Permeability and electrical conductivity of porous media from 3D stochastic replicas of the microstructure

In this paper we report on the application of low-order statistical information (porosity, two-point correlation function), obtained from 2D micrographs of real porous media, to derive stochastic replicas of their 3D pore networks. The main focus is on assessing the usefulness of stochastic reconstruction as a means of relating macroscopic transport coefficients (intrinsic permeability and effective electrical conductivity) to the geometry and topology of the pore space. To this end we employ newly developed algorithms, based on morphological skeletonization, to obtain a comprehensive geometric and topological description of each simulated pore network. Using the skeleton or graph of the pore space as a basis, detailed geometrical measurements are performed to estimate the effective hydraulic and electrical conductance of individual flow paths, identified with skeleton links. In combination with exact knowledge of the network topology, these measurements enable the specification of equivalent resistor-type network models for the calculation of intrinsic permeability and formation factor. Consistently successful predictions of permeability over a wide range of values are obtained for five reservoir rock samples of diverse origin and lithology. Predictions of formation factor are within a factor of three of the experimental values. These predictions are, however, inconsistent, a fact attributed to the inability of the reconstruction method to accurately reflect the contributions of smaller pores and throats to electrical conductivity. Additionally, it is shown that the hydraulic conductance of pore space channels in stochastically simulated pore networks is spatially correlated over distances equal to the characteristic length scale of the two-point correlation function. The effect of spatial resolution and sample size on the prediction of macroscopic properties is also investigated. Finally, the physical meaning of various length scales relating flow permeability to effective electrical conductivity is elucidated.

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