Speeding-up image-based simulation of two-phase flow in porous media with lattice-Boltzmann method using three-dimensional curvelet transforms

Abstract

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 multirelaxation 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.