A suspension filtration problem with modified deposition kinetics in a porous medium is considered. A new model developed, in which “aging” and “charging” phenomena are taken into account in the kinetics of deposition. It is suggested that the process of deposition forming happens with “charging”, transient, “aging” and breakthrough stages and stops when the capacity of filter fills with deposition. To solve the formed system of partial differential equations an algorithm based on finite difference schemes is developed. Based on numerical results the influences of “aging” and “charging” phenomena on suspended particle transport, attachment and detachment characteristics are analysed.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 3
Year: 2020

DOI: 10.12732/ijam.v33i3.10

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  1. [1] M. Elimelech, J. Gregory, X. Jia, R.A. Williams, Particle Deposition and Aggregation: Measurement, Modelling, and Simulation. Colloid and Surface Engineering Series, Butterworth-Heinemann, Oxford (1989).
  2. [2] V. Gitis, et. al., Deep-bed filtration model with multistage deposition kinetics, Chemical Engineering Journal, 163, No 1-2 (2010), 78-85; doi: 10.1016/j.cej.2010.07.044.
  3. [3] A. Zamani, B. Maini, Flow of dispersed particles through porous media - deep bed filtration, Journal of Petroleum Science and Engineering, 69 (2009), 71-88; doi:10.1016/j.petrol.2009.06.016.
  4. [4] V. Jegatheesan, S. Vigneswaran, Deep bed filtration: mathematical models and observations, Critical Reviews in Environmental Science and Technology, 35 (2005), 515-569; doi:10.1080/10643380500326432.
  5. [5] A. Adin, E.R. Baumann, J.L. Cleasby, The application of filtration theory to pilot-plant design, Journal American Water Works Association, 71 (1979), 17-27; doi:10.1002/j.1551-8833.1979.tb04285.x.
  6. [6] K.J. Ives, Rapid filtration, Water Research, 4 (1970), 201-223; doi:10.1016/0043-1354(70)90068-0.
  7. [7] D.M. Mintz, Kinetics of filtration of low-concentration water suspensions in water purification filters, Doklady Akademii Nauk SSSR, 78 (1951), 315318 (in Russian).
  8. [8] R.G. Guedes, F. Al-Abduwani, P. Bedrikovetsky, P. K. Currie, Deepbed filtration under multiple particle-capture mechanisms, Society of Petroleum Engineers Journal, 14 (2009), 477-487; doi:10.2118/98623-PA.
  9. [9] T. Iwasaki, Some notes on sand filtration, Journal of American Water Works Association, 29 (1937), 1591-1602; doi:10.1002/j.15518833.1937.tb14014.x.
  10. [10] C.R. Ison, K.J. Ives, Removal mechanisms in deep bed filtration, Chemical Engineering Science, 24 (1969), 717-729; doi:10.1016/0009-2509(69)800643.
  11. [11] C. Tien, B.V. Ramarao, Granular Filtration of Aerosols and Hydrosols 2nd ed, Elsevier, Amsterdam (2007).
  12. [12] E.V. Venetsianov, R. Rubinshtein, Dynamic of Sorption from Liquid Media Nauka, Moscow (1983) (in Russian).
  13. [13] J.M. Kavanagh, et. al., Particle capture models: Comparison with experimental data, ANZIAM J., 53 (2011), 249-265; doi:10.21914/anziamj.v53i0.5072.
  14. [14] ] A. Hammadi, N.D. Ahfir, A. Alem, H. Wang, Effects of particle size nonuniformity on transport and retention in saturated porous media, Transport in Porous Media, 118 (2017), 1-14; doi:10.1007/s11242-017-0848-6.
  15. [15] L. Kuzmina, Y. Osipov, Particle transport in a porous medium with initial deposit, IOP Conf. Ser.: Mater. Sci. Eng., 365 (2018), 042003; doi:10.1088/1757-899X/365/4/042003.
  16. [16] L. Kuzmina, Y. Osipov, Particle capture in porous medium, IOP Conf. Ser.: Mater. Sci. Eng., 661 (2019), 012122; doi:10.1088/1757899X/661/1/012122.
  17. [17] B. Khuzhayorov, B. Fayziev, A model of suspension filtration in porous media with multistage accumulation kinetics, Internat. J. of Advanced Research in Science, Engineering and Technology, 4 (2017), 4643-4648.
  18. [18] B. Khuzhayorov, A model of multicomponent grouting and suffosion filtration, J. of Engineering Physics and Thermophysics, 66 (1994), 373-379; doi:10.1007/BF00853459.
  19. [19] B. Khuzhayorov, Model of colmatage-suffosion filtration of disperse systems in a porous medium, J. of Engineering Physics and Thermophysics, 73 (2000), 668-673; doi:10.1007/s10891-000-0073-x.
  20. [20] A.A. Samarskii, The Theory of Difference Schemes, CRC Press, New York (2001).
  21. [21] B. Fayziev, G. Ibragimov, B. Khuzhayorov, I.A. Alias, Numerical study of suspension filtration model in porous medium with modified deposition kinetics, Symmetry, 12 No 5 (2020), 696; doi:10.3390/sym12050696.
  22. [22] J.W.Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer, New York (1995).