Study and analysis of mathematical models of groundwater filtration processes in multilayer heterogeneous porous media
DOI:
https://doi.org/10.71310/pcam.1_63.2025.04Keywords:
mathematical model, filtration, groundwater, heterogeneous porous mediumAbstract
Modeling of nonlinear filtration processes in multilayer heterogeneous porous media is a complex area that combines various mathematical and physical principles to understand the dynamics of fluid in porous structures. The complexity of these processes is influenced by the heterogeneity of the medium, the nonlinear nature of the fluid flow and the interaction between different layers of porous materials. The paper presents a detailed analysis of the obtained fundamental and applied research in the field of groundwater filtration in homogeneous, heterogeneous and multilayer porous media based on the laws of A. Darcy, J. Dupuis, N.E. Zhukovsky, F. Forchheimer and others.
References
Dassargues A. Hydrogeology. First Edition // Boca Raton (USA): Taylor Francis, 2019.
Baev O.A. Calculations of steady free seepage from unlined canals // L. Reclam. Hydraul. Eng. – 2022. – No. 3.
Павловский Н.Н. Неравномерное движение грунтовых вод. – Ленинград: КУБУЧ, 1932. – 80 с.
Костякoв А.Н. Основы мелиораций. – М.: СЕЛЬХОЗГИЗ, 1938. – 747 с.
Abdrazakov F.K. et al. Theoretical studies of filtration from irrigation channels // L. Reclam. Hydraul. Eng. – 2024. – Vol. 14, No. 4. – P. 390-402.
Suo S., Liu M., Gan Y. Modelling Imbibition Processes in Heterogeneous Porous Media // Porous Media. – 2019. – Vol. 126, No. 3. – P. 615-631.
Zhang C. et al. A chaotic dynamical approach to simulate heterogeneous groundwater flow movement // 3rd Int. Conf. on Comp. Sys. and Com. (ICCSC 2017). – 2017.
Michuta O.R., Martyniuk P.M. Nonlinear Evolutionary Problem of Filtration Consolidation With the Non-Classical Conjugation Condition // J. Optim. Differ. Equations Their Appl. – 2022. – Vol. 30, No. 1.
Kayumov S. et al. A multiparameter mathematical model for the problem of nonlinear filtration of fluids in two-layer media // J. Phys. Conf. Ser. – 2024. – Vol. 2697, No. 1.
Arbabi S., Sahimi M. The Transition from Darcy to Nonlinear Flow in Heterogeneous Porous Media: I—Single-Phase Flow // Transp. Porous Media. – 2024. – Vol. 151, No. 4. – P. 795- 812.
Ku C.Y. et al. 2020. Modeling Transient Flows in Heterogeneous Layered Porous Media Using the Space–Time Trefftz Method // Appl. Sci. – 2021. – Vol. 11, No. 8.
Natalia I., Petro M., Olga M. Mathematical model of filtration under conditions of variable porosity taking into account biocolmatage // Model. Control Inf. Technol. – 2020. – No. 4. – P. 43-46.
Abubakar A.D. et al. Mathematical Modeling of Effect of Pumping Rate on Contaminant Transport in Riverbank Filtration System // J. Appl. Sci. Environ. Manag. – 2021. – Vol. 25, No. 2. – P. 199-208.
Michuta O. et al. A finite-element study of elastic filtration in soils with thin inclusions // Eastern-European J. Enterp. Technol. – 2020. – Vol. 5, No. 5(107). – P. 41-48.
Benes M., Pazanin I. Homogenization of degenerate coupled transport processes in porous media with memory terms // Math. Methods Appl. Sci. – 2019. – Vol. 42, No. 18. – P. 6227-6258.
Ravshanov N. et al. Numerical study of fluid filtration in three-layer interacting pressure porous formations // E3S Web Conf. – 2021. – Vol. 264. – 01018.
Simpson M.J. Calculating Groundwater Response Times for Flow in Heterogeneous Porous Media // Groundwater. – 2018. – Vol. 56, No. 2. – P. 337-342.
Равшанов Н. Математическое моделирование изменения уровня грунтовых вод в двухслойных средах // J. Innov. RESEACH Econ. – 2022. – Vol. 1, No. 1.
Djumanov J.X. et al. Development Of A Hydrogeological Simulation Model Of Geofiltration Processes In Regional Aquifers Of Fergana Valley // IEEE Int. Conf. on Infor. Sci. and Commu. Tech. (ICISCT). – 2019. – P. 1-5.
Cayar M., Kavvas M.L. Ensemble average and ensemble variance behavior of unsteady, onedimensional groundwater flow in unconfined, heterogeneous aquifers: an exact second-order model // Stoch. Environ. Res. Risk Assess. – 2009. – Vol. 23, No. 7. – P. 947-956.
Daliev S. et al. Numerical study of filtration process of ground and pressure waters in multilayer porous media // IOP Conf. Ser. Mater. Sci. Eng. – 2020. – Vol. 896, No. 1. – 012069.
