Inclusion of Microporosity in Numerical Simulation of Relative Permeability Curves

Abstract

Abstract Advances in high-resolution micro computed tomography (micro-CT) allow obtaining high-quality rock images with a resolution of up to a few micrometres. Novel direct numerical simulation methods provide the opportunity to precisely predict the flow properties in the resolved pore space. However, a large fraction of porosity lies below the resolution of modern micro-CT scanners. These, so called, micro-pores may significantly affect the physics of flow in geologically complex dual-porosity heterogeneous formations (carbonates, shales, and coals) and are currently not accounted for in traditional micro-CT based simulations. In this work, we have employed a multiphase multi-scale Darcy-Brinkman approach to simulate immiscible two-phase flow in a hybrid system containing both macro-porous solid-free regions and a micro-porous permeable matrix. This approach solves the Navier-Stokes based volume of fluid equations system in macro-pores and accounts for multiphase Darcy equations in micro-porous regions. By combining available information on micro-porosity with relative permeability curves estimated from the synthetically generated image with both macro- and micro-porous regions fully resolved, we solve the inverse problem to account for micro-porous contribution in our Darcy-Brinkman simulation. This approach allows us to estimate relative-permeability curves in the micro-porous region and correct the multi-scale simulation so it coincides with the data from the fully-resolved image. As a result, we were able to account for the impact of micro-porosity on the residual saturation and correct the shape of relative permeability curves and their end-points in the micro-porous domain. The proposed approach provides a workflow which can be used to history-match the Darcy-Brinkman pore-scale simulation with core-scale petrophysical data with respect to the relative permeability. Thus, it is possible to account for heterogeneity in complex rock formations by incorporating the whole range of porosity. The inclusion of micro-porosity in pore-scale image-based simulations for predicting relative permeability curves may help in a more reliable modelling and estimation of filed-scale subsurface flows, production profiles, recoverable reserves and carbon capture and storage mechanisms.