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Russia Cheboksary
Section Mechanics
Title Investigation of the filtration coefficient of elastic-porous medium at plane deformation
Author(-s) Mikishanina E.A.a
Affiliations Chuvash State Universitya
Abstract The value of the filtration coefficient is determined empirically due to its physical and chemical properties of the medium and the filtered liquid. However, the experimental data obtained can vary significantly depending on the applied loads. The paper proposes a new hypothesis about the linear dependence of the medium filtration coefficient on the first invariant of the stress tensor arising in the region due to the hydraulic head at the boundary. Within the framework of this hypothesis, the change of the region filtration coefficient under plane deformation is investigated. The appearance of hydraulic head on the border leads to the appearance of elastic perturbations in the environment. Since the velocity of the latter is much higher than the velocity of the liquid filtration, the change in the stress state of the region will lead to a change in the pore space, and, consequently, to a change in the filtration coefficient. Thus, the initial problem is reduced to the solution of the classical problem of elasticity theory, namely, to the solution of the boundary value problem for the Erie function, and then to the definition of the filtration coefficient as the solution of the boundary value problem for the harmonic equation. A numerical algorithm for solving harmonic and biharmonic equations based on the boundary element method is constructed, which ultimately reduces the original problem to a system of linear algebraic equations. As shown by the numerical results of studies, the change in the filtration coefficient of some materials under operating loads reaches 20 percent at some points of the region. These results are especially relevant when using pipes, hoses, water hoses made of various polymeric materials, fiberglass, as well as in the operation of hydraulic engineering and treatment facilities. The change in the filtering capacity of the medium at low elastic deformations makes it possible at the appropriate pressures to filter even in those environments that are usually considered impervious to the liquid. The paper presents the results of numerical experiments to study the filtration coefficient of polyurethane (flexible irrigation hose) and butyl rubber. Graphs of the required mechanical parameters are constructed. Calculations were performed in the Maple software package.
Keywords filter coefficient, plane strain, stresses, filtration, harmonic equation, biharmonic equation, numerical algorithm
UDC 532.685
MSC 76S05, 65R20
DOI 10.20537/vm190309
Received 4 July 2019
Language Russian
Citation Mikishanina E.A. Investigation of the filtration coefficient of elastic-porous medium at plane deformation, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 3, pp. 396-407.
  1. Bridgman P.W. Recent work in the field of high pressures, Reviews of Modern Physics, 1946, vol. 18, issue 1, pp. 1-93.
  2. Golubev G.V., Tumashev G.G. Fil'tratsiya neszhimaemoi zhidkosti v neodnorodnoi poristoi srede (Filtration of incompressible fluid in a heterogeneous porous medium), Kazan: Kazan State University, 1972.
  3. Kadyrov F.M., Kosterin A.V. The filtration consolidation of an elastic porous medium with discontinuous initial conditions, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2016, vol. 158, book 2, pp. 262-275 (in Russian).
  4. Kazakova A.O., Terent'ev A.G. Numerical modelling of the plane problem of the stress state of a tube immersed in a liquid, Journal of Applied Mathematics and Mechanics, 2014, vol. 78, no. 5, pp. 518-523.
  5. Loitsyanskii L.G. Mekhanika zhidkosti i gaza (Fluid mechanics), Moscow-Leningrad: Gostekhizdat, 1950.
  6. Leibenzon L.S. Dvizhenie prirodnykh zhidkostei i gazov v poristoi srede (Movement of natural liquids and gases in a porous medium), Moscow-Leningrad: Gostekhteorizdat, 1947.
  7. Mikishanina E.A., Terentiev A.G. On determination of the stress state of an elastic-porous medium, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, vol. 159, no. 2, pp. 204-215 (in Russian).
  8. Mikishanina E.A. Computer simulation of planar solutions of the boundary value problem of filtration theory, Vestnik Chuvashskogo Universiteta, 2016, no. 1, pp. 145-152 (in Russian).
  9. Mikishanina E.A. Research of filtration coefficient of elastic-porous plate under loading, Vestnik Chuvashskogo Gosudarstvennogo Pedagogicheskogo Universiteta imeni I.Ya. Yakovleva. Ser. Mekhanika Predel'nogo Sostoyaniya, 2017, no. 2 (32), pp. 65-70 (in Russian).
  10. Nevmerzhitskii Ya.V. Application of the streamline method for nonlinear filtration problems acceleration, Computer Research and Modeling, 2018, vol. 10, no. 5, pp. 709-728 (in Russian).
  11. Polubarinova-Kochina P.Ya. Teoriya dvizheniya gruntovykh vod (Theory of ground water movement), Moscow: Nauka, 1977.
  12. Engel'gardt V. Porovoe prostranstvo osadochnykh porod (Pore space of sedimentary rocks). Мoscow: Nedra, 1964.
  13. Sheidegger A.E. Fizika techeniya zhidkostei cherez poristye sredy (Physics of fluid flow through porous media), Moscow: Gostoptekhizdat, 1960.
  14. Akhmetzyanov A.V., Kushner A.G., Lychagin V.V. Control of displacement front in a model of immiscible two-phase flow in porous media, Doklady Mathematics, 2016, vol. 94, no. 1, pp. 378-381.
  15. Biot M.A. General solutions of the equations of elasticity and consolidation for a porous materials, J. Appl. Mech., 1956, vol. 23, no. 1, pp. 91-96.
  16. Boronin S.A., Osiptsov A.A., Tolmacheva K.I. Multy-fluid model of suspension filtration in a porous medium, Fluid Dynamics, 2015, vol. 50, no. 6, pp. 759-768.
  17. Dullien F.A.L., Batra V.K. Determination of the structure of porous media, Industrial and Engineering Chemistry, 1970, vol. 62, no. 10, pp. 25-53.
  18. Fatt I. The network model of porous media. I. Cappillary pressure characteristics, Transactions of the American Institute of Mining, Metallurgical, and Petroleum Engineers, 1956, vol. 207. P. 144-159.
  19. Fatt I. The network model of porous media. II. Dynamic properties of a single size tube network, Transactions of the American Institute of Mining, Metallurgical, and Petroleum Engineers, 1956, vol. 207, pp. 160-177.
  20. Fusi L., Farina A., Rosso F. Mathematical models for fluids with pressure-dependent viscosity flowing in porous media, International Journal of Engineering Science, 2015, vol. 87, pp. 110-118.
  21. Kozeny J. Grundwasserbewegung bei freiem Spiegel, Fluss und Kanalversickerung, Wasserkraft und Wasserwirtschaft, 1931, vol. 26, no. 3, pp. 28-31.
  22. Terentiev A.G., Kirschner I.N., Uhlman J.S. The hydrodynamics of cavitating flows, Hoboken, New Jersey: Backbone, 2011.
  23. You Zh., Osipov Yu., Bedrikovetsky P., Kuzmina L. Asymptotic model for deep bed filtration, Chemical Engineering Journal, 2014, vol. 258, pp. 374-385.
  24. Zhang J., Sinha N., Ross M., Tejada-Martínez A.E. Computational fluid dynamics analysis of the hydraulic (filtration) efficiency of a residential swimming pool, Journal of Water and Health, 2018, vol. 16, no. 5, pp. 750-761.
  25. Tang T., McDonough J.M. A theoretical model for the porosity-permeability relationship, International Journal of Heat and Mass Transfer, 2016, vol. 103, pp. 984-996.
  26. Verruijt А. An introduction to soil dynamics, Dordrecht: Springer, 2010.
  27. Coussy O. Poromechanics, New York: John Wiley and Sons, 2004.
  28. Dietrich P., Helmig R., Sauter M., Hötzl H., Köngeter J., Teutsch G. Flow and transport in fractured porous media, Berlin: Springer, 2005.
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