For a mathematical model with internal-diffusion kinetics and an oxidation-reduction reaction, we consider two inverse problems of determining the sorption isotherm or the redox reaction rate constant from the output dynamic curve. A numerical method for the solution of these inverse problems is proposed, computational results are reported, and its potential is investigated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. V. Venetsianov and R. N. Rubinshtein, Dynamics of Sorption from Liquids [in Russian], Nauka, Moscow (1983).
V. I. Gorshkov, M. S. Safonov, and N. M. Voskresenskii, Ion Exchange in Counter-Current Columns [in Russian], Nauka, Moscow (1981).
T. A. Kravchenko and N. I. Nikovalev, Kinetics and Dynamics of Processes in Redoxites [in Russian], Khimiya, Moscow (1982).
V. V. Kafarov, Cybernetic Methods in Chemistry and Chemical Engineering [in Russian], Khimiya, Moscow (1976).
E. N. Korzhov, Mathematical Modeling of Redox-Sorption Processes [in Russian], Izd. Dom VGU, Voronezh (2016).
A. M. Denisov, “Uniqueness of solution of some inverse problems for nonlinear models of sorption dynamics,” in: Conditionally Well-Posed Problems of Mathematical Physics and Analysis [in Russian], Nauka, Novosibirsk (1992), pp. 73–84.
A. M. Denisov, “Uniqueness of determination of a nonlinear coefficient in a system of partial differential equations in the small and in the large,” Dokl RAN, 388, No. 4, 444–447 (1994).
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).
A. M. Denisov and A. Lorenzi, “Recovering an unknown coefficient in an absorption model with diffusion,” J. Inverse and Ill-Posed Problems,15, No. 6, 599–610 (2007).
S. R. Tuikina, “Inverse problems for a mathematical model of redox sorption,” Computational Mathematics and Modeling, 18, No. 1, 10–18 (2007).
V. A. Ivanov, N. P. Nikolaev, and V. I. Gorshkov, “A method for the determination of the dynamic parameters of counter-current ion-exchange columns,” Teoret. Osnovy Khim. Tekhnol.,26, No. 1, 43–49 (1992).
S. R. Tuikina, “Inverse problems for a mathematical model of ion exchange in a compressible ion exchanger column,” Computational Mathematics and Modeling, 13, No. 2, 159–168 (2002).
S. R. Tuikina and S. I. Solov’eva, “Numerical determination of two characteristics of a compressible ion exchanger,” Computational Mathematics and Modeling, 15, No. 2, 138–149 (2004).
S. R. Tuikina and S. I. Solov’eva, “Numerical determination of coefficients in some mathematical models of nonisothermal sorption dynamics,” Computational Mathematics and Modeling, 21, No. 2, 117–126 (2010).
S. R. Tuikina, “Numerical determination of two sorbent characteristics from dynamic observations,” Computational Mathematics and Modeling, 29, No. 3, 299–306 (2018).
S. R. Tuikina, “A numerical method for determining two sorbent characteristics in case of decreasing porosity,” Computational Mathematics and Modeling, 30, No. 2, 155–163 (2019).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Matematika i Informatika, No. 62, 2019, pp. 95–102.
Rights and permissions
About this article
Cite this article
Tuikina, S.R. A Numerical Method for the Solution of Two Inverse Problems in the Mathematical Model of Redox Sorption. Comput Math Model 31, 96–103 (2020). https://doi.org/10.1007/s10598-020-09478-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10598-020-09478-8