Numerical Solution of the Inverse Problem of Solute Transport in Non-Homogeneous Porous Media
Keywords:
Adsorption, approximation, fractional derivative, porous media, retardation factor, mobile zone.
Abstract
In this paper, a solute transport problem with non-equilibrium adsorption in a non-homogeneous porous medium consisting of two zones, one with high permeability (mobile zone) and another one with low permeability (immobile liquid zone) are considered. In the mobile zone, there are two zones in both of which adsorption of solute with reversible kinetics occurs. The results of this approach are compared with known, traditional approaches. It is shown that this method of modeling the process gives a satisfactory result. By appropriate selection of the parameters of the source term, one can obtain results close to those of the well-known bicontinuum approach.
References
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Danilaev P.G. On the filtration non–homogeneous porous stratum parameters identification problem, The International Symposium on Inverse Problems in Engineering Mechanics (ISIP'98), March 24–27, 1998, Nagano City, Japan.
Kravaris Costas, Seinfeld John H. Distributed parameter identification in geophysics–petroleum reservoirs and aquifers, In «Disributed Parameter Control Systems», (S. Tzafestas, Ed.). New York: Pergamon, 1982. P. 367–390.
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Van Golf–Racht T.D. Fundamentals of Fractured Reservoir Engineering, Developments in Petroleum Science, Elsevier, Vol.12, 1982, 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 Verlag GmbH&Co. KGaA (Weinheim, Germany), 2011.
Leij F.L., Bradford S.A. Colloid transport in dual–permeability media, Journal of Contaminant Hydrology, 150, 2013, pp. 65−76.
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, pp. 2242–2250.
Leij F.J., Bradford S.A. Combined physical and chemical nonequilibrium transport model: analytical solution, moments, and application to colloids, Journal of Contaminant Hydrology, 110, 2009. pp. 87–99.
Alifanov O.M. Klibanov M.V. Uniqueness conditions and method of solution of the coefficient inverse problem of thermal conductivity, Journal of engineering physics, Vol. 48, No 6, 1985, 730–735 pp.
Alifanov O.M. Inverse heat transfer problems. Springer–Verlag, New–York, 1994, 280 p.
Alifanov O.M. Artyukhin E.A. and Rumiantsev S.V. Extreme methods for solving III–posed problems with applications to inverse problems, Begell House, New–York, 1995.
Golubev G.V. Danilayev P.G. Tumashev G.G. Determination of hydroconductivity of inhomogeneous oil reservoirs by nonlocal methods, Kazan, Kazan university, Published, 1978, 168 p. (In Russian).
Lavrentiev M.M., Romanov V.G., Vasiliev V.G. Multidimensional inverse problems for differential equations. Springer–Verlag Berlin, Heidelberg, New York, 1970, 59 p.
Makarov A. M., Romanovskii M. R. Solution of inverse coefficient problems by the regularization method using spline functions, Journal of Engineering Physics, Vol. 34, No.2, 1978.
Romanov V.G. Inverse Problems of Mathematical Physics. VNU Science Press, 1987, 239 Pp.
Chavent G. Une methode de resolution de probleme inverse dans les equations aux derivees partielles, Bulletin de l' Academie Polonaise des Sciences, Serie des Sciences Techniques, V. XYIII, № 8, 1970, pp. 99–105.
Danilaev P.G. On the filtration non–homogeneous porous stratum parameters identification problem, The International Symposium on Inverse Problems in Engineering Mechanics (ISIP'98), March 24–27, 1998, Nagano City, Japan.
Kravaris Costas, Seinfeld John H. Distributed parameter identification in geophysics–petroleum reservoirs and aquifers, In «Disributed Parameter Control Systems», (S. Tzafestas, Ed.). New York: Pergamon, 1982. P. 367–390.
Kravaris Costas, Seinfeld John H. Identification of parameters in distributed parameter systems by regularization, SIAM Journal on Control and Optimization, 1985. V.23, No. 2. 1985, pp.217–241.
Kravaris Costas, Seinfeld John H. Identification of spatially varying parame¬ters in distributed parameters systems by discrete regularization, Journal of Mathematical Analysis and Applications, V. 119, 1986, pp. 128–152.
Schumer R. and Benson D.A. Fractal mobile/immobile solute transport, Water resources research, Vol. 39, No. 10, 2003. pp. 1296.
Fomin S.A., Chugunov V.A. and Hashida T. “The effect of non-Fickan diffusion into surrounding rocks on contaminant transport in a fractured porous aquifer”, Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences, 461, 2005, pp. 2923-2939.
Khuzhayorov B.Kh., Dzhiyanov T.O. and Eshdavlatov Z.Z. Numerical Investigation of Solute transport in a non-homogeneous porous medium using nonlinear kinetics, International Journal of Mechanical Engineering and Robotics Research, Vol. 11. No. 2, 2022, pp. 79–85.
Published
2023-06-19
How to Cite
Dzhiyanov T.O., & Xoliqov J. (2023). Numerical Solution of the Inverse Problem of Solute Transport in Non-Homogeneous Porous Media. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 4(6), 45-52. Retrieved from https://cajmtcs.centralasianstudies.org/index.php/CAJMTCS/article/view/472
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