Skip to main content
Log in

Identifying kinetic parameters of mass transfer in components of multicomponent heterogeneous nanoporous media of a competitive diffusion system

  • Systems Analysis
  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The identification of diffusion parameters of a two-component solution in heterogeneous nanoporous materials is analyzed. The gradient of the residual functional is obtained based on optimal control theory. The results of numerical experiments are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. J. Kärger and D. Ruthven, “Diffusion and adsorption in porous solids,” in: F. Shuth, K. W. Sing, and J. Weitkamp (eds.), Handbook of Porous Solids, Wiely-VCH, Wenheim (2002), pp. 2089–2173.

    Google Scholar 

  2. J. Kärger and D. Ruthven, Diffusion in Zeolites and Other Microporous Solids, John Wiley & Sons, New York (1992).

    Google Scholar 

  3. N. Y. Chen, T. F. Degnan, and M. C. Smith, Molecular Transport and Reaction in Zeolites: Design and Application of Shape Selective Catalysis, Wiley, New York (1994).

    Google Scholar 

  4. D. Ruthven, Principles of Adsorption and Adsorption Processes, Wiley Interscience, New York (1984).

    Google Scholar 

  5. P. N’Gokoli-Kekele, M.-A. Springuel-Huet, and J. Fraissard, “An analytical study of molecular transport in a zeolite crystallite bed,” Adsorption, 8, No. 3, 35–44 (2002).

    Article  Google Scholar 

  6. J. Kärger, F. Grinberg, and P. Heitjans, Diffusion Fundamentals, Leipziger Univ., Leipzig (2005).

    Google Scholar 

  7. E. L. Cussler, Diffusion: Mass Transfer in Fluid Systems, Cambridge Univ. Press, Cambridge (2008).

    Google Scholar 

  8. H. Mehrer, Diffusion in Solids, Springer, Berlin–Heidelberg–New York (2007).

    Google Scholar 

  9. F. D. Magalhães, R. L. Laurence, W. C. Conner, et al., “Study of molecular transport in beds of zeolite crystallites: Semi-quantitative modeling of 129Xe NMR experiments,” J. Phys. Chem., B., 101, 2277–2284 (1997).

    Article  Google Scholar 

  10. M. Petryk, S. Leclerc, D. Canet, and J. Fraissard, “Mathematical modeling and visualization of gas transport in a zeolite bed using a slice selection procedure,” Diffus. Fundam., 4, 11.1–11.23 (2007).

    Google Scholar 

  11. M. Petryk, J. Fraissard, S. Leclerc, and D. Canet, “Modeling of gas transport in a microporous solid using a slice selection procedure: Application to the diffusion of benzene in ZSM5,” Catalysis Today, 139, No. 3, 234–240 (2008).

    Article  Google Scholar 

  12. M. R. Petryk and J. Fraissard, “Mathematical modeling of nonlinear competitive two-component diffusion in media of nanoporous particles,” J. Autom. Inform. Sci., 41, Issue 3, 37–55 (2009).

    Article  Google Scholar 

  13. I. V. Sergienko and V. S. Deineka, “Using gradient methods to identify parameters of diffusion problems for two-component substances in nanoporous media,” Dop. NANU, No. 2, 42–49 (2010).

  14. M. R. Petryk, J. Fraissard, and D. M. Mikhalik, “Modeling and analysis of concentration fields of nonlinear competitive two-component diffusion in medium of nanoporous particles,” J. Autom. Inform. Sci., 41, Issue 8, 13–23 (2009).

    Article  Google Scholar 

  15. M. R. Petryk and J. Fraissard, “Mathematical modeling and visualization of multilevel mass transfer system in heterogeneous catalytic media of nanoporous particles,” J. Autom. Inform. Sci., 40, Issue 10, 1–41 (2008).

    Article  Google Scholar 

  16. M. R. Petryk, “Mathematical modeling of mass transfer in symmetric heterogeneous and nanoporous media with a system of n-interface interactions,” Cybern. Syst. Analysis, 43, No. 1, 94–111 (2007).

    Article  MATH  Google Scholar 

  17. M. Petryk and E. Vorobiev, “Liquid flowing from porous particles during the pressing of biological materials,” Computer and Chem. Eng., 31, 1336–1345 (2007).

    Article  Google Scholar 

  18. M. Petryk, O. Shabliy, M. Leniyk, and P. Vasylyuk, “Mathematical modeling and research for diffusion process in multilayer and nanoporous media,” in: W. C. Conner and J. Fraissard (eds.), Fluid Transport in Nanoporous Materials, NATO Sci. Series, Series II, Mathematics, Physics, and Chemistry, 219, Springer Publ., Amsterdam (2006), pp. 685–655.

    Chapter  Google Scholar 

  19. M. P. Lenyuk and M. R. Petryk, Integral Fourier and Bessel Transforms with Spectral Parameter in Problems of Mathematical Modeling of Mass Transfer in Heterogeneous Media [in Ukrainian], Naukova Dumka, Kyiv (2000).

    Google Scholar 

  20. V. S. Deineka and I. V. Sergienko, Optimal Control of Heterogeneous Distributed Systems [in Russian], Naukova Dumka, Kyiv (2003).

    Google Scholar 

  21. I. V. Sergienko and V. S. Deineka, Optimal Control of Distributed Systems with Conjugation Conditions, Kluwer Academic Publishers, New York (2005).

    MATH  Google Scholar 

  22. V. S. Deineka and I. V. Sergienko, Analysis of Multicomponent Distributed Systems and Optimal Control [in Russian], Naukova Dumka, Kyiv (2007).

    Google Scholar 

  23. I. V. Sergienko and V. S. Deineka, “Solving combined inverse problems for multicomponent parabolic distributed systems,” Cybern. Syst. Analysis, 43, No. 5, 655–674 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  24. V. S. Deineka and N. A. Veshchunova, “Numerical solution of inverse problems of transient heat conduction for a plate,” Komp. Matematika, No. 2, 32–43 (2008).

  25. I. V. Sergienko and V. S. Deineka, Systems Analysis of Multicomponent Distributed Systems [in Russian], Naukova Dumka, Kyiv (2009).

    Google Scholar 

  26. I. V. Sergienko and V. S. Deineka, “Parameter identification by gradient methods of the problems of substance diffusion in nanoporous medium,” J. Autom. Inform. Sci., 42, Issue 11, 1–17 (2010).

    Article  Google Scholar 

  27. I. V. Sergienko, V. V. Skopetskyy, and V. S. Deineka, Mathematical Modeling and Analysis of Processes in Heterogeneous Media [in Russian], Naukova Dumka, Kyiv (1991).

    Google Scholar 

  28. M. A. Lavrent’ev and B. V. Shabat, Methods of Complex Analysis [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  29. I. G. Petrovskii, Lectures on Partial Differential Equations [in Russian], Fizmatgiz, Moscow (1961).

    Google Scholar 

  30. J.-L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York (1971).

    MATH  Google Scholar 

  31. O. M. Alifanov, S. V. Artyukhin, and S. V. Rumyantsev, Extremum Methods to Solve Ill-Posed Problems [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  32. V. S. Deineka and E. A. Evdin, “Modifying the Crank–Nicholson scheme to solve convection–diffusion transfer equations,” Komp. Matematika, No. 3, 15–26 (2006).

  33. V. A. Ditkin and A. P. Prudnikov, A Handbook on Operator Calculus [in Russian], Vysshaya Shkola, Moscow (1965).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. S. Deineka.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 45–64, September–October 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deineka, V.S., Petryk, M.R. & Fraissard, J. Identifying kinetic parameters of mass transfer in components of multicomponent heterogeneous nanoporous media of a competitive diffusion system. Cybern Syst Anal 47, 705–723 (2011). https://doi.org/10.1007/s10559-011-9350-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-011-9350-2

Keywords

Navigation