Correspondence between one- and two-equation models for solute transport in two-region heterogeneous porous media
In this work, we study the transient behavior of upscaled models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the s...
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| Materialtyp: | Journal article |
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2012
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| _version_ | 1826279666611126272 |
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| author | Davit, Y Wood, B Debenest, G Quintard, M |
| author_facet | Davit, Y Wood, B Debenest, G Quintard, M |
| author_sort | Davit, Y |
| collection | OXFORD |
| description | In this work, we study the transient behavior of upscaled models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the time scale of interest (t) is smaller than the characteristic time (T1) for the relaxation of the effective macroscale parameters (i.e., when t ≤ T1); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (T1) (i.e., when t » T1); and (3) a one-equation, time-asymptotic formulation (1eq∞). This model can be adopted when (t) is significantly larger than the time scale (T2) associated with exchange processes between the two regions (i.e., when t » T2). In order to obtain some physical insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in simple cases. The main result of this paper is to show that there is weak long-time convergence of the solution of (2eq) toward the solution of (1eq∞) in terms of standardized moments but, interestingly, not in terms of centered moments. Physically, our interpretation of this result is that the spreading of the solute is dominating higher order non-zero perturbations in the asymptotic regime. |
| first_indexed | 2024-03-07T00:02:11Z |
| format | Journal article |
| id | oxford-uuid:7653c272-a19c-4217-be7b-0d91b71d10b0 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:02:11Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:7653c272-a19c-4217-be7b-0d91b71d10b02022-03-26T20:15:08ZCorrespondence between one- and two-equation models for solute transport in two-region heterogeneous porous mediaJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7653c272-a19c-4217-be7b-0d91b71d10b0Mathematical Institute - ePrints2012Davit, YWood, BDebenest, GQuintard, MIn this work, we study the transient behavior of upscaled models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the time scale of interest (t) is smaller than the characteristic time (T1) for the relaxation of the effective macroscale parameters (i.e., when t ≤ T1); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (T1) (i.e., when t » T1); and (3) a one-equation, time-asymptotic formulation (1eq∞). This model can be adopted when (t) is significantly larger than the time scale (T2) associated with exchange processes between the two regions (i.e., when t » T2). In order to obtain some physical insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in simple cases. The main result of this paper is to show that there is weak long-time convergence of the solution of (2eq) toward the solution of (1eq∞) in terms of standardized moments but, interestingly, not in terms of centered moments. Physically, our interpretation of this result is that the spreading of the solute is dominating higher order non-zero perturbations in the asymptotic regime. |
| spellingShingle | Davit, Y Wood, B Debenest, G Quintard, M Correspondence between one- and two-equation models for solute transport in two-region heterogeneous porous media |
| title | Correspondence between one- and two-equation models for solute
transport in two-region heterogeneous porous media |
| title_full | Correspondence between one- and two-equation models for solute
transport in two-region heterogeneous porous media |
| title_fullStr | Correspondence between one- and two-equation models for solute
transport in two-region heterogeneous porous media |
| title_full_unstemmed | Correspondence between one- and two-equation models for solute
transport in two-region heterogeneous porous media |
| title_short | Correspondence between one- and two-equation models for solute
transport in two-region heterogeneous porous media |
| title_sort | correspondence between one and two equation models for solute transport in two region heterogeneous porous media |
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