## 4 Microstructural Analysis
### Pore Scale Network Model  
The pore network plays a vital role in determining the permeability and the storage capacity of rock masses. As trailblazing work, [PERSON] [27] proposed the modeling of porous media using a network of tubes when deriving capillary pressure curves. Based upon this concept, two different methods were proposed by researchers to model the network of pores in porous media. In the first method, 3D images of porous media are obtained from process-based reconstructions and X-ray microtomography. Then the complete pore network representations are extracted from the 3D images. It is applied to the study of  
Figure 8: Representative elementary volumes (REV) that are chosen for each test sample. Figure 9: The 3D reconstructed model of REV2 of sample A and the extraction of pore network and solid. (**a**) Total. (**b**) Pore network. (**c**) Solid. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Rock Sample**} & \multicolumn{4}{c}{**Carbonate**} & \multicolumn{4}{c}{**Sandstone**} \\ \cline{2-7}  & **A** & **B** & **C** & **D** & **E** & **S** \\ \hline Porosity of REV1 (\%) & 19.91 & 4.86 & 18.16 & 7.30 & 12.01 & 0.43 \\ Porosity of REV2 (\%) & 23.99 & 8.58 & 7.59 & 5.85 & 6.73 & 0.83 \\ Porosity of REV3 (\%) & 28.48 & 5.13 & 10.30 & 6.63 & 4.36 & 2.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Porosity of REVs. both sandstones and carbonates [28]. The second method is a process-based method for reconstructing the full three-dimensional microstructure of sandstones, which includes the network of pores. It utilizes petrographical information obtained from two-dimensional thin sections to stochastically model sandstone forming processes--sedimentation, compaction, and diagenesis. It was shown that the process-based reconstruction was able to reproduce adequately accurate properties of the sandstone [29]. However, the sedimentary process of carbonate rocks can be too complicated for the process-based method. Therefore, the network of pores in carbonate rocks need to be extracted from 3D images, for which algorithms that extract simplified networks of pores and throats with parametrized geometry and interconnectivity are indispensable. Among the algorithms that extract topology from 3D images of porous media, the maximum ball algorithm is the most widely used one. Being initially proposed by [PERSON] et al. [30; 31], the maximum ball method produces a stick-and-ball diagram of the pore network. The balls and sticks are used to represent the \"pore bodies\" and \"pore throats\", through which their respective volumes and connectivity are established. The balls and the sticks thus indicate the porosity and the permeability of the porous media. Using the concept of maximal balls, [PERSON] and [PERSON] [32] extended the pore network extraction algorithm of [PERSON] et al. [30] by replacing the original master-slave hierarchy of maximal balls by a refined master-slave-cluster hierarchy. Their model was successfully tested on sandstone and carbonate samples. However, their proposed algorithm precluded the extraction of large networks using standard computer resources. [PERSON] and [PERSON] [33] proposed a modified maximal ball algorithm, extending the work of [PERSON] et al. [30; 31], to extract simplified networks of pores and throats with parametrized geometry and interconnectivity. The parameters of the pore networks, including the coordination number, the pore and throat size distributions were computed and compared to benchmark data derived from other methods as well as the experimental data. Good agreement was observed in most cases allowing pore networks derived from a wide variety of rock types to be used for predictive modeling. In the following, the major aspects of [PERSON] and [PERSON]'s [33] maximum ball algorithm are revisited.