An optimal method of Galerkin type for diffusion-dispersion problems.
An optimal viscosity profile in the secondary oil recovery
An up-wind finite element method for a filtration problem
Analyse mathématique de modèles variationells en simulation pétrolière. Le cas du modèle black-oil pseudo-compositionnel standard isoterme.
The aim of the paper is an analytical and numerical approach to the pseudo-compositional black-oil model for simulating a 3-D isothermal constrained polyphasic flow in porous media, taking into account realistic boundary conditions. The handling of the component conservation laws leads to a strongly coupled system including parabolic quasilinear degenerated equations and first-order hyperbolic inequalities: the introduction of unilateral problems arises from the nature of the thermodynamical equilibrium...
Analysis of a multiple-porosity model for single-phase flow through naturally fractured porous media.
Analyticity of the interface in a free boundary problem.
Application of a multiphase flow code for investigation of influence of capillary pressure parameters on two-phase flow
We have developed a multiphase flow code that has been applied to study the behavior of non-aqueous phase liquids (NAPL) in the subsurface. We describe model formulation, discretization, and use the model for numerical investigation of sensitivity of the NAPL plume with respect to capillary parameters of the soil. In this paper the soil is assumed to be spatially homogeneous. A 2-D reference problem has been chosen and has been recomputed repeatedly with modified parameters of the Brooks–Corey capillary...
Application of homogenization theory related to Stokes flow in porous media
We consider applications, illustration and concrete numerical treatments of some homogenization results on Stokes flow in porous media. In particular, we compute the global permeability tensor corresponding to an unidirectional array of circular fibers for several volume-fractions. A 3-dimensional problem is also considered.
Approximate ad hoc parametric solutions for nonlinear first-order PDEs governing two-dimensional steady vector fields.
Approximation of the Heaviside function and uniqueness results for a class of quasilinear elliptic-parabolic problems.
In this paper, we concern ourselves with uniqueness results for an elliptic-parabolic quasilinear partial differential equation describing, for instance, the pressure of a fluid in a three-dimensional porous medium: within the frame of mathematical modeling of the secondary recovery from oil fields, the handling of the component conservation laws leads to a system including such a pressure equation, locally elliptic or parabolic according to the evolution of the gas phase.
Asymptotic analysis of incompressible and viscous fluid flow through porous media. Brinkman's law via epi-convergence methods
Asymptotic and numerical modelling of flows in fractured porous media
This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale, so that we can asymptotically reduce them to immersed polygonal fault interfaces and the model finally consists in a coupling between...
Asymptotic behaviour of a viscoplastic bingham fluid in porous media with periodic structure
Asymptotic behaviour of one-dimensional flows through porous media
Asymptotic behaviour of the porous media equation in an exterior domain
Asymptotic Expansions of the Pressure and the Free Boundary for Flows through Porous Media.
Automatic simplification of Darcy’s equations with pressure dependent permeability
We consider the flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with mixed boundary conditions. Since the boundary pressure can present high variations, the permeability of the medium also depends on the pressure, so that the model is nonlinear. A posteriori estimates allow us to omit this dependence where the pressure does not vary too much. We perform the numerical analysis of a spectral element discretization of the simplified model. Finally we propose a strategy...
Axissymmetric Free Surface Seepage