Peculiarities of calculating the value of the air bubble surface renewal coefficient
https://doi.org/10.31660/2782-232X-2023-4-55-63
Abstract
The resource intensity of biological wastewater treatment is reduced by increasing the energy efficiency of the pneumatic aeration systems used in the aeration tank. Modernisation of the aeration process is possible with the development of an adequate mathematical model describing the process of mass transfer from air bubble to water the oxygen required for biological oxidation of wastewater pollutants. The analysis of the LewisWhitman two-film theory, Higbee's penetration theory, and P. W. Dankwerts' theory of deformed bubble surface renewal describing the process of mass transfer of air oxygen into water showed the peculiarities of their application to gas-liquid systems. The factor of renewal of deformed surface of air bubbles is of great importance for describing the processes of mass transfer of air oxygen to water when using pneumatic aeration system in aeration tanks. In turbulent flow at continuous renewal of interfacial surface created by air bubbles, there is intensification of mass transfer process due to turbulent diffusion, which is reflected in calculated mathematical dependences. The use of mathematical dependences determining the rate of mass transfer of air oxygen to water through the deformable surface of bubbles formed in the aeration volume of the aeration tank will make it possible to take into account the change in their shape. This will increase the accuracy of determining the values of technological characteristics of pneumatic aeration systems.
About the Authors
S. Yu. Andreev
Penza State University of Architecture and Construction
Russian Federation
Russian Federation
Sergey Yu. Andreev, D. Sc. in Engineering, Professor, Professor at the Department of Water Supply, Water Dump and Hydraulic Engineering
L. V. Belova
Industrial University of Tyumen
Russian Federation
Russian Federation
Larisa V. Belova, Cand. Sc. In Engineering, Associate Professor, Associate Professor at the Department of Engineering Systems and Structures, Head of the Department of Descriptive Geometry and Graphics
References
1. Fick, A. (1855). On Liquid Diffusion. London, Publ. Taylor & Francis, 39 p. (In English).
2. Noyes, A. A., & Whitney, W. R. (1897). The rate of solution of solid substances in their own solutions. Journal of the American Chemical Society, 19(12), pp. 930-934. (In English). DOI 10.1021/ja02086a003.
3. Nernst, W. (1904). Theory of reaction rates in heterogeneous systems [Theorie der Reaktionsgeschwindigkeit in heterogenen Systemen]. Zeitschrift für Physikalische Chemie, 47U(1), pp. 52-55. (In German). DOI 10.1515/zpch1904-4704.
4. Lewis, W. K., & Whitman, W. G. (1924). Principles of Gas Absorption. Industrial & Engineering Chemistry, 16(12), 1215-1220. (In English). DOI 10.1021/ie50180a002.
5. Higbie, R. (1935). The Rate of Absorption of a Pure Gas into a Still Liquid during Short Periods of Exposure. AIChE Journal, 31, 365-389. (In English).
6. Popkovich, G. S., & Repin, B. N. (1986). Sistemy aeratsii stochnykh vod. Moscow, Stroyizdat Publ., 133 p. (In Russian).
7. Pan, Yu., & Dagnew, M. (2022). A new approach to estimating oxygen off-gas fraction and dynamic alpha factor in aeration systems using hybrid machine learning and mechanistic models. Journal of Water Process Engineering, 48:102924. (In English). DOI 10.1016/j.jwpe.2022.102924. Available at: https://www.sciencedirect.com/science/ article/pii/S2214714422003683 (accessed 23.10.2023).
8. Jiang, L.-M., Garrido-Baserba, M., Nolasco, D., Al-Omari, A., DeClippeleir, H., Murthy, S., & Rosso, D. (2017). Modelling oxygen transfer using dynamic alpha factors. Water Research, (124), pp. 139-148. (In English). DOI 10.1016/j. watres.2017.07.032. Available at: https://www.sciencedirect.com/science/article/pii/S004313541730605X (accessed 23.10.2023).
9. Danckwerts, P. V. (1951). Significance of liquid-film coefficients in gas absorption. Industrial & Engineering Chemistry, 43(6), pp. 1460-1467. (In English).
10. Kishinevskiy, M. Kh., & Kornienko, T. S. (1967). Issledovanie teploi massoobmena. Kishinev, Kartya moldovenyaske Publ., 16 p. (In Russian).
11. Andreev, S. Y., Garkina, I. A., & Yakhkind, M. I. (2019). Evaluating the patterns of air bubble rise in water-air mixtures used in natural and waste water treatment processes. IOP Conference Series: Materials Science and Engineering: International Conference on Construction, Architecture and Technosphere Safety. Chelyabinsk, Institute of Physics Publ., 687(6), P. 066054. (In English). DOI 10.1088/1757-899X/687/6/066054.
12. Deryagin, B. V., Dukhin, S. S., & Rulev, N. N. (1982). Kinetic theory of the flotation of small particles. Russian Chemical Reviews, (51), pp. 92-118. (In English). DOI 10.1070/RC1982V051N01ABEH002791.
13. Okazaki, S. (1964). The velocity of ascending air bubbles in aqueous solution of a surface active substance and the life of the bubble on the same solution. Bulletin of the Chemical Society of Japan, (37), pp. 144-150. (In English).
14. Meshengisser, Yu. M. (2005). Teoreticheskoe obosnovanie i razrabotka novykh polimernykh aeratorov dlya biologicheskoy ochistki stochnykh vod. Avtoref. diss. … dokt. tekhn. nauk. Moscow, NII VODGEO, 48 p. (In Russian).
15. Khudenko, B. M., & Shpirt, E. A. (1973). Aeratory dlya ochistki stochnykh vod. Moscow, Stroyizdat Publ., 112 p. (In Russian).
16. Braginskiy, L. N., Evilevich, M. A., & Begachev, V. I. (1980). Modelirovanie aeratsionnykh sooruzheniy dlya ochistki stochnykh vod. Leningrad, Khimiya Publ., 144 p. (In Russian).
17. Karaichev, I. E. (2019). Sovershenstvovanie metodov rascheta aeratsii vodnykh ob"ektov. Avtoref. diss. … kand. tekhn. nauk. Moscow, 23 p. (In Russian).
18. Horvath, I. R., & Chatterjee, S. G. (2018). A surface renewal model for unsteady-state mass transfer using the generalized Danckwerts age distribution function. The Royal Society Publishing, (5). (In English). DOI 10.1098/ rsos.172423. Available at: https://royalsocietypublishing.org/doi/10.1098/rsos.172423 (accessed 23.10.2023).
Review
For citations:
Andreev S.Yu., Belova L.V. Peculiarities of calculating the value of the air bubble surface renewal coefficient. Architecture, Construction, Transport. 2023;(4):55–63. (In Russ.) https://doi.org/10.31660/2782-232X-2023-4-55-63
Views:
21
Email this article 