Reduced Model for Properties of Multiscale Porous Media with Changing Geometry
In this paper, we consider an important problem for modeling complex coupled phenomena in porous media at multiple scales. In particular, we consider flow and transport in the void space between the pores when the pore space is altered by new solid obstructions formed by microbial growth or reactive...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-03-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/9/3/28 |
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| author | Malgorzata Peszynska Joseph Umhoefer Choah Shin |
| author_facet | Malgorzata Peszynska Joseph Umhoefer Choah Shin |
| author_sort | Malgorzata Peszynska |
| collection | DOAJ |
| description | In this paper, we consider an important problem for modeling complex coupled phenomena in porous media at multiple scales. In particular, we consider flow and transport in the void space between the pores when the pore space is altered by new solid obstructions formed by microbial growth or reactive transport, and we are mostly interested in pore-coating and pore-filling type obstructions, observed in applications to biofilm in porous media and hydrate crystal formation, respectively. We consider the impact of these obstructions on the macroscopic properties of the porous medium, such as porosity, permeability and tortuosity, for which we build an experimental probability distribution with reduced models, which involves three steps: (1) generation of independent realizations of obstructions, followed by, (2) flow and transport simulations at pore-scale, and (3) upscaling. For the first step, we consider three approaches: (1A) direct numerical simulations (DNS) of the PDE model of the actual physical process called BN which forms the obstructions, and two non-DNS methods, which we call (1B) CLPS and (1C) LP. LP is a lattice Ising-type model, and CLPS is a constrained version of an Allen–Cahn model for phase separation with a localization term. Both LP and CLPS are model approximations of BN, and they seek local minima of some nonconvex energy functional, which provide plausible realizations of the obstructed geometry and are tuned heuristically to deliver either pore-coating or pore-filling obstructions. Our methods work with rock-void geometries obtained by imaging, but bypass the need for imaging in real-time, are fairly inexpensive, and can be tailored to other applications. The reduced models LP and CLPS are less computationally expensive than DNS, and can be tuned to the desired fidelity of the probability distributions of upscaled quantities. |
| first_indexed | 2024-03-09T05:47:39Z |
| format | Article |
| id | doaj.art-ea983ebaf39b47619156c32fe6e54346 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-09T05:47:39Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-ea983ebaf39b47619156c32fe6e543462023-12-03T12:19:58ZengMDPI AGComputation2079-31972021-03-01932810.3390/computation9030028Reduced Model for Properties of Multiscale Porous Media with Changing GeometryMalgorzata Peszynska0Joseph Umhoefer1Choah Shin2Department of Mathematics, Oregon State University, Corvallis, OR 97331, USADepartment of Mathematics, Oregon State University and Solid Modeling Solutions, Corvallis, OR 97331, USADepartment of Mathematics, Oregon State University, Corvallis, OR 97331, USAIn this paper, we consider an important problem for modeling complex coupled phenomena in porous media at multiple scales. In particular, we consider flow and transport in the void space between the pores when the pore space is altered by new solid obstructions formed by microbial growth or reactive transport, and we are mostly interested in pore-coating and pore-filling type obstructions, observed in applications to biofilm in porous media and hydrate crystal formation, respectively. We consider the impact of these obstructions on the macroscopic properties of the porous medium, such as porosity, permeability and tortuosity, for which we build an experimental probability distribution with reduced models, which involves three steps: (1) generation of independent realizations of obstructions, followed by, (2) flow and transport simulations at pore-scale, and (3) upscaling. For the first step, we consider three approaches: (1A) direct numerical simulations (DNS) of the PDE model of the actual physical process called BN which forms the obstructions, and two non-DNS methods, which we call (1B) CLPS and (1C) LP. LP is a lattice Ising-type model, and CLPS is a constrained version of an Allen–Cahn model for phase separation with a localization term. Both LP and CLPS are model approximations of BN, and they seek local minima of some nonconvex energy functional, which provide plausible realizations of the obstructed geometry and are tuned heuristically to deliver either pore-coating or pore-filling obstructions. Our methods work with rock-void geometries obtained by imaging, but bypass the need for imaging in real-time, are fairly inexpensive, and can be tailored to other applications. The reduced models LP and CLPS are less computationally expensive than DNS, and can be tuned to the desired fidelity of the probability distributions of upscaled quantities.https://www.mdpi.com/2079-3197/9/3/28flow in porous mediapore-scale with obstructionsupscalingreduced order model |
| spellingShingle | Malgorzata Peszynska Joseph Umhoefer Choah Shin Reduced Model for Properties of Multiscale Porous Media with Changing Geometry Computation flow in porous media pore-scale with obstructions upscaling reduced order model |
| title | Reduced Model for Properties of Multiscale Porous Media with Changing Geometry |
| title_full | Reduced Model for Properties of Multiscale Porous Media with Changing Geometry |
| title_fullStr | Reduced Model for Properties of Multiscale Porous Media with Changing Geometry |
| title_full_unstemmed | Reduced Model for Properties of Multiscale Porous Media with Changing Geometry |
| title_short | Reduced Model for Properties of Multiscale Porous Media with Changing Geometry |
| title_sort | reduced model for properties of multiscale porous media with changing geometry |
| topic | flow in porous media pore-scale with obstructions upscaling reduced order model |
| url | https://www.mdpi.com/2079-3197/9/3/28 |
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