Constructing a mathematical model and studying numerically the effect of bio-clogging on soil filtration consolidation

Authors

DOI:

https://doi.org/10.15587/1729-4061.2021.230238

Keywords:

excess heads, bio-clogging, organic waste, finite element method, filtration consolidation

Abstract

Mathematical modeling and computer simulation methods have been used to investigate the extent of influence exerted by bio-clogging on the dynamics of excess head scattering in the soil massif. To this end, the classical equation of filtration consolidation has been modified for the case of variable porosity resulting from changes in the biomass. The numerical solution to the constructed mathematical model in the form of a nonlinear boundary problem was derived by a finite-element method. Numerical experiments were carried out and their analysis was performed. Specifically, this paper shows the charts of pressure differences in the soil array when neglecting bio-clogging and when estimating the effects exerted by bio-clogging at specific points in time. The numerical experiments demonstrated that in two years after the onset of the consolidation process in the neighborhood of the lower limit of the examined soil mass with a thickness of 10 meters, excess heads fall from the initial value of 10 m to 4 m. The greatest impact from the clogging of pores by microorganisms is revealed in the neighborhood of an upper limit. At a depth of 1 m, at t=180 days, the pressure difference reaches 2.4 m. This is about 200 % of the pressure distribution without taking into account the effects of bio-clogging. Over time, the effect of bacteria on the distribution of pressures in the neighborhood of the upper boundary decreases. However, this effect extends to the entire soil mass, up to the lower limit. Thus, at t=540 days, at the lower limit, the effect of bio-clogging leads to that excess heads are 1.8 m greater than for the case of pure water filtration (a relative increase of about 80 %).

Bio-clogging processes are intensified as a result of the development of microorganisms when organic chemicals enter the porous environment. Therefore, from a practical point of view, studying them is especially relevant for household waste storage facilities and the stability of their soil bases. It is advisable to undertake research by using the methods of mathematical modeling and computer simulation

Author Biographies

Natalia Ivanchuk, National University of Water and Environmental Engineering

PhD

Department of Computer Science and Applied Mathematics

Petro Martyniuk, National University of Water and Environmental Engineering

Doctor of Technical Sciences, Professor

Department of Computer Science and Applied Mathematics

Olga Michuta, National University of Water and Environmental Engineering

PhD, Associate Professor

Department of Computer Science and Applied Mathematics

Yevhenii Malanchuk, National University of Water and Environmental Engineering

Doctor of Technical Sciences, Professor

Department of Automation, Electrical and Computer-Integrated Technologies

Hanna Shlikhta, Rivne State University of Humanities

PhD, Associate Professor

Department of Information and Communication Technologies and Computer Science Teaching Methods

References

  1. Zaretskii, Yu. K. (1972). Theory of soil consolidation. Israel Program for Scientific Translation.
  2. DBN V.2.4-3:2010 (2010). Derzhavni budivelni normy Ukrainy. Hidrotekhnichni, enerhetychni ta melioratyvni systemy i sporudy, pidzemni hirnychi vyrobky. Hidrolohichni sporudy. Osnovni polozhennia. Kyiv: Minrehionbud Ukrainy. Available at: https://dbn.co.ua/load/normativy/dbn/1-1-0-802
  3. DBN V.2.1-10-2009 (2009). Derzhavni budivelni normy Ukrainy. Obiekty budivnytstva ta promyslova produktsiya budivelnoho pryznachennia. Osnovy ta fundamenty budynkiv i sporud. Osnovy ta fundamenty sporud. Osnovni polozhennia proektuvannia. Kyiv: Minrehionbud Ukrainy. Available at: https://dbn.co.ua/load/normativy/dbn/dbn_v21_10_2009/1-1-0-319
  4. Park, S., Hong, S. (2021). Nonlinear Modeling of Subsidence From a Decade of InSAR Time Series. Geophysical Research Letters, 48 (3). doi: http://doi.org/10.1029/2020gl090970
  5. Widada, S., Zainuri, M., Yulianto, G., Satriadi, A., Wijaya, Y. (2020). Estimation of Land Subsidence Using Sentinel Image Analysis and Its Relation to Subsurface Lithology Based on Resistivity Data in the Coastal Area of Semarang City, Indonesia. Journal of Ecological Engineering, 21 (8), 47–56. doi: http://doi.org/10.12911/22998993/127394
  6. Knabe, D., Kludt, C., Jacques, D., Lichtner, P., Engelhardt, I. (2018). Development of a Fully Coupled Biogeochemical Reactive Transport Model to Simulate Microbial Oxidation of Organic Carbon and Pyrite Under Nitrate‐Reducing Conditions. Water Resources Research, 54 (11), 9264–9286. doi: http://doi.org/10.1029/2018wr023202
  7. Moshynsky, V., Riabova, O. (2013). Approaches to Aquatic Ecosystems Organic Energy Assessment and Modelling. Black Sea Energy Resource Development and Hydrogen Energy Problems. NATO Science for Peace and Security Series C: Environmental Security. Dordrecht: Springer, 125–135. doi: http://doi.org/10.1007/978-94-007-6152-0_12
  8. Michuta, O. R., Vlasyuk, A. P., Martinyuk, P. N. (2013). Influence of chemical erosion on filtration consolidation of saline soils in nonisothermal conditions. Matematicheskoe modelirovanie, 25 (2), 3–18. Available at: http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=mm&paperid=3327&option_lang=rus
  9. Gui, R., Pan, Y., Ding, D., Liu, Y., Zhang, Z. (2018). Experimental Study on Bioclogging in Porous Media during the Radioactive Effluent Percolation. Advances in Civil Engineering, 2018, 1–6. doi: http://doi.org/10.1155/2018/9671371
  10. Wang, Y., Huo, M., Li, Q., Fan, W., Yang, J., Cui, X. (2018). Comparison of clogging induced by organic and inorganic suspended particles in a porous medium: implications for choosing physical clogging indicators. Journal of Soils and Sediments, 18 (9), 2980–2994. doi: http://doi.org/10.1007/s11368-018-1967-6
  11. Thullner, M., Regnier, P. (2019). Microbial Controls on the Biogeochemical Dynamics in the Subsurface. Reviews in Mineralogy and Geochemistry, 85 (1), 265–302. doi: http://doi.org/10.2138/rmg.2019.85.9
  12. Glatstein, D. A., Montoro, M. A., Carro Pérez, M. E., Francisca, F. M. (2017). Hydraulic, Chemical and Biological Coupling on Heavy Metals Transport Through Landfills Liners. The Journal of Solid Waste Technology and Management, 43 (3), 261–269. doi: http://doi.org/10.5276/jswt.2017.261
  13. Mohanadhas, B., Kumar, G. S. (2019). Numerical Experiments on Fate and Transport of Benzene with Biological Clogging in Vadoze Zone. Environmental Processes, 6 (4), 841–858. doi: http://doi.org/10.1007/s40710-019-00402-w
  14. Lopez-Peña, L. A., Meulenbroek, B., Vermolen, F. (2019). A network model for the biofilm growth in porous media and its effects on permeability and porosity. Computing and Visualization in Science, 21 (1-6), 11–22. doi: http://doi.org/10.1007/s00791-019-00316-y
  15. Bohaienko, V., Bulavatsky, V. (2020). Fractional-Fractal Modeling of Filtration-Consolidation Processes in Saline Saturated Soils. Fractal and Fractional, 4 (4), 59. doi: http://doi.org/10.3390/fractalfract4040059
  16. Józefiak, K., Zbiciak, A., Brzeziński, K., Maślakowski, M. (2021). A Novel Approach to the Analysis of the Soil Consolidation Problem by Using Non-Classical Rheological Schemes. Applied Sciences, 11 (5), 1980. doi: http://doi.org/10.3390/app11051980
  17. Tian, Y., Wu, W., Jiang, G., El Naggar, M. H., Mei, G., Xu, M., Liang, R. (2020). One‐dimensional consolidation of soil under multistage load based on continuous drainage boundary. International Journal for Numerical and Analytical Methods in Geomechanics, 44 (8), 1170–1183. doi: http://doi.org/10.1002/nag.3055
  18. Vlasyuk, A. P., Martynyuk, P. M. (2010). Numerical solution of three-dimensional problems of filtration consolidation with regard for the influence of technogenic factors by the method of radial basis functions. Journal of Mathematical Sciences, 171 (5), 632–648. doi: http://doi.org/10.1007/s10958-010-0163-z
  19. Vlasyuk, A. P., Martynyuk, P. M., Fursovych, O. R. (2009). Numerical solution of a one-dimensional problem of filtration consolidation of saline soils in a nonisothermal regime. Journal of Mathematical Sciences, 160 (4), 525–535. doi: http://doi.org/10.1007/s10958-009-9518-8
  20. Glatstein, D. A., Francisca, F. M. (2014). Hydraulic conductivity of compacted soils controlled by microbial activity. Environmental Technology, 35 (15), 1886–1892. doi: http://doi.org/10.1080/09593330.2014.885583
  21. Tang, Q., Gu, F., Zhang, Y., Zhang, Y., Mo, J. (2018). Impact of biological clogging on the barrier performance of landfill liners. Journal of Environmental Management, 222, 44–53. doi: http://doi.org/10.1016/j.jenvman.2018.05.039
  22. Ulyanchuk-Martyniuk, O., Michuta, O., Ivanchuk, N. (2020). Biocolmation and the finite element modeling of its influence on changes in the head drop in a geobarrier. Eastern-European Journal of Enterprise Technologies, 4 (10 (106)), 18–26. doi: http://doi.org/10.15587/1729-4061.2020.210044
  23. Gerus, V. A., Martyniuk, P. M. (2015). Generalization of the soil consolidation equation taking into account the influence of physicochemical factors .Bulletin of VN Karazin Kharkiv National University. Series: Mathematical modeling. Information Technology. Automated control systems, 27, 41–52. Available at: http://nbuv.gov.ua/UJRN/VKhIMAM_2015_27_7
  24. Bulavatsky, V. M., Bohaienko, V. O. (2020). Some Consolidation Dynamics Problems within the Framework of the Biparabolic Mathematical Model and its Fractional-Differential Analog. Cybernetics and Systems Analysis, 56 (5), 770–783. doi: http://doi.org/10.1007/s10559-020-00298-7
  25. Wang, H.-X., Xu, W., Zhang, Y.-Y., Sun, D.-A. (2021). Simplified solution to one-dimensional consolidation with threshold gradient. Computers and Geotechnics, 131, 103943. doi: http://doi.org/10.1016/j.compgeo.2020.103943
  26. Araujo, F., Fantucci, H., Nunes, E., Santos, R. M. (2020). Geochemical Modeling Applied in Waste Disposal, and Its Relevance for Municipal Solid Waste Management. Minerals, 10 (10), 846. doi: http://doi.org/10.3390/min10100846
  27. Rodrigo-Ilarri, J., Rodrigo-Clavero, M.-E., Cassiraga, E. (2020). BIOLEACH: A New Decision Support Model for the Real-Time Management of Municipal Solid Waste Bioreactor Landfills. International Journal of Environmental Research and Public Health, 17 (5), 1675. doi: http://doi.org/10.3390/ijerph17051675
  28. Sergienko, I. V., Skopetskiy, V. V., Deyneka, V. S. (1991). Matematicheskoe modelirovanie i issledovanie protsessov v neodnorodnykh sredakh. Kyiv: Naukova dumka, 432.
  29. Ulianchuk-Martyniuk, O. V. (2020). Numerical simulation of the effect of semipermeable properties of clay on the value of concentration jumps of contaminants in a thin geochemical barrier. Eurasian Journal of Mathematical and Computer Applications, 8 (1), 91–104. doi: http://doi.org/10.32523/2306-6172-2020-8-1-91-104
  30. Šimůnek, J., van Genuchten, M. T., Šejna, M. (2016). Recent Developments and Applications of the HYDRUS Computer Software Packages. Vadose Zone Journal, 15 (7). doi: http://doi.org/10.2136/vzj2016.04.0033
  31. Clement, T. P., Hooker, B. S., Skeen, R. S. (1996). Macroscopic Models for Predicting Changes in Saturated Porous Media Properties Caused by Microbial Growth. Ground Water, 34 (5), 934–942. doi: http://doi.org/10.1111/j.1745-6584.1996.tb02088.x
  32. Manfred, B., Jaap, B., Klaus, M., Rolf, M. (2006). Enumeration and Biovolume Determination od Microbial Cells. Microbiological Methods for Assessing Soil Quality. CABI Publishing, 93–113. doi: https://doi.org/10.1079/9780851990989.0093

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Published

2021-04-30

How to Cite

Ivanchuk, N., Martyniuk, P., Michuta, O., Malanchuk, Y., & Shlikhta, H. (2021). Constructing a mathematical model and studying numerically the effect of bio-clogging on soil filtration consolidation. Eastern-European Journal of Enterprise Technologies, 2(10 (110), 27–34. https://doi.org/10.15587/1729-4061.2021.230238

Issue

Vol. 2 No. 10 (110) (2021): Ecology

Section

Ecology

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Copyright (c) 2021 Наталія Віталіївна Іванчук, Петро Миколайович Мартинюк, Ольга Романівна Мічута, Євгеній Зіновійович Маланчук, Ганна Олександрівна Шліхта

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