Simulation of Flow and Dispersion on Pore-Space Images

Abstract

Summary We simulate flow and transport directly on pore-space images obtained from a microcomputed-tomography (micro-CT) scan of rock cores. An efficient Stokes solver is used to simulate low-Reynolds-number flows. The flow simulator uses a finite-difference method along with a standard predictor/corrector procedure to decouple pressure and velocity. An algebraic multigrid technique solves the linear systems of equations. We then predict permeability, and the results are compared with lattice-Boltzmann-method (LBM) numerical results and available experimental data. For solute transport, we apply a streamline-based algorithm that is similar to the Pollock algorithm common in field-scale reservoir simulation, but which uses a novel semianalytic formulation near solid boundaries to capture, with subgrid resolution, the variation in velocity near the grains. A random-walk method accounts for molecular diffusion. The streamline-based algorithm is validated by comparison with published results for Taylor-Aris dispersion in a single capillary with a square cross section. We then predict accurately the available experimental data in the literature for the longitudinal dispersion coefficient for a range of Péclet numbers (10–2 to 105). We introduce a characteristic length on the basis of the ratio of volume to pore/grain surface area that can be used for consolidated porous media to calculate the Péclet number.