Calculation of colloids filtration in a porous medium

Galaguz, Yuri; Safina, Galina

doi:10.1088/1757-899x/365/4/042005

Cited by 5 publications

(6 citation statements)

References 19 publications

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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%

“…Conditions ( 3) and (5) take 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: Mathematical Modelmentioning

confidence: 99%

“…The solution to the system ( 6), ( 7) is obtained in the form [22,23] Substitute the expansions (10), (11) into the equations ( 6), (7) and equate the terms at the same powers of ε. We obtain a recurrent system of differential equations…”

Section: A S Y M P T O T I C S F O R a L M O S T Constant Coefficientsmentioning

confidence: 99%

“…Substitute the expansions ( 10), (11) into the equations ( 6), ( 7) and equate the terms at the same powers of H. We obtain a recurrent system of differential equations Conditions for the equations ( 12) -( 15) follow from ( 8) and ( 9)…”

Section: S Y S Y S Y C Y C Y C Ymentioning

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%

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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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Section: Consider the Condition On The Concentrations Frontmentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

Section: A S Y M P T O T I C S F O R a L M O S T Constant Coefficientsmentioning

confidence: 99%

Section: S Y S Y S Y C Y C Y C Ymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotics of the Filtration Problem With Almost Constant Coefficients

Кузьмина

Osipov

2021

IJCCSE

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Global asymptotics of filtration in porous media

2019

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Filtration problems are actual for the design of underground structures and foundations, strengthening of loose soil and construction of watertight walls in the porous rock. A liquid grout pumped under pressure penetrates deep into the porous rock. Solid particles of the suspension retained in the pores, strengthen the loose soil and create watertight partitions. The aim of the study is to construct an explicit analytical solution of the filtration problem. A one-dimensional model of deep bed filtration of a monodisperse suspension in a homogeneous porous medium with size-exclusion mechanism of particles retention is considered. Solid particles are freely transferred by the carrier fluid through large pores and get stuck in the throats of small pores. The mathematical model of deep bed filtration includes the mass balance equation for suspended and retained particles and the kinetic equation for the deposit growth. The model describes the movement of concentrations front of suspended and retained particles in an empty porous medium. Behind the concentrations front, solid particles are transported by a carrier fluid, accompanied by the formation of a deposit. The complex model has no explicit exact solution. To construct the asymptotic solution in explicit form, methods of nonlinear asymptotic analysis are used. The new coordinate transformation allows to obtain a parameter that is small at all points of the porous sample at any time. In this paper, a global asymptotic solution of the filtration problem is constructed using a new small parameter. Numerical calculations are performed for a nonlinear filtration coefficient found experimentally. Calculations confirm the closeness of the asymptotics to the solution in the entire filtration domain. For a nonlinear filtration coefficient, the asymptotics is closer to the numerical solution than the exact solution of the problem with a linear coefficient. The analytical solution obtained in the paper can be used to analyze solutions of problems of underground fluid mechanics and fine-tune laboratory experiments.

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