We have studied the electrical transport properties of porous media and the physical meaning of Archie's parameters with 2D lattice gas automata (LGA). On the basis of our simulations, we have developed a set of new equations to calculate fluid saturation from electrical measurements. The calculations from the new equations show very good agreement with laboratory measurements and published data on sandstone samples. There are limitations for this study in applying mesoscale modeling to the resistivity-index/ water-saturation (I/Sw) relationship for porous rocks because only 2D models of sandstone rock were simulated. Some important factors like wettability were not modeled. However, current flow simulations on the 3D digital rock samples of various types reconstructed from thin sections and high-resolution CT scans of real rocks have been ongoing in our laboratory as the next step to address these issues.
Archie's (1942) equations (F = aF-m and I = bSw-n, where a, b, m, and n are constants and called Archie parameters) have been the fundamental equations used to calculate fluid saturation of porous rocks from electrical well logs. There have long been questions and arguments about the true physical meaning of the Archie parameters because the micropore structure, the flow of fluid, and the electrical current in a porous medium cannot be directly observed and controlled in laboratory measurements. In oilfield electrical-logging-data interpretation, non-Archie behavior of the porous rocks (i.e., the I/Sw relationship not being linear on a log-log scale) has been increasingly observed and reported by log analysts and petroleum engineers (Diederix 1982).
Diederix (1982), Li (1989), Worthington and Pallatt (1992), and Jing et al. (1993), among others, have studied this so-called "non-Archie phenomenon" of porous rocks extensively. The non-Archie phenomenon generally becomes more evident as the water saturation decreases further. However, because of the limitations of macroscale laboratory experiments, it is not possible to quantify the factors that influence the I/Sw relation. Many researchers have tried to simulate the behavior numerically at the pore scale. Schopper (1966) used a resistor network to study the formation factor/porosity relationship. Yale (1984) developed a 3D pore-network model to simulate the transport properties of porous rocks. Tao et al. (1995) used Yale's model to interpret electrical-conductivity and elastic-wave data simultaneously measured on fluid-saturated sandstone samples. Man and Jing (2001) further developed Yale's model to account for the electrical transport properties of multiphase-fluid-saturated porous media. Jonas et al. (2000) used a statistical network to study the physical basis of Archie's first equation. However, because these models do not simulate closely enough the real pore structures and fluid distributions, the theoretical modeling has achieved only limited success.