the best to charge this material with thermal energy.