Advertisement

Computational Mathematics and Modeling

, Volume 30, Issue 2, pp 155–163 | Cite as

A Numerical Method for Determining Two Sorbent Characteristics in Case of Decreasing Porosity

  • S. R. TuikinaEmail author
Article
  • 23 Downloads

For a mathematical model that incorporates internal-diffusion kinetics and sorbent swelling, we consider the inverse problem of determining the sorption isotherm and the porosity coefficient from two output dynamic curves. A gradient-type iterative method utilizing the conjugate problem technique is proposed and results of numerical experiments are reported. The results are used to investigate the features of the proposed method.

Keywords

inverse problems numerical methods mathematical models of sorption 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. V. Venetsianov and R. N. Rubinshtein, The Dynamics of Sorption from Liquid Media [in Russia], Nauka, Moscow (1983).Google Scholar
  2. 2.
    V. I. Gorshkov, M. S. Safonov, and N. M. Voskresenskii, Ion Exchange in Counter-Current Columns [in Russian], Nauka, Moscow (1981).Google Scholar
  3. 3.
    P. P. Zolotarev, “Problems of sorption dynamics and chromatography in stationary layers,” ZhFKh, 59, No. 6, 1342–1351 (1985).Google Scholar
  4. 4.
    V. A. Ivanov, N. P. Nikolaev, and V. I. Gorshkov, “A method for the determination of dynamic parameters in counter-current ionexchange columns,” Teoret. Osnovy Khim. Tekhnol., 26, No. 1, 43–49 (1992).Google Scholar
  5. 5.
    S. R. Tuikina, “Solving some inverse problems of sorption dynamics by gradient methods,” Vestnik MGU. Ser. 15: Vychil. Matem. Kibern., No. 4, 33–39 (1990).Google Scholar
  6. 6.
    S. R. Tuikina and S. I. Solov’eva, “Inverse problems for a mathematical model of redox sorption,” Comput. Math. Model., 18, No. 1, 10–18 (2007).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    S. R. Tuikina and S. I. Solov’eva, “Mathematical modeling numerical determination of coefficients in some mathematical models of nonisothermal sorption dynamics,” Comput. Math. Model., 21, No. 2, 117–126 (2010).CrossRefzbMATHGoogle Scholar
  8. 8.
    A. M. Denisov, “Unique solvability of some inverse problems for nonlinear sorption-dynamics models,” in: Conditionally Well-Posed Problems of Mathematical Physics and Analysis [in Russian], Nauka, Novosibirsk (1993), pp. 73–84.Google Scholar
  9. 9.
    A. M. Denisov, “Unique determination of the nonlinear coefficient in a system of partial differential equations in the small and in the large,” Dokl. RAN, 338, No. 4, 444–447 (1994).Google Scholar
  10. 10.
    A. M. Denisov and V. A. Leshchenko, “Uniqueness theorems for problems of determining the coefficients in nonlinear systems of equations of sorption dynamics,” J. Inv. Ill-Posed Problems, 2, No. 1, 15–32 (1994).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    S. R. Tuikina, “Determining the sorption coefficient from the solution of the inverse problem,” Mat. Modelirovanie, 9, No. 8, 95–104 (1997).MathSciNetGoogle Scholar
  12. 12.
    S. R. Tuikina, “Numerical determination of two sorbent characteristics from dynamic observations,” Comput. Math. Model., 29, No. 3, 299–306 (2018).MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    S. R. Tuikina, “Inverse problems for a mathematical model of ion exchange in a compressible ion exchanger,” Comput. Math. Model., 13, No. 2, 159–168 (2002).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    S. R. Tuikina and S. I. Solov’eva, “Numerical determination of two characteristics of a compressible ion exchanger,” Comput. Math. Model., 15, No. 2, 137–149 (2004).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia

Personalised recommendations