# Estimation of Sedimentary Rock Porosity Using a Digital Image Analysis
## 3 Results and Discussion
### Mercury Intrusion Porosimetry (MIP)  
The results of the MIP tests (Figure 4a) provide the reference data of the porosity and pore size diameter (PSD) for each tested rock. As the specimens were of irregular shapes, the surface features such as cracks created by the tensile fracture might have an impact on the mercury intrusion data at the low pressures applied, known as 'consistency' errors [37]. To account for this inconsistency, the comparisons between the initial mass and the mass sent back in the MIP experiments were made to identify the surface voids. The original data were then re-plotted in Figure 4b to represent the corrected pore size distributions of each rock. It is evident from Figure 4b that the MIP curves of siltstone and sandstone are similar, with the pore distribution being in the range of 1000 nm and 50,000 nm. In contrast, the pore size diameter of the coal specimen varied from 3 nm to 10,000 nm. In the MIP test, the values of the surface tension of mercury (\(\gamma\)) and the contact angle of mercury (\(\theta\)) were constant factors. For this reason, Equation (1) can be converted into a linear equation that relates the pressure (\(P\)) with the pore size, as given in Equation (6):  
\[P=-4\gamma cos\theta/d \tag{6}\]  
Figure 3: TGA tests results of specimens: (**a**) sandstone, (**b**) siltstone and (**c**) coal. Figure 5 depicts the pore volume in 1 g of material for each pressure level and pore size. The PSD curves provide the data on the peaks and distribution of voids. It appears that the sandstone and siltstone exhibit differences in the pore size in the region of large pores (>100,000 nm), but only minor changes in the range of relatively smaller pores. For the coal specimen, a more uniform distribution of voids was observed, as shown in Figure 5. To better understand the pore distribution in the specimens, the original data were replotted in Figure 6, with the focus on the larger pore sizes, and in Figure 7, where the distribution of the smaller-sized pores was analysed. Figure 4 shows that the sandstone and siltstone have similar distribution patterns, while the data obtained for the coal specimen have the largest correction due to the effect of surface fractures and voids. The highest point in the curve is known as the most probable pore size [43], which correlates to the pore sizes that have the greatest mercury intrusion. The original data for the sandstone siltstone and coal had the same value of 700 microns as the most probable pore size. However, the modified data showed that the actual most probable pore size of the sample was smaller than the original data; that is, about 500 microns for the sandstone and siltstone, and 3 nm for the coal specimen. This difference can be attributed to two major factors: (1) the consistency errors, and (2) the presence of a certain amount of voids smaller than 3 nm in the coal specimen. Figure 7a shows that no change in the pore size diameter for the sandstone was observed at 6000 nm, while for the siltstone, this occurred at approximately 15 nm (Figure 7b). Figure 4: Results from MIP tests for sandstone, siltstone, and coal: (**a**) original data; and (**b**) data corrected to the consistency errors. Three types of sedimentary samples were examined in this study using high-pressure mercury intrusion porosimetry (MIP). The two different advanced mathematical forms of MIP data presentation, differential pore volume versus diameter (_DV/Dd_), and the log differential pore volume versus diameter (_DV/Dlogd_) were used to analyse pore size distribution. The findings of the comparison revealed a difference in the range of pore size diameter. For example, smaller pore ranges would be encouraged by the _DV/Dd_ curve, but greater pore ranges would be encouraged by the _DV/Dlogd_ curve. Additionally, the _DV/Dlogd_ approach is appropriate for all specimens, and the _DV/Dd_ approach is only appropriate for the coal specimen.