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arXiv · 2505.17943

Well-posedness and Fingering Patterns in $A + B \rightarrow C$ Reactive Porous Media Flow

Sahil Kundu·Surya Narayan Maharana·Manoranjan Mishra
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Abstract

The convection-diffusion-reaction system governing incompressible reactive fluids in porous media is studied, focusing on the \( A + B \to C \) reaction coupled with density-driven flow. The time-dependent Brinkman equation describes the velocity field, incorporating permeability variations modeled as an exponential function of the product concentration. Density variations are accounted for using the Oberbeck-Boussinesq approximation, with density as a function of reactants and product concentration. The existence and uniqueness of weak solutions are established via the Galerkin approach, proving the system's well-posedness. A maximum principle ensures reactant nonnegativity with nonnegative initial conditions, while the product concentration is shown to be bounded, with an explicit upper bound derived in a simplified setting. Numerical simulations are performed using the finite element method to explore reactive fingering instabilities and illustrate the effects of density stratification, differential product mobility, and two- or three-dimensionality. Two cases with initial flat and elliptic interfaces further demonstrate the theoretical result that solutions continuously depend on initial and boundary conditions. These theoretical and numerical findings provide a foundation for understanding chemically induced fingering patterns and their implications in applications such as carbon dioxide sequestration, petroleum migration, and rock dissolution in karst reservoirs.

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Sahil Kundu, Surya Narayan Maharana, Manoranjan Mishra. 2025-05-23. Well-posedness and Fingering Patterns in $A + B \rightarrow C$ Reactive Porous Media Flow. https://doi.org/10.1016/j.cnsns.2025.109493

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