Finite Analytic Method for 2d Fluid Flow in Porous Media With Permeability in Tensor Form

Liu, Zhifan; Wang, Xiaohong

doi:10.1615/jpormedia.v19.i6.50

Cited by 6 publications

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“…Then the potential has linear piecewise distributions. The details of the derivation can be found out in the paper [13].…”

Section: Appendixmentioning

confidence: 99%

“…The cause of this difficulty is that the harmonic mean algorithm is based upon the linear distribution assumption of the potential, but in fact, the distribution is power‐law. Actually, the potential will have the power‐law behavior and its gradient will diverge as approaching the node joining the different permeability areas for the 2D case . This specific behavior causes the traditional numerical method to converge very slowly in the case of the strong conductivity heterogeneity.…”

Section: Introductionmentioning

confidence: 99%

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Finite analytic numerical method for three‐dimensional quasi‐laplace equation with conductivity in tensor form

Wang

Liu

et al. 2017

Numerical Methods Partial

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The finite analytic numerical method for 3D quasi‐Laplace equation with conductivity in full tensor form is constructed in this article. For cubic grid system, the gradient of the potential variable will diverge when tending to the common edge joining the four grids with different conductivities. However, the potential gradient along the tangential direction is of limited value. As a consequence, the 3D quasi‐Laplace equations will behave as a quasi‐2D one. An approximate analytical solution of the 3D quasi‐Laplace equation can be found around the common edge, which is expressed as a combination of a power‐law function and a linear function. With the help of this approximate analytical solution, a 3D finite analytical numerical scheme is then constructed. Numerical examples show that the proposed numerical scheme can provide rather accurate solutions only with 3 × 3 × 3 or 4 × 4 × 4 subdivisions. More important, the convergent speed of the numerical scheme is independent of the conductivity heterogeneity. In contrast, when using the traditional numerical schemes, typically such as the MPFA method, the refinement ratio for the grid cell needs to increase dramatically to get an accurate result for the strong heterogeneous case.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1475–1492, 2017

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“…Then the potential has linear piecewise distributions. The details of the derivation can be found out in the paper [13].…”

Section: Appendixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite analytic numerical method for three‐dimensional quasi‐laplace equation with conductivity in tensor form

Wang

Liu

et al. 2017

Numerical Methods Partial

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“…It is known that the harmonic mean algorithm underestimates the interface flux, especially for strong heterogeneities, and the error is unbounded. To improve the accuracy of calculating the internodal transmissibility, the FAM for the flow in heterogeneous porous media was constructed by Liu and Wang 12–19 . The local analytical solution of the quasi‐Laplacian equation containing the singular point was found, and based on this, the internodal transmissibility of the two adjacent cells can be calculated accurately.…”

Section: Introductionmentioning

confidence: 99%

“…To improve the accuracy of calculating the internodal transmissibility, the FAM for the flow in heterogeneous porous media was constructed by Liu and Wang. [12][13][14][15][16][17][18][19] The local analytical solution of the quasi-Laplacian equation containing the singular point was found, and based on this, the internodal transmissibility of the two adjacent cells can be calculated accurately. The effect of applying the interface transmissibility calculated from FAM is amazing, and its biggest advantage is that its accuracy is independent of the strength of heterogeneity.…”

Section: Introductionmentioning

confidence: 99%

Finite analytical method on corner‐point grid for fluid flow in heterogeneous porous media

Liu,

Wang,

Liu

et al. 2023

Num Anal Meth Geomechanics

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The three‐dimensional (3D) corner‐point grid system, as an industrial standard, has been widely used in oil reservoir geological modeling and numerical simulation due to its versatility compared to traditional orthogonal grids. The finite analytical method (FAM) is proposed for corner‐point grid systems in this article, which can greatly improve the simulation accuracy, especially for strongly heterogeneous porous media. Based on the approximate analytical solution around the edge of the corner‐point cells, the internodal transmissibility of two adjacent cells is recalculated to replace the traditional one. The traditional internodal transmissibility is calculated based on the harmonic mean of the permeabilities of the two adjacent cells, which will greatly underestimate the transmissibility and lead to an uncontrollable error as the strength of heterogeneity increases. The proposed FAM can calculate the internodal transmissibility rather accurately, and its accuracy is irrelevant to the strength of the heterogeneity, which is the main advantage of FAM. Numerical tests show that the simulation results of the proposed FAM converge much faster than the traditional method as the cells are refined. The proposed FAM can be easily extended to the simulation of multiphase flow and be easily embedded in commercial reservoir numerical simulation software.

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“…Being unconditionally stable, it allows for selecting large time steps which are able to solve years of operation of complete reservoirs with dozens of producers and injectors in a few hours of computational time [Künze et al, 2013;Liu et al, 2016]. However, FIM is not well suited for detailed simulation, as required in the near wellbore region, where smaller time steps are needed to capture fast dynamic behaviour and coupling with pipe simulators.…”

Section: Motivationmentioning

confidence: 99%

A fast IMPES multiphase flow solver in porous media for reservoir simulation

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Finite Analytic Method for 2d Fluid Flow in Porous Media With Permeability in Tensor Form

Cited by 6 publications

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Finite analytic numerical method for three‐dimensional quasi‐laplace equation with conductivity in tensor form

Finite analytic numerical method for three‐dimensional quasi‐laplace equation with conductivity in tensor form

Finite analytical method on corner‐point grid for fluid flow in heterogeneous porous media

A fast IMPES multiphase flow solver in porous media for reservoir simulation

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