# Compressible multi-component flow in porous media with Maxwell-Stefan diffusion

## TL;DR

This paper develops a Darcy-scale model for compressible multi-component flow in porous media using Maxwell-Stefan diffusion, ensuring thermodynamic consistency and analyzing solution behavior over time.

## Contribution

It introduces a new thermodynamically consistent Darcy-scale model incorporating Maxwell-Stefan diffusion for multi-component flow in porous media.

## Key findings

- Existence of global classical solutions near equilibrium.
- Solutions tend to a parabolic limit system over time.
- Model captures cross-diffusive effects accurately.

## Abstract

We introduce a Darcy-scale model to describe compressible multi-component flow in a fully saturated porous medium. In order to capture cross-diffusive effects between the different species correctly, we make use of the Maxwell--Stefan theory in a thermodynamically consistent way. For inviscid flow the model turns out to be a nonlinear system of hyperbolic balance laws. We show that the dissipative structure of the Maxwell-Stefan operator permits to guarantee the existence of global classical solutions for initial data close to equilibria. Furthermore it is proven by relative entropy techniques that solutions of the Darcy-scale model tend in a certain long-time regime to solutions of a parabolic limit system.