On the solvability of the Brinkman-Forchheimer-extended Darcy equation

TL;DR

This paper investigates the existence and uniqueness of solutions for a nonlinear flow model in porous media, and presents finite element approximations for various flow conditions in packed bed reactors.

Contribution

It provides new theoretical results on solution solvability and offers finite element methods for simulating flows in non-Darcy regimes.

Findings

Existence and uniqueness of weak solutions established for nonlinear flows.

Finite element approximations demonstrated for different Reynolds numbers.

Results applicable to chemical reactor design and analysis.

Abstract

The nonlinear Brinkman-Forchheimer-extended Darcy equation is used to model some porous medium flow in chemical reactors of packed bed type. The results concerning the existence and uniqueness of a weak solution are presented for nonlinear convective flows in medium with nonconstant porosity and for small data. Furthermore, the finite element approximations to the flow profiles in the fixed bed reactor are presented for several Reynolds numbers at the non-Darcy's range.