## 3 Results
### Pore Structure Characterization
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample** & **Discretization,** & **CT Resolution,** & **Total** & **Effective** & **Mean Pore** & **Mean Pore** \\  & **Voxels** & **\(\mathbf{\mathrm{\SIUnitSymbolMicro m}}\)/Voxel** & **Porosity, \%** & **Porosity, \%** & **Radius \(\langle d\rangle\)**, \(\mathbf{\mathrm{\SIUnitSymbolMicro m}}\)** & **Radius \(\langle d^{\prime}\rangle\)**, **Voxel** \\ \hline \hline \multicolumn{6}{c}{Group 2 (select sandstones and carbonates from ICL dataset [37])} \\ \hline
2\_BS (\mathrm{\SIUnitSymbolMicro b}\) & 10003 & 3.00 & 21.6 & 21.6 & 21.13 & 7.04 \\
2\_DS (\mathrm{\SIUnitSymbolMicro c}\) & 10003 & 2.69 & 19.5 & 19.5 & 19.18 & 7.13 \\
2\_EC (\mathrm{\SIUnitSymbolMicro d}\) & 10003 & 3.31 & 10.9 & 10.9 & 19.90 & 6.01 \\
2\_KC (\mathrm{\SIUnitSymbolMicro e}\) & 10003 & 3.00 & 12.3 & 12.3 & 18.02 & 6.00 \\ \hline \hline \multicolumn{6}{c}{Group 3 (tight pore Achimov sandstones [43])} \\ \hline
3\_A & 6003 & 1.2 & 6.5 & 5.8 & 3.15 & 2.63 \\
3\_B & 6003 & 1.2 & 5.3 & 4.4 & 5.05 & 4.2 \\
3\_C & 6003 & 1.2 & 5.8 & 5.3 & 3.75 & 3.13 \\
3\_D & 6003 & 1.2 & 9.9 & 9.7 & 5.3 & 4.42 \\
3\_E & 6003 & 1.2 & 7 & 6.4 & 4.65 & 3.88 \\ \hline \hline \multicolumn{6}{c}{Group 4 (tight pore Achimov sandstones [43])} \\ \hline
4\_A & 14003 & 1.2 & 8.9 & 8.1 & 7.15 & 5.95 \\
4\_B & 14003 & 1.2 & 6.5 & 5.1 & 7.01 & 5.84 \\
4\_D & 14003 & 1.2 & 10.8 & 10.2 & 7.12 & 5.93 \\ \hline \hline \end{tabular}  
* Berea sandstone; \(\mathrm{\SIUnitSymbolMicro b}\) Bentheimer sandstone; \(\mathrm{\SIUnitSymbolMicro c}\) Doddington sandstone; \(\mathrm{\SIUnitSymbolMicro d}\) Estaillades carbonate; \(\mathrm{\SIUnitSymbolMicro e}\) Ketton carbonate.  
\end{table} 
Table 1: _Cont._  
Figure 2: Pore volume distributions for samples of Groups 2 and 3 (**A**) in voxels and (**B**) in \(\mathbf{\mathrm{\SIUnitSymbolMicro m}}\)3. All Achimov sandstones have unimodal pore volume distributions with the mode at 420-900 um\({}^{3}\) (Table A1), which approximately corresponds to an 8 um pore radius. The mode of the pore volume distribution only slightly varies with the overall porosity. The reference samples (group 2) are more diverse. 2_BS and 2_KC samples (Bentheimer sandstone and Ketton carbonate) have a large share of very small pores that have a low influence on overall permeability. At the same time, they have a higher fraction of pores of much high volume compared to Achimov sandstones. The other two samples, 2_EC and 2_DS (also one sandstone and one carbonate), have unimodal pore volume distributions similar to the Achimov sandstones, but the modes are shifted to volumes 2-3 orders of magnitude larger, with the 3_DS sandstone having the largest average pore size. It is peculiar that within groups 2 (we do not of course pretend on any generalization) neither the prevailing mineral nor the overall porosity correlate with the type of pore volume distribution. The pore coordination number \(C_{\text{p}}\) refers to the compartmentalized representation of the pore space obtained with the MISA algorithm and measures the number of pores with which a given pore shares throat voxels [6] (Table A1). \(C_{\text{t}}\) is the pore throat coordination number, which is the number of effective pores connected by each junction connects. Most junctions, of course, only connect two neighboring pores, which basically means a narrowing in the channel through which the fluid flows. Since the ratio between junction diameter and channel diameter is unknown, it is difficult to say how narrows affect flow. The connectivity \(R\) is characterized by the concentration of junctions connecting more than two pores, and can be represented as:  
\[R(C_{t})=\frac{\sum_{i=C_{\text{t}}}^{j}\delta_{ji}}{V_{\text{s}}}\langle V_{ \text{p}}\rangle, \tag{1}\]  
where \(V_{\text{s}}\) is the total volume of the system, \(\langle V_{\text{p}}\rangle\) is the average pore volume, and \(j\) is the index of junction. Such a normalization by a characteristic pore volume makes the concentration independent of spatial resolution.