We consider coupled hydrodynamic and biochemical phenomena that occur in an underground porous reservoir, in which a mixture of hydrogen with other gases has been injected. The presence of methanogenic bacteria in geological strata initiates the natural underground methanation, i.e., the conversion of the mixture of H2 and CO2 into methane. Such a transformation increases the energy of the stored gas, as the energy potential of methane is higher than that of hydrogen. Consequently, such an underground methanation can represent the basis of a new industrial technology of energy storing and enrichment. In the present paper, we give the mathematical model of bacterial kinetics, closely related to the metabolism of bacteria. We formulate the mathematical model of the process and give qualitative mathematical analysis of various scenarios of gas behavior. In practice, the mixture of hydrogen with other gases is produced by the underground coal gasification, which gives syngas (H2, CO and CO2) or town gas (H2, CO, CH4 and CO2). After storing, the enriched mixture can be extracted and used as fuel or transformed into electricity in gas-fired turbines. The same processes also occur when pure hydrogen is injected in underground storage of natural gas. Such technique is applied to store exceedingly produced electricity: electricity is converted to hydrogen by electrolyzers and injected into geological strata.