Analytical model for deep bed filtration with multiple mechanisms of particle capture

Кузьмина, Людмила Ивановна; Osipov, Yu. V.; Zheglova, Yulia

doi:10.1016/j.ijnonlinmec.2018.05.015

Cited by 29 publications

(8 citation statements)

References 35 publications

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“…The problem (1)-(4) of one-dimensional filtration of a monodisperse suspension in a porous medium with variable porosity and accessible fractional flow does not have an explicit analytical solution. The paper considers the transition from system (1)-(2) to the equivalent equation (5) and the solution of this equation by the characteristics method. The obtained transcendental system of equations (18)-(19) is solved numerically at each node of the rectangular grid in the domain 1…”

Section: Discussionmentioning

confidence: 99%

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Numerical solution of filtration in porous rock

Safina

2019

E3S Web Conf.

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The filtration problem is one of the most relevant in the design of retaining hydraulic structures, water supply channels, drainage systems, in the drainage of the soil foundation, etc. Construction of transport tunnels and underground structures requires careful study of the soil properties and special work to prevent dangerous geological processes. The model of particle transport in the porous rock, which is based on the mechanical-geometric interaction of particles with a porous medium, is considered in the paper. The suspension particles pass freely through large pores and get stuck in small pores. The deposit concentration increases, the porosity and the permissible flow of particles through large pores changes. The model of one-dimensional filtration of a monodisperse suspension in a porous medium with variable porosity and fractional flow through accessible pores is determined by the quasi-linear equation of mass balance of suspended and retained particles and the kinetic equation of deposit growth. This complex system of differential equations has no explicit analytical solution. An equivalent differential equation is used in the paper. The solution of this equation by the characteristics method yields a system of integral equations. Integration of the resulting equations leads to a cumbersome system of transcendental equations, which has no explicit solution. The system is solved numerically at the nodes of a rectangular grid. All calculations are performed for non-linear filtration coefficients obtained experimentally. It is shown that the solution of the transcendental system of equations and the numerical solution of the original hyperbolic system of partial differential equations by the finite difference method are very close. The obtained solution can be used to analyze the results of laboratory research and to optimize the grout composition pumped into the porous soil.

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Section: Discussionmentioning

confidence: 99%

“…A mathematical model of particle motion in a filter based on size-exclusion mexanism of particle retention in a porous medium is considered in [5], [6] . The suspension particles freely pass through large pores and lock pores that are smaller than the particle size.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of filtration in porous rock

Safina

2019

E3S Web Conf.

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“…In the domain ͞ Ω 1 , the solution to problem (1)-( 4) coincides with the solution to the Goursat problem (1)-( 3), (5). In characteristic variables τ = t -x/v, y = x, the Goursat problem takes the form numerical and analytical methods are used [11][12][13][14][15][16]. Analytical methods allow to obtain exact and asymptotic solutions and their dependence on parameters.…”

Section: Consider the Condition On The Concentrations Frontmentioning

confidence: 99%

“…The mathematical model of deep bed filtration includes the equation for the balance of the masses of suspended and retained particles and the kinetic equation of deposit growth, which form a quasilinear hyperbolic system of the first order partial differential equations [10]. To solve filtration problems, both numerical and analytical methods are used [11][12][13][14][15][16]. Analytical methods allow to obtain exact and asymptotic solutions and their dependence on parameters.…”

Section: Introductionmentioning

confidence: 99%

Asymptotics of the Filtration Problem With Almost Constant Coefficients

Кузьмина

Osipov

2021

IJCCSE

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During the construction of hydraulic and underground structures, a grout solution is pumped into the ground to create waterproof partitions. The liquid grout is filtered in the porous rock and clogs the pores when hardened. The mathematical model of deep bed filtration describes the transfer of suspension particles and colloids by a fluid flow through the pores of a rock. For a one-dimensional filtration problem in a homogeneous porous medium with almost constant coefficients, an asymptotic solution is constructed. The asymptotics is compared with the numerical solution.

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“…The mass balance equation for suspended and retained particles is an analogue of the continuity equation; the kinetic equation determines the deposit growth rate [5]. More sophisticated filtration models for particles and pores of various sizes, constructed on the basis of the balance of suspended and retained particles, are given in [6].…”

Section: Introductionmentioning

confidence: 99%

Filtration in porous rock with initial deposit

Osipov

Galaguz

2019

E3S Web Conf.

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The problems of underground fluid mechanics play an important role in the design and preparation for the construction of tunnels and underground structures. To strengthen the insecure soil a grout solution is pumped under pressure in the porous rock. The liquid solution filters in the pores of the rock and strengthens the soil after hardening. A macroscopic model of deep bed filtration of a monodisperse suspension in a porous medium with a size-exclusion mechanism for the suspended particles capture in the absence of mobilization of retained particles is considered. The solids are transported by the carrier fluid through large pores and get stuck at the inlet of small pores. It is assumed that the accessibility factor of pores and the fractional flow of particles depend on the concentration of the retained particles, and at the initial moment the porous medium contains an unevenly distributed deposit. The latter assumption leads to inhomogeneity of the porous medium. A quasilinear hyperbolic system of two first-order equations serves as a mathematical model of the problem. The aim of the work is to obtain the asymptotic solution near the moving curvilinear boundary - the concentration front of suspended particles of the suspension. To obtain a solution to the problem, methods of nonlinear asymptotic analysis are used. The asymptotic solution is based on a small-time parameter, measured from the moment of the concentration front passage at each point of the porous medium. The terms of the asymptotics are determined explicitly from a recurrent system of ordinary differential and algebraic equations. The numerical calculation is performed by the finite difference method using an explicit TVD scheme. Calculations for three types of microscopic suspended particles show that the asymptotics is close to the solution of the problem. The time interval of applicability of the asymptotic solution is determined on the basis of numerical calculation. The constructed asymptotics, which explicitly determines the dependence on the parameters of the system, allows to plan experiments and reduce the amount of laboratory research.

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Analytical model for deep bed filtration with multiple mechanisms of particle capture

Cited by 29 publications

References 35 publications

Numerical solution of filtration in porous rock

Numerical solution of filtration in porous rock

Asymptotics of the Filtration Problem With Almost Constant Coefficients

Filtration in porous rock with initial deposit

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