Nonlinear wave interactions in geochemical modeling

TL;DR

This paper investigates nonlinear wave interactions in geochemical conservation laws, focusing on surface complex effects, developing a Riemann solver, and analyzing wave bifurcations relevant to oil recovery modeling.

Contribution

It introduces a new Riemann solver that accounts for complex nonlinear wave interactions and bifurcations in geochemical models involving surface complexes.

Findings

Development of a Riemann solver for complex wave interactions

Analysis of bifurcations at inflection and resonance surfaces

Application to oil recovery modeling with surface complexes

Abstract

This paper is concerned with the study of the main wave interactions in a system of conservation laws in geochemical modeling. We study the modeling of the chemical complexes on the rock surface. The presence of stable surface complexes affects the relative permeability. We add terms representing surface complexes to the accumulation function in the model presented in \cite{lambert2019nonlinear1}. This addition allows to take into account the interaction of ions with the rock surface in the modeling of the oil recovery by the injection of carbonated water. Compatibility hypotheses with the modeling are made on the coefficients of the system to obtain meaningful solutions. We developed a Riemann solver taking into account the complexity of the interactions and bifurcations of nonlinear waves. Such bifurcations occur at the inflection and resonance surfaces. We present the solution of a generalized eigenvalue problem in a (n+1)-dimensional case, which allows the construction of rarefaction curves. A method to find the discontinuous solutions is also presented. We find the solution path for some examples.