Asymptotics for filtration of polydisperse suspension with small impurities

Кузьмина, Людмила Ивановна; Osipov, Yu. V.; Gorbunova, Tatiana

doi:10.1007/s10483-021-2690-6

Cited by 13 publications

(7 citation statements)

References 35 publications

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“…) To find the asymptotics [26,27], we will seek a solution to problem (1), (2) as a series in decreasing exponents:…”

Section: Asymptotic Solution For a Long Timementioning

confidence: 99%

Traveling Wave Solution to Filtration Model in Porous Medium

Kuzmina,

Osipov

2023

Advances in Transdisciplinary Engineering

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Suspension and colloid filtration in porous rocks is encountered in problems of underground hydromechanics associated with construction. The formation of grout sediment in the pores of loose rock increases the water resistance of the soil and strengthens the foundation. A one-dimensional model of filtration in a porous medium considers the particles transport by the flow of a carrier fluid and the deposition of particles on the framework of a porous medium. The purpose of the work is to study the concentrations of suspended and settled particles of a suspension over a long time. Exact and asymptotic methods are used to obtain a solution to the model. The exact solution is presented in an implicit integral form. A set of solutions in the form of traveling waves with an arbitrary initial condition and their asymptotics are constructed. An explicit second-order asymptotic solution for a long time is obtained as an expansion in decreasing exponents. Comparison of the asymptotic solution with the traveling waves makes it possible to choose a single traveling wave corresponding to the exact solution. The closeness of the traveling wave to the exact solution of the filtration model is verified numerically. The traveling wave found determines the explicit asymptotics of the concentration of deposited particles for a long time.

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“…) To find the asymptotics [26,27], we will seek a solution to problem (1), (2) as a series in decreasing exponents:…”

Section: Asymptotic Solution For a Long Timementioning

confidence: 99%

Traveling Wave Solution to Filtration Model in Porous Medium

Kuzmina,

Osipov

2023

Advances in Transdisciplinary Engineering

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“…Let us construct the asymptotics of the solution near the concentration front [29,30]. Expand the functions ( ), ( ) S S O / in Taylor series in powers of S:…”

Section: Asymptotic Solutionmentioning

confidence: 99%

Filtration in Porous Medium with Particle Release

Кузьмина

Osipov

2022

Advances in Transdisciplinary Engineering

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The transport of small particles in soil voids is a common problem in construction. Filtering determines the creation of foundations by pumping liquid grout and building watertight walls in the soil. A 1-D model of depth filtration for a slurry in a porous medium is considered. It is assumed that the velocity of the carrier liquid is high enough to detach the deposited particles from the carcass of the porous medium. To take into account the effect of sediment lifting, the particle release function is introduced into the standard filtration model. For the filtration model with deposit release, analytic solutions are found at the inlet of the porous sample and at the concentration front. An asymptotics near the concentration front and a traveling wave solution are constructed.

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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 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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Asymptotics for filtration of polydisperse suspension with small impurities

Cited by 13 publications

References 35 publications

Traveling Wave Solution to Filtration Model in Porous Medium

Traveling Wave Solution to Filtration Model in Porous Medium

Filtration in Porous Medium with Particle Release

Asymptotics of the Filtration Problem With Almost Constant Coefficients

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