3. EXPERIMENTAL RESULT
3.1 Influences of injection location
The result of measurement on sample A, sample B, and sample C are displayed in Figure 3 as plots of log electrical resistivity (\(\rho_r\)) versus brine saturation (Sw). Figure 3a shows data from sample Ax and Ay; Figure 3b from Sample Bx and By; Figure 3c from Sample Cx and Cy. In the three sample categories, log \(\rho_r\) dependency on Sw is quite similar. The resistivity of the samples that are injected with brine from the bottom position is always higher than the samples that are injected from the middle position until it reaches a certain point. We defined this point as critical brine saturation \(S_{w^{ }}^o\) in which for sample A and sample C, critical brine saturation is approximately at \(S_w^{o_{ }}\)= 0.70; for sample B, the critical brine saturation is about \(S_w^o\) = 0.6. Beyond this critical brine saturation, the resistivity of the three sample categories is relatively the same up to the full saturation state. Based on these results, the three regions can be defined in the data as follows: region 1, at low brine saturation; region 2, at intermediate brine saturation; region 3, at the highest brine saturation. Regions 1 and 2 are prior to the critical brine saturation, while region 3 is beyond the critical brine saturation up to the fully saturated state.
In region 1, the electrical resistivity decreases with increasing brine saturation for the three data sets. There are differences in the pattern of the decrease in the resistivity between each sample that are injected brine from the bottom position which will be further referred as samples X (Ax, Bx, and Cx) and the samples that are injected brine from the bottom position which will be further referred as samples Y (Ay, By, and Cy). In this region, the resistivity of samples X is slowly decreasing, on the other hand, the resistivity of samples Y decreases rapidly. In region 2, the opposite condition occurs where the resistivity of samples X decreases dramatically by approximately two orders of magnitude, while the resistivity of samples Y decreases monotonously. Region 3 is initiated with a critical brine saturation until the state of full saturation: sample A in the range Sw = 0.78-1.00; sample B in the range Sw = 0.59-1.00; sample C in the range Sw = 0.73-1.00. In this region, the change of resistivity of all samples is considered insignificant, compared to other regions.
3.2 Influence of grain size
In this study, we also plotted log electrical resistivity ( \(\rho_r\) ) versus brine saturation (Sw) as a function of grain size, as displayed in Figure 4. Figures 4a and 4b are the data obtained from the samples that are injected with brine from the bottom position (Samples X) and middle positions (Samples Y) respectively. The results show that Sample X and Y have different ρ vs Sw pattern. For Samples X (Figure 4a), we can define three regions in the data to explain the relationship between resistivity vs brine saturation. In the region 1 (at low saturations, Sw = 0-0.4), the electrical resistivity decreases gradually. In the region 2 (at intermediate saturation, Sw = 0.4-0.8), the resistivity decreases rapidly approximately in three orders of magnitude. In the region 3, at higher saturation, the resistivity tends not to change, even almost constant. For Samples Y (Figure 4b), the resistivity decreases significantly up to saturation of 0.8. Afterwards, the resistivity changes gradually until the state of full saturation for all samples. For both Samples X and Samples Y, the critical brine saturation occurs at approximately saturation of 0.8. While the log \(\rho_r\) vs Sw pattern of the two sample categories is unique, there are similarities between the two sample categories. In region before the critical brine saturation, the resistivity of samples with larger grain size is always higher than that of with the smaller grain size.
3.3 Physical properties of sample from digital images
The results of the three samples scanning can be seen in Figure 5. Based on the digital images, it can be seen that Sample A has the largest grain size compared to Sample B and Sample C. The grain size of Sample B seems to be slightly larger than the grain size of Sample C, although no significant difference can be seen. Estimation of porosity through digital images and measurement showed good agreement, as shown in Table 4.
Beside calculating the bulk porosity, 2D porosity analysis was also performed on each vertical slice of the image. 2D porosity calculation results show that the samples are quite homogeneous (see Figure 6b). Thus, the injected brine is assumed to have the same behaviour in all pores of the sample. In addition, the pore size distribution of the samples was also analysed (see Fig. 6a). The pore size distribution which was calculated is both the connected and isolated pores. However, the isolated pores are most unlikely exist due to the fact that the sample is constructed from unconsolidated sand. In Sample A, the pore size is quite large, as the consequences of large grain sizes. As for Sample B and C, the pore size distribution is quite similar, although for Sample B it is slightly larger than Sample C. Pore size distribution shows a similar tendency, where the peak is higher for the smaller grain size.
The result from digital image analysis of the scanned samples is summarized in Table 4. The specific surface area S is defined as the ratio between the surface area of the grains to the total total volume of the sample. Specific surfaces area is used to calculate the permeability which obtained through the Kozeny-Carman equation, as shown in the equation (3) (Mavko, Murkeji and Dvorkin 2009)