Filtration in Porous Medium with Particle Release

Кузьмина, Людмила Ивановна; Osipov, Yu. V.

doi:10.3233/atde220849

Cited by 2 publications

(1 citation statement)

References 23 publications

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“…To determine the behavior of solutions for long time, consider a traveling wave on the plane ( , ) x t [24,25] ( ), ( ),…”

Section: -D Model Of Deep Bed Filtration Determines the Concentration...mentioning

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 determine the behavior of solutions for long time, consider a traveling wave on the plane ( , ) x t [24,25] ( ), ( ),…”

Section: -D Model Of Deep Bed Filtration Determines the Concentration...mentioning

confidence: 99%

Traveling Wave Solution to Filtration Model in Porous Medium

Kuzmina,

Osipov

2023

Advances in Transdisciplinary Engineering

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Characteristic Method for Solving Filtration Problem

Kuzmina,

Osipov,

Pesterev

2023

IJCCSE

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During construction, a liquid solution of a grout or waterproof filler is pumped into porous rock to improve its properties. The filtration of a suspension moving at a variable speed in a porous medium is simulated. A one-dimensional problem of filtration in a homogeneous porous medium with a curvilinear concentration front of suspended and retained particles is considered. For the numerical solution of the problem by the method of finite differences, the method of characteristics is used. The transition to characteristic variables allows one to straighten the front and construct a discrete grid with a constant step. When calculating the solution using an explicit difference scheme, additional points are used that do not coincide with the grid nodes. A detailed description of the algorithm for calculating a solution at the grid nodes and an example of a numerical solution of the problem are given.

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Filtration in Porous Medium with Particle Release

Cited by 2 publications

References 23 publications

Traveling Wave Solution to Filtration Model in Porous Medium

Traveling Wave Solution to Filtration Model in Porous Medium

Characteristic Method for Solving Filtration Problem

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