Unlike natural gas, hydrogen gas mixtures stored in underground reservoirs undergo active chemical transformations under the influence of methanogenic microorganisms inhabiting in porous reservoirs. They lead to reduction of hydrogen and carbon dioxide concentrations and increase methane concentration. This chemical activity coupled with bacterial dynamics and gas/water flow through porous medium causes the phenomenon of self-organization such as the occurrence of autowave spatial structures, whose dynamics is characterized by a multiplicity of scenarios and bifurcations between them. In this paper we continue to develop the qualitative theory of self-organization in underground hydrogen storage, for more complicated cases that include the mechanism of chemotaxis, which is one of the main types of bacterial movement, and takes into account the flow of both phases. The analysis of scenarios is based on the model of two-phase compositional flow coupled with population dynamics.