The intermittent production of the renewable energy imposes the necessity to temporarily store it. Large amount of exceeding electricity can be stored in geological strata in the form of hydrogen. The conversion of hydrogen to electricity and vice versa can be performed in electrolysers and fuel elements by chemical methods. The nowday thecnical solution accepted by the European industry consists of injecting small amounts of hydrogen in the existing storages of natural gas. The progressive development of this technology will finally lead to the creation of underground storage of pure hydrogen. The main problem encountered in the case of storage of hydrogen mixtures with other gases in geological strata consists of the chemical reactivity induced by various classes of bacteria that consume hydrogen for their methabolism. One of the products of such reactions is methane, having higher energy potential than hydrogen, and produced from Sbatiers's reaction between H2 and CO2. The fundamental problem thus consists of intensifying the useful biotic reaction of methanogenesis and suppressing other hydrogenotrophic reactions caused by other colonies (sulphate-reducing, iron-reducing, acetogen bacteria). The kinetics of all these reactions represents the key element of all the theory. Multiple experimental data reveal important memory effects reflecting the non-instantaneous reaction of bacteria to sharp variation of the environment. Such memory effects give rise to the phenomena of self-organization and qualitatively change the behaviour of the system. We developed the new memory model of bacterail kinetics and biotic reactions, which is characterized by: the long memory ; the presence of several types of nutrients; different types of the metabolism as respiration and biomass production ; the concurrence between various colonies for nutrients. The kernel of the integral operator has been obtained by solving the inverse problem and fitting experimental data. Such a model has been integrated in the numerical simulator of the compositional multiphase flow based on the DuMux software (the open source, developed by Stuttgart university). The obtained DuMux-Biotic version has been used to model the evolution of a hypothetical underground storage of hydrogen. We have revealed the appearance of non-attenuating oscillatory regimes and chaotic behaviour caused by the memory effects, the different rates of bacterial growth and gas injection, and by the competition between various colonies for nutrients. The additional injection of CO2 was analysed with the objective to intensify the Sabatier's reaction. The research was performed within the framework of the German project H2STORE.