DOI 10.35776/VST.2022.12.05
UDC 628.35

Andreev Sergei, Stepanov S. V., Strelkov A. K.

Mathematical modeling of the wastewater biological treatment process in a plug flow aeration tank


The results of theoretical studies of the kinetics of the processes of biochemical oxidation of organic wastewater pollution by activated sludge microorganisms are presented. It is shown that the value of the average effective value of the specific rate of organic wastewater pollution oxidation by the activated sludge in a plug flow aeration tank can be determined using the theorem on the average value of the continuous function f(L) integrated in a certain range of its variable from Lн to Lк. By integrating the Michaelis–Menten equation, a mathematical model was obtained based on the fundamental regularities of enzymatic kinetics that describes the process of biological oxidation of organic pollutants in a plug flow aeration tank. The use of the proposed equations will provide for determining the average effective values ​​of the specific oxidation rates of various organic pollutants (BOD, oil products, surfactants, phenols, etc.), the estimated duration of aerobic processes; and thereby, optimizing the design and operation of biological wastewater treatment facilities in plug flow aeration tanks.

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  1. Iakovlev S. V., Kariukhina T. A. Biokhimicheskie protsessy ochistki stochnykh vod [Biochemical processes of wastewater treatment. Moscow, Stroiizdat Publ., 1980, 200 p.].
  2. Evilevich M. A., Brachinskii L. N. Optimizatsiia biokhimicheskoi ochistki stochnykh vod [Optimization of biochemical wastewater treatment. Leningrad, Stroiizdat Publ., 1979, 160 p.].
  3. Michaelis L., Menten M. L. Die Kinetik der Invertinwirkung. Biochemische Zeitschrift, 1913, z. 49, pp. 333–369.
  4. Henze M., Armoes P., La Cour Jansen J., Arvin E. Ochistka stochnykh vod. Biologicheskie i khimicheskie protsessy [Wastewater treatment. Biological and chemical processes. Translated from English, Мoscow, Mir Publ., 2006, 480 p.].
  5. Stepanov S. V. Tekhnologicheskii raschet aerotenkov i membrannykh bioreaktorov: Uchebnoe posobie [Technological calculation of aeration tanks and membrane bioreactors: Textbook. Moscow, ASV Publ., 2020, 224 p.].
  6. Karelin Ia. A., Zhukov D. D., Zhurov V. N., Repin B. N. Ochistka proizvodstvennykh stochnykh vod v aerotenkakh [Industrial wastewater treatment in aeration tanks. Moscow, Stroiizdat Publ., 1979, 223 p.].
  7. Spravochnoe posobie k SNiP. Proektirovanie sooruzhenii dlia ochistki stochnykh vod [Reference Manual to SNiP. Designing facilities for wastewater treatment. Moscow, Stroiizdat Publ., 1990, 192 p.].
  8. Skirdov I. V. Issledovanie i razrabotka metodov intensifikatsii raboty sooruzhenii biologicheskoi ochistki stochnykh vod [Research and development of methods for enhancing the operation of biological wastewater treatment facilities. Dissertation for the degree of PhD in Engineering. Moscow, VNII VODGEO, 1977, 400 p.].
  9. Khar’kina O. V. Effektivnaia ekspluatatsiia i raschet sooruzhenii biologicheskoi ochistki stochnykh vod [Efficient operation and calculation of wastewater biological treatment facilities. Volgograd, Panorama Publ., 2015, 433 p.].

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