Pore connectivity, electrical conductivity, and partial water saturation: Network simulations

The electrical conductivity of brine-saturated rock is predominantly dependent on the geometry and topology of the pore space. When a resistive second phase (e.g., air in the vadose zone and oil/gas in hydrocarbon reservoirs) displaces the brine, the geometry and topology of the pore space occupied by the electrically conductive phase are changed. We investigated the effect of these changes on the electrical conductivity of rock partially saturated with brine. We simulated drainage and imbibition as invasion and bond percolation processes, respectively, in pipe networks assumed to be perfectly water-wet. The simulations included the formation of a water film in the pipes invaded by the nonwetting fluid. During simulated drainage/imbibition, we measured the changes in resistivity index as well as a number of relevant microstructural parameters describing the portion of the pore space saturated with water. Except Euler topological number, all quantities considered here showed a significant level of universality, i.e., insensitivity to the type of lattice used (simple cubic, body-centered cubic, or face-centered cubic). Hence, the coordination number of the pore network appears to be a more effective measure of connectivity than Euler number. In general, the simulated resistivity index did not obey Archie's simple power law. In log-log scale, the resistivity index curves displayed a substantial downward or upward curvature depending on the presence or absence of a water film. Our network simulations compared relatively well with experimental data sets, which were obtained using experimental conditions and procedures consistent with the simulations. Finally, we verified that the connectivity/heterogeneity model proposed by Bernabe et al. (2011) could be extended to the partial brine saturation case when water films were not present.