Hertz‐Mindlin Theory of Contacting Grains and the Effective‐Medium Approximation for the Permeability of Deforming Porous Media
Abstract Estimating flow and transport properties of porous media that undergo deformation as a result of applying an external pressure or stress is important to a wide variety of processes, ranging from shale formations into which a fracking liquid is injected to CO2 sequestration in geological for...
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| Format: | Article |
| Language: | English |
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Wiley
2019-07-01
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| Series: | Geophysical Research Letters |
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| Online Access: | https://doi.org/10.1029/2019GL083727 |
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| author | Samuel Richesson Muhammad Sahimi |
| author_facet | Samuel Richesson Muhammad Sahimi |
| author_sort | Samuel Richesson |
| collection | DOAJ |
| description | Abstract Estimating flow and transport properties of porous media that undergo deformation as a result of applying an external pressure or stress is important to a wide variety of processes, ranging from shale formations into which a fracking liquid is injected to CO2 sequestration in geological formations. We propose a novel model for estimating the effective permeability of such porous media. Given the pore‐size distribution (PSD) of a porous medium before deformation, as well as the Young's modulus of its grains, the model uses 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 to estimate the effective permeability at P. Comparison between the predictions and experimental data for several types of sandstones indicates excellent agreement between the two. |
| format | Article |
| id | doaj-art-fd8a4e8b2ddf4930b941715a820e9f46 |
| institution | OA Journals |
| issn | 0094-8276 1944-8007 |
| language | English |
| publishDate | 2019-07-01 |
| publisher | Wiley |
| record_format | Article |
| series | Geophysical Research Letters |
| spelling | doaj-art-fd8a4e8b2ddf4930b941715a820e9f462025-08-20T02:09:04ZengWileyGeophysical Research Letters0094-82761944-80072019-07-0146148039804510.1029/2019GL083727Hertz‐Mindlin Theory of Contacting Grains and the Effective‐Medium Approximation for the Permeability of Deforming Porous MediaSamuel Richesson0Muhammad Sahimi1Mork Family Department of Chemical Engineering and Materials Science University of Southern California Los Angeles CA USAMork Family Department of Chemical Engineering and Materials Science University of Southern California Los Angeles CA USAAbstract Estimating flow and transport properties of porous media that undergo deformation as a result of applying an external pressure or stress is important to a wide variety of processes, ranging from shale formations into which a fracking liquid is injected to CO2 sequestration in geological formations. We propose a novel model for estimating the effective permeability of such porous media. Given the pore‐size distribution (PSD) of a porous medium before deformation, as well as the Young's modulus of its grains, the model uses 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 to estimate the effective permeability at P. Comparison between the predictions and experimental data for several types of sandstones indicates excellent agreement between the two.https://doi.org/10.1029/2019GL083727deformationporous mediaeffective‐medium approximationpermeability |
| spellingShingle | Samuel Richesson Muhammad Sahimi Hertz‐Mindlin Theory of Contacting Grains and the Effective‐Medium Approximation for the Permeability of Deforming Porous Media Geophysical Research Letters deformation porous media effective‐medium approximation permeability |
| title | Hertz‐Mindlin Theory of Contacting Grains and the Effective‐Medium Approximation for the Permeability of Deforming Porous Media |
| title_full | Hertz‐Mindlin Theory of Contacting Grains and the Effective‐Medium Approximation for the Permeability of Deforming Porous Media |
| title_fullStr | Hertz‐Mindlin Theory of Contacting Grains and the Effective‐Medium Approximation for the Permeability of Deforming Porous Media |
| title_full_unstemmed | Hertz‐Mindlin Theory of Contacting Grains and the Effective‐Medium Approximation for the Permeability of Deforming Porous Media |
| title_short | Hertz‐Mindlin Theory of Contacting Grains and the Effective‐Medium Approximation for the Permeability of Deforming Porous Media |
| title_sort | hertz mindlin theory of contacting grains and the effective medium approximation for the permeability of deforming porous media |
| topic | deformation porous media effective‐medium approximation permeability |
| url | https://doi.org/10.1029/2019GL083727 |
| work_keys_str_mv | AT samuelrichesson hertzmindlintheoryofcontactinggrainsandtheeffectivemediumapproximationforthepermeabilityofdeformingporousmedia AT muhammadsahimi hertzmindlintheoryofcontactinggrainsandtheeffectivemediumapproximationforthepermeabilityofdeformingporousmedia |