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- Title
Vanishing adsorption limit of Riemann problem solutions for the polymer model.
- Authors
Petrova, Yulia; Plohr, Bradley J.; Marchesin, Dan
- Abstract
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.
- Subjects
ADSORPTION (Chemistry); RIEMANN-Hilbert problems; PETROLEUM reservoirs; CHEMICAL models; PETROLEUM chemicals
- Publication
Journal of Hyperbolic Differential Equations, 2024, Vol 21, Issue 2, p299
- ISSN
0219-8916
- Publication type
Article
- DOI
10.1142/S0219891624500103