Vadym Polyakov, Andriy Kravchuk, Gennadii Kochetov, Oleksandr Kravchuk


The presented work is devoted to solving the actual problem of increasing the efficiency of rapid sand filters with granular filling, which operate at a constant filtration rate when cleaning suspensions with a relatively high concentration of contaminants. The proposed mathematical model for clarifying the suspension by filtration consists of three interconnected blocks: clarified, filtration, and hydraulic. Convenient dimensionless mathematical dependencies are obtained for calculating the concentrations of contaminants and sediment from the height of the filter and suspension in the filtrate; head loss in the filter loading; the effective time of the filter (the duration of the filter cycle). The design of the experimental setup and the methodology for conducting experimental studies and mathematical processing of the results are valid. The results of experimental studies of the suspension filtering process through the granular loading are presented, and the obtained data is analyzed. Measurement of pressure losses in the filter loading is performed when a suspension is passed with a relatively high concentration of contaminants at various filtration rates. The nature of the change in the filtration rate with time and height (length) loading at various filtration rates and initial contamination concentrations is determined. Measured variable concentration of suspended matter in filtered water and retained contamination over time. As a result of the experiments, it is confirmed that an increase in the concentration of retained contaminants S leads to an increase in the parameter Δn/n. Upon reaching a certain value of the concentration of the retained sediment S (in our case S=30 g/dm3), an increase in the relative specific volume of the sediment greater than Δn/n0=0.65 is not observed. It is established that an important characteristic of the retained sediment is the ratio of the volume concentration of the sediment to the volume concentration of solid particles in this sediment γ=Csds. The values of the adhesion and detachment of particles of contaminant in the particles of the material loading =4,9; =0,009. The results of experimental studies in general confirm the correctness and reliability of the obtained analytical dependencies.


filtration rate; loading porosity; filtration rate; contaminant concentration; contaminant adhesion factor; contaminant detachment factor

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DBN V.2.5-74:2013. Vodopostachannia. Zovnishni merezhi ta sporudy (2013). Minrehion Ukrainy.

Orlov, V. O. (2005). Vodoochysni filtry iz zernystoiu zasypkoiu. Rivne: NUVHP, 163.

Hudson, H. E. (1959). Declining rate filtration. Journal American Water Works Association, 51 (11), 42–50.

Zhurba, M. (2011). Vodoochistnye fil'try s plavayushchey zagruzkoy. Moscow: RIO VoGTU.

Minc, D. M. (1964). Teoreticheskie osnovy tekhnologi ochistki vody. Moscow: Stroyizdat, 156.

Shevchuk, E. A., Mamchenko, A. V., Goncharuk, V. V. (2005). Tekhnologiya pryamotochnogo fil'trovaniya prirodnyh i stochnyh vod cherez zernistye zagruzki. Himiya i tekhnologiya vody, 27 (4), 369–383.

Ives, K. J. (1970). Rapid filtration. Water Research, 4 (3), 201–223. doi:

Jegatheesan, V., Vigneswaran, S. (2005). Deep Bed Filtration: Mathematical Models and Observations. Critical Reviews in Environmental Science and Technology, 35 (6), 515–569. doi:

Saatçi, A. M. (1990). Application of Declining Rate Filtration Theory – Continuous Operation. Journal of Environmental Engineering, 116 (1), 87–105. doi:

O’Melia, C. R., Ali, W. (1979). The role of retained particles in deep bed filtration. Ninth International Conference on Water Pollution Research, 167–182. doi:

Noskov, M. D., Zayceva, M. S., Istomin, A. D., Lukashevich, O. D. (2008). Mathematical modelling of butterfly filter work. Vestnik TGASU, 2, 126–137.

Grabovskyi, P. A. (2016). Water filtration through a grainy layer with decreasing rate. Reports of the National Academy of Sciences of Ukraine, 8, 40–45. doi:

Gurinchik, N. A. (2010). Opredelenie prodolzhitel'nosti raboty fil'trov dlya raznyh rezhimov fil'trovaniya. Visnyk ODABA, 42, 56–62.

Polyakov, V. L. (2012). Suspension filtration at declining rate and linear mass-exchange kinetics. Himiya i tekhnologiya vody, 34 (2), 107–130.

Polyakov, V. L., Kravchuk, O. A. (2015). Matematicheskoe modelirovanie osvetleniya suspenzii fil'trovaniem s sushchestvenno peremennoy skorost'yu. Visnyk Odeskoi derzhavnoi akademiyi budivnytstva ta arkhitektury, 59, 331–337.

Zhurba, M. G. (1980). Ochistka vody na zernistyh fil'trah. Lviv: Vyshcha shkola, 199.

Girikov, O. G., Nikolaev, E. Yu. (1999). Intensifikaciya raboty skoryh vodoprovodnyh fil'trov. Izvestiya vuzov. Stroitel'stvo, 7, 128–131.

Saiers, J. E., Hornberger, G. M., Liang, L. (1994). First- and second-order kinetics approaches for modeling the transport of colloidal particles in porous media. Water Resources Research, 30 (9), 2499–2506. doi:

Polyakov, V. L. (2009). Filtration of a suspension with variable content of suspended particles through a uniform filter medium at a nonlinear mass-exchange kinetics. Reports of the National Academy of Sciences of Ukraine, 12, 61–68.

Ojha, C. S. P., Graham, N. J. D. (1993). Theoretical estimates of bulk specific deposit in deep bed filters. Water Research, 27 (3), 377–387. doi:

Polyakov, V. L. (2009). Teoreticheskiy analiz dlitel'nosti fil'trocikla. Himiya i tekhnologiya vody, 31 (6), 605–618.

Polyakov, V. L. (2010). On the prediction of the head loss dynamics within a filter medium. Reports of the National Academy of Sciences of Ukraine, 3, 70–76.

Polyakov, V. L. (2011). Calculation of suspension filtration through two-layer filter medium at linear mass-exchange kinetics. Himiya i tekhnologiya vody, 33 (4), 367–380.



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