PORE-SCALE ANALYSIS OF THE WAXMAN-SMITS SHALY SAND CONDUCTIVITY MODEL

摘要

Waxman-Smits and dual-water models of electrical conductivity in 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 shalefree rocks. These empirical models have enjoyed great success in the interpretation of electric-log responses of 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. This paper quantifies the influence of petrophysical, textural, and fluid factors on the electrical conductivity of shaly siliciclastic rocks by calculating excess conductivities associated with clay minerals for explicit pore geometries of brine- and hydrocarbon-saturated shaly granular rocks. We construct synthetic pore-scale models to represent homogeneous shaly sands that include the structural effects of compaction, cementation, and distribution of dispersed clay minerals. Exchange cations associated with these clay mineral distributions in the pore space are assigned effective conductivities which vary with brine salinity. Two-phase immiscible fluids are also geometrically distributed in the pore space consistent with capillary pressure and drainage cycles. Waxman- Smits Formation Factors and Resistivity Indices are calculated from the late-time diffusion asymptotes of random walks enforced within the conductive space formed by the pore water and clay mineral exchange cations. The fully explicit pore-scale geometrical approach developed in this paper allows one to calculate accurate rock conductivity as function of amount and spatial distribution of clay minerals and their exchange cations, fluid saturation, and brine salinity for the homogeneous shaly sand case. We show that significant changes in excess electrical conductivity can be observed with realistic perturbations of water saturation, salinity, and clay mineral distribution.