Unlike natural gas, gaseous mixtures of hydrogen stored in underground reservoirs undergo active chemical transformations under the influence of methanogenic microorganisms inhabiting in geological strata. In the present paper, we extend the qualitative theory of self-organization in underground hydrogen storage for more complicated cases, which take into account the two-phase flow in porous medium and include chemotaxis, which is one of the main types of bacterial movement. The analysis of scenarios is based on the model of two-phase compositional flow coupled to the population dynamics. We show analytically and numerically that the chemotaxis retains the effects of self-organization, but leads to the appearance of non-periodicity in the structure of spatial oscillations.