Mathematical modeling of suspension clarification in a dynamic layer
DOI:
https://doi.org/10.15407/dopovidi2019.12.033Keywords:
concentration, mathematical modeling, moving boundary, pressure difference, rate, surface filtration, suspensionAbstract
A non-linear non-steady task of undetachable cake filtration at a constant pressure difference at moving and stationary cake layer boundaries is formulated and solved exactly. Sorption and conductivity possibilities are described by arbitrary functions. The solution obtained in the parametric form enables one to predict reliably chan ges in time of the filtrate quantity and productivity of a cake filtration installation. The effects of layer sorption pro perties, autocatalysis, and rate of cake formation on the main filtration characteristics are analyzed for a number of test examples. It is established that a considerable decrease in the suspended substance content in a filtrate, and filtration rate occurs during a short time, and the deposition is distributed along the dynamic layer height essentially unevenly with the maximum at its exit.
Downloads
References
Mints, D. M. (1964). Theoretical fundamentals of water purification technology. Moscow: Stroyizdat (in Russian).
Jegatheesan, V. & Vigneswaran, S. (2005). Deep bed filtration: mathematical models and observations. Crit. Rev. Environ. Sci. Technol., 35(6), pp. 515-569. Doi: https://doi.org/10.1080/10643380500326432
Benesch, T., Meier, U. & Schutz, W. (2004) Modelling filtration with superimposed sedimentation. Separat. Purific. Technol., 35, pp. 37-46. Doi: https://doi.org/10.1016/S1383-5866(03)00114-X
Zee, D. J. & Wang, C. H. (2000). Theories of cake filtration and consolidation and implications to sludge dewatering. Water Res., 34, pp. 1-20. Doi: https://doi.org/10.1016/S0043-1354(99)00096-2
Zee, S., Park, P.-K., Kim, J.-H., Yeon, K.-M. & Lee, C.-H. (2008). Analysis of filtration in submerged microfiltration for drinking water treatment. Water Res., 42, pp. 3109-3121. Doi: https://doi.org/10.1016/j.watres.2008.03.001
Mota, M., Teixeira, J. A. & Yelshin, A. (2002). Influence of cell-shape on the cake resistance in dead-end and cross-flow filtrations. Separat. Purific. Technol., 27, pp. 137-144. Doi: https://doi.org/10.1016/S1383-5866(01)00202-7
Wakeman, R. (2007). The influence of particle properties on filtration. Separat. Purific. Technol., 58, pp. 234-241. Doi: https://doi.org/10.1016/j.seppur.2007.03.018
Akgiray, O. & Saatci, A.M. (1998). An algorithm for bank operation of declining rate filters. Water Res., 3, pp. 2095-2105. Doi: https://doi.org/10.1016/S0043-1354(97)00459-4
Bai, R. & Tien, C. (2000). Effect of deposition in deep-bed filtration: determination and search of rate parameters. J. Colloid Interface Sci., 231, pp. 299-311. Doi: https://doi.org/10.1006/jcis.2000.7130
Chaundry, F. H. (1987). Theory of declining rate filtration. I. Continuous operation. J. Environ. Eng. Din. ASCE, 113(4), pp. 834-851. Doi: https://doi.org/10.1061/(ASCE)0733-9372(1987)113:4(834)
Ojha, C. S. & Graham, N. J. D. (1993) Theoretical estimates of bulk specific deposit in deep bed filters. Water Res., 27, pp. 377-387. Doi: https://doi.org/10.1016/0043-1354(93)90037-I
Polyakov, V., Kravchuk, A., Kochetov, G. & Kravhuk, O. (1993). Clarification of aqueous suspensions with a high content of suspended solids in rapid sand filters. Eureka: Physics and Engineering, No. 1, pp. 28-45. Doi: https://doi.org/10.21303/2461-4262.2019.00827
Venitsianov, E. V. & Rubinshteyn, R. N. (1983). Sorption dynamics from aqueous media. Moscow: Nauka (in Russian).
Boller, M. A. & Kavanauch, M. C. (1995). Particle characteristics and headloss increase in granular media filtration. Water Res., 29, pp. 1139-1149. Doi: https://doi.org/10.1016/0043-1354(94)00256-7
Saatci, A. M. (1990). Application of the declining rate filtration theory — Continuous operation. J. Environ. Eng. Div. ASCE, 116(1), pp. 87-105. Doi: https://doi.org/10.1061/(ASCE)0733-9372(1990)116:1(87)
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
