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Flow and Transport Properties of Deforming Porous Media. I. Permeability

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Abstract

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\(_2\) 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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Availability of data and material

The experimental data referenced and plotted throughout this work can be found from their respective published source that is listed in the reference section. For example, much of the data are acquired from Yale, D.P. 1984.

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Acknowledgements

Partial support of this work by the Petroleum Research Fund, administered by the American Chemical Society, as well as the National Science Foundation, is gratefully acknowledged. The first author is also grateful to Chevron Oil Company for a Ph.D. scholarship. We thank three anonymous reviewers whose comments and suggestions helped us to greatly improve the manuscript.

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Partial support of this work is by the Petroleum Research Fund, administered by the American Chemical Society, as well as be the National Science Foundation.

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  1. Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA, 90089-1211, USA

    Samuel Richesson & Muhammad Sahimi

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Richesson, S., Sahimi, M. Flow and Transport Properties of Deforming Porous Media. I. Permeability. Transp Porous Med 138, 577–609 (2021). https://doi.org/10.1007/s11242-021-01633-y

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