## 4 Discussion
### Influence of Rock Structure on Electrical Properties
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Nb** & **Equation** & **Rock Type** & **Variables** & \(k\) **(mD) Calculated** & \(k\) **(mD) Measured** & **References** \\ \hline \multirow{3}{*}{1} & \multirow{3}{*}{\(k\propto\phi^{n}\)} & chalk & \(n=4\) & 4–22 & 4–40 & \multirow{3}{*}{[15; 16]} \\  & & limestone & \(n=2.5\) & 4–8 & 2–26 & \\  & & dolomite & \(n=2.5\) & 5–16 & & \\ \hline \multirow{3}{*}{2} & \multirow{3}{*}{\(k=(\phi-\phi_{c})^{n}\)} & chalk & \(n=4\); \(\phi_{c}=1\%\) & 3–20 & 4–40 & \multirow{3}{*}{[54]} \\  & & limestone & \(n=4\); \(\phi_{c}<1\%\) & \(<\)1 & & \\  & & dolomite & \(n=4\); \(\phi_{c}<1\%\) & \(<\)1 & & \\ \hline \multirow{3}{*}{3} & \multirow{3}{*}{\(k=\frac{d^{2}}{180}\frac{\phi^{3}}{(1-\phi)^{2}}\)} & chalk & \(d=5\upmu\)m & 3–20 & 4–40 & \multirow{3}{*}{[15; 16]} \\  & & limestone & \(d=20\upmu\)m & 4–10 & 2–26 & \\  & & dolomite & \(d=30\upmu\)m & 15–50 & & \\ \hline \multirow{3}{*}{4} & \multirow{3}{*}{\(k=d^{2}\phi^{n}\)} & chalk & \(d=5\upmu\)m; \(n=6\) & 7–85 & 4–40 & \multirow{3}{*}{[22]} \\  & & limestone & \(d=20\upmu\)m; \(n=5\) & 7–30 & 2–26 & \\  & & dolomite & \(d=30\upmu\)m; \(n=6\) & 3–45 & & \\ \hline \multirow{3}{*}{5} & \multirow{3}{*}{\(k=\frac{1}{32}\phi(\frac{d_{c}}{2})^{2}\)} & chalk & \(d_{c}=3.5\upmu\)m & 30 & 4–40 & \multirow{3}{*}{[24]} \\  & & limestone & \(d_{c}=9\upmu\)m & 80 & 2–26 & \\  & & dolomite & \(d_{c}=11.5\upmu\)m & 170 & & \\ \hline \multirow{3}{*}{6} & \multirow{3}{*}{\(k=\frac{1}{226}\frac{d_{c}^{2}}{F}\)} & chalk & \(d_{c}=3.5\upmu\)m & 4 & 4–40 & \multirow{3}{*}{[23]} \\  & & limestone & \(d_{c}=9\upmu\)m & 3 & 2–26 & \\ \cline{1-1}  & & dolomite & \(d_{c}=11.5\upmu\)m & 8 & & \\ \hline \end{tabular}
\end{table} 
Table 4: Summary of permeability results calculated from literature. equation [23]). Based on results obtained for limestone, dolomite is more likely to have low permeability. Applying these different relationships to our data enable us to take into account the critical pore size \(d_{c}\) with porosity (equation in line 5 from Table 4) [24] but gives overestimated permeability. On one hand, including grains diameter or critical pore size in permeability calculations is relevant. On the other hand, calculated permeabilities using formation factor are more consistent with measured data (Table 1). Consequently, transport properties in carbonate rocks seem to be mainly correlated with the rock structure, in particular the grain diameter. However, adding a fractal dimension seems tricky for carbonate rocks because of the importance of microstructure, at the contrary of sandstones [57] and vesicular rocks [58]. Additionally, the specific surface, which can be compared to the pond surface accessible by the fluid, and by extension to our \(\frac{\hat{S}}{\hat{V}}\)[27], does not seem correlated with porosity and permeability for our data set [27; 59; 60; 61]. These failed correlations support the idea that microstructure plays a very important role. Indeed, \(\frac{\hat{S}}{\hat{V}}\) is calculated from tomography images with a pixel resolution of 12 \(\upmu\)m, which seems too large and inappropriate in transport properties determination.