Filtration model of the unsteady suspension flow in a porous medium

Кузьмина, Людмила Ивановна; Osipov, Yu. V.

doi:10.1051/matecconf/201711700097

Cited by 3 publications

(1 citation statement)

References 15 publications

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“…There are various filtration models of monodisperse and polydisperse suspensions [7], [8]. In a number of important special cases, it is possible to obtain an exact or asymptotic solution of the problem [9], [10].…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Numerical solution of filtration in porous rock

Safina

2019

E3S Web Conf.

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Model of grout filtration in a porous soil

Gorbunova

2018

IOP Conf. Ser.: Mater. Sci. Eng.

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A chemical reaction model in a porous medium

Кузьмина

Osipov

2020

IOP Conf. Ser.: Mater. Sci. Eng.

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Chemical reactions in a porous medium are found in many natural phenomena and technological processes. Reactive substances dissolved in groundwater can significantly change the soil strength. The precipitate formed as a result of the reaction changes the porous medium structure and affects the porosity and permeability. A one-dimensional model of the reaction of two reagents in a homogeneous porous medium with a linear reaction function is considered. The model includes the mass balance equations of each reagent and precipitate, and the kinetic equation of precipitate growth. It is assumed that the precipitate is stationary and the growth rate of the precipitate is proportional to the reagents’ concentration. A carrier fluid with constant concentration reagents is injected at the empty porous medium entrance. The reaction front moves in a porous medium at a constant speed. The exact solution to the problem is constructed by eliminating the unknown functions and lowering the equations’ order. A Riemann invariant that relates the concentration of sediment and reagents to the system’s characteristics was found. The reaction’s numerical simulation is performed. It is shown that, for a long time, the reagents’ concentrations and the precipitate tend to final limit values. Sediment profiles always decrease monotonously, and the type of the profiles’ convexity changes.

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Filtration model of the unsteady suspension flow in a porous medium

Cited by 3 publications

References 15 publications

Numerical solution of filtration in porous rock

Numerical solution of filtration in porous rock

Model of grout filtration in a porous soil

A chemical reaction model in a porous medium

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