Une méthode mixte multi-échelles pour un simulateur de réservoir biphasé

A multiscale hybrid mixed finite element method is presented in this paper to solve two-phase flow equations on heterogeneous media under the effect of gravitational segregation. It is designed to cope with the complex geometry and inherent multiscale nature of the rocks, leading to stable and accurate multi-physics reservoir simulations. This multiscale approach makes use of coarse scale fluxes between subregions (macro domains) that allow to reduce substantially the dominant computational costs associated with the flux/pressure kernel embedded in the numerical model. As such, larger scale problems can be approximated in a reasonable computational time. Dividing the problems into macro domains leads to a hierarchy of meshes and approximation spaces, allowing the efficient use of static condensation and parallel computation strategies. The method documented in this work utilizes discretizations based on a general domain partition formed by poly-hedral subregions. The normal flux between these subregions is associated with a finite dimensional trace space. The global system to be solved for the fluxes and pressures is expressed only in terms of the trace variables and of a piecewise constant pressure associated with each subregion. The fine scale features are resolved by mixed finite element approximations using fine flux and pressure representations inside each subregion, and the trace variable (i.e. normal flux) as Neumann boundary conditions. This property implies that the flux approximation is globally H(div)-conforming, and, as in classical mixed formulations, local mass conservation is observed at the micro-scale elements inside the subregions, an essential property for flows in heterogeneous media

Sub-grid models for multiphase fluid flow inside fractures in poroelastic media

Models have been developed for the simulation of multiphase fluid flow within fractured poroelastic media. They allow for the fluid phases to interact inside fractures, without requiring explicit simulations in the interior of the fractures. The models retain the ability to retrieve the fluid velocity profile in the fracture by post-processing. The models for flow within a fracture are combined with a formulation for multiphase flow within the poroelastic medium. They have been implemented using isogeometric analysis, cast into a traditional finite element format using Bézier extraction. Pressure oscillations around the fracture are prevented by using a lumped integration scheme for the pressure capacity. The effect of interactions between the fluid phases is first demonstrated for a single fracture through parameter studies. Next, two cases with a more practical orientation are simulated. They show, inter alia, that the inclusion of interactions between the fluid phases can result in fluid back-flow