| Full text | |
| Author(s): |
Abreu, Eduardo
[1]
Total Authors: 1
|
| Affiliation: | [1] Univ Campinas UNICAMP, Dept Appl Math, IMECC, BR-13083970 Campinas, SP - Brazil
Total Affiliations: 1
|
| Document type: | Journal article |
| Source: | MATHEMATICS AND COMPUTERS IN SIMULATION; v. 97, p. 234-259, MAR 2014. |
| Web of Science Citations: | 13 |
| Abstract | |
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. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 12/19874-8 - Design of a well-balanced scheme for the numerical approximation of a three-phase flow model with discontinuous flux functions |
| Grantee: | Eduardo Cardoso de Abreu |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 11/11897-6 - Numerical analysis and mathematical modeling of non-linear PDEs applied to fluid dynamics in porous media |
| Grantee: | Eduardo Cardoso de Abreu |
| Support Opportunities: | Regular Research Grants |