Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media

2014 ◽  
Vol 30 (5) ◽  
pp. 1674-1699 ◽  
Author(s):  
Jisheng Kou ◽  
Shuyu Sun
Keyword(s):  
Porous Media ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Two Phase Flow ◽  
Mass Conservation ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Galerkin Methods ◽  
Two Phase

A novel discontinuous Galerkin model for two-phase flow in porous media using an improved IMPES method

2016 ◽  
Vol 26 (1) ◽  
pp. 284-306 ◽  
Author(s):  
Mehdi Jamei ◽  
H Ghafouri
Keyword(s):  
Porous Media ◽  
Discontinuous Galerkin ◽  
Numerical Scheme ◽  
Two Phase Flow ◽  
Weighted Average ◽  
Computation Time ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Content Type

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.

An efficient discontinuous Galerkin method for two-phase flow modeling by conservative velocity projection

2016 ◽  
Vol 26 (1) ◽  
pp. 63-84 ◽  
Author(s):  
Mehdi Jamei ◽  
H Ghafouri
Keyword(s):  
Porous Media ◽  
Discontinuous Galerkin ◽  
Two Phase Flow ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Content Type ◽  
Proposed Model ◽  
Dg Method ◽  
Velocity Projection

Purpose – The purpose of this paper is to present a novel sequential implicit discontinuous Galerkin (DG) method for two-phase incompressible flow in porous media. It is based on the wetting phase pressure-saturation formulation with Robin boundary condition (Klieber and Riviere, 2006) using H(div) velocity projection. Design/methodology/approach – The local mass conservation and continuity of normal component of velocity across elements interfaces are enforced by a simple H(div) velocity projection in lowest order Raviart-Thomas (RT0) space. As further improvements, the authors use the weighted averages and the scaled penalties in spatial DG discretization. Moreover, the Chavent-Jaffre slope limiter, as a consistent non-oscillatory limiter, is used for saturation values to avoid the spurious oscillations. Findings – The proposed model is verified by a pseudo 1D Buckley-Leverett problem in homogeneous media. Two homogeneous and heterogeneous quarter five-spot benchmark problems and a random permeable medium are used to show the accuracy of the method at capturing the sharp front and illustrate the impact of proposed improvements. Research limitations/implications – The work illustrates incompressible two-phase flow behavior and the capillary pressure heterogeneity between different geological layers is assumed to be negligible. Practical implications – The proposed model can efficiently be used for modeling of two-phase flow in secondary recovery of petroleum reservoirs and tracing the immiscible contamination in porous media. Originality/value – The authors present an efficient sequential DG method for immiscible incompressible two-phase flow in porous media with improved performance for detection of sharp frontal interfaces and discontinuities.

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