Analysis of a combined mixed finite element and discontinuous Galerkin method for incompressible two-phase flow in porous media

Kou, Jisheng; Sun, Shuyu

doi:10.1002/mma.2854

Cited by 14 publications

(7 citation statements)

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“…Over the past decade or so, research attention has focused on conditioning simulator forecasts to data and, to a lesser extent, on characterizing the uncertainty in forecasts, usually with few data to inform flow simulator parameters. Typically, the commonly used governing principles fall in the realm of multiphase flow in porous media [7,[9][10][11][12]16,17], in which the subsurface flow and transport of multiple components are governed by coupled differential equations of different type: an elliptic equation for pressure and a sequence of hyperbolic equations for component concentrations. Further complication arises from the heterogeneous and multiscale nature presented in the permeability field.…”

Section: Introductionmentioning

confidence: 99%

On Application of the Weak Galerkin Finite Element Method to a Two-Phase Model for Subsurface Flow

2015

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This paper presents studies on applying the novel weak Galerkin finite element method (WGFEM) to a two-phase model for subsurface flow, which couples the Darcy equation for pressure and a transport equation for saturation in a nonlinear manner. The coupled problem is solved in the framework of operator decomposition. Specifically, the Darcy equation is solved by the WGFEM, whereas the saturation is solved by a finite volume method. The numerical velocity obtained from solving the Darcy equation by the WGFEM is locally conservative and has continuous normal components across element interfaces. This ensures accuracy and robustness of the finite volume solver for the saturation equation. Numerical experiments on benchmarks demonstrate that the combined methods can handle very well two-phase flow problems in high-contrast heterogeneous porous media.

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Section: Introductionmentioning

confidence: 99%

On Application of the Weak Galerkin Finite Element Method to a Two-Phase Model for Subsurface Flow

2015

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“…A simple illustration of why local conservation property is required in multiphase flow simulation is shown in Figure 1. Instead of using the standard CGFEMs for such application problems, many endeavors have utilized mixed finite element methods (MFEMs) (see for example [4,6,22,26,15,30,36]), FVM (see for example [16,24,25,29]), and discontinuous Galerkin (DG) methods (see for example [12,13,17,20,27]).…”

Section: Introductionmentioning

confidence: 99%

“…The paper [22] analyzed a combined method for incompressible two-phase flow in porous media. The method consists of the MFEM for Darcy equation and DG for the transport equation.…”

Section: Introductionmentioning

confidence: 99%

Locally Conservative Continuous Galerkin FEM for Pressure Equation in Two-Phase Flow Model in Subsurfaces

Deng

Ginting

2017

J Sci Comput

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A typical two-phase model for subsurface flow couples the Darcy equation for pressure and a transport equation for saturation in a nonlinear manner. In this paper, we study a combined method consisting of continuous Galerkin finite element methods (CGFEMs) followed by a post-processing technique for Darcy equation and finite volume method (FVM) with upwind schemes for the saturation transport equation, in which the coupled nonlinear problem is solved in the framework of operator decomposition. The postprocessing technique is applied to CGFEM solutions to obtain locally conservative fluxes which ensures accuracy and robustness of the FVM solver for the saturation transport equation. We applied both upwind scheme and upwind scheme with slope limiter for FVM on triangular meshes in order to eliminate the non-physical oscillations. Various numerical examples are presented to demonstrate the performance of the overall methodology.

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“…In [31], the combination of the finite element method and the finite difference method has been used to simulate the wormhole generation and propagation in carbonate rocks. In this paper, we use mixed finite element methods [2,3,12,13] to simulate wormhole propagation. The advantages of mixed finite element methods can be listed as below: firstly, they are capable to achieve very accurate and stable approximations for both pressure variables and flux variables across grid-cell interfaces; secondly, they also have the local mass conservation property.…”

Section: Introduction Matrix Acidization Technique Plays An Importanmentioning

confidence: 99%

Mixed finite element-based fully conservative methods for simulating wormhole propagation

Kou

Sun

2016

Computer Methods in Applied Mechanics and Engineering

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. MIXED FINITE ELEMENT-BASED FULLY CONSERVATIVE METHODS FOR SIMULATING WORMHOLE PROPAGATION *JISHENG KOU † , SHUYU SUN ‡ , AND YUANQING WU § Abstract. Wormhole propagation during reactive dissolution of carbonates plays a very important role in the product enhancement of oil and gas reservoir. Because of high velocity and nonuniform porosity, the Darcy-Forchheimer model is applicable for this problem instead of conventional Darcy framework. We develop a mixed finite element scheme for numerical simulation of this problem, in which mixed finite element methods are used not only for the Darcy-Forchheimer flow equations but also for the solute transport equation by introducing an auxiliary flux variable to guarantee full mass conservation. In theoretical analysis aspects, based on the cut-off operator of solute concentration, we construct an analytical function to control and handle the change of porosity with time; we treat the auxiliary flux variable as a function of velocity and establish its properties; we employ the coupled analysis approach to deal with the fully coupling relation of multivariables. From this, the stability analysis and a priori error estimates for velocity, pressure, concentration and porosity are established in different norms. Numerical results are also given to verify theoretical analysis and effectiveness of the proposed scheme.

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Analysis of a combined mixed finite element and discontinuous Galerkin method for incompressible two-phase flow in porous media

Cited by 14 publications

References 50 publications

On Application of the Weak Galerkin Finite Element Method to a Two-Phase Model for Subsurface Flow

On Application of the Weak Galerkin Finite Element Method to a Two-Phase Model for Subsurface Flow

Locally Conservative Continuous Galerkin FEM for Pressure Equation in Two-Phase Flow Model in Subsurfaces

Mixed finite element-based fully conservative methods for simulating wormhole propagation

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