## 3 Results and Discussion  
### Loss of \(H_{2(g/\rm aq)}\) by Bacterial Conversion to CH\({}_{4(g)}\) and \(H_{2}S_{(g)}\)  
The modeling results of the reference scenario (defined in Section 2.2; input file S1) show that the maximum amount of bacterial-converted H\({}_{2(g/\rm aq)}\) to CH\({}_{4(g)}\) and H\({}_{2}\)S\({}_{(g)}\) depends on the amount of available (and reactive) electron acceptors, carbon dioxide and sulfate, and on the amount of available H\({}_{2(g/\rm aq)}\). Figure 1 shows selected reactions and processes that are coupled to bacterial sulfate reduction and methanogenesis. When CO\({}_{2}\) and SO\({}_{4}\)\({}^{2-}\) are fully consumed, methanogenesis and BSR will not proceed. The stored gas is composed of 96% hydrogen and 4% carbon dioxide (residual gas is still available). Therefore, CO\({}_{2}\) is available as electron acceptor for the methanogenesis and CH\({}_{4(g)}\) is generated. After less than 3 years of storage, the injected CO\({}_{2(g)}\) is completely consumed, but an ongoing supply of CO\({}_{2}\) is provided by the dissolution of carbonate-bearing minerals (such as calcite, for example). Consequently, the amount of generated CH\({}_{4(g)}\) is limited by the assumed storage time of 30 years and the time-dependent kinetics of methanogenesis. The available sulfate for BSR in the reservoir rock results from anhydrite dissolution. If anhydrite is still present in a depleted natural gas reservoir, it is not reactive (e.g., it is coated by other minerals). Otherwise, the sulfate would have been catalyzed by bacterial sulfate reduction, with methane--the main component of natural gas--as electron donor. The same applies to hydrogen storage in depleted natural gas reservoirs. However, the creation of new fractures and natural faults or the dissolution of carbonate cements (pore-filling cements) leads to contact of reactive anhydrite with the stored hydrogen. To simulate this \"worst-case\" scenario, a small amount of reactive anhydrite is assumed in this model. The dissolution of anhydrite provides SO\({}_{4}\)\({}^{2-}\)\({}_{(\rm aq)}\) for H\({}_{2}\)S\({}_{(\rm g)}\) generation and Ca\({}^{2+}\)\({}_{(\rm aq)}\) for calcite precipitation. Additionally, the dissolution of anhydrite creates porosity, which in turn can be superseded by the precipitation of other minerals (see Section 3.2). The reactive anhydrite is in solution equilibrium with the brine. The consumption of sulfate\({}_{(\rm aq)}\) by BSR is accompanied by ongoing anhydrite dissolution and more sulfate becomes available for BSR until the reactive anhydrite is completely dissolved. As a product of BSR and methanogenesis, small amounts of water (0.007 kg) are formed (Equations (2) and (3)). This increases the water content in the reservoir rock (1.0 kg initial water + 0.007 kg generated water = 1.007 kg total water mass per cell after 30 years). The water will probably be suppressed by the gas along the reservoir/cap rock boundary. However, the small increase in the mass of water could increase the anhydrite dissolution, resulting in a higher amount of sulfate ions that are available for BSR. Additional sulfate is delivered by diffusion from the cap rock and the underlying rock, where the dissolution of anhydrite acts as a sulfate source. The amount of generated H\({}_{2}\)S\({}_{(\rm g)}\) depends on the storage time, the amount of available and reactive anhydrite, the diffusion, and the time-dependent kinetic rate constant. However, the last three mentioned factors depend on pressure and/or temperature. Two hotspot regions with higher amounts of generated H\({}_{2}\)S\({}_{(\rm g)}\) (related to a higher loss of hydrogen) are identified: the contact area of the reservoir rock and the cap rock and the contact area of the reservoir rock and the underlying rock. These are the regions where additional sulfate is delivered into the reservoir rock by diffusion.