Filtration of 2-particles suspension in a porous medium

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

doi:10.1088/1742-6596/1926/1/012001

Cited by 6 publications

(4 citation statements)

References 19 publications

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“…At the concentration front Γ, the solutions

c_{i}

are discontinuous, and the solutions

s_{i}

are continuous and have discontinuous derivatives. Since systems () and () with conditions () and () do not have smooth solutions in the domain Ω, weak solutions are used (see Nazaikinskii et al [38] and Kuzmina et al [31]). Consider piecewise continuous functions in the domain Ω that are continuous in the closures

{\overset{Ω}{true}}_{0}

and

{\overset{Ω}{true}}_{1}

of both the domains

{normalΩ}_{0}

and

{normalΩ}_{1}

and are discontinuous at the boundary Γ of these domains.…”

Section: Exact Solution and Retention Profilesmentioning

confidence: 99%

“…To solve problems ( 28)- (31) in the domain Ω 1 , pass to the characteristic variables τ, y. The system takes the form…”

Section: System For Total Concentrationsmentioning

confidence: 99%

“…Experimental studies and numerical calculations show that for a bidisperse suspension consisting of both large and small particles, the retention profile can be nonmonotonic (see experiments of Wang et al [24], Leisi et al [25], and studies of the mathematical models [26][27][28][29][30]. Kuzmina et al [31,32] obtained the exact solutions of the two-particle filtration problem. It was proven that the retention profile of large particles decreases monotonically, while the retention profile of small particles is nonmonotonic.…”

Section: Introductionmentioning

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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“…At the concentration front Γ, the solutions

c_{i}

are discontinuous, and the solutions

s_{i}

{\overset{Ω}{true}}_{0}

and

{\overset{Ω}{true}}_{1}

of both the domains

{normalΩ}_{0}

and

{normalΩ}_{1}

and are discontinuous at the boundary Γ of these domains.…”

Section: Exact Solution and Retention Profilesmentioning

confidence: 99%

“…To solve problems ( 28)- (31) in the domain Ω 1 , pass to the characteristic variables τ, y. The system takes the form…”

Section: System For Total Concentrationsmentioning

confidence: 99%

Section: Introductionmentioning

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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“…Since in the process of filtering, the sediment-suspension interface is mobile, the models are usually reduced to Stefan problems [1,4,7], the numerical solution of which, as is known, has a number of specific features [18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

An Axi-Symmetric Problem of Suspensions Filtering with the Formation of a Cake Layer

et al. 2023

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In this paper, we consider a vertically positioned cylindrical filtering element. Filtering occurs in the radial direction, therefore, the direction of the velocities of the liquid and suspended particles coincide with this radial direction. The flow can be considered to be one-dimensional and radially axisymmetric. To describe such a filtering process, the axisymmetric Stefan problem will be formulated. The radial mass balance formalism and Darcy’s law are utilized to obtain a basic equation for cake filtration. The boundary condition at the moving surface is derived and the cake filtration is formulated in a Stefan problem. Equations are derived that describe the dynamics of cake growth in the cake filtration, and they are numerically solved. The influence of different model parameters on the compression and fluid pressure across the cake and the growth of its thickness are studied.

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Inverse Filtration Problem of a Bidisperse Suspension

Kuzmina,

Osipov

2024

Lecture Notes in Civil Engineering

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Filtration problems of suspensions and colloids in porous media are considered when designing tunnels and underground structures. To strengthen weak soil, a liquid solution is injected into the rock, the particles of which are filtered in the pores and distributed far from the well. A deep bed filtration model of 2-particle suspension in a porous material is considered. The purpose of the work is to determine the model parameters from the measured outlet concentration of suspended particles. Using an explicit solution to the direct filtration problem on the concentration front, the inverse problem is reduced to a system of nonlinear algebraic equations, which is a special case of the moment problem. The system is solved by passing to a canonical basis in the space of symmetric polynomials. Conditions for the existence of a solution are obtained. An explicit solution is constructed. The inverse filtration problem of a suspension with particles of two types is solved, determining the initial partial concentrations and filtration coefficients.

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Filtration of 2-particles suspension in a porous medium

Cited by 6 publications

References 19 publications

Retention profiles of multiparticle filtration in porous media

Retention profiles of multiparticle filtration in porous media

An Axi-Symmetric Problem of Suspensions Filtering with the Formation of a Cake Layer

Inverse Filtration Problem of a Bidisperse Suspension

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