## 3 Model Concept  
For the sake of completeness, we explain the model's full capability. However, in this study, the terms related to two-phase effects and temperature-induced precipitation have no relevance for the given experimental conditions. Our EICP model concept accounts for two-phase, multicomponent, non-isothermal reactive transport on the scale of a representative elementary volume (REV) where flow is modeled using Darcy's Law. It includes pH-dependent dissociation reactions, temperature-dependent urease inactivation, as well as temperature-dependent enzymatically catalyzed ureolysis. Mass transfer may occur between both fluid phases by mutual dissolution of water and CO\({}_{2}\) in the gas or the aqueous phases or between the aqueous phase and the two \"solid\" phases adsorbed urease (au) and calcium carbonate (c) by adsorption or desorption of urease and precipitation or dissolution of calcium carbonate. We assume all calcium carbonate precipitates as calcite, as in [21]. The components considered mobile are denoted by superscripts \(\kappa\): water (w), dissolved inorganic carbon (C\({}_{\text{tot}}\)), sodium (Na), chloride (Cl), calcium (Ca), urea (u), ammonium and ammonia (N\({}_{\text{tot}}\)), and suspended urease (su). While our model employs an REV-scale and thus a volume-averaged approach, a pore-scale representation of the relevant processes and phases is shown in Figure 1.  
The balance equations for the mobile components are solved for the primary variables \(p_{\text{w}}\) (aqueous-phase pressure) and \(x_{\text{w}}^{\kappa}\) (mole fractions of component \(\kappa\) in the water phase). For the solid phases, we use their volume fractions \(\phi_{\lambda}\). However, the gas-phase saturation \(S_{\text{g}}=\
icefrac{{\text{gas volume}}}{{\text{pore volume}}}\) is used as a primary variable instead of the mole fraction of total inorganic carbon in water \(x_{\text{w}}^{\text{Ctot}}\) whenever both fluid phases are present within the same control volume. All reactive and mass-transfer processes are incorporated in the component balance Equations (5) and (6) using component-specific source and sink terms. \[\sum_{\alpha}\left[\frac{\partial}{\partial t}\left(\phi p_{\alpha}x_{\alpha} ^{\kappa}S_{\alpha}\right)+\
abla\cdot\left(\rho_{\alpha}x_{\alpha}^{\kappa} \mathbf{v}_{\alpha}\right)-\
abla\cdot\left(\rho_{\alpha}D_{\text{pm,ff}}^{ \kappa}\
abla x_{\alpha}^{\kappa}\right)\right]=q^{\kappa}. \tag{5}\]  
Here, \(t\) is time; \(\phi\) is porosity; \(\rho_{\alpha}\), \(S_{\alpha}\), and \(\mathbf{v}_{\alpha}\) are the density, saturation, and velocity of phase \(\alpha\), respectively; \(x_{\alpha}^{\kappa}\) is the mole fraction of component \(\kappa\) in phase \(\alpha\); \(D_{\text{pm,ff}}^{\kappa}\) is the diffusion coefficient  
Figure 1: Schematic view of relevant processes and phases considered in the conceptual model, modified from [29]. for component \(\kappa\) in phase \(\alpha\) in the porous medium; and \(q^{\kappa}\) is the source term of component \(\kappa\) due to biochemical reactions. The mass balances for the solid phases calcite and adsorbed urease contain only storage and source terms since they are assumed immobile. \[\frac{\partial}{\partial t}\left(\phi_{\lambda}\rho_{\lambda}\right)=q^{ \lambda}. \tag{6}\]  
Here, \(\phi_{\lambda}=\
icefrac{{\mathrm{volume}_{\lambda}}}{{\mathrm{total\ volume}}}\) is the volume fraction of the solid phase \(\lambda\), \(\rho_{\lambda}\) is the solid-phase density, and \(q^{\lambda}\) is the source term of phase \(\lambda\) due to bio- or geochemical reactions.