DOI: 10.12732/ijam.v37i1.2
INTEGRAL CONJUGATION
CONDITIONS FOR A
DISCONTINUOUS FILTRATION
FLOW VIA A GEOBARRER IN THE
CASE OF ITS BIOCOLMATATION
Petro Martyniuk §, Oksana Ulianchuk-Martyniuk,
Volodymyr Herus, Oksana Pryshchepa
National University of Water and Environmental Engineering
11 Soborna St., Rivne – 33028, UKRAINE
Abstract. In the article, modified conjugation conditions of non-ideal contact have been derived for the filtration rate when passing through a thin porous geobarrier. Their feature is taking into account the influence on the change in the porosity of the geo-barrier by the dynamic bioclamation processes. Accounting for this effect leads to the appearance under conjugation conditions of time derivatives on microbial biomass concentration. As a result, the filtration flow
of the pore fluid may be discontinuous when passing through the geo-barrier. The case of conjugation conditions has been considered when the concentration of microorganisms over the thickness of the inclusion can be approximated by a linear dependence.
How
to cite this paper?
DOI: 10.12732/ijam.v37i1.2
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 1
References
[1] S. Nanda, F. Berruti, Municipal solid waste management and landfilling technologies: a review, Environmental Chemistry Letters, 19 (2021), 1433–1456; doi: 10.1007/s10311-020-01100-y
[2] G. Kumar, Kevin B. Kopp, Krishna R. Reddy, James L. Hanson, N. Yesiller, Influence of waste temperatures on long-term landfill performance: coupled numerical modeling, J. Environ. Eng., 147(3) (2021), 04020158; doi: 10.1061/(ASCE)EE.1943-7870.0001855
[3] J.C. Evans, D.G. Ruffing, K.R. Reddy, G. Kumar, J.K. Chetri, Sustainability of vertical barriers for environmental containment, Sustainable Environmental Geotechnics. Lecture Notes in Civil Engineering, 89 (2020), 271–283; doi: 10.1007/978-3-030-51350-4-29
[4] W.W. Ng Charles, R. Chen, J.L. Coo, J. Liu, J.J. Ni, Y.M. Chen, L.-t. Zhan, H.W. Guo, B.W. Lu, A novel vegetated three-layer landfill cover system using recycled construction wastes without geomembrane, Can. Geotech. J., 56 (2019), 1863–1875; doi: 10.1139/cgj-2017-0728
[5] Chun-Hui Peng, Shi-Jin Feng, Qi-Teng Zheng, Xiang-Hong Ding, Zhang-Long Chen, Hong-Xin Chen, A two-dimensional analytical solution for organic contaminant diffusion through a composite geomembrane cut-off wall and an aquifer, Computers and Geotechnics, 119 (2020), 103361; doi: 10.1016/j.compgeo.2019.103361
[6] N. Hassannayebi, B. Jammernegg, J. Schritter, P. Arnold, F. Enzmann, M. Kersten, A.P. Loibner, M. Ferno, H. Ott, Relationship between microbial growth and hydraulic properties at the sub-pore scale, Transport in Porous Media, 139 (2021), 579–593; doi: 10.1007/s11242-021-01680-5
[7] Qiang Tang, Shenjie Shi, Jiannan Chen, Qi Xu, Xinyu Luo, Modeling the influence of microbial growth on the hydraulic properties of porous media, Computers and Geotechnics, 147 (2022), 104786; doi: 10.1016/j.compgeo.2022.104786
[8] M. Thullner, J. Zeyer, W. Kinzelbach, Influence of microbial growth on hydraulic properties of pore networks, Transport in Porous Media, 49 (2002), 99–122; doi: 10.1023/A:1016030112089
[9] Y.V. Chui, V.S. Moshynskyi, P.M. Martyniuk, O.M Stepanchenko, On conjugation conditions in the filtration problems upon existence of semipermeable inclusions, JP Journal of Heat and Mass Transfer, 15 (2018), 609–619; doi: 10.17654/HM015030609
[10] Y. Chui, P. Martyniuk, M. Kuzlo, O. Ulianchuk-Martyniuk, The conditions of conjugation in the tasks of moisture transfer on a thin clay inclusion taking into account salt solutions and temperature, Journal of Theoretical and Applied Mechanics, 49 (2019), 28–38; doi:
10.7546/JTAM.49.19.01.03
[11] O. Ulianchuk-Martyniuk, O. Michuta, Conjugation conditions in the problem of filtering chemical solutions in the case of structural changes to the material and chemical suffusion in the geobarrier, JP Journal of Heat and Mass Transfer, 19 (2020), 141–154; doi: 10.17654/HM019010141
[12] O. Stepanchenko, P. Martyniuk, O. Belozerova, L. Shostak, Balance boundary conditions for thin boundary layers: derivation from the integral conjugation conditions, International Journal of Applied Mathematics, 36, No 1 (2023), 107–116; doi: 10.12732/ijam.v36i1.9
[13] O.V. Ulianchuk-Martyniuk, O.R. Michuta, N.V. Ivanchuk, Finite element analysis of the diffusion model of the bioclogging of the geobarrier, Eurasian Journal of Mathematical and Computer Applications, 9 (2021), 100–114; doi: 10.32523/2306-6172-2021-9-4-100-114
[14] O. Ulianchuk-Martyniuk, O. Michuta, N. Ivanchuk, Biocolmatation and the finite element modeling of its influence on changes in the head drop in a geobarrier, Eastern-European Journal of Enterprise Technologies, 4 (2020), 18–26; doi: 10.15587/1729-4061.2020.210044
[15] V.A. Herus, N.V. Ivanchuk, P.M. Martyniuk, A system approach to mathematical and computer modeling of geomigration processes using freefem++ and parallelization of computations, Cybernetics and Systems Analysis, 54 (2018), 284–294;
doi: 10.1007/s10559-018-0030-3
[16] N. Ivanchuk, P. Martyniuk, O. Michuta, Y. Malanchuk, H. Shlikhta, Constructing a mathematical model and studying numerically the effect of bio-clogging on soil filtration consolidation, Eastern-European Journal of Enterprise Technologies, 2 (2021), 27–34;
doi: 10.15587/1729-4061.2021.230238
[17] P. Martyniuk, O. Michuta, N. Ivanchuk, Mathematical model of filtration under conditions of variable porosity taking into account biocolmatage, Modeling, Control and Information Technologies: Proceedings of IV International Scientific and Practical Conference, 4 (2020),
43–46; doi: 10.31713/MCIT.2020.36
[18] M. Bolter, J. Bloem, K. Meiners, R. Moller, Enumeration and biovolume determination of microbial cells, In: Microbiological Methods for Assessing Soil Quality, CABI Publishing, UK (2006), 93–113.
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