Mathematical model of transport of degrading substance in a two-zone porous medium
DOI:
https://doi.org/10.71310/pcam.2_64.2025.01Keywords:
adsorption, finite differences, mathematical model, multistage kinetics, porous mediumAbstract
In the paper developed and numerically solved the problem of solute transport in a porous medium consisting of active and passive zones, taking into account the multi-stage nature of adsorption kinetics. A mathematical model of the process is compiled based on general conservation laws and additional phenomenological assumptions. The influence of initial conditions on the characteristics of transfer and adsorption is analyzed. The results of numerical modeling are presented, confirming the influence of system parameters on the concentration dynamics in the active and passive zones. TThe obtained results can be used to predict the spread of pollutants in underground reservoirs and develop strategies for its control.
References
Zeng L., Yuan C., Xiang T., Guan X., Dai L., Xu D., Yang D., Li L., Tian C. Research on the Migration and Adsorption Mechanism Applied to Microplastics in Porous Media: A Review Nanomaterials,– 2024. Vol. 14(12):1060. doi: http://dx.doi.org/10.3390/nano14121060.
Fetter C.W. Contaminant hydrogeology, — Long Grove, Ill: Waveland Press, – 2018.
Bear J. Theory and applications of transport in Porous Media 5. modeling and applications of transport phenomena in Porous Media — Dordrecht; Boston; London: Kluwer,– 1991.
Tien C., Ramarao B.V. Granular Filtration of Aerosols and Hydrosols, 2nd ed. — Elsevier: Amsterdam, The Netherlands,– 2007.
van Genuchten M.Th., Wagenet R.J. Two– Site / Two– Region Models for Pesticide Transport and Degradation: Theoretical Development and Analytical Solutions Soil Science Society of America Journal,– 1989. Vol.53(5):– P. 1303–1310. doi: http://dx.doi.org/10.2136/sssaj1989.03615995005300050001x.
Berkowitz B., Ishai D., Scott K.H., Harvey S. Measurements and Models of Reactive Transport in Geological Media, Reviews of Geophysics, – 2016. Vol. 54., no. 4– P. 930–986. doi: http://dx.doi.org/10.1002/2016rg000524
Ogram A.V., Jessup R.E., Ou L.T., Rao P.S. Effects of sorption on biological degradation rates of (2,4-dichlorophenoxy) acetic acid in soils, Applied and Environmental Microbiology,– 1985. Vol.49(3),– P. 582–587. doi: http://dx.doi.org/10.1128/AEM.49.3.582-587. 1985
Mover J.R., Hance R.J., McKone C.E. The effect of adsorbents on the rate of degradation of herbicides incubated with soil, Soil Biology and Biochemistry,– 1972.– Vol. 4.– P. 307–311. doi: http://dx.doi.org/10.1016/0038-0717(72)90026-0.
Brusseau M.L., Xie L.H., LiL. Biodegradation during contaminant transport in porous media: 1. mathematical analysis of controlling factors, Journal of Contaminant Hydrology,– 1999. Vol. 37.– P. 269–293. doi: http://dx.doi.org/10.1016/S0169-7722(99)00005-4
Kammouri S.A., El Hatri M., Crolet J.M. Modeling Contaminant Transport and Biodegradation in a Saturated Porous Media, In: Crolet, J.M. (eds) Computational Methods for Flow and Transport in Porous Media. Theory and Applications of Transport in Porous Media,– 2000. doi: http://dx.doi.org/10.1007/978-94-017-1114-2_16.
Chamkha A.J., Al-Humoud J. Deep bed filtration with time-dependent input conditions, Special Topics and Reviews in Porous Media: An International Journal,– 2015. Vol. 6.– P. 343–352. doi: http://dx.doi.org/10.1615/SpecialTopicsRevPorousMedia.v6.i4.30.
Ma E., Ouahbi T., Wang H., Ahfir N.D., Alem A., Hammadi A. Modeling of retention and re-entrainment of mono- and poly-disperse particles: Effects of hydrodynamics, particle size and interplay of different-sized particles retention Sci. Total Environ. 596-597:– 2017.– P. 222–229. doi: http://dx.doi.org/10.1016/j.scitotenv.2017.03.254.
Веницианов Е.В., Рубинштейн Р.Н. ДинамикасорбцииизжидкихсредМосква:Наука,– 1983.
Gitis V., Rubinstein I., Livshits M., Ziskind M. Deep– bed filtration model with multistage deposition kinetics, Chemical Engeneering Journal,– 2010. Vol. 163.– P. 78–85.
Fayziev B., Ibragimov G., Khuzhayorov B., Alias IA. 2020. Numerical study of suspension filtration model in porous medium with modified deposition kinetics Symmetry 12 No. 5, 696. doi: http://dx.doi.org/10.3390/sym12050696.
Khuzhayorov B.K., Makhmudov J.M., Fayziev B.M., Begmatov T.I. Some Model of a Suspension Filtration in a Porous Media That Accounts for the Two-Zone and Multistage Character of Deposition Kinetics Journal of Applied and Industrial Mathematics,– 2020. Vol. 14 No. 3,– P. 513–523. doi: http://dx.doi.org/10.1134/S1990478920030102.
Samarskii A.A. The Theory of Difference Schemes CRC Press: New York, NY, USA,– 2001.
