Coupling compositional liquid gas Darcy and free gas flows at porous and free-flow domains interface

Abstract

This paper proposes an efficient splitting algorithm to solve coupled liquid gas Darcy and free gas flows at the interface between a porous medium and a free-flow domain. This model is compared to the reduced model introduced in [6] using a 1D approximation of the gas free flow. For that purpose, the gas molar fraction diffusive flux at the interface in the free-flow domain is approximated by a two point flux approximation based on a low-frequency diagonal approximation of a Steklov-Poincaré type operator. The splitting algorithm and the reduced model are applied in particular to the modelling of the mass exchanges at the interface between the storage and the ventilation galleries in radioactive waste deposits.

A domain decomposition method to couple nonisothermal compositional gas liquid Darcy and free gas flows

“…This is motivated by the small perturbation of the free-flow velocity and pressure induced by the coupling with the porous medium. In practice we will use the Prandtl algebraic turbulent model as in [5] (see the numerical Section 5).…”

“…At the interface Γ between the free-flow and the porous-medium domains, the coupling conditions are those stated in [7,15,5] where we have replaced the Beaver Joseph condition by the simpler no slip condition due to the low permeability of the porous medium in our application.…”

“…In the free-flow domain, the turbulent viscosity µ t used to define the RANS stress tensor (6) is given by the Prandtl algebraic turbulent model as in [5] and computed once and for all from the uncoupled solution in the free-flow model. The turbulent diffusivity…”

“…Following [5], a Cartesian mesh uniform in the x direction and refined at the interface Γ on both sides is used. The Darcy problem (11) and the convection diffusion equations (14) are solved using a two-point flux approximation scheme given in [32] with additional face unknowns at the interface Γ to discretize the boundary conditions.…”

“…Modeling the exchange processes at the interface between a free flow and a flow in a porous medium appears in a wide range of applications from food processing [1], wood or paper production [2], salinization of agricultural land [3], prediction of convective heat and moisture transfer at exterior building surfaces [4], to the study of the mass and energy exchanges at the interface between a nuclear waste disposal and the ventilation galleries [5,6]. This latter is the main focus of this paper in terms of application.…”