Approximating Permeability of Microcomputed-Tomography Images Using Elliptic Flow Equations

Abstract

Summary Direct simulation of flow on microcomputed-tomography (micro-CT) images of rocks is widely used for the calculation of permeability. However, direct numerical methods are computationally demanding. A rapid and robust method is proposed to solve the elliptic flow equation. Segmented micro-CT images are used for the calculation of local conductivity in each voxel. The elliptic flow equation is then solved on the images using the finite-volume method. The numerical method is optimized in terms of memory usage using sparse matrix modules to eliminate memory overhead associated with both the inherent sparsity of the finite-volume two-point flux-approximation (TPFA) method, and the presence of zero conductivity for impermeable grain cells. The estimated permeabilities for a number of sandstone and carbonate micro-CT images are compared against estimation of other solvers, and results show a difference of approximately 11%. However, the computational time is 80% lower. Local conductivity can furthermore be assigned directly into matrix voxels without a loss in generality, hence allowing the pore-scale finite-volume solver (PFVS) to be able to solve for flow in a permeable matrix as well as open pore space. This has been developed to include the effect of microporosity in flow simulation.