Modeling of filtration of 2-types particles suspension in a porous medium

Galaguz, Yuri; Safina, Galina

doi:10.1051/matecconf/201711700053

Cited by 9 publications

(3 citation statements)

References 20 publications

(19 reference statements)

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“…To test the obtained solution the problem (1)-(4) was numerically solved by the method of finite differences, similarly to [14]- [16]. The integrals from the left side of equation 1over a rectangular grid cell were approximated by the formulas of trapezoids and rectangles, which have a second order of accuracy.…”

Section: Methodsmentioning

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: Methodsmentioning

confidence: 99%

“…,(17) is solved under the assumption that functions ( ), ( ), ( ) filtration coefficient is zero at a certain positive value S , otherwise the concentration of retained particles increases indefinitely and is infinite in the limit.Then the cubic polynomial () equations(16),(17) can be represented as a sum of elementary fractions that can be integrated easily:…”

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confidence: 99%

Numerical solution of filtration in porous rock

Safina

2019

E3S Web Conf.

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“…For a monodisperse suspension, the retention profiles decrease monotonically (see, e.g., earlier studies [21][22][23]). Experimental studies and numerical calculations show that for a bidisperse suspension consisting of both large and small particles, the retention profile can be nonmonotonic (see experiments of Wang et al [24], Leisi et al [25], and studies of the mathematical models [26][27][28][29][30]. Kuzmina et al [31,32] obtained the exact solutions of the two-particle filtration problem.…”

Section: Introductionmentioning

confidence: 99%

Retention profiles of multiparticle filtration in porous media

Kuzmina,

Osipov,

Astakhov

2024

Math Methods in App Sciences

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A one‐dimensional deep bed filtration model of a polydisperse suspension or colloid in a porous medium is considered. The model includes a quasilinear system of 2n equations for concentrations of suspended and retained particles of n types. The problem is reduced to a closed 3 × 3 system for total concentrations of suspended and retained particles and of occupied rock surface area, which allows an exact solution. The exact solution to the n‐particle problem is derived, the existence and uniqueness of the solution are proven, and the solution in the form of a traveling wave is obtained. The retention profiles (dependence of the deposit concentration on the coordinate at a fixed time) of different size particles and the total profile are studied. It is shown that the profile of large particles decreases monotonically, while the profile of small particles is nonmonotonic. Conditions for the monotonicity/nonmonotonicity of the intermediate particle profiles and the total profile are obtained. The maximum point of the small particles profile tends to infinity with unlimited growth of time, and the maximum points of nonmonotonic profiles of intermediate particles are limited. The asymptotical expansion of the maximum points of nonmonotonic profiles is constructed.

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