In Figure 3, the resistivity of samples Y is always lower than that of samples X. The results indicate that there are areas in between the two potential electrodes that significantly reduce the resistivity. To confirm this, we present the measurement results on sample C at sat 1 (see Table 3), with direct measurements right after the brine injection. Figure 7 shows the change of resistivity over time for Sample C, on the first brine injection (sat1). In the initial measurements, assuming the fluid is right at the injection site, it shows a noticeable difference that the brine in the area of two potential electrodes significantly decreases the electrical resistivity.
To strengthen this hypothesis, measurements were taken on three samples that were horizontally positioned. All the three samples were injected with 10 ml brine in three different positions: on the left side of the sample; on the middle of the sample; and on the right side of the sample. Resistivity measurements were made just after the brine injection, assuming the brine is still right at the injection site. Figure 8 shows the results of from the measurement of the three samples in a dry and partially saturated state. In the dry condition, all the three samples have the same resistivity, but just after the brine injection, the resistivity of the middle sample drops intensely, while for the left and the right samples, the resistivity only decrease slightly and both the left and the right-side samples have almost equal resistivity.
The result strongly suggests that the area between the two potential electrodes is the area which significantly contributes for reducing electrical resistivity. Consequently, in the measurement of the resistivity, the samples that were injected with brine from the middle is always lower than that of injected with brine from bottom. This behaviour only applies up to the critical brine saturation, the area beyond the critical brine saturation, the resistivity tends to be relatively the same for all samples, both the ones that are injected from the middle and the bottom.
Referring to Figure 3, if it is assumed that the injected brine occupies uniformly into the pores of the samples, it can be predicted that the critical brine saturation occurs when the distribution of the brine has passed through the area above the potential electrode (see Figure 9). Based on this analysis, we can say that after passing through the area above the upper potential electrode (P2), the critical brine saturation occurs, where the potential will change gradually, and the resistivity tends to be the same between the samples that injected with brine from the middle and bottom positions. This explains the trend in the ρ vs Sw for all sample X (see Figure 4a). In region 1, the brine is still below the potential electrode (P1), characterized by the monotonically decreased in resistivity. For region 2, the brine has entered the area between the two potential electrodes (P1 & P2), which is the area which significantly contributes for reducing the resistivity. It can be seen that the slope of the graph in region two is steep. In region 3, the brine has passed the upper potential electrode (P2), thus the resistivity changes gradually. See Figure 9 for an illustration of the brine state for each region of plot in Figure 4a.
4.2 Influence of grain size
One of the objectives of this study is to investigate the effect of grain size to the resistivity of partially saturated samples. Figure 4 shows \(\rho_r\) vs Sw for three different grain sizes, where the resistivity of the samples with smaller grains is always lower than samples with larger grains in the area before the critical brine saturation. The difference in pore structure in the sample that must be considered in assessing changes in the resistivity of the samples. The physical properties of the samples which are listed in Table 1 and Table 4 are important for analysing the samples’ structure. One of the prominent physical properties between samples A, B, and C is the permeability, where the samples that have the largest grain size have the highest permeability. Note that permeability is the ability of the medium to allow fluid to pass through the medium. Thus, referring to Table 4, the injected brine in sample A has the tendency of flowing more easily compared to the other samples.
A notable observation in samples Y at saturation of 0.2 is the fact that in sample Ay, the brine (marked in green) tends to flow immediately and settles in the lower area until a particular time. In contrast, to sample Cy, which has a low permeability, brine tends not to flow and settles right at the injection site. As for Sample By, the permeability is not as large as Sample Ay and also not smaller than Sample Cy, the brine partly flows towards the bottom of the sample and partly holds it right at the injection site (see figure 10).
This phenomenon where the fluid has the tendency of settling in a certain part of the sample, can also be explained by surface tension, which can be calculated by the Wilhelmy equation (Abe, Takiguchi and Tamada 2000)