A percolation study of wettability effect on the electrical properties of reservoir rocks

Measurements of the electrical resistivity of oil reservoirs are commonly used to estimate other properties of reservoirs, such as porosity and hydrocarbon reserves. However, the interpretation of the measurements is based on empirical correlations, because the underlying mechanisms that control the electrical properties of oil bearing rocks have not been well understood. In this paper, we employ percolation concepts to investigate the effect of wettability on the electrical conductivity of a reservoir formation. A three-dimensional simple cubic network is used to represent an ideal reservoir formation, for which the effect of the wettability can be isolated from the others. The phase distribution in the network is analyzed for different flow processes, and the conductivity is then estimated using a power law approximation of the percolation quantities. The proposed conceptual model predicts the generic behavior of reservoir resistivities of different wettabilities. It demonstrates that the resistivity index depends on saturation history and wettability. For strongly oil-wet systems, significant hysteresis is expected, while there is little hysteresis for strongly water-wet systems, and some hysteresis is also expected for intermediate wet systems. One of the interesting results from this study is that for intermediate wet systems, Archie's saturation exponent is between 1.9 and 3.0.