## 2 Samples and Methods
### Sample Classification  
To determine the pore structures of these sandstones and classify them by their permeability, all the sandstone samples were transported to a laboratory without disturbance and processed to undergo the four types of laboratory tests before the formal seepage experiment.  
1. The first type of test was to obtain the porosity and permeability with STY-2 gas permeability and porosity meters. Standard plunger rock samples with a diameter of 25.4 mm and heights of 25.4-50.8 mm were made by nondestructive wire cutting for porosity and permeability tests (see Figure 2).
2. The second type of test was used to test the pore throat size of the sandstone with a MAP 9500 mercury porosimeter. Samples with heights of 7.0-12.0 mm and a diameter of 25.4 mm were prepared for mercury injection testing (see Figure 2).
3. The third type of test was used to observe the composition and texture of grains and pore structure of sandstone by a Zeiss Imaging 2 M polarizing microscope and Nova Nano SEM450. Casting thin slices were used for polarizing microscope observation, and samples with a height of 6.0 mm and diameter of 4.0 mm were used for SEM observation (see Figure 2).  
* The fourth type of test was used to analyze the sandstone grain size with a Mastersizer 3000 E laser grain size analyzer. The samples were processed by crushing, grinding, removing cement with hydrochloric acid and drying before grain size analysis (see Figure 2).  
Figure 1: A general overview of the flow of this study.  
Based on the four recognized indicators that can reflect pore permeability, namely permeability, porosity, average pore throat radius and sorting coefficient, k-means clustering analysis was conducted for all samples. The results showed that the sandstone samples could be divided into four subcategories (I\({}_{1}\), I\({}_{2}\), II\({}_{1}\) and II\({}_{2}\)), which belonged to two categories (I and II), as shown in Table 2. The characteristics of the four subcategories of sandstone in terms of the optical microscope, SEM and MICP test results are shown in Figures 3-5, respectively.  
Figure 3: Comparisons of pores, throats and connectivities among the four subcategories of sandstone in casting thin slices under a polarizing microscope. (Note that the deep blue colors are mostly intergranular pores; the light blue colors are mostly intragranular pores and micropores).  
Figure 4: Comparison of pores, throats and connectivities among the four subcategories of sandstone under SEM. (Note that the images (**a–d**) in Figure 4 correspond to the images (**a–c**) and (**d**) in Figure 3, respectively).  
Figure 5: _Cont_.  
Figure 5: Comparison of the capillary pressure curves of four subcategories showing the differences in the pores, throats and their permeability contributions among the four subcategories of sandstone: (**a**) subcategory **I1** sandstone showed a lower left distribution, well-sorted pore throats, coarse throat peaks at 4 to 6 \(\upmu\)m, and a higher peak, and nearly all of the pore throats contributed to the permeability; (**b**) subcategory **I2** sandstone showed a slight lower left distribution, well-to-moderately sorted pore throats, coarse throat peaks at 1.6 to 4 \(\upmu\)m, and a high peak, and most of the pore throats contributed to the permeability; (**c**) subcategory **II1** sandstone showed a slight upper right distribution, moderately to poorly sorted pore throats, coarse throat peaks at 1 to 1.6 \(\upmu\)m, and a moderate to low peak, and approximately half of the pore throats contributed to the permeability, but with large differences; (**d**) subcategory **II2** sandstone showed an upper right distribution, poorly sorted pore throats, coarse throat peaks at 0.0063-0.1 \(\upmu\)m, and a lower peak, and minute amounts of pore throats contributed to the permeability.