Sedimentation of heterogeneous particles in a porous material

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Abstract

Filtration of suspensions and colloids in porous materials occurs during the construction and operation of hydraulic structures, tunnels and underground storage facilities. Filtration models are used to calculate the penetration of grout into loose soil, when treating drinking water and industrial wastewater. During the filtration process, suspended particles pass through large pores and get stuck at the entrance of small-diameter pores. The trapped particles form a stationary deposit. A model of filtration of a polydisperse suspension in a porous material is considered. The purpose of the work is to study sediment profiles – the dependence of the concentration of deposited particles on the distance to the porous material inlet at a fixed time. An exact solution to the model was constructed using the method of characteristics. It has been shown that when filtering a polydisperse suspension, the distribution of sediment differs for different types of particles. The sediment profile of the largest particles always decreases monotonically, but the sediment profile of the smallest particles is not monotonic. It decreases at short times, then a maximum point appears on the graph, moving along the porous medium as time increases. After the maximum point reaches the porous material exit, the sediment profile becomes monotonically increasing. The sediment profiles of intermediate size particles and the total sediment profile are either monotonic or non-monotonic depending on the model parameters. The behavior of maximum points of non-monotonic profiles has been studied.

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About the authors

L. I. Kuzmina

National Research University Higher School of Economics

Author for correspondence.
Email: lkuzmina@hse.ru

Candidate of Sciences (Physics and Mathematics), Associate Professor

Russian Federation, 0, Myasnitskaya Street, Moscow, 101000

Yu. V. Osipov

Moscow State University of Civil Engineering

Email: yuri-osipov@mail.ru

Candidate of Sciences (Physics and Mathematics), Professor

Russian Federation, 26, Yaroslavskoe Highway, Moscow, 129337

References

  1. Zhu G., Zhang Q., Liu R., Bai J., Li W., Xiao Feng X. Experimental and numerical study on the permeation grouting diffusion mechanism considering filtration effects. Geofluids, 2021. https://doi.org/10.1155/2021/6613990
  2. Ibragimov M.N., Semkin V.V., Shaposhnikov A.V. Tsementatsiya gruntov inektsiei rastvorov v stroitel’stve [Cementation of soils by injection of solutions in construction]. Moscow: ASV. 2017. 266 p.
  3. Christodoulou D., Lokkas P., Droudakis A., Spiliotis X., Kasiteropoulou D., Alamanis N. The development of practice in permeation grouting by using fine-grained cement suspensions. Asian Journal of Enginee- ring and Technology. 2021. Vol. 9 (6), pp. 92–101. https://doi.org/10.24203/ajet.v9i6.6846
  4. Mammadov H.N., Suleimanova I.H., Tahirov B.M. High-effective lightweight aggregate obtained from glass-containing waste. Stroitel’nye Materialy [Construction Materials]. 2020. No. 12, pp. 66–71. (In Russian). https://doi.org/10.31659/0585-430X-2020-787-12-66-71
  5. Fedorova G.D., Aleksandrov G.N., Scryabin A.P. Activation of structure-forming properties of graphene oxide in cement composites. Stroitel’nye Materialy [Construction Materials]. 2020. No. 1–2, pp. 17–23. (In Russian). DOI: https://doi.org/10.31659/0585-430X-2020-778-1-2-17-23
  6. Fedorova G.D., Skriabin A.P., Aleksandrov G.N. The study of the influence of graphene oxide on the strength of cement stone using river sand. Stroitel’nye Materialy [Construction Materials]. 2019. No. 1–2, pp. 16–22. (In Russian). https://doi.org/10.31659/0585-430X-2019-767-1-2-16-22
  7. Guedes R.G., Al-Abduwani F., Bedrikovetsky P., Currie P.K. Deep bed filtration under multiple particle-capture mechanisms. SPE Journal. 2009. Vol. 14. No. 3, pp. 477–487. https://doi.org/10.2118/98623-PA
  8. Kuzmina L.I., Osipov Yu.V., Shaydullina A.M. Particle dynamics in a porous medium. Promyshlennoe i grazhdanskoe stroitel’stvo. 2021. No. 10, pp. 72–77. (In Russian). https://doi.org/10.33622/0869-7019.2021.10.72-77
  9. Osipov Yu.V., Zheglova Yu.G. Modelling of transport and retention of particles in porous media. Promyshlennoe i grazhdanskoe stroitel’stvo. 2019. No. 11, pp. 56–60. (In Russian). https://doi.org/10.33622/0869-7019.2019.11.56-60
  10. Santos A., Bedrikovetsky P., Fontoura S. Analytical micro model for size exclusion: Pore blocking and permeability reduction. Journal of Membrane Science. 2008. Vol. 308, pp. 115–127. https://doi.org/10.1016/j.memsci.2007.09.054
  11. Bashtani F., Ayatollahi S., Habibi A., Masihi M. Permeability reduction of membranes during particulate suspension flow; analytical micro model of size exclusion mechanism. Journal of Membrane Science. 2013. Vol. 435, pp. 155–164. https://doi.org/10.1016/j.memsci.2013.01.043
  12. Gitis V., Rubinstein I., Livshits M., Ziskind G. Deep-bed filtration model with multistage deposition kinetics. Chemical Engineering Journal. 2010. Vol. 163, pp. 78–85. https://doi.org/10.1016/j.cej.2010.07.044
  13. Safina G.L. Modelling of filtration of a two-particle suspension in a porous medium. Promyshlennoe i grazhdanskoe stroitel’stvo. 2022. No. 2, pp. 31–35. (In Russian). https://doi.org/10.33622/0869-7019.2022.02.31-35
  14. Sun N.Z. Mathematical modeling of groundwater pollution. New York: Springer. 2014. 377 p.
  15. Herzig J.P., Leclerc D.M., le Goff P. Flow of suspensions through porous media–application to deep filtration. Industrial & Engineering Chemistry Research. 1970. Vol. 62. No. 5, pp. 8–35. https://pubs.acs.org/doi/abs/10.1021/ie50725a003
  16. 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. https://doi.org/10.1007/s11242-008-9228-6
  17. Kuzmina L.I., Osipov Yu.V. Determining the Lengmur coefficient of the filtration problem. International Journal for Computational Civil and Structural Engineering. 2020. Vol. 16. No. 4, pp. 48–54. https://doi.org/10.22337/2587-9618-2020-16-4-48-54
  18. Kuzmina L.I., Osipov Yu.V. Filtration of suspension in a porous material. Stroitel’nye Materialy [Construction Materials]. 2023. No. 9, pp. 89–93. (In Russian). https://doi.org/10.31659/0585-430X-2023-817-9-89-93
  19. 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. https://doi.org/10.1134/S0040579507050168
  20. Zhang H., Malgaresi G.V.C., Bedrikovetsky P. Exact solutions for suspension colloidal transport with multiple capture mechanisms. International Journal of Non-Linear Mechanics. 2018. Vol. 105, pp. 27–42. https://doi.org/10.1016/j.ijnonlinmec.2018.07.007
  21. Polyanin A.D. Tochnye resheniya differentsial’nykh, integral’nykh, funktsional’nykh i drugikh matematicheskikh uravnenii [Exact solutions to differential, integral, functional and other mathematical equations]. Moscow: IPMech RAN. 2023. 600 p.
  22. Polyanin A.D., Zhurov A.I. Metody razdeleniya peremennykh i tochnye resheniya nelineinykh uravnenii matematicheskoi fiziki [Methods of separation of variables and exact solutions to nonlinear equations of mathematical physics]. Moscow: IPMech RAN. 2021. 383 p.
  23. Kuzmina L.I., Osipov Yu.V., Tsareva V.I. Inverse problem for a linear filtration function. Promyshlennoe i grazhdanskoe stroitel’stvo. 2020. No. 6, pp. 64–68. (In Russian). https://doi.org/10.33622/0869-7019.2020.06.64-68
  24. Alvarez A.C., Hime G., Marchesin D., Bedriko- vetsky P.G. The inverse problem of determining the filtration function and permeability reduction in flow of water with particles in porous media. Transport in Porous Media. 2007. Vol. 70. No. 1, pp. 43–62. https://doi.org/10.1007/s11242-006-9082-3
  25. Safina G.L. Calculation of deposit profiles of a two-particle suspension in a porous medium // Promyshlennoe i grazhdanskoe stroitel’stvo. 2020. No. 11, pp. 110–114. (In Russian).
  26. Malgaresi G., Collins B., Alvaro P., Bedrikovetsky P. Explaining non-monotonic retention profiles during flow of size-distributed colloids. Chemical Engineering Journal. 2019. Vol. 375. 121984. https://doi.org/10.1016/j.cej.2019.121984
  27. Osipov Yu.V., Astakhov M.D. Calculation of filtration of bidisperse suspension in a porous medium. Inzhenerno-stroitel’nyj vestnik Prikaspiya. 2020. Vol. 31. No. 1, pp. 69–72. (In Russian).

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2. Fig. 1. Sediment profiles at fixed time: a – t=0.1; b – t=0.5; c – t=3

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3. Fig. 2. Sediment profiles at fixed time: a – t=0.1; b – t=0.5; c – t=3

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4. Fig. 3. Sediment profiles of three particle types: a – t=1; b – t=10; c – t=25; d – t=50

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5. Fig. 4. Sediment profiles of three particle types: a – t=1; b – t=10; c – t=25; d – t=90

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