Pore Scale Modeling of Rock Properties and Comparison to Laboratory Measurements

The microstructure of a porous medium and the physical characteristics of the solid and fluid phases determine the macroscopic transport properties of the medium. The purpose of this paper is to test numerical calculations of the geometrical and transport properties (electrical conductivity, permeability, specific surface area, and surface conductivity) of porous, permeable rocks, given their 3D digital microtomography (μCT) images. We focus on μCT data for a 23.6% porosity sample of Berea Sandstone 500 (BS500) with 2.8 micron resolution. Finite difference methods are used to solve the Laplace and Stokes equations for electrical and hydraulic conductivities. We show that the permeability and formation factor are well correlated using a hydraulic radius computed from the digitized image. Electrical transport in the BS500 sample is complicated by the presence of clays. A three phase conductivity model, which includes the double layer length and counter-ion mobility, is developed to compute interface conductivity ~
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 from the μCT image and measured values of the cation exchange capacity (CEC). Our calculations compare well with the laboratory measurements on cm core samples. Finally, we examine the influence of image size and image resolution on our numerical results. Introduction Understanding the interaction between rock matrix, pore space, and pore fluids at microscopic scale is crucial to better interpretation of macroscopic geophysical measurements. With the development of modern imaging techniques, such as advanced X-ray CT and laser confocal microscopy, direct image of the 3D pore structure of sedimentary rock at micrometer resolution could be obtained. Accurate representation of porous material in digital space makes it possible to compute rock properties according to the physical laws controlling characteristics such as fluid flow and electrical currents (Hazlett, 1995; Coles et al., 1996; Pal et al., 2002). Computational rock physics has become a significant complement to core-derived laboratory measurements and the use of empirical rock physics in the interpretation of logging measurements and resulting reservoir description. Effective characterization of complex rock microstructure at pore scale enables better prediction of physical properties. It reduces the ambiguity of parameters in empirical rock physics models and minimizes the physical and chemical changes of core samples during experimental processes (Klinkenberg, 1941; Amaefule et al., 1986; Li et al., 1995). Advances in computer hardware and computational algorithms make it possible to calculate transport properties on large three dimensional volumes. Increasing the pore space image will reduce the fluctuations of computed properties from small sub-fragments ~
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 and minimize the difference between calculated and measured results. In this study, finite difference (FD) techniques are employed to solve the Laplace equation for electrical conductivity and the Stokes equation for single phase fluid flow (Roberts and Garboczi, 2000). The 3D microstructure is converted into a network of electrical and hydraulic resistors. For the Laplace equation, the boundary conditions (BC) are current and electrical potential normal to the fluid-solid interface are continuous. For the Stokes equation, the boundary condition (BC) is the no-flow condition. In addition to providing the effective value for electrical conductivity and hydraulic permeability, FD techniques could also give the current and flow field distribution at each voxel within the 3D structure. Thus, it is possible to solve multiphysics coupling, such as electrokinetic problems on a microstructure (Pride et al., 1997). Predicting the formation factor of saturated rocks, particularly with high porosity Fontanbleau sandstones, from a binary image has been successful (Arns et al., 2001, 2005; Pal et al., 2002). The most fundamental empirical relation between brine conductivity and brine saturated rock conductivity is Archie’s law (Archie, 1942),