A Phenomenological Model of Suspension Filtration in Porous Medium

Fayziev, Bekzodjon

doi:10.12732/ijam.v33i3.10

Cited by 3 publications

(3 citation statements)

References 4 publications

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“…Some results of numerical calculations according to (11) are shown in Figs. 1-18. The following values of the initial parameters were used in the calculations: k = 10 −13 m 2 ; μ = 10 −4 P a • s; p 0 = 5 • 10 5 P a; β * = 3 • 10 −8 P a −1 ; L = 40m.…”

Section: Resultsmentioning

confidence: 99%

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Generalized Relaxation Fractional Differential Model of Fluid Filtration in a Porous Medium

Khuzhayorov,

Djiyanov,

Zokirov

2024

Int. J. of Appl. Math.

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The process of anomalous filtration of a homogeneous liquid in a porous medium is modeled by differential equations with a fractional derivative. Fractional derivatives are used as defined by Caputo. The problem of filtration in a finite homogeneous reservoir is posed and numerically solved. The influence of process abnormality on filtration characteristics was estimated. It is shown that a decrease in the exponent of the derivative in the relaxation term with respect to pressure leads to the decrease of the pressure distribution up to a certain distance from the beginning of the medium, and then to an increase. Reducing the order of the derivative in the relaxation term with respect to the filtration velocity acts inversely. The corresponding dynamics with decreasing orders of derivatives las the filtration velocity. As a special case, the case with the predominance of the filtration velocity relaxation time over the pressure relaxation time is singled out, in particular, when the latter is equal to zero. In this case, the solution of the filtration equation acquires a wave character. With an increase in the difference between relaxation times in terms of filtration velocity and pressure, the propagation velocity of pressure waves decreases.

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Section: Resultsmentioning

confidence: 99%

“…When approximating the fractional derivatives in (11), the methodology of [11,[13][14][15][16][17][21][22][23]28,29] was used.…”

Section: Numerical Solution Of the Problemmentioning

confidence: 99%

Generalized Relaxation Fractional Differential Model of Fluid Filtration in a Porous Medium

Khuzhayorov,

Djiyanov,

Zokirov

2024

Int. J. of Appl. Math.

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“…When a medium undergoes deformation, its properties undergo changes, especially through compaction, which results in a decrease in porosity. Consequently, the reduction in fluid pathways causes a decline in permeability [9,21]. Therefore, it becomes essential to incorporate the correlation between conductivity and tissue tension into the primary equations [17].…”

Section: Introductionmentioning

confidence: 99%

Modeling of Two-Phase Filtration in Deformable Porous Media

Burnashev,

Kaytarov,

Akramov

2023

Int. J. of Appl. Math.

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The paper considers the process of two-phase filtration in a porous medium, taking into account the compressibility of the medium. The process mathematically modeled and solved by the large particle method. The effect of changing the distance between oil wells on the filtration process has been investigated. According to the results obtained, the correct choice of the distance between oil wells has a positive effect on the oil production process.

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