Due to the thermodynamic conditions prevailing at very shallow depths of calcite stone oil fields, molecular hydrogen has been reported to be released from hydrocarbon or heavy oil located on the surface of the calcite stone. Since this region is physically inaccessible, there is a need to realize modeling and simulation of the hydrogen adsorption and storage process under reservoir conditions. Motivated by the previous problem, in this work, based on recent reports of hydrogen production from oil fields, we present a theoretical methodology to describe the process of hydrogen adsorption on naturally fractured and carbonated (limestone (CaCO3)) reservoirs and to quantify their storage capacity. Firstly, the calcite rock model was optimized inside a simulation cell containing a vacuum layer, for which energy optimization techniques based on density functional theory were used. Subsequently, using ab initio methods also based on DFT, calcite rock was characterized obtaining structural, electronic, vibrational, thermodynamic properties, and Mulliken population analysis of CaCO3. Finally, molecular dynamics simulations were performed in order to simulate the adsorption process and obtain percentages of hydrogen adsorption on (110) surface of the (2 × 2) CaCO3 supercell, for N = 3, 5, 10 hydrogen molecules. The molecular dynamics simulations showed that the surface of CaCO3 rock has hydrogen capacity of only 0.42 mass %.