Solute Transport in a Nonhomogeneous Porous Medium
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Samarkand State University, Samarkand, UzbekistanAbstract
The paper considers the solute transport in a heterogeneous porous medium consisting of well-permeable and poorly permeable zones, taking into account nonequilibrium adsorption in the zones. In a well-permeable zone, there are two areas, in each of which there is an adsorption of a substance with reversible nonequilibrium kinetics. The exchange of solute with the second zone is modeled by the source term in the form of a fractional time derivative of the concentration of the substance in the first zone. The numerical implementation of the model is carried out and the effect of mass transfer to the second zone on the characteristics of the solute transport in the first zone is estimated.
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Barenblatt G.I., Entov V.M. and Ryzhik V.M. Theory of Fluid Flow Through Natural Rocks. Kluwer Academic, Dordrecht, The Netherlands. 1990.
Van Golf-Racht T.D. Fundamentals of Fractured Reservoir Engineering. Developments in Petroleum Science, Vol. 12. Elsevier. 1982 y. 732 p.
Sahimi M. Flow and Transport in Porous Media and Fractured Rock. From Classical Methods to Modern Approaches. Second, Revised and Enlarged Edition. WILEY-VCH VerlagGmbH&Co. KGaA. 2011.
Leij F.L., Bradford S.A. Colloid transport in dual-permeability media // Journal of Contaminant Hydrology. 150.- 2013.-P. 65–76.
Cey E.E., Rudolph D.L. Field study of macropore flow processes using tension infiltration of a dye tracer in partially saturated soils // Hydrological Processes. 23.- 2009.-P. 1768–1779.
Jarvis N.J. A review of non-equilibrium water flow and solute transport in soil macropores: principles, controlling factors and consequences for water quality // European Journal of Soil Science. 58.- 2007.- P. 523–546.
Pang L., McLeod M., Aislabie J., Simunek J., Close M., Hector R. Modeling transport of microbes in ten undisturbed soils under effluentirrigation // Vadose Zone Journal 7. -2008.- P. 97–111.
Passmore J.M., Rudolph D.L., Mesquita M.M.F., Cey E.E., Emelko M.B. The utility of microspheres as surrogates for the transport of E. coli RS2gin partially saturated agricultural soil // Water Research 44.-2010.- P. 1235–1245.
Gerke H.H., van Genuchten M.T. Macroscopic representation of structural geometry for simulating water and solute movement in dual porosity media // Advances in Water Resources. 19. -1996. -P. 343–357.
Selim H.M., Ma L. Physical Nonequilibrium in Soils: Modeling and Applications. Ann Arbor Press, Chelsea, MI. -1998.
Simunek J., van Genuchten M.Th. Modeling nonequilibrium flow andtransport processes using HYDRUS //Vadose Zone Journal 7.- 2008. -P. 782–797.
Toride N., Leij F.J., van Genuchten M.Th. The CXTFIT code for estimating transport parameters from laboratory or field tracer experiments. Version 2.0.Res. Rep. 137. U.S. Salinity Lab, Riverside, CA.- 1995.
Coats K.H., Smith B.D. Dead-end pore volume and dispersion in porous media // Soc.Pet.Eng.J. -1964. No. 4.-P. 73−84.
Van Genuchten M.Th., Wierenga P.J. Mass Transfer Studies in Sorbing Porous media.I. Analytical Solution // Soil Science Society of America Journal, 1976.-Vol.40, N.4.- P.473−480.
Leij F.J., Bradford S.A. Combined physical and chemical non equilibrium transport model: analytical solution, moments, and application to colloids //Journal of Contaminant Hydrology. 110.- 2009.- P. 87–99.
Bradford S.A., Simunek J., Bettahar M., van Genuchten M.T., Yates S.R. Modeling colloid attachment, straining, and exclusion in saturated porous media // Environmental Science & Technology. 37.-2003.- P. 2242–2250.
Bradford S.A., Torkzaban S. Colloid transport and retention inunsaturated porous media: A review of interface-, collector-, and pore-scale processes and models //Vadose Zone Journal. 7.- 2008.- P. 667–681.
Elimelech M. et al. Particle Deposition and Aggregation: Measurement, Modelling, and Simulation. Butterworth-Heinemann.- Oxford, England,1995.
Gitis V., Rubinstein I., Livshits M.,Ziskind M. Deep-bed filtration model with multistage deposition kinetics // Chemical Engineering Journal. 163.- 2010.- P. 78-85.
Khuzhayorov B. Kh, Djiyanov T.O. Solute Transport with nonequilibrium adsorption in an inhomogeneous porous medium // Scientific journal «problems of computational and applied mathematics». -2017. -№ 3(9). – P. 63-70.
Samarskiy A.A. The theory of difference scheme. М. The science. 1977. P. 656
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