Pore-Scale Analysis of the Waxman-Smits Shaly-Sand Conductivity Model

摘要

Waxman-Smits and dual-water models of electrical conductivity of shaly sands account for the dual conductive pathways formed by pore brine and clay mineral exchange cations, while Archie's equations describe the electrical conductivity behavior of clay-free rocks. These empirical models are widely used in the interpretation of resistivity logs acquired in homogeneous reservoir rocks. However, the models are not explicit in their predictions of electrical conductivity with respect to rock structure, spatial fluid distribution in the pore space, wettability, or clay mineral distribution. The objective of this paper is to quantify the influence of exchange cations associated with hydrated clay minerals, salinity of pore bulk water, and water saturation on the electrical conductivity of shaly siliciclastic rocks. We accomplish this objective by calculating excess conductivities associated with hydrated clay minerals for explicit pore geometries of brine- and hydrocarbon-saturated shaly granular rocks. In so doing we introduce synthetic pore-scale representations intended to reproduce experimental observations of electrical conductivity of shaly sands.The synthetic pore-scale models are constructed to represent homogeneous shaly sands that include the structural effects of compaction, cementation, and distribution of grain-coating clay minerals. Our pore-scale model is implemented on the digitized representative of rock samples, which allows us to consider arbitrary media boundaries. Two-phase immiscible fluids are geometrically distributed in the pore space using the ordinary percolation algorithm. We introduce grain-coating hydrated clay minerals and their corresponding electric double layer in the synthetic rock models with a grain "shell" of variable dimensions and diffusivity with respect to those of pore-filling brine. Waxman-Smits formation factors and resistivity indices are calculated directly with random walk simulations of late-time diffusion within the conductive space formed by the pore water and clay mineral exchange cations in the digitized shaly-sand samples. Simulations with this simple model correctly reproduce the nonlinear behavior of rock conductivity at low and high salinity, and are consistent with reported laboratory measurements.