## 3 Results  
### Pore Structure Characterization  
The porosity of the samples is estimated as the fraction of the void space in the sample map. More important is the effective porosity that only accounts for the open pores' space (all isolated voids are excluded). Both quantities are shown in Table 1. The samples from group 1 are the most porous, and the Achimov samples from groups 3 and 4 are the least porous among the sandstones considered here: for example, sample 1_LV60A is 8.5 times more porous than sample 3_B. Carbonates from the ICL database (group 2) are also relatively low in porosity compared to other samples from groups 1 and 2, but still more porous than the Achimov sandstones (groups 3, 4). We also estimate the mean pore size from PSD, calculated using the machine learning framework [53]. The mean pore radius ranges from 5 to 9 voxels, which is sufficient for performing the simulations [52]. As mentioned, the samples from group 1 are the most porous, and their digital maps are the smallest. The pore morphologies of wide pore sandstones were extensively studied by [PERSON] et al. [54]. For these reasons, we do not discuss the pore characteristics of this group here. For finer discretized maps of the samples from groups 2, 3 and 4, we calculate pore volume distributions and characterize the pore connectivity and pore network tortuosity. Using the Euclidean distance transform (EDT) [55], for each pore voxel, the largest sphere non-overlapping with the walls is found. Each pore space voxel is assigned the radius of the maximum inscribed sphere (MISA). The field contains as many maximum spheres as the binary image contains pore space voxels. Clearly, some void voxels would be part of multiple spheres. The set of maximum spheres has to be reduced to a subset of containing spheres by searching for each void voxel for the largest sphere in which this voxel was contained. This implies that the spheres contained within a larger sphere are eliminated. This method enables the dissection of a continuous pore space to an integer number of effective pores and thus calculates the pore volume distribution (PVD), as well as characterizes the connectivity and tortuosity. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **Discretization,** & **CT Resolution,** & **Total** & **Effective** & **Mean Pore** & **Mean Pore** \\  & **Voxels** & **\(\mu\)m/Voxel** & **Porosity, \%** & **Porosity, \%** & **Radius \(\langle d\rangle\), \(\mu\)m** & **Radius \(\langle d^{\prime}\rangle\), Voxel** \\ \hline \hline \multicolumn{8}{c}{Group \(1\) (sandstones from ICL database [37])} \\ \hline
1\_BS (\({}^{\text{a}}\)) & 400\({}^{\text{3}}\) & 5.345 & 19.6 & 19.6 & 31.67 & 5.92 \\
1\_LV60A & 450\({}^{\text{3}}\) & 10.0 & 37.7 & 37.7 & 62.074 & 6.21 \\
1\_S1 & 300\({}^{\text{3}}\) & 8.683 & 14.1 & 14.1 & 52.96 & 6.09 \\
1\_S2 & 300\({}^{\text{3}}\) & 4.956 & 24.6 & 24.6 & 31.59 & 6.37 \\
1\_S9 & 300\({}^{\text{3}}\) & 3.398 & 22.2 & 22.2 & 24.42 & 7.18 \\
1\_C1 & 400\({}^{\text{3}}\) & 2.85 & 23.3 & 23.3 & 17.47 & 5.14 \\
1\_A1 & 300\({}^{\text{3}}\) & 3.85 & 42.9 & 42.9 & 24.658 & 6.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Samples used in the present study: discretization, resolutions and porosity. Figure 2 shows the pore volume distribution obtained from the MISA analysis. There is a visible difference between the pore structure of the reference sandstones and carbonates from the ICL database (group 2) and the Achimov sandstones (groups 3 and 4).