## 2 Super-Sized Pore-Throat Network Generation Method
### Mineral Growth Simulation  
The number of pores, throats, and mineral particles is important. In a given partition, porosity is related to the radius and quantity of pores, throats, and mineral particles. The number of mineral cores needs to be determined before applying the QSGS method \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbol** & **Physical Meaning** \\ \hline core distribution & \(c_{d}\) & The probability that a pixel in the image becomes a mineral core whose value is less than the volume fraction of that kind of mineral theoretically. \\ \hline directional growth & \(D_{i}\) & The probability that a pixel grows in the \(i\)th direction, which controls the shape of the mineral particle. \\ \hline phase volume fraction & \(P^{n}\) & The volume fraction of a kind of mineral. If all the kinds of minerals are considered as one phase its value is equal to the porosity. \\ \hline phase interaction growth probability & \(I_{i}^{n,m}\) & When considering the interaction (repulsion or attraction) between different minerals or phases, the pixel grows in the \(i\)th direction with the probability of \(I_{i}^{n,m}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Symbols and meanings of four parameters in the QSGS algorithm. Consider the random distribution of \(N\) pores in a region of area S, when ignoring the throat area, the following occurs:  
\[S\cdot\phi\ \approx N\pi\overline{R_{p}}^{-2} \tag{1}\]  
where \(S\) is the area of the partition, \(N\) is the number of pores, \(\phi\) is the porosity, and \(\overline{R_{p}}\) is the weighted pore radius. According to a large number of micropore structure analyses of real cores by our CT laboratory, it is found that the pore number of real cores is 1.3 times that of mineral particles. Thus, on the basis of determining the pore number, the number of mineral particles can be further obtained. According to the real micropore characteristics of the core, the pores develop at the junction of mineral particles [30; 31]. The QSGS algorithm is used to simulate the overgrowth of minerals to fill the entire partition and then treats the intersection of mineral particles as a potential pore position, thus obtaining the distribution position of each pore in the region. In order to ensure the independence and integrity of each mineral particle, each particle is treated as a mineral, and the interaction between minerals is ignored to accelerate the model generation speed. The growth flow chart of mineral particles is shown in Figure 3. In order to simulate the heterogeneous characteristics of the reservoir, multiple partitions can be set up. Different zones have different macroscopic and microscopic characteristics, which are manifested by different porosity and microscopic parameters [32]. The simulation generates a 0.25 mm\({}^{2}\) region in which the number of mineral particles is calculated to be 25 according to the ideal model. Figure 2: Eight growth directions of each point in 2D systems and Algorithm flow chart. As shown in Figure 4a, 25 mineral particle cores overgrow and fill the entire region based on the QSGS algorithm. The green boundary lines indicate the positions of the throats. The intersections of the boundary lines, marked in blue in Figure 4b, represent the potential pore positions [33]. Later, each line and each point are numbered by the connected domain analysis algorithm, which helps the program analyze the distribution of the coordination number of each pore. The next step is to calculate the length of each line. When the length of the throat is less than the value \(l\), it is changed into a pore, with the pore equivalent radius \(R_{p}\) and the pore area \(S_{p}\):  
\[S_{p}=\pi{R_{p}}^{2} \tag{2}\]  
When the coordination number is 3, as shown in Figure 5a, there is \(l/R_{p}=2\).