Vanishing adsorption limit of Riemann problem solutions for the polymer model

Author:

Petrova Yulia1ORCID,Plohr Bradley J.2ORCID,Marchesin Dan3ORCID

Affiliation:

1. Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), R. Marquês de São Vicente, 124 – Gávea, Rio de Janeiro – RJ 22451-040, Brazil

2. Los Alamos National Laboratory, Los Alamos, NM, USA

3. Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina, 110 – Jardim Botânico, Rio de Janeiro – RJ 22460-320, Brazil

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.

Funder

Bolsa de Excelncia at IMPA

Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior — Brasil

FAPERJ

Publisher

World Scientific Pub Co Pte Ltd

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