Numerical scheme for coupling two-phase compositional porous-media flow and one-phase compositional free flow

Purpose – The purpose of this paper is to present an efficient improved version of Implicit Pressure-Explicit Saturation (IMPES) method for the solution of incompressible two-phase flow model based on the discontinuous Galerkin (DG) numerical scheme. Design/methodology/approach – The governing equations, based on the wetting-phase pressure-saturation formulation, are discretized using various primal DG schemes. The authors use H(div) velocity reconstruction in Raviart-Thomas space (RT_0 and RT_1), the weighted average formulation, and the scaled penalties to improve the spatial discretization. It uses a new improved IMPES approach, by using the second-order explicit Total Variation Diminishing Runge-Kutta (TVD-RK) as temporal discretization of the saturation equation. The main purpose of this time stepping technique is to speed up computation without losing accuracy, thus to increase the efficiency of the method. Findings – Utilizing pressure internal interpolation technique in the improved IMPES scheme can reduce CPU time. Combining the TVD property with a strong multi-dimensional slope limiter namely, modified Chavent-Jaffre leads to a non-oscillatory scheme even in coarse grids and highly heterogeneous porous media. Research limitations/implications – The presented locally conservative scheme can be applied only in 2D incompressible two-phase flow modeling in non-deformable porous media. In addition, the capillary pressure discontinuity between two adjacent rock types assumed to be negligible. Practical implications – The proposed numerical scheme can be efficiently used to model the incompressible two-phase flow in secondary recovery of petroleum reservoirs and tracing immiscible contamination in aquifers. Originality/value – The paper describes a novel version of the DG two-phase flow which illustrates the effects of improvements in special discretization. Also the new improved IMPES approach used reduces the computation time. The non-oscillatory scheme is an efficient algorithm as it maintains accuracy and saves computation time.

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Coupling of two-phase flow in fractured-vuggy reservoir with filling medium

Open Physics ◽

10.1515/phys-2017-0002 ◽

2017 ◽

Vol 15 (1) ◽

pp. 12-17 ◽

Cited By ~ 5

Author(s):

Haojun Xie ◽

Aifen Li ◽

Zhaoqin Huang ◽

Bo Gao ◽

Ruigang Peng

Keyword(s):

Porous Media ◽

Oil Recovery ◽

Two Phase Flow ◽

Water Injection ◽

Free Flow ◽

Flow In Porous Media ◽

Free Fluid ◽

Phase Flow ◽

Fluid Exchange ◽

Two Phase

AbstractCaves in fractured-vuggy reservoir usually contain lots of filling medium, so the two-phase flow in formations is the coupling of free flow and porous flow, and that usually leads to low oil recovery. Considering geological interpretation results, the physical filled cave models with different filling mediums are designed. Through physical experiment, the displacement mechanism between un-filled areas and the filling medium was studied. Based on the experiment model, we built a mathematical model of laminar two-phase coupling flow considering wettability of the porous media. The free fluid region was modeled using the Navier-Stokes and Cahn-Hilliard equations, and the two-phase flow in porous media used Darcy's theory. Extended BJS conditions were also applied at the coupling interface. The numerical simulation matched the experiment very well, so this numerical model can be used for two-phase flow in fracture-vuggy reservoir. In the simulations, fluid flow between inlet and outlet is free flow, so the pressure difference was relatively low compared with capillary pressure. In the process of water injection, the capillary resistance on the surface of oil-wet filling medium may hinder the oil-water gravity differentiation, leading to no fluid exchange on coupling interface and remaining oil in the filling medium. But for the water-wet filling medium, capillary force on the surface will coordinate with gravity. So it will lead to water imbibition and fluid exchange on the interface, high oil recovery will finally be reached at last.

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Convergence of an MPFA finite volume scheme for a two‐phase porous media flow model with dynamic capillarity

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drx078 ◽

2018 ◽

Cited By ~ 3

Author(s):

X Cao ◽

S F Nemadjieu ◽

I S Pop

Keyword(s):

Porous Media ◽

Finite Volume ◽

Flow Model ◽

Porous Media Flow ◽

Finite Volume Scheme ◽

Two Phase ◽

Volume Scheme ◽

Dynamic Capillarity

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Degenerate two-phase porous media flow model with dynamic capillarity

Journal of Differential Equations ◽

10.1016/j.jde.2015.10.008 ◽

2016 ◽

Vol 260 (3) ◽

pp. 2418-2456 ◽

Cited By ~ 16

Author(s):

X. Cao ◽

I.S. Pop

Keyword(s):

Porous Media ◽

Flow Model ◽

Porous Media Flow ◽

Two Phase ◽

Dynamic Capillarity

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Controllability and observability in two-phase porous media flow

Computational Geosciences ◽

10.1007/s10596-013-9355-1 ◽

2013 ◽

Vol 17 (5) ◽

pp. 773-788 ◽

Cited By ~ 4

Author(s):

Jorn F. M. Van Doren ◽

Paul M. J. Van den Hof ◽

Okko H. Bosgra ◽

Jan Dirk Jansen

Keyword(s):

Porous Media ◽

Porous Media Flow ◽

Two Phase ◽

Controllability And Observability

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Convergence of nonlinear finite volume schemes for two-phase porous media flow on general meshes

IMA Journal of Numerical Analysis ◽

10.1093/imanum/draa064 ◽

2020 ◽

Author(s):

Léo Agélas ◽

Martin Schneider ◽

Guillaume Enchéry ◽

Bernd Flemisch

Keyword(s):

Porous Media ◽

Finite Volume ◽

A Priori ◽

Porous Media Flow ◽

Finite Volume Schemes ◽

Two Phase ◽

Finite Volume Discretization ◽

Flux Approximation ◽

Specific Scheme ◽

Flow Through

Abstract In this work we present an abstract finite volume discretization framework for incompressible immiscible two-phase flow through porous media. A priori error estimates are derived that allow us to prove the existence of discrete solutions and to establish the proof of convergence for schemes belonging to this framework. In contrast to existing publications the proof is not restricted to a specific scheme and it assumes neither symmetry nor linearity of the flux approximations. Two nonlinear schemes, namely a nonlinear two-point flux approximation and a nonlinear multipoint flux approximation, are presented, and some properties of these schemes, e.g. saturation bounds, are proven. Furthermore, the numerical behavior of these schemes (e.g. accuracy, coercivity, efficiency or saturation bounds) is investigated for different test cases for which the coercivity is checked numerically.

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