Percolation-based Effective Permeability Estimation in Real Heterogeneous Porous Media

Abstract

It has long been understood that flow behavior in heterogeneous porous media is largely controlled by the continuity of permeability contrasts. With this in mind, we are looking in new methods for a fast estimation of the effective permeability which concentrates on the properties of the percolating cluster. From percolation concepts we use a threshold permeability value (K_th) by which the gridblocks with the highest permeability values connect two opposite side of the system in the direction of the flow. Those methods can be applied to heterogeneous media of a range of permeabilities distribution and various underlying structures. We use power law relations and weighted power averages that can be inferred either from the statistics and the properties of percolation sub-networks at the threshold point. This approach does not need fitting to the experimental data of conductivity measurements to estimate the model parameter as is done in empirical methods. We examine the order of accuracy of these methods on some layers of 10th SPE model and found very good agreements with the values determined from the commercial flow simulators. The results of this work open insights on new methods in estimating the effective permeability using percolation concepts.