Eng During last 365 days Approved articles: 2088,   Articles in work: 317 Declined articles: 839 
Articles and journals | Tariffs | Payments | Your profile

Back to contents

Construction and investigation of a filtration model for a suspension in a porous soil
Gorbunova Tatiana Nikolaevna

PhD in Technical Science

associate professor of the Department of Applied Mathematics, Moscow State University of Civil Engineering, Department of Information Systems and Technolologies, Moscow Polytechnic University

107023, Russia, g. Moscow, ul. B.semenovskaya, 38, of. 4603





The subject of the study is the filtration problem, which describes the distribution of suspended solids in a loose porous soil. The urgency of constructing a model is determined by the need to strengthen loose soil by pumping under pressure a solution in the form of a suspension that, when hardened, forms a waterproof layer. The author's main goal is to construct a model for the motion of suspended particles of a suspension and colloids and to form a sediment in a porous ground for various filtration regimes. The distributions of solid particles of various sizes carried by the carrier liquid and settled on the framework of the porous medium are studied at different rates of precipitate growth.The one-dimensional filtration model with the particle retention mechanism includes a hyperbolic system of first-order equations with inconsistent initial and boundary conditions that generate discontinuous solutions. For polydisperse media, a modified mathematical model describing the competition of particles of different sizes for small pores is considered. The computer circuit for finding the numerical solution is constructed by the method of finite differences. The optimization of the method is used to improve convergence and reduce computation time. The main results of the study are a multi-particle model of solution filtration in a porous soil, taking into account the variety of sizes of suspended particles. A numerical calculation of the problem is performed for various blocking filter coefficients. Solutions are obtained with a discontinuity at the concentration front. Approbation of the found numerical solutions is carried out. Plots of the dependence of the concentrations of suspended and sedimented particles on time and coordinates are constructed.

Keywords: finite-difference methods, numerical solution, mathematical model, suspended particles, porous medium, deep bed filtration, grout, discontinuous solutions, retained particles, Euler's method



Article was received:


Review date:


Publish date:


This article written in Russian. You can find full text of article in Russian here .

Yoon J., Mohtar El C.S. Groutability of Granular Soils Using Bentonite Grout Based on Filtration Model // Transp Porous Med. 2014. 102(3) pp. 365-385.
Shucai Li, Rentai Liu, Qingsong Zhang, Xiao Zhang Protection against water or mud inrush in tunnels by grouting: a review // Journal of Rock Mechanics and Geotechnical Engineering. 2016. 8 pp. 753-766.
Bedrikovetsky P.G. Upscaling of Stochastic Micro Model for Suspension Transport in Porous Media // Transport in Porous Media. 2008. 75 pp. 335369.
You Z., Badalyan A., Bedrikovetsky P. Size-exclusion colloidal transport in porous media stochastic modeling and experimental study. // SPE Journal. 2013. 18. pp. 620633.
Vyazmina E.A., Bedrikovetsky 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. 41(5). pp. 556564.
You Z., Osipov Y., Bedrikovetsky P., Kuzmina L. Asymptotic model for deep bed filtration. // Chemical Engineering Journal. 2014. 258. pp. 374-385.
Herzig J.P., Leclerc D.M., le Goff P. Flow of suspensions through porous mediaapplication to deep filtration. // Industrial and Engineering Chemistry. 1970. 62(8). pp. 835.
Osipov Yu. Calculation of the filtration of polydisperse suspension with a small rate. // Matec Web of Conferences. 2017, vol. 117, 00131, 6 p
Kuzmina L.I., Osipov Y.V., Galaguz Y.P. A model of two-velocity particles transport in a porous medium. // International Journal of Non-Linear Mechanics. 2017. 93. pp. 16.
E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, 3 ed., Springer, Dordrecht, 2009.
Kuzmina L.I., Osipov Y.V. Filtration model of the unsteady suspension flow in a porous medium. // Matec Web of Conferences. 2017. v. 117, 00097
You Z., Bedrikovetsky P., Kuzmina L. Exact Solution for Long-Term Size Exclusion Suspension-Colloidal Transport in Porous Media. // Abstract and Applied Analysis. 2013. pp. 19.
Bedrikovetsky P., You Z., Badalyan A., Osipov Yu., Kuzmina L. Analytical model for straining-dominant large-retention depth filtration. // Chemical Engineering Journal. 2017. 330. pp.11481159.
Kuz'mina L.I., Osipov Yu.V. Asimptotika zadachi fil'tratsii suspenzii v poristoi srede. // Vestnik MGSU. 2015. 1. pp. 54-62
Kuzmina L.I., Osipov Y.V. Asymptotics of a particles transport problem. // Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2017. 11. pp. 1278-1283.
Kuzmina L.I., Osipov Y.V. Asymptotic Solution For Deep Bed Filtration With Small Deposit. // Procedia Engineering. 2015. 111. pp.491494.
Galaguz Y., Safina G. Calculation of the filtration in a heterogeneous porous medium. // Matec Web of Conferences. 2017. vol. 117, 00052, 6 p.
Galaguz Y., Safina G.. Modeling of Fine Migration in a Porous Medium. // MATEC Web of Conferences. 2016. vol. 86, 03003.
Galaguz Y.P., Safina G.L. Modeling of Particle Filtration in a Porous Medium with Changing Flow Direction. // Procedia Engineering. 2016. 153. pp.157161.
Galaguz Yu P. Realizatsiya TVD-skhemy chislennogo resheniya zadachi fil'tratsii. // International Journal for Computational Civil and Structural Engineering. 2017. 13(2). pp. 93-102.