Numerical simulation of two-phase flows in 2-D petroleum reservoirs using a very high-order CPR method coupled to the MPFA-D finite volume scheme

Galindez-Ramirez, G.; Contreras, Fernando Raul Licapa; Carvalho, Darlan Karlo Elisiário de; Lyra, Paulo Roberto Maciel

doi:10.1016/j.petrol.2020.107220

Cited by 10 publications

(2 citation statements)

References 50 publications

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“…Finally, to examine the capability of the proposed limiting scheme to produce a correct and bound‐preserving solution for strongly anisotropic permeability fields, we present the results for the boundary‐value problem illustrated in Figure 16, which was adopted from References 26 and 27. The permeability matrix is defined as follows:

K=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ {}\sin \theta & \cos \theta \end{array}\right]\left[\begin{array}{cc}{k}_1& 0\\ {}0& {k}_2\end{array}\right]\left[\begin{array}{cc}\cos \theta & \sin \theta \\ {}-\sin \theta & \cos \theta \end{array}\right],

where principal permeabilities are set to

{k}_1=2.25\times 1{0}^{-12}

and

{k}_2=2.25\times 1{0}^{-14}

.…”

Section: Numerical Resultsmentioning

confidence: 99%

Bound‐preserving discontinuous Galerkin methods for compressible two‐phase flows in porous media

Sarraf Joshaghani,

Riviere

2023

Numerical Meth Engineering

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This paper presents a numerical study of immiscible, compressible two‐phase flows in porous media, that takes into account heterogeneity, gravity, anisotropy and injection/production wells. We formulate a fully implicit stable discontinuous Galerkin solver for this system that is accurate, that respects maximum principle for the approximation of saturation, and that is locally mass conservative. To completely eliminate the overshoot and undershoot phenomena, we construct a flux limiter that produces bound‐preserving elementwise average of the saturation. The addition of a slope limiter allows to recover a pointwise bound‐preserving discrete saturation. Numerical results show that both maximum principle and monotonicity of the solution are satisfied. The proposed flux limiter does not impact the local mass error and the number of nonlinear solver iterations.

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K=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ {}\sin \theta & \cos \theta \end{array}\right]\left[\begin{array}{cc}{k}_1& 0\\ {}0& {k}_2\end{array}\right]\left[\begin{array}{cc}\cos \theta & \sin \theta \\ {}-\sin \theta & \cos \theta \end{array}\right],

where principal permeabilities are set to

{k}_1=2.25\times 1{0}^{-12}

and

{k}_2=2.25\times 1{0}^{-14}

.…”

Section: Numerical Resultsmentioning

confidence: 99%

Bound‐preserving discontinuous Galerkin methods for compressible two‐phase flows in porous media

Sarraf Joshaghani,

Riviere

2023

Numerical Meth Engineering

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“…We refer the reader to the seminal work [27] for a strong background in reservoir simulation, comprising physical principles, mathematical models, and numerical resolution by finite-difference formulations. There is also some literature on the application of finitevolume numerical methods in the field of reservoir simulation, see for instance [6,11,14,18,20,23].…”

Section: Introductionmentioning

confidence: 99%

Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media

Luna

Hidalgo

2022

Commun. Appl. Math. Comput.

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Two-phase flow in porous media is a very active field of research, due to its important applications in groundwater pollution, $${\text {CO}}_2$$ CO 2 sequestration, or oil and gas production from petroleum reservoirs, just to name a few of them. Fractional flow equations, which make use of Darcy’s law, for describing the movement of two immiscible fluids in a porous medium, are among the most relevant mathematical models in reservoir simulation. This work aims to solve a fractional flow model formed by an elliptic equation, representing the spatial distribution of the pressure, and a hyperbolic equation describing the space-time evolution of water saturation. The numerical solution of the elliptic part is obtained using a finite-element (FE) scheme, while the hyperbolic equation is solved by means of two different numerical approaches, both in the finite-volume (FV) framework. One is based on a monotonic upstream-centered scheme for conservation laws (MUSCL)-Hancock scheme, whereas the other makes use of a weighted essentially non-oscillatory (ENO) reconstruction. In both cases, a first-order centered (FORCE)-$$\alpha$$ α numerical scheme is applied for intercell flux reconstruction, which constitutes a new contribution in the field of fractional flow models describing oil-water movement. A relevant feature of this work is the study of the effect of the parameter $$\alpha$$ α on the numerical solution of the models considered. We also show that, in the FORCE-$$\alpha$$ α method, when the parameter $$\alpha$$ α increases, the errors diminish and the order of accuracy is more properly attained, as verified using a manufactured solution technique.

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Numerical simulation for a incompressible miscible displacement problem using a reduced-order finite element method based on POD technique

Song

Rui

2021

Comput Geosci

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Numerical simulation of two-phase flows in 2-D petroleum reservoirs using a very high-order CPR method coupled to the MPFA-D finite volume scheme

Cited by 10 publications

References 50 publications

Bound‐preserving discontinuous Galerkin methods for compressible two‐phase flows in porous media

Bound‐preserving discontinuous Galerkin methods for compressible two‐phase flows in porous media

Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media

Numerical simulation for a incompressible miscible displacement problem using a reduced-order finite element method based on POD technique

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