Conservation laws of mixed type describing three-phase flow in porous media
SIAM Journal on Applied Mathematics
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Transitional waves for conservation laws
SIAM Journal on Mathematical Analysis
Comparison of various formulations of three-phase flow in porous media
Journal of Computational Physics
Corrected Operator Splitting for Nonlinear Parabolic Equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Formulations and Numerical Methods of the Black Oil Model in Porous Media
SIAM Journal on Numerical Analysis
Capillary instability in models for three-phase flow
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
The sequential method for the black-oil reservoir simulation on unstructured grids
Journal of Computational Physics
Three-phase immiscible displacement in heterogeneous petroleum reservoirs
Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
Adaptive Semidiscrete Central-Upwind Schemes for Nonconvex Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Journal of Computational Physics
A Fast Explicit Operator Splitting Method for Passive Scalar Advection
Journal of Scientific Computing
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This paper presents a new numerical formulation for the simulation of immiscible and incompressible three-phase water-gas-oil flows in heterogeneous porous media. We take into account the gravitational effects, both variable permeability and porosity of porous medium, and explicit spatially varying capillary pressure, in the diffusive fluxes, and explicit spatially varying flux functions, in the hyperbolic operator. The new formulation is a sequential time marching fractional-step procedure based in a splitting technique to decouple the equations with mixed discretization techniques for each of the subproblems: convection, diffusion, and pressure-velocity. The system of nonlinear hyperbolic equations that models the convective transport of the fluid phases is approximated by a modified central scheme to take into account the explicit spatially discontinuous flux functions and the effects of spatially variable porosity. This scheme is coupled with a locally conservative mixed finite element formulation for solving parabolic and elliptic problems, associated respectively with the diffusive transport of fluid phases and the pressure-velocity problem. The time discretization of the parabolic problem is performed by means of an implicit backward Euler procedure. The hybrid-mixed formulation reported here is designed to handle discontinuous capillary pressures. The new method is used to numerically investigate the question of existence, and structurally stable, of three-phase flow solutions for immiscible displacements in heterogeneous porous media with gravitational effects. Our findings appear to be consistent with theoretical and experimental results available in the literature.