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Estimating flow and transport properties of porous media that undergo deformation as a result of applying an external pressure or force is important to a wide variety of processes, ranging from injecting a fracking liquid into shale formations, to CO sequestration in spent oil reservoirs. We propose a novel model for estimating the effective flow and transport properties of such porous media. Assuming that the solid matrix of a porous medium undergoes elastic deformation, and given its initial porosity before deformation, as well as the Young’s modulus of its grains, the model uses an extension of the Hertz–Mindlin theory of contact between grains to compute the new PSD that results from applying an external pressure P to the medium, and utilizes the updated PSD in the effective-medium approximation (EMA) to estimate the effective flow and transport properties at pressure P. In the present part of this series, we use the theory to predict the effective permeability as a function of the applied pressure. Comparison between the predictions and experimental data for twenty-four types of sandstones indicates excellent agreement between the two.
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This content will become publicly available on April 1, 2026
Predicting Elastic Moduli of Heterogeneous Porous Media by Percolation Theory and Effective‐Medium Approximation
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 CO2sequestration, 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.
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- Award ID(s):
- 2000968
- PAR ID:
- 10625552
- Publisher / Repository:
- AGU
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Solid Earth
- Volume:
- 130
- Issue:
- 4
- ISSN:
- 2169-9313
- Subject(s) / Keyword(s):
- Porous media, Deformation Elastic moduli effective-medium approximation
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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