Vanishing adsorption limit of Riemann problem solutions for the polymer model

TL;DR

This paper investigates the behavior of solutions to the Riemann problem in a chemical flooding model for petroleum reservoirs as adsorption effects vanish, establishing criteria for admissible discontinuities and validating previous criteria.

Contribution

It provides a rigorous justification for the admissibility criteria of contact discontinuities in the polymer model, especially under vanishing adsorption limits and monotonic fractional flow functions.

Findings

Admissibility criteria are justified for vanishing adsorption limits.

The criterion correctly selects undercompressive contact discontinuities.

Results apply to models with non-monotone chemical concentration dependence.

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.