Predicting Elastic Moduli of Heterogeneous Porous Media by Percolation Theory and Effective‐Medium Approximation

Abstract Predicting geomechanical properties of rock and other types of porous media is essential to accurate modeling of many important processes, such as wave propagations, seismic events, and underground gas storage, and CO 2 sequestration, all of which involve deformation of the pore space. We propose a model to predict the porosity dependence of the Young's and bulk moduli in heterogeneous porous media by combining the universal power law, predicted by percolation theory that describes the behavior of elastic moduli near the percolation threshold of the solid skeletons, and the effective‐medium approximation (EMA) for elastic materials that is accurate away from the threshold. The parameters of the model have unambiguous physical meanings, and can, in principle, be measured. We estimate the parameters ‐ the percolation threshold , crossover point between the EMA and percolation power law, the average particle coordination number , and the elastic moduli of the solid skeleton by using experimental data or numerical simulations for a wide variety of porous media in both two and three dimensions. Whenever data are available, the predictions are consistent with them. We then predict the elastic moduli for another 10 porous media using the proposed model and the estimated parameters without adjusting any new parameter. The predictions are in most cases in agreement with the data, hence indicating the accuracy of the approach.