Numerical simulation of the two-phase fluid filtration in heterogeneous media

Васильев, В. И.; Васильева, М. А.; Laevsky, Yu. M.; Тимофеева, Т. С.

doi:10.1134/s1990478917020156

Cited by 3 publications

(1 citation statement)

References 7 publications

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“…С одной стороны, наличие диффузионного члена играет роль естественной регуляризации, но с другой стороны, самым существенным образом усиливает ограничение на шаг интегрирования, обусловленное условием устойчивости явной схемы, используемой в IMPES методе. В связи с этим возникли модификации IMPES метода в сторону повышения неявности схемы с целью ослабления ограничений на шаг интегрирования (см., например, [13]), вплоть до чисто неявной схемы [15,19,41]. В случае отсутствия в модели капиллярных сил шаг по времени явной семы регламентируется только условием Куранта, что вполне соответствует физическим представлениям о процессе.…”

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On the streamline upwind scheme of solution to the filtration problem

Ivanov¹,

Kremer²,

Laevsky³

2019

Sib. Elektron. Mat. Izv.

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The work is devoted to one of the approaches in the numerical simulation of filtration processes of a two-phase incompressible fluid. Bukley -Leverett problem is considered with solutions of a shock wave type. Within the mixed finite element method upwind algorithm for solution to equation for saturation is proposed, which gives solutions without numerical oscillations at the discontinuity. Special attention is paid to a new approach to solving the degenerate Neumann problem in a mixed formulation for the pressure and total flow velocity. The work is accompanied by an illustration of the results of numerical experiments for 3D problem.

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unclassified

On the streamline upwind scheme of solution to the filtration problem

Ivanov¹,

Kremer²,

Laevsky³

2019

Sib. Elektron. Mat. Izv.

Self Cite

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One-Dimensional Mathematical Model and a Numerical Solution Accounting Sedimentation of Clay Particles in Process of Oil Filtering in Porous Medium

Nazirova

Nematov

Sadikov

et al. 2021

Intelligent Human Computer Interaction

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Two-phase flow simulation algorithm for numerical estimation of relative phase permeability curves of porous materials

Khachkova,

Lisitsa,

Gondul

et al. 2024

Russian Journal of Numerical Analysis and Mathematical Modelling

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The paper presents an algorithm for three-dimensional modelling of two-phase flows on the scale of pore size order for numerical evaluation of relative phase permeability curves of porous materials. Such an evaluation is performed based on the results of numerical simulation of primary drainage with subsequent waterflooding. In this case, models of porous materials based on three-dimensional tomographic images of rocks are used. The simulation of the flow considers the Stokes equation and the Cahn–Hilliard equation for modelling phase transfer, which allows us to determine phases using the concentration function. The combination of the phase field method and finite difference method makes it possible to correctly take into account the contact angle and stably calculate surface tension forces in domains with complex topology.

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Numerical simulation of the two-phase fluid filtration in heterogeneous media

Cited by 3 publications

References 7 publications

On the streamline upwind scheme of solution to the filtration problem

On the streamline upwind scheme of solution to the filtration problem

One-Dimensional Mathematical Model and a Numerical Solution Accounting Sedimentation of Clay Particles in Process of Oil Filtering in Porous Medium

Two-phase flow simulation algorithm for numerical estimation of relative phase permeability curves of porous materials

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