A Pore-Skeleton-Based Method for Calculating Permeability and Capillary Pressure

Abstract

We have developed a new method for calculating permeability and capillary pressure from the pore skeleton that is extracted from a fractured rock model, which might comprises medial axes of matrix pores and/or medial surfaces of fracture voids. Such a skeleton, therefore, is able to encapsulate the total connected fluid flow paths in the pore-void space. To do pore-network flow simulations, the pore skeleton needs to be further “discretised” into a network of interconnected nodes and bonds to capture local pore morphology. Jiang et al. (Adv Water Resour 107:280–289, 2017) developed a method to extract pore skeletons of this type and a discretisation to construct a pore-network model that is optimal in many aspects. In this work, we develop a new in-place discretisation method, by simply inserting a virtual link, a bond, between every pair of skeleton voxels, nodes, which are either face or only edge adjacent under certain conditions. This new method results in a simpler pore-network model, i.e. a virtual network, in which each node or bond is assumed as either a cylinder or a tiny fracture, as well as prescribed with length and inscribed radius/aperture only. As a result, a simpler pore-network simulator is also developed using improved formulae of conductance and capillary pressure according to where each virtual link falls, appropriately distinguishing every local configuration within matrixes or fractures. We verify our methods by comparing the simulation results against with those of lattice Boltzmann methods and a laboratory flooding experiment and demonstrate the accuracy and efficiency of our methods with sensitivity analysis.