A Nonlinear Domain Decomposition Method to Couple Compositional Gas Liquid Darcy and Free Gas Flows

Abstract

A domain decomposition algorithm is proposed to couple at the interface a gas liquid compositional Darcy flow and a compositional free gas flow. At each time step, our algorithm solves iteratively the nonlinear system coupling the compositional Darcy flow in the porous medium, the RANS gas flow in the free flow domain, and the convection diffusion of the species in the free flow domain. In order to speed up the convergence of the algorithm, the transmission conditions at the interface are replaced by Robin boundary conditions. Each Robin coefficient is obtained from a diagonal approximation of the Dirichlet to Neumann operator related to a scalar simplified model in the neighbouring subdomain. The efficiency of our domain decomposition algorithm is assessed in the case of the modelling of the mass exchanges at the interface between the geological formation and the ventilation galleries of geological radioactive waste disposal.

Non-isothermal compositional liquid gas Darcy flow: formulation, soil-atmosphere boundary condition and application to high-energy geothermal simulations

“…We consider a 2D test case from [7] which simulates the mass and energy exchanges occurring within deep geological radioactive waste disposal at the interface between a geological formation with low permeable porous medium and a ventilation excavated gallery. The data set is derived from lab experiments and in accordance with the deep disposal center for French radioactive waste project.…”

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

“…The results are compared to the isothermal counterpart of this test case which has been presented in [6] with no energy conservation and a fixed temperature T = 303 K.…”

“…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.…”