Numerical analysis of a finite volume scheme for two incompressible phase flow with dynamic capillary pressure

Bouadjila, Khaled; Mokrane, Abdellah; Saâd, Ali; Saad, Mazen

doi:10.1016/j.camwa.2018.02.021

Cited by 7 publications

(4 citation statements)

References 17 publications

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“…The theoretical results above are independent of the spatial discretization. For Richards' equation and two-phase flow models with equilibrium capillary pressure as well as dynamic capillarity, the (mixed) finite element method is used in [2][3][4], the discontinuous Galerkin method in [5,62] and the finite volume method in [6,[63][64][65]. General gradient schemes are considered in [60,66].…”

Section: Numerical Experimentsmentioning

confidence: 99%

Linearized domain decomposition methods for two-phase porous media flow models involving dynamic capillarity and hysteresis

Lunowa

Pop

Koren

2020

Computer Methods in Applied Mechanics and Engineering

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Section: Numerical Experimentsmentioning

confidence: 99%

Linearized domain decomposition methods for two-phase porous media flow models involving dynamic capillarity and hysteresis

Lunowa

Pop

Koren

2020

Computer Methods in Applied Mechanics and Engineering

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“…Many works [9][10][11][12] are devoted to the numerical implementation of the two-phase fluid flow model with the nonequilibrium law from [4]. For example, in [9], a second-order numerical scheme for both spatial and temporal variables is proposed using a mixed finite element method with the lowest order Thomas-Raviar elements and an implicit Euler scheme.…”

Section: Introductionmentioning

confidence: 99%

“…The paper [12] analyzes the convergence of a "two-point flow" finite volume scheme to approximate the flow of two incompressible phases with dynamic capillary pressure in porous media. In that work, a fully implicit scheme is based on a non-standard approximation of mobility and capillary pressure on a double grid is proposed.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a finite volume element scheme for solving the model two-phase nonequilibrium flow problem

Omariyeva

Yergaliyev

2022

JMMCS

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The paper proposes a hybrid numerical method for solving a model problem of two-phase nonequilibrium flow of an incompressible fluid in a porous medium. This problem is relevant in the modern theory of the motion of multiphase fluids in porous media and has many applications. The studied model is based on the assumption that the relative phase permeabilities and capillary pressure depend not only on saturation, but also on its time derivative. The saturation equation in this problem refers to the type of convection-diffusion with a predominance of convection, which also includes a third-order term to account for the nonequilibrium effects. Due to the hyperbolic nature of the equation, its solution is accompanied by a number of difficulties that lead to the need for an appropriate choice of the solution method. In contrast to previous works, this paper uses a finite volume element method for solving the problem, the construction of which is based on integral balance equations, and an approximate solution is chosen from the finite element space. To discretize the problem, two different dual grids are used based on the main triangulation. In this paper, a number of a priori estimates are obtained which yields the unconditional stability of the scheme as well as its convergence with the second order. The advantages of the approach used include the local conservatism of the scheme, as well as the comparative simplicity of the software implementation of the method. These results are confirmed by a numerical test carried out on the example of a model problem.

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“…Abbasi et al (2018) applied the same approach to incorporate the dynamic capillary pressure effects in their one-dimensional vertical imbibition model for a high permeability case. Bouadjila et al (2018) proposed and analyzed the convergence of a two-point flux approximation finite volume scheme to approximate the incompressible two-phase flow with dynamic capillary pressure in porous media. Tian et al (2018) coupled the dynamic capillary pressure with gas production models to predict reservoir performance in tight sandstone reservoirs.…”

Section: Introductionmentioning

confidence: 99%

Two-Phase Fluid Flow Characterizations in a Tight Rock: A Fractal Bundle of the Capillary Tube Model

Liu¹,

Li²,

Chen

et al. 2019

Ind. Eng. Chem. Res.

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The multiphase fluid flow in the tight rocks can be affected by the existence of the dynamic effect, boundary slip, and boundary layer. In this work, a fractal bundle of the capillary tube model is proposed to incorporate the above-mentioned factors into the two-phase fluid flow characterization in tight porous media. The model has been successfully validated by the experimental data from core-flooding tests, demonstrating its effectiveness to describe the production behavior in tight reservoirs. In addition, sensitivity analysis is conducted to quantify the effects of the dynamic effect, boundary slip, boundary layer, and injection pressure on the oil recovery of the tight formations. Results indicate that the dynamic effect and boundary layer should be taken into consideration when predicting the production behavior, while the boundary slip can be neglected. The predicted recovery can be as high as 23% higher than its actual value if neglecting the dynamic effect while the existence of the boundary layer can decrease the oil recovery by up to 7%.

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Numerical analysis of a finite volume scheme for two incompressible phase flow with dynamic capillary pressure

Cited by 7 publications

References 17 publications

Linearized domain decomposition methods for two-phase porous media flow models involving dynamic capillarity and hysteresis

Linearized domain decomposition methods for two-phase porous media flow models involving dynamic capillarity and hysteresis

Analysis of a finite volume element scheme for solving the model two-phase nonequilibrium flow problem

Two-Phase Fluid Flow Characterizations in a Tight Rock: A Fractal Bundle of the Capillary Tube Model

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