Influence of wettability on phase connectivity and electrical resistivity

Experimental results have shown that resistivity index can deviate from Archie's law at low conductive phase saturation. Previous works have claimed that wettability and flow history are the two main factors causing this phenomenon. Herein, we investigate how the underlying fluid morphology influences electrical resistivity. We start from digital synchrotron x-ray microcomputed tomography images at different conductive phase saturations. We then simulate two-phase flow at different Capillary numbers and wettabilities to investigate deviations in resistivity index. We discover that other than water saturation the connectivity of water quantified by Euler characteristic is an important parameter in determining electrical resistivity for intermediate to purely oil-wet conditions. Deviations in electrical resistivity are found to start at low Capillary number ($\mathrm{Ca}\sim {10}^{-5}$) for intermediate and oil-wet conditions for the full range of water saturations. We study correlations between resistivity index, saturation, and Euler characteristic by using the Pearson product-moment correlation and a linear regression model. We find a strong correlation between water saturation and resistivity index for the water-wet case while for the intermediate and oil-wet cases a strong correlation between Euler characteristic and resistivity index was observed. The results are explained in terms of percolation theory and a general relationship for resistivity index is proposed for intermediate-wet to oil-wet systems whereby the percolation parameter is normalized Euler characteristic. The findings explain previously observed deviations in resistivity index measurements and allow for a means to predict Euler characteristic from laboratory core-scale experiments using the proposed percolation model.

Figure 1

Resistivity model of a core with different fluid arrangements, blue is the conductive phase (brine) and yellow is the non-conductive phase (oil).

Figure 2

(a) A 3D rendering of pore space from a $200\times 200\times 200$ subset of Robuglass, (b) the conductive phase at $\text{Ca}=3.1\times {10}^{-6}$ for the 100% oil-wet condition and (c) the conductive phase at $\text{Ca}=1.1\times {10}^0$ for the 100% oil-wet condition. Fluid connectivity changes with Ca as seen with red and green circles in (b) and (c).

Figure 3

$R_i-S_w$ curve: data points of different size and color correspond to different Ca at (a) 100% water-wet condition, (b) 100% oil-wet condition, (c) 50% water-wet condition, and (d) 50% oil-wet condition. The dashed line is the power-law fit of function $R_i=S_w^n$.

Figure 4

$R_i-{\chi }_w/{\chi }_p$ curve: data points of different size and color correspond to different Ca at (a) 100% water-wet condition, (b) 100% oil-wet condition, (c) 50% water-wet condition, and (d) 50% oil-wet condition. The dashed line is the power-law fit of function $R_i=a{({\chi }_w/{\chi }_p)}^b$, where $a$ is a proportionality constant and $b$ is the scaling exponent.

Figure 5

Comparison between fully saturated and partially saturated porous system. (a) 2D simplified model (solid phase consists of four grains) of fully water saturated porous media at 100% water-wet condition, (b) 2D simplified model of partially saturated porous media (oil trapped in four grains) at 100% water-wet condition, (c) 3D rendering of fully water saturated Robuglass, ${\chi }_w={\chi }_p=-257$, (d) 3D rendering of partially water saturated Robuglass, ${\chi }_w=-1283$. 3D image size is ${200}^3$.