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Multiphase fluid flow in porous media is relevant to many fundamental scientific problems as well as numerous practical applications. With advances in instrumentations, it has become possible to obtain high-resolution three-dimensional (3D) images of complex porous media and use them directly in the simulation of multiphase flows. A prime method for carrying out such simulations is the color-fluid lattice Boltzmann method with multi-relaxation time (CFLB-MRT) collision operator. The simulations are, however, time consuming and intensive. We propose a method to accelerate image-based computations with the CFLB-MRT method, in which the 3D image is preprocessed by curvelet transforming it and eliminating those details that do not contribute significantly to multiphase flow. The coarsening is done by thresholding the image. After inverting the coarser image back to the real space, it is utilized in the simulation of multiphase flow by the CFLB-MRT approach. As the test of the method, we carry out simulation of a two-phase flow problem in which the porous media are initially saturated by brine or water, which is then displaced by CO2 or oil, injected into the pore space. The simulations are carried out with two types of sandstone. We show that the method accelerates the computations significantly by a factor of up to 35. 

In Part I of this series, we presented a new theoretical approach for computing the effective permeability of porous media that are under deformation by a hydrostatic pressure P. Beginning with the initial pore-size distribution (PSD) of a porous medium before deformation and given the Young’s modulus and Poisson’s ratio of its grains, the model used an extension of the Hertz–Mindlin theory of contact between grains to compute the new PSD that results from applying the pressure P to the medium and utilized the updated PSD in the effective-medium approximation (EMA) to estimate the effective permeability. In the present paper, we extend the theory in order to compute the electrical conductivity of the same porous media that are saturated by brine. We account for the possible contribution of surface conduction, in order to estimate the electrical conductivity of brine-saturated porous media. We then utilize the theory to update the PSD and, hence, the pore-conductance distribution, which is then used in the EMA to predict the pressure dependence of the electrical conductivity. Comparison between the predictions and experimental data for twenty-six sandstones indicates agreement between the two that ranges from excellent to good. 

Multiphase fluid flow in porous media is important to a wide variety of processes of fundamental scientific and practical importance. Developing a model for the pore space of porous media represents the first step for simulating such flows. With rapid increase in the computation power and advances in instrumentation and imaging processes, it has become feasible to carry out simulation of multiphase flow in two- and three-dimensional images of porous media, hence dispensing with development of models of pore space that are based on approximating their morphology. Image-based simulations are, however, very time consuming. We describe an approach for speeding-up image-based simulation of multiphase flow in porous media based on curvelet transformations, which are specifically designed for processing of images that contain complex curved surfaces. Most porous media contain correlations in their morphology and, therefore, their images carry redundant information that, in the curvelet transform space, can be removed efficiently and accurately in order to obtain a coarser image with which the computations are far less intensive. We utilize the methodology to simulate two-phase flow of oil and water in two-dimensional digital images of sandstone and carbonate samples, and demonstrate that while the results with the curvelet-processed images are as accurate as those with the original ones, the computations are speeded up by a factor of 110–150. Thus, the methodology opens the way toward achieving the ultimate goal of simulation of multiphase flow in porous media, namely, making image-based computations a standard practice.