## 2 Materials and Methods
### Numerical Model  
As was presented above, the reactive transport modelling requires information on flow conditions, which are governed by materials' hydraulic properties (intrinsic and relative permeability, initial porosity, and water retention curve), transport-related properties (fortuosity, solute diffusivity in water, and saturation), chemistry-related data (equilibrium constants of chemical reactions considered in the analysis, and activity coefficients) as well as porewater solution composition, amount of minerals in the porous medium, exchanged ion concentrations, data on surface complexation sites, and initial and boundary conditions. Data on hydraulic, thermal, and transport-related properties of liquid, gas, and bentonite are provided in Table 3. \begin{table}
\begin{tabular}{c c} \hline
**Parameter [13; 18; 29]** & **Value or Dependence** \\ \hline Initial porosity of bentonite & 0.41 \\ Solid density (kg/m\({}^{3}\)) (T in Celsius) & 2780\(e^{(-2\cdot 10^{-5}(T-12))}\) \\ Water density (kg/m\({}^{3}\)) (T in Celsius) & \(\rho_{w}=998.2\exp\left(5\cdot 10^{-7}(\mathrm{P}_{L}-100)-2.1\cdot 10^{-4}( \mathrm{T}-12)\right)\) \\ \(\rho_{g}=\rho_{v}+\rho_{A}\) \\ Vapour and air density (kg/m\({}^{3}\)) (T in Celsius) & \(\rho_{v}=\frac{e^{(0.00547-41584-10^{-3}T^{2})}}{194.4}e^{-(2.16677(\mathrm{P }_{g}-\mathrm{P}_{L}))/(\rho_{w}(\mathrm{T}+273.15))}\) \\  & \(\rho_{A}=\frac{\mathrm{M}_{p}P_{A}}{RT}\) \\ \hline Thermal properties [13; 18; 29] & \\ \hline Thermal conductivity of the liquid (W/m \({}^{\circ}\)C) & 1.5 \\ Thermal conductivity of the air (W/m \({}^{\circ}\)C) & 2.6\(\cdot 10^{-2}\) \\ Thermal conductivity of the vapour (W/m \({}^{\circ}\)C) & 4.2\(\cdot 10^{-2}\) \\ Thermal conductivity of the solid (W/m \({}^{\circ}\)C) & 1.23 \\ Specific heat of the water (J/kg \({}^{\circ}\)C) & 4202 \\ Specific heat of the air (J/kg \({}^{\circ}\)C) & 1000 \\ Specific heat of the vapour (J/kg \({}^{\circ}\)C) & 1620 \\ Specific heat of the solid (J/kg \({}^{\circ}\)C) & 835.5 \\ Vaporisation enthalpy (J/kg) & 2.45\(\cdot 10^{6}\) \\ Thermal compressibility of the water (\({}^{\circ}\)C\({}^{-1}\)) & 2.1\(\cdot 10^{-4}\) \\ Thermal compressibility of the solid (\({}^{\circ}\)C\({}^{-1}\)) & 2\(\cdot 10^{-5}\) \\ \hline Hydraulic properties [13; 18] & \\ \hline Intrinsic permeability for liquid flow (m\({}^{2}\)) & \(k_{L}=k_{o}\frac{\rho^{3}}{(1-\rho)^{2}}\frac{(1-\rho_{v})^{2}}{\rho_{v}}\), \(k_{o}=3.75\;10^{-21}\;\mathrm{m}^{2}\) \\ Relative permeability to liquid & \(k_{TL}=S_{w}3\) \\ Intrinsic permeability for gas flow (m\({}^{2}\)) & 5\(\cdot 10^{-10}\) \\ Relative permeability to gas (m\({}^{2}\)) & \(k_{rG}=(1-S_{W})3\) \\  & \(S_{w}=S_{r}+\frac{S_{s}-S_{r}}{\left(1+\left(a\left(P_{g}-P_{s}\right)\frac{1 }{r+1}\right)^{s}\right)}\) \\ Van [PERSON] retention curve & \(S_{r}=0.05\), \(S_{s}=0.95\) \\  & \(\alpha=5\cdot 10^{-5}\;\mathrm{kPa}^{-1},\;b=0.21\) \\ Liquid viscosity (kg/m\(\cdot\)s) (T in Celsius) & \(661.2\cdot 10^{-3}(T+44)^{-1.562}\) \\ Gas viscosity (kg/m\(\cdot\)s) & 1.76\(\cdot 10^{-5}\) \\ Vapour tortuosity factor & 0.10 \\ [PERSON]’s constant for air (T in Celsius) & \(\mathrm{H}=\rho^{1}\cdot(\mathrm{T}+273.15)\cdot 7.1281183\cdot 10^{-11}\cdot e^{ \frac{\mathrm{mW}\mathrm{W}\mathrm{W}}{(17+273.15)}}\) \\ [PERSON]’s constant for CO\({}_{2}\) at 25 \({}^{\circ}\)C (mol/(m\({}^{3}\):Pa)) & 3.4\(\cdot 10^{-4}\) \\ \hline Transport-related properties [18; 29] & \\ \hline Molecular diffusion in water \(D_{0}(T)\) (m\({}^{2}\)/s) & \(D_{o}(T)=D_{o}\left(T_{ref}\right)\frac{T}{T_{ref}}\frac{k_{U}^{2}}{T^{2}}\), \(D_{o}\left(T_{ref}\right)=2\cdot 10^{-11},\;T_{ref}=25\;^{\circ}\)C \\ Longitudinal dispersivity (m) & 0.01 \\ Molecular diameter of the gases species (m) & \(10^{-10}\) \\ Vapour diffusivity (m\({}^{2}\)/s) & \(D_{V}=5.9\cdot 10^{-6}\frac{T^{23}}{T_{C}}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Data on hydraulic, thermal, transport related properties of liquid, gas, and bentonite used in the study.