Vanishing adsorption limit of Riemann problem solutions for the polymer model
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912011414142976 |
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| author | Petrova, Yulia Plohr, Bradley J. Marchesin, Dan |
| author_facet | Petrova, Yulia Plohr, Bradley J. Marchesin, Dan |
| contents | We examine the vanishing adsorption limit of solutions of Riemann problems for the Glimm-Isaacson model of chemical flooding of a petroleum reservoir. A contact discontinuity is deemed admissible if it is the limit of traveling waves or rarefaction waves for an augmented system that accounts for weak chemical adsorption onto the rock. We prove that this criterion justifies the admissibility criteria adopted previously by Keyfitz-Kranzer, Isaacson-Temple, and de Souza-Marchesin, provided that the fractional flow function depends monotonically on chemical concentration. We also demonstrate that the adsorption criterion selects the undercompressive contact discontinuities required to solve the general Riemann problem in an example model with non-monotone dependence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_10326 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Vanishing adsorption limit of Riemann problem solutions for the polymer model Petrova, Yulia Plohr, Bradley J. Marchesin, Dan Analysis of PDEs Primary 35L65, secondary 35L67, 76L05 We examine the vanishing adsorption limit of solutions of Riemann problems for the Glimm-Isaacson model of chemical flooding of a petroleum reservoir. A contact discontinuity is deemed admissible if it is the limit of traveling waves or rarefaction waves for an augmented system that accounts for weak chemical adsorption onto the rock. We prove that this criterion justifies the admissibility criteria adopted previously by Keyfitz-Kranzer, Isaacson-Temple, and de Souza-Marchesin, provided that the fractional flow function depends monotonically on chemical concentration. We also demonstrate that the adsorption criterion selects the undercompressive contact discontinuities required to solve the general Riemann problem in an example model with non-monotone dependence. |
| title | Vanishing adsorption limit of Riemann problem solutions for the polymer model |
| topic | Analysis of PDEs Primary 35L65, secondary 35L67, 76L05 |
| url | https://arxiv.org/abs/2211.10326 |