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Particles Transport with Deposit Release in Porous Media
P. 539–547.
Kuzmina L., Osipov Y.
Models of transport and filtration of fine particles in porous media are used in the design of foundations, tunnels and hydraulic structures. During the particles transport, some of the particles get stuck in narrow pores and form a sediment. The suspension or colloid flow washes out the retained particles and increases the concentration of suspended particles. Consider a model of the suspension/colloid transport in one-dimensional homogeneous porous media with the simultaneous action of forces aimed at sedimentation and release of particles. The model consists of an equation for mass exchange between particles and an equation describing the rate of sediment formation, taking into account the retention and release of particles. Exact solutions are obtained at entrance of the porous medium, on the front separating the injected fluid and the clean water, and ahead of the front. A solution to the problem is found in the form of a traveling wave.
In book
Vol. 170. , Springer, 2022.
Liudmila I. Kuzmina, Osipov Y., , in: Proceedings of the 10th International Conference on Civil Engineering.: Singapore: Springer, 2024. P. 585–593.
Filtration problems of suspensions and colloids in porous media are considered when designing tunnels and underground structures. To strengthen weak soil, a liquid solution is injected into the rock, the particles of which are filtered in the pores and distributed far from the well. A deep bed filtration model of 2-particle suspension in a porous ...
Added: October 31, 2024
Liudmila I. Kuzmina, Osipov, Y., Pesterev, A., International Journal of Non-Linear Mechanics 2024 Vol. 167 Article 104905
We consider filtration of a suspension in a homogeneous porous medium which is described by a macroscopic 1-D model including the mass exchange equation and the kinetic equation for deposit growth. The standard model assumes that suspended particles move at the same speed as the carrier fluid. However, in some experiments, a lag between the ...
Added: October 31, 2024
Khazali N., Malgaresi G., Russell T. et al., Chemical Engineering Journal 2024 Vol. 496 Article 153973
Modelling of colloidal and nano-suspension transport in porous media has garnered significant attention due to the prevalence of these processes in many engineering applications. A number of experimental studies have reported retention profiles after coreflooding that are hyper-exponential, a feature that the traditional models for deep bed filtration are unable to capture. The aim of ...
Added: October 31, 2024
Kuzmina L., Osipov, Y. V., Astakhov, M. D., Mathematical Methods in the Applied Sciences 2024 Vol. 47 No. 11 P. 8319–8341
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 ...
Added: June 27, 2024
L.I. Kuzmina, Osipov, Y. V., International Journal of Non-Linear Mechanics 2023 Vol. 150 Article 104363
Many technological processes of chemical and environmental engineering are associated with the filtration of fine particles in porous media, specifically in heterogeneous reservoirs. A one-dimensional model of deep bed filtration of suspensions and colloids in a heterogeneous porous medium is derived. The model includes the mass balance equation with variable porosity for the concentrations of ...
Added: May 19, 2023
Kuzmina L., Osipov, Y. V., Astakhov, M. D., Annali di Matematica Pura ed Applicata 2022 Vol. 201 No. 6 P. 2943–2964
During deep bed filtration of suspensions and colloids in a porous medium, some particles are retained in the pores and form a fixed deposit. A one-dimensional mathematical model of filtration with particles of two types is considered. Exact solution is derived. The existence and the uniqueness of the solution are proved by the method of ...
Added: October 26, 2022
Liudmila I. Kuzmina, Osipov Y., Astakhov M., International Journal for Computational Civil and Structural Engineering 2022 Vol. 18 No. 3 P. 86–94
During the construction of ground and underground structures, filtration of a liquid grout in loose soil makes it possible to strengthen the foundation and create underground waterproof partitions. A one-dimensional problem of filtering a bidisperse suspension in a homogeneous porous medium with size-exclusion particle capture mechanism is considered. The article is devoted to the calculation ...
Added: October 26, 2022
Yang S., Osipov Y., Xu C. et al., Chemical Engineering Journal 2022 Vol. 430 No. 2 Article 132812
We discuss reactive flows in porous media that exhibit an irreversible chemical reaction between two components, resulting in large solid-product deposition. Previous works used the analytical solution for the linear problem with low deposition to determine model parameters from the reactant breakthrough concentrations and pressure drop growth across the core during laboratory coreflood. The present ...
Added: March 4, 2022
LIUDMILA I. KUZMINA, OSIPOV Y., International Journal for Computational Civil and Structural Engineering 2021 Vol. 17 No. 2 P. 43–49
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 ...
Added: October 18, 2021
Mironov M., Pislyakov V., Journal of Sound and Vibration 2020 Vol. 473 Article 115223
We discuss results of experiments made in the 2000s with two different models of acoustic (sonic) black holes. Both structures provide linear decrease of sound velocity. The first one is a series of rigid discs fixed on a rod and placed inside the tube, diameters of discs gradually increase according to a parabolic law. The ...
Added: February 19, 2020
Abrashkin A. A., Chaos, Solitons and Fractals 2019 Vol. 118 P. 152–158
We present an analytical description of the class of unsteady vortex surface waves generated by non- uniformly distributed, time-harmonic pressure. The fluid motion is described by an exact solution of the equations of hydrodynamics generalizing the Gerstner solution. The trajectories of the fluid particles are circumferences. The particles on a free surface rotate around circumferences ...
Added: December 17, 2018
Irina Utkina, Mikhail Batsyn, , in: Models, Algorithms and Technologies for Network Analysis, Springer Proceedings in Mathematics & StatisticsVol. 156.: Switzerland: Springer, 2016. P. 115–124.
The cell formation problem (CFP) is an NP-hard optimization problem considered for cell manufacturing systems. Because of its high computational complexity several heuristics have been developed for solving this problem. In this paper we present a branch and bound algorithm which provides exact solutions of the CFP. This algorithm finds optimal solutions for 13 problems ...
Added: October 23, 2018
Liudmila Kuzmina, Bedrikovetsky P., You Z. et al., Chemical Engineering Journal 2017 Vol. 330 P. 1148–1159
A method for determining pore size distribution for a porous medium from long-time straining-dominant mono-sized suspension injection is proposed. The aim is avoiding using multiple-size particle suspensions in short-term challenge tests. We derive an exact solution for long-time non-linear injection of particles with the same size, where the non-linearity is determined by accumulation of strained ...
Added: September 7, 2017
Abrashkin A. A., Yakubovich E. I., Radiophysics and Quantum Electronics 2016 Vol. 58 No. 11 P. 852–857
We show that the discrete frequency spectrum of a plane hydrodynamic flow of ideal incompressible liquid with localized trajectories of the liquid particles can contain only one, two, or an infinite number of harmonics. ...
Added: November 17, 2016
Abrashkin A. A., Oshmarina O. E., Communications in Nonlinear Science and Numerical Simulation 2016 Vol. 34 P. 66–76
The process of rogue wave formation on deep water is considered. A wave of extreme amplitude is born against the background of uniform waves (Gerstner waves) under the action of external pressure on free surface. The pressure distribution has a form of a quasi-stationary “pit”. The fluid motion is supposed to be a vortex one ...
Added: November 3, 2015
Tamm M., Stadnichuk V., Ilyina A. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2014 Vol. 89 P. 042137
We consider two random walkers starting at the same time t = 0 from different points in space separated by a given distance R. We compute the average volume of the space visited by both walkers up to time t as a function of R and t and dimensionality of space d. For d < 4, this volume, after proper renormalization, is shown to be ...
Added: May 23, 2014
You Z., Bedrikovetsky P., Kuzmina L., Abstract and Applied Analysis 2013 Vol. 2013 P. 1–9
Long-term deep bed filtration in porous media with size exclusion particle capture mechanism is studied. For mono dispersed suspension and transport in porous media whit distributed pore sizes, the micro stochastic model allows for upscaling and the exact solution is derived for the obtained macro scale equation system. Results show that transient pore size distribution ...
Added: December 27, 2013
Malkov A., Zinkina J. V., Korotayev A., Physica A: Statistical Mechanics and its Applications 2012 Vol. 391 No. 21 P. 5215–5229
A society is a medium with a complex structure of one-to-one relations between people. Those could be relations between friends, wife-husband relationships, relations between business partners, and so on. At a certain level of analysis, a society can be regarded as a gigantic maze constituted of one-to-one relationships between people. From a physical standpoint it ...
Added: February 4, 2013