As the interest in hydrogen as an energy carrier, for an energy storage, grows, with it grows the effort for a better understanding of the working environment and the conditions that can be encountered. Depleted natural gas reservoirs are so far considered the best option for underground hydrogen storage. Seeing how they bring an option for a large storage volume, whose rocks have a history of being in contact with the gas. An extensive library of collected data and knowledge about the reservoir, throughout the years of production, only adds to the favorability of such storage. In the reservoirs where such implementation has been carried out an interesting phenomenon has been observed, namely various species of microorganisms that thrive at the rough reservoir conditions have been using stored hydrogen as an energy source for their metabolism. The focus of this work is set on a certain species of these microorganisms called methanogenic archaea, which are producing methane as they consume hydrogen. In other words, stored hydrogen gas is converted to methane in the presence of these microorganisms. Little is known about the underlying physics and influencing parameters on the microbial conversion of underground hydrogen storage. Therefore, many laboratory tests, as well as simulations, are being done in order to broaden our knowledge and familiarize ourselves with the expected outcomes when it comes to these types of microorganisms and their activity. We intend to implement a developed mathematical model into the MRST (The MATLAB Reservoir Simulation Toolbox) code and therefore simulate a one-dimensional injection of the nutrient gas mixture into the core sample that has been populated with methanogenic archaea. The model consists of two equations, one describing the population growth of the microbial species and the other describing the effects of metabolic bioreaction (called methanogenesis), those being nutrient (H2 and CO2) consumption and methane production. Once developed, this code can serve as an assisting tool for future laboratory experiments and a basis for full reservoir scale simulations that could predict the expected effects in a more realistic environment.