Two-phase flow in a chemically active porous medium

TL;DR

This paper models and analyzes the transformation of reactants into immiscible products in a chemically active porous medium, deriving governing equations, identifying key parameters, and exploring flow behavior and optimization strategies.

Contribution

It introduces a one-dimensional macroscopic model for reactive multiphase flow in porous media, including new equations, dimensionless analysis, and insights into flow transformation dynamics.

Findings

The spatial transformation rate is non-monotonous with an inflection point.

Scaling laws for the inflection point location are established.

Viscous coupling terms significantly influence flow behavior.

Abstract

We study the problem of the transformation of a given reactant species into an immiscible product species, as they flow through a chemically active porous medium. We derive the equation governing the evolution of the volume fraction of the species -- in a one-dimensional macroscopic description --, identify the relevant dimensionless numbers, and provide simple models for capillary pressure and relative permeabilities, which are quantities of crucial importance when tackling multiphase flows in porous media. We set the domain of validity of our models and discuss the importance of viscous coupling terms in the extended Darcy's law. We investigate numerically the steady regime and demonstrate that the spatial transformation rate of the species along the reactor is non-monotonous, as testified by the existence of an inflection point in the volume fraction profiles. We obtain the scaling of the location of this inflection point with the dimensionless lengths of the problem. Eventually, we provide key elements for optimization of the reactor.