Analysis of the Filtration Problem by Bitwise Search Method

Кузьмина, Людмила Ивановна; Osipov, Yu. V.; Astakhov, Maxim

doi:10.22337/2587-9618-2022-18-3-86-94

Cited by 2 publications

(3 citation statements)

References 2 publications

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“…Solutions () and () were calculated using the bitwise search method described in detail by Kuzmina et al [40].…”

Section: Numerical Calculationsmentioning

confidence: 99%

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Retention profiles of multiparticle filtration in porous media

Kuzmina,

Osipov,

Astakhov

2024

Math Methods in App Sciences

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A one‐dimensional deep bed filtration model of a polydisperse suspension or colloid in a porous medium is considered. The model includes a quasilinear system of 2n equations for concentrations of suspended and retained particles of n types. The problem is reduced to a closed 3 × 3 system for total concentrations of suspended and retained particles and of occupied rock surface area, which allows an exact solution. The exact solution to the n‐particle problem is derived, the existence and uniqueness of the solution are proven, and the solution in the form of a traveling wave is obtained. The retention profiles (dependence of the deposit concentration on the coordinate at a fixed time) of different size particles and the total profile are studied. It is shown that the profile of large particles decreases monotonically, while the profile of small particles is nonmonotonic. Conditions for the monotonicity/nonmonotonicity of the intermediate particle profiles and the total profile are obtained. The maximum point of the small particles profile tends to infinity with unlimited growth of time, and the maximum points of nonmonotonic profiles of intermediate particles are limited. The asymptotical expansion of the maximum points of nonmonotonic profiles is constructed.

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“…Solutions () and () were calculated using the bitwise search method described in detail by Kuzmina et al [40].…”

Section: Numerical Calculationsmentioning

confidence: 99%

“…Various cases of profiles monotonicity are presented below (Table 1). Solutions ( 20) and ( 21) were calculated using the bitwise search method described in detail by Kuzmina et al [40].…”

Section: Consider the Convergent Integralsmentioning

confidence: 99%

Retention profiles of multiparticle filtration in porous media

Kuzmina,

Osipov,

Astakhov

2024

Math Methods in App Sciences

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“…Solving the filtration problem [16,17] in a porous medium is an integral part of achieving the efficiency of the injection process. Currently, many papers are devoted to the problems of monodisperse [18][19][20] and polydisperse [21][22][23] suspension filtration. Suspension filtration in a porous medium with several types of particles is the process of passing a liquid with particles through a porous medium in which particles of various sizes and shapes may be present.…”

Section: Figure 1 Soil Stabilization By Injectionmentioning

confidence: 99%

Modelling of a Three-Dispersed Suspension Filtration

Safina¹

2023

IJCCSE

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The injection method of soil stabilization is one of the methods to improve the soil base during the road construction. This method consists in the introduction of special compounds into the ground with the help of special equipment. Such compositions, as a rule, are solutions of polymers or cement, which harden, forming a solid base. The advantages of the injection method of soil stabilization for roads include rapid completion of work, minimal environmental impact, the possibility of application in difficult geological conditions, as well as strengthening the soil base at great depth. Injection solutions penetrate into microcracks and micropores of soils, forming a deposition. The study of liquid filtration in a porous soil system is of great practical importance. The paper considers the filtration of liquid in a porous medium with three types of particles. In the considered problem, each of the three types of suspension particles is characterized by its linear filtration function. It determines the size-exclusion particle capture mechanism, in which particles whose diameter exceeds the size of the pores get stuck in them, the rest pass through them unhindered. Numerical solutions are obtained for the concentrations of suspended particles of three types, as well as the total deposition. Depending on the initial parameters of the problem, the concentrations of suspended particles are either monotonic functions or non-monotonic, reaching the maximum value. In this paper, asymptotic solutions are constructed for the concentrations of suspended and retained particles near the concentration front, which are compared with numerical ones. The solution is obtained at infinity using a traveling wave.

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Analysis of the Filtration Problem by Bitwise Search Method

Cited by 2 publications

References 2 publications

Retention profiles of multiparticle filtration in porous media

Retention profiles of multiparticle filtration in porous media

Modelling of a Three-Dispersed Suspension Filtration

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