In-situ fluid saturations are conventionally determined from resistivity measurements using Archie?s power-laws with default exponents. However, rock-core measurements have consistently shown that the saturation exponent n can vary drastically depending on water saturation, wettability and rock morphology. Such an abnormal, non-Archie behavior, frequently takes place in rocks exhibiting oil wettability or irregular pore morphology. These last two factors may cause opposite effects on the electrical resistivity of rocks and hence their interplay remains difficult to understand and/or predict using standard pore-scale petrophysical models of electrical conduction. This paper introduces and validates a new pore-scale approach for the simulation of DC electrical resistivity measurements. The approach explicitly incorporates specific two-phase fluid distributions that are consistent with capillary pressure, saturation history, and percolation principles. Moreover, the simulation methodology properly reproduces pore-level fluid wettability, complex rock structure, and presence of conductive clay. We make use of a dynamic random-walk diffusion technique to simulate DC resistivity measurements via statistical averages of long-time diffusivity asymptotes. This strategy readily lends itself to accurately simulate the effects of explicit geometrical distributions of wetting films, pendular rings and snap-offs on DC resistivity measurements. We reproduce sequential drainage/imbibition cycles and their corresponding resistivity-index cycles for both water-wet and oil-wet generic clean rocks. To our knowledge, this has not been achieved by any previously published pore-scale simulation method. The simulation methodology introduced in this paper can therefore be used as a tool to assess the influence of wettability and saturation history for specific conditions of grain size distributions. Classical values of n within specific ranges (less than 2, about 2, about 3, and larger are all justified making use of wettability arguments. Non-constant values of n through the complete saturation range can therefore be explained and even predicted for simple rocks when given their saturation history; conversely, their saturation history can be inferred from simulations of resistivity index performed with similar models.

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