The problem of mathematical simulation of the vertical migration of radionuclides in a catalytic porous medium under nonisothermal conditions is considered. A numerical solution of the corresponding one-dimensional nonlinear boundary-value problem is obtained by the finite difference method. Numerical experiments are carried out and their analysis is made.
Similar content being viewed by others
References
V. Entov, S. Numerov, P. Polubarinova-Kochina, and I. Charnyi (Eds.), Development of Studies in the USSR on the Theory of Filtration (1917–1967) [in Russian], Nauka, Moscow (1969).
N. N. Verigin and B. S. Sherzhukov, Diffusion and mass transfer during filtration of liquids in porous media, in: Development of Studies in the USSR on the Theory of Filtration (1917–1967) [in Russian], Nauka, Moscow (1969), pp. 237–313.
I. V. Sergienko, V. V. Skopetskii, and V. S. Deineka, Mathematical Simulation and Investigation of the Processes Proceeding in Inhomogeneous Media [in Russian], Naukova Dumka, Kiev (1991).
S. I. Lyashko, Optimization and Mathematical Simulation of Underground Water Mass Transfer [in Russian], Naukova Dumka, Kiev (1998).
A. P. Vlasyuk and M. Kuzlo, Experimental investigations of some of the parameters of filtration of salt solutions in sandy soils, in: Melioration and Water Handling Facilities: Interdepartmental Thematic Scientific Collection [in Russian] (2000), pp. 43–46.
V. M. Prokhorov (R. M. Aleksakhin Ed.), Migration of Radioactive Foulings in Soils [in Russian], Énergoizdat, Moscow (1981).
Ya. I. Burak and E. Ya. Chaplya, The starting principles of the mathematical model of heterodiffusional transfer of radionuclides in the near-surface layers of Earth, Dop. Nats. Akad. Nauk Ukrainy, 10, 59–63 (1993).
P. Bossew and G. Kirchner, Modelling the vertical distribution of radionuclides in soil. Part 1: The convection–dispersion equation revisited, J. Environ. Radioactivity, 73, 127–150 (2004); doi:https://doi.org/10.1016/j.jenvrad.2003.08.006.
A. P. Vlasyuk and O. P. Ostapchuk, Mathematical Simulation of Salt Solution Transfer during Filtration of Underground Water in Large Masses of Ground [in Russian], Nats. Univ. Vodn. Khoz. i Prirodopol′z., Rovno (2015).
P. P. Zolotarev and M. M. Dubinin, About the equations describing internal diffusion in adsorbent granules, Dokl. Akad. Nauk SSSR, 210, No. 1, 136–139 (1973).
E. Ruckenstein, A. Vaidyanathan, and G. Youngquist, Sorption by solids with bidisperse pore structures, Chem. Eng. Sci., 26, 1305–1318 (1971); doi:https://doi.org/10.1016/0009-2509(71)80051-9.
I. N. Bekman, The Theory of Diffusion in Dispersion Media [in Russian], Moskovsk. Gos. Univ., Moscow–Nal′chik (2008).
W. C. Conner and J. P. Fraissard, Fluid Transport in Nanoporous Materials, Springer in cooperation with NATO Public Diplomacy Division, Dordrecht, The Netherlands (2006).
J. Kärger, D. M. Ruthven, and D. N. Theodorou, Diffusion in Nanoporous Materials, Wiley-VCH, Weinheim, Germany (2012).
M. R. Petryk, J. Fraissard, and D. M. Mykhalyk, Modeling and analysis of concentration fields of nonlinear competitive two-component diffusion in medium of nanoporous particles, J. Automat. Inform. Sci., 41, 13–23 (2009); doi:https://doi.org/10.1615/JAutomatInfScien.v41.i8.20.
J. Rouquerol, D. Avnir, C. W. Fairbridge, D. H. Everett, J. M. Haynes, N. Pernicone, et al., Recommendations for the characterization of porous solids (Technical Report), Pure Appl. Chem., 66, No. 8, 1739−1758 (1994); doi:https://doi.org/10.1351/pac199466081739.
N. Natarajan and G. Suresh Kumar, Radionuclide and colloid co-transport in a coupled fracture–skin–matrix system, Colloids Surf. A: Physicochem. Eng. Aspects, 370, Issues 1−3, 49–57 (2010); doi:https://doi.org/10.1016/j.colsurfa.2010.08.045.
T. Cheng and J. E. Saiers, Colloid-facilitated transport of cesium in vadose-zone sediments: the importance of flow transients, Environ. Sci. Technol., 44, 7443–7449 (2010); doi:https://doi.org/10.1021/es100391j.
O. Klimenko, A machine for inserting meliorants in a liquid state, Vestn. Rovensk. Gos. Tekh. Univ., Collect. of Sci. Works, Issue 1 (3), 161–166 (2000).
A. P. Vlasyuk, V. V. Zhukovskyy, and M. M. Bondarchuk, Mathematical modelling of vertical migration of radionuclides in catalytic porous media with traps in linear case, in: Proc. 5th Int. Sci. Conf. of Students and Young Scientists "Theoretical and Applied Aspects of Cybernetics" (2015), pp. 208–219.
A. P. Vlasyuk and V. V. Zhukovskyy, Mathematical modelling of vertical migration of radionuclides in unsaturated porous media in non-isothermal conditions one-dimensional case, Abstr. XXIV Int. Conf. "Problems of Decision Making under Uncertainties" (2014), pp. 110–111.
A. P. Vlasyuk and V. V. Zhukovskii, Mathematical simulation of vertical migration of radionuclides in a catalytic porous medium, Vestn. Kievsk. Nats. Univ., Ser. Fiz.-Mat. Nauk, Issue 1, 89–95 (2015).
A. P. Vlasyuk and V. V. Zhukovskii, Mathematical simulation of vertical migration of radionuclides in a catalytic porous medium in a nonlinear case, in: Mathematical and Computer Simulation, Series: Technical Sciences, Collect. of Sci. Works, Issue 12, 161–172 (2015).
J. Simunek, D. Jacques, G. Langergraber, S. A. Bradford, M. Šejna, and M. T. van Genuchten, Numerical modeling of contaminant transport using HYDRUS and its specialized modules, J. Indian Inst. Sci., 93, 265–284 (2013).
B. P. Demidovich, I. A. Maron, and É. Z. Shuvalova, Numerical Methods of Analysis [in Russian], Nauka, Moscow (1967).
A. A. Samarskii, The Theory of Difference Schemes, Textbook for universities specializing in "Applied Mathematics" [in Russian], Nauka, Moscow (1989).
A. P. Vlasyuk and P. M. Martynyuk, Numerical Solution of the Problems of Consolidation and Filtration-Induced Disturbance of Soils under Heat and Mass Transfer Conditions by the Method of Radial Basis Functions [in Russian], Nats. Univ. Vodn. Khoz. i Prirodopol′z., Rovno (2010).
Modelling the Migration and Accumulation of Radionuclides in Forest Ecosystems, Report, International Atomic Energy Agency, Vienna (2002).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 90, No. 6, pp. 1457–1469, November–December, 2017.
Rights and permissions
About this article
Cite this article
Vlasyuk, A.P., Zhukovskii, V.V. Mathematical Simulation of the Migration of Radionuclides in a Soil Medium Under Nonisothermal Conditions with Account for Catalytic Microparticles and Nonlinear Processes. J Eng Phys Thermophy 90, 1386–1398 (2017). https://doi.org/10.1007/s10891-017-1697-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-017-1697-4