Today, the global trend in the development of renewable energy sources is the implementation of integrated processing of organic waste with the production of biogenic gases such as biomethane. In this case, an essential focus is the study of biogas purification processes to methane. This paper focuses on the process of modeling biochemical purification of biogas from hydrogen sulfide to develop the direction of biomethane production. Simulation of hydrogen sulfide bio-oxidation process with the use of granulated carrier based on phosphogypsum was conducted using experimental data from previous studies to verify the adequacy of the proposed mathematical model. Thus, to implement the process of phosphogypsum utilization in technological systems of biogas purification, it is important to consider the level of bioactivity in the immobilization of bacteria on the loading surface of phosphogypsum and the degree of biotransformation of phosphogypsum components in the oxidation of carbon dioxide and hydrogen sulfide impurities to achieve the highest ecological effect. Also, the use of overlay visualization allowed to form the main clusters of development of research potential in the field of biogas technologies for Ukraine.