ASYMPTOTICS OF a PARTICLES TRANSPORT PROBLEM

Вестник МГСУ 11/2017 Том 12
  • Kuzmina Ludmila Ivanovna - National Research University Higher School of Economics Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Applied Mathematics, National Research University Higher School of Economics, 20 Myasnitskaya st., Moscow, 101000, Russian Federation.
  • Osipov Yuri Viktorovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Applied Mathematics, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.

Страницы 1278-1283

Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.

DOI: 10.22227/1997-0935.2017.11.1278-1283

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Asymptotics of the filtration problem for suspension in porous media

Вестник МГСУ 1/2015
  • Kuzmina Ludmila Ivanovna - Higher School of Economics Department of Applied Mathematics, Moscow Institute of Electronics and Mathematics, Higher School of Economics, 20 Myasnitskaya str., Moscow, 101000, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Osipov Yuri Viktorovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Computer Science and Applied Mathematics, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe Shosse, Moscow, 129337, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 54-62

The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and are stuck at the inlet of pores that are smaller than the particle size. It is considered that one particle can clog only one small pore and vice versa. The particles stuck in the pores remain motionless and form a deposit. The concentrations of suspended and retained particles satisfy a quasilinear hyperbolic system of partial differential equations of the first order, obtained as a result of macro-averaging of micro-stochastic diffusion equations. Initially the porous media contains no particles and both concentrations are equal to zero; the suspension supplied to the porous media inlet has a constant concentration of suspended particles. The flow of particles moves in the porous media with a constant speed, before the wave front the concentrations of suspended and retained particles are zero. Assuming that the filtration coefficient is small we construct an asymptotic solution of the filtration problem over the concentration front. The terms of the asymptotic expansions satisfy linear partial differential equations of the first order and are determined successively in an explicit form. It is shown that in the simplest case the asymptotics found matches the known asymptotic expansion of the solution near the concentration front.

DOI: 10.22227/1997-0935.2015.1.54-62

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  23. You Z., Osipov Y., Bedrikovetsky P., Kuzmina L. Asymptotic Model for Deep Bed Filtration. Chemical Engineering Journal. 2014, vol. 258, pp. 374—385. DOI: http://dx.doi.org/10.1016/j.cej.2014.07.051.
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Asymptotic solution of the filtration equation

Вестник МГСУ 2/2016
  • Kuzmina Ludmila Ivanovna - Higher School of Economics Department of Applied Mathematics, Moscow Institute of Electronics and Mathematics, Higher School of Economics, 20 Myasnitskaya str., Moscow, 101000, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Osipov Yuri Viktorovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Computer Science and Applied Mathematics, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe Shosse, Moscow, 129337, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 49-61

The problem of filtering a suspension of tiny solid particles in a porous medium is considered. The suspension with constant concentration of suspended particles at the filter inlet moves through the empty filter at a constant speed. There are no particles ahead of the front; behind the front of the fluid flow solid particles interact with the porous medium. The geometric model of filtration without effects caused by viscosity and electrostatic forces is considered. Solid particles in the suspension pass freely through large pores together with the fluid flow and are stuck in the pores that are smaller than the size of the particles. It is considered that one particle can clog only one small pore and vice versa. The precipitated particles form a fixed deposit increasing over time. The filtration problem is formed by the system of two quasi-linear differential equations in partial derivatives with respect to the concentrations of suspended and retained particles. The boundary conditions are set at the filter inlet and at the initial moment. At the concentration front the solution of the problem is discontinuous. By the method of potential the system of equations of the filtration problem is reduced to one equation with respect to the concentration of deposit with a boundary condition in integral form. An asymptotic solution of the filtration equation is constructed near the concentration front. The terms of the asymptotic expansions satisfy linear ordinary differential equations of the first order and are determined successively in an explicit form. For verification of the asymptotics the comparison with the known exact solutions is performed.

DOI: 10.22227/1997-0935.2016.2.49-61

Библиографический список
  1. Barenblatt G.I., Entov V.M., Ryzhik V.M. Theory of Fluid Flows through Natural Rocks. Dordrecht, Kluwer Academic Publishers, 1990, 396 p.
  2. Bedrikovetsky P. Mathematical Theory of Oil and Gas Recovery with Applications to Ex-USSR Oil and Gas Fields. Dordrecht, Kluwer Academic, 1993, 576 p. DOI: http://www.doi.org/10.1007/978-94-017-2205-6.
  3. Khilar K.C., Fogler H.S. Migrations of Fines in Porous Media. Dordrecht, Kluwer Academic Publishers, 1998, 173 p. DOI: http://www.doi.org/10.1007/978-94-015-9074-7.
  4. Tien C., Ramarao B.V. Granular Filtration of Aerosols and Hydrosols. 2nd ed. Amsterdam, Elsevier, 2007, 512 p.
  5. Baveye P., Vandevivere P., Hoyle B.L., DeLeo P.C., Sanchez De Lozada D. Environmental Impact and Mechanisms of the Biological Clogging of Saturated Soils and Aquifer Materials. Critical Reviews in Environmental Science and Technology. 1998, vol. 28, pp. 123—191. DOI: http://www.doi.org/10.1080/10643389891254197.
  6. Jeong S., Vigneswaran S. Assessment of Biological Activity in Contact Flocculation Filtration Used as a Pretreatment in Seawater Desalination. Chemical Engineering Journal. 2013, vol. 228, pp. 976—983. DOI: http://www.doi.org/10.1016/j.cej.2013.05.085.
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  11. Chalk P., Gooding N., Hutten S., You Z., Bedrikovetsky P. Pore Size Distribution from Challenge Coreflood Testing by Colloidal Flow. Chemical Engineering Research and Design. 2012, vol. 90. Pp. 63—77.
  12. Santos A., Bedrikovetsky P. A Stochastic Model for Particulate Suspension Flow in Porous Media. Transport in Porous Media. 2006, vol. 62, pp. 23—53.
  13. Vollebregt H.M., Van der Sman R.G.M., Boom R.M. Model for Particle Migration in Bidisperse Suspensions by Use of Effective Temperature. Faraday Discussions. 2012, vol. 158, pp. 89—103. DOI: http://dx.doi.org/10.1039/C2FD20035J.
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  17. Yuan H., You Z., Shapiro A., Bedrikovetsky P. Improved Population Balance Model for Straining-Dominant Deep Bed Filtration Using Network Calculations. Chemical Engineering Journal. 2013, vol. 226, pp. 227—237. DOI: http://dx.doi.org/10.1016/j.cej.2013.04.031.
  18. Gitis V., Rubinstein I., Livshits M., Ziskind G. Deep-bed Filtration Model with Multistage Deposition Kinetics. Chemical Engineering Journal. 2010, vol. 163, no. 1—2, pp. 78—85. DOI: http://dx.doi.org/10.1016/j.cej.2010.07.044.
  19. You Z., Osipov Y., Bedrikovetsky P., Kuzmina L. Asymptotic Model for Deep Bed Filtration. Chemical Engineering Journal. 2014, vol. 258, pp. 374—385. DOI: http://dx.doi.org/10.1016/j.cej.2014.07.051.
  20. Yuan H., Shapiro A., You Z., Badalyan A. Estimating Filtration Coefficients for Straining from Percolation and Random Walk Theories. Chemical Engineering Journal. 2012, vol. 210, pp. 63—73. DOI: http://dx.doi.org/10.1016/j.cej.2012.08.029.
  21. Kuzmina L.I., Osipov Yu.V. Inverse Problem of Filtering the Suspension in Porous Media. International Journal for Computational Civil and Structural Engineering. 2015, vol. 11, no. 1, pp. 34—41.
  22. Bedrikovetsky P. Upscaling of Stochastic Micro Model for Suspension Transport in Porous Media. Transport in Porous Media. 2008, vol. 75, no. 3, pp. 335—369. DOI: http://dx.doi.org/10.1007/s11242-008-9228-6.
  23. Kuzmina L.I., Osipov Yu.V. Particle Transportation at the Filter Inlet. International Journal for Computational Civil and Structural Engineering. 2014, vol. 10, no. 3, pp. 17—22.
  24. Herzig J.P., Leclerc D.M., Legoff P. Flow of Suspensions Through Porous Media — Application to Deep Filtration. Industrial and Engineering Chemistry. 1970, vol. 62 (5), pp. 8—35. DOI: http://dx.doi.org/10.1021/ie50725a003.
  25. Vyazmina E.A., Bedrikovetskii P.G., Polyanin A.D. New Classes of Exact Solutions to Nonlinear Sets of Equations in the Theory of Filtration and Convective Mass Transfer. Theoretical Foundations of Chemical Engineering. 2007, vol. 41, no. 5, pp. 556—564. DOI: http://dx.doi.org/10.1134/S0040579507050168.
  26. Bedrikovetsky P.G., Marchesin D., Checaira F., Serra A.L., Resende E. Characterization of Deep Bed Filtration System from Laboratory Pressure Drop Measurements. Journal of Petroleum Science and Engineering. 2001, vol. 32, no. 3, pp. 167—177. DOI: http://dx.doi.org/10.1016/S0920-4105(01)00159-0.
  27. Yuan H., Shapiro A., You Z., Badalyan A. Estimating Filtration Coefficients for Straining from Percolation and Random Walk Theories. Chemical Engineering Journal. 2012, vol. 210, pp. 63—73. DOI: http://dx.doi.org/10.1016/j.cej.2012.08.029.
  28. Fallah H., Fathi H.B., Mohammadi H. The Mathematical Model for Particle Suspension Flow through Porous Medium. Geomaterials. 2012, vol. 2, no. 3, pp. 57—62. DOI: http://dx.doi.org/10.4236/gm.2012.23009.

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TECHNOLOGY OF ALIGNMENT OF THE BUILDING OF ZAGORSK PUMPED STORAGE STATION BY COMPENSATION GROUTING METHOD

Вестник МГСУ 4/2018 Том 13
  • Kharchenko Aleksey Igorevich - ZAO InGeoStroy; Institute of Expert Evaluation and Engineering, Moscow State University of Civil Engineering (National Research University) (MGSU) general manager; Candidate of Technical Sciences, Chief Executive, ZAO InGeoStroy; Institute of Expert Evaluation and Engineering, Moscow State University of Civil Engineering (National Research University) (MGSU), 7 Kalitneykovskaya, Moscow, 109147, Russian Federatio; 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Kharchenko Igor’ Yakovlevich - Research and Development Institute of Expert Evaluation and Engineering, Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, Head of Division, Research and Development Institute of Expert Evaluation and Engineering, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Panchenko Aleksandr Ivanovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences. Professor, Department of Binders and Concretes Technology, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Gazdanov David Vladimirovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Master Student, Department of Reinforced Concrete and Stone Structures, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 490-498

Subject: elimination of excessive non-uniform deformations of the building of Zagorsk pumped storage station unit (pumped-storage hydroelectric power station) under construction by using the method of compensation grouting. Research objectives: development of a methodology for assigning optimal values of the main technological parameters, such as pressure, intensity of injected mixture, consumption of the mixture per unit volume of soil, based on experimental data of tests of various types of soil on the model; justification of the method for calculation of pressure for fracturing the casing layer of the tube-a-manchette before injection. Materials and methods: the following materials were used: high permeability grouts “KN-1” with adjustable structural strength for primary impregnation of the soil massif; injection material “KN-2” with increased viscosity and a slow strength gain to create a stressed state in the soil and ensure leveling of the building; casing grout “Solidur” for fixing the tube-a-manchette in the borehole. Kinetics of impregnation and the nature of distribution of the material “KN-1” were studied on a unidirectional model. Results: on the laboratory unidirectional model, the main technological parameters were worked out for alignment of the building of Zagorsk pumped storage station unit using the technology of compensation grouting at the experimental site located in immediate vicinity of the main facility. Nomograms for assignment of optimal technological parameters of the compensation grouting process were developed. Conclusions: tested mineral-based injection systems fully comply with the technological requirements for production of works on compensation grouting. The results of experimental and theoretical studies allow us to reasonably assign optimal values of the main parameters of technological regulations for all stages of production of works on compensation grouting.

DOI: 10.22227/1997-0935.2018.4.490-498

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FEATURES OF PERMEABILITY CALCULATION FOR CONCRETE-LINED FACING WITH SEALED SEAMS TAKING INTO ACCOUNT THE GROUND PERMEABILITY

Вестник МГСУ 5/2018 Том 13
  • Kosichenko Yuriy Mikhaylovich - Russian Scientific Research Institute of Land Improvement Problems (RSRILIP) Doctor of Technical Sciences, Professor, Chief Scientific Officer, Russian Scientific Research Institute of Land Improvement Problems (RSRILIP), 190 Baklanovskiy, Novocherkassk, Rostov oblast, 346400, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Baev Oleg Andreevich - Russian Scientific Research Institute of Land Improvement Problems (RSRILIP) Candidate of Technical Sciences, Senior Researcher, Russian Scientific Research Institute of Land Improvement Problems (RSRILIP), 190 Baklanovskiy, Novocherkassk, Rostov oblast, 346400, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Garbuz Aleksandr Yur’evich - Russian Scientific Research Institute of Land Improvement Problems (RSRILIP) Postgraduate Student, Junior Researcher, Russian Scientific Research Institute of Land Improvement Problems (RSRILIP), 190 Baklanovskiy, Novocherkassk, Rostov oblast, 346400, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 633-642

Subject: calculation of filtration through concrete-lined facings with the subsequent construction of diagrams of excess pressure when sealing the seams. The considered case of water permeability of the sealed seam of the facing refers to a two-layer medium with a sealed screen and an underlying base in which three types of excess pressure diagrams can be formed depending on the ratio of the filtration coefficient of the ground-soil to that of the sealed layer. Research objectives: investigation of cases of water permeability of the sealed seam of the facing in a two-layer medium where the top layer constitutes a sealed screen of soil in which three types of excess pressure diagrams can be formed depending on the ratio of the filtration coefficient of the ground-soil to that of the sealed layer. Materials and methods: dependencies of specific flow through the sealed seam are considered. Results: for the analyzed cases of water permeability of the sealed seam, it was established that for the ratio of ground soil filtration coefficient to that of the sealed layer the following values are obtained: 1) when , the excess pressure would be positive and the filtration in the foundation would proceed with complete saturation of pores with water; 2) when , the diagram corresponds to such a degree of seam sealing, at which the excess pressure at its base falls to zero; 3) when , there is a negative excess pressure (i.e., vacuum), and the filtration with full pore saturation transitions to motion with partial saturation of pores. Conclusions: The obtained value of the speed of spreading of seepage flow under the sealed seam in the first case when is (1.0> 0.274 m/day), in the second case when - (1.0 ≅ 1.02 m/day), and in the third case, when - (1.0 < 2.48 m/day). These data confirm the nature of the filtration process in the ground-soil under the seam: in the first case - with complete saturation of pores, in the second case, there is a boundary with the transition from complete saturation of the soil to partially saturated soil, and in the third case - with partial saturation of the ground-soil, which corresponds to previously established concepts of filtration nature for infiltration basins.

DOI: 10.22227/1997-0935.2018.5.633-642

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