Efficient Image-Based Simulation of Flow and Transport in Heterogeneous Porous Media: Application of Curvelet Transforms

Flow, transport, reaction, adsorption, and deformation (FTRAD) are phenomena that occur in a wide variety of heterogeneous porous media and have been studied for decades. Models of heterogeneous porous formations involve approximations, simplifications, and even unjustified assumptions. With advances in instrumentation, obtaining highly resolved images of such media has become feasible, opening the way to direct image-based simulation of the FTRAD. Such simulations require, however, intensive computations, limiting their utility. We propose a novel methodology whereby (i) the image is taken to the curvelet space, (ii) all the curvelet coefficients that are smaller than a threshold are set to 0, and (iii) the image is reconstructed. By carrying out image-based simulations of diffusion and fluid flow in two distinct types of heterogeneous porous media, we demonstrate that simulations in the reconstructed images yield as accurate results as those in the original ones while speeding up the computation by 2 orders of magnitude or better. Thus, the methodology represents a significant step toward the ultimate goal of making direct image-based simulation of the FTRAD in heterogeneous porous media a standard practice.