Effective Conductivity Modeling of a Fluid Saturated Porous Rock

The microstructure of a porous medium and physical characteristics of the solid and the fluids that occupy the pore space determine the macroscopic transport properties of the medium. The computation of macroscopic properties from the rock microtomography is becoming an increasingly studied topic. The transport properties are especially difficult to determine at the microscopic scale. In this paper, we will focus on modeling the electric conductivity from the X-ray CT microtomograhpy of a 1mm 3 Fontainbleau Sandstone sample. To accomplish this, we modified the finite difference Laplace solver developed at NIST (National Institute of Standards and Technology, Gaithersburg, MD 20899-8621, U.S.A). Our modified finite difference code can calculate the effective conductivity of random materials with different levels of conductivity contrasts. The effective conductivity and the current density distribution of gas, oil and different salinity brine saturated Fontainbleau Sandstone are calculated using a two-phase model. When we compare our numerical results with experimental results from previous studies, the numerically resolved conductivity is almost 100% lower than the experimental data. This is the case for all of the previous work on the numerical computation of electric conductivity from digital images of rocks. Our explanation for this large discrepancy is due to the exclusion of the surface conductivity in the electric double layer (EDL) at the rock-electrolyte interface. Thus, we develop a three phase conductivity model to include the surface conductivity and determine the effective conductivity of the numerical grids containing the EDL from the Waxman-Smits equation. By adding the surface conductivity into our numerical modeling, the calculated conductivity from rock microtomography is much closer to the experimental data.