Optimized calculation of adsorption process through the nozzle adsorber by the cell model method
Abstract
This paper considers the main theoretical calculations of adsorption kinetics, time of the flow in the nozzle adsorber, time of protective action of the adsorbent layer, average speed of adsorption process and the differential equation of the adsorption process according to initial and boundary conditions. Graphically, C-curve has been obtained, which is presented in dimensionless coordinates and demonstrates a mathematical model of adsorption process. The optimal number of cells is calculated by comparing the experimentally obtained response curve with the curves calculated according to the equation of the cell model at different values. In addition, the amount of heat according to the Langmuir's law for adsorption on activated carbon and the dependence of the amount of heat adsorbed on temperature using the Truton's equation have been determined. A mathematical model of the adsorption process, which has been studied using the cell model method and software, is presented. Using the MathCAD application package and the Langmuir's equation, this model has been solved by comparing the required number of cells n, which is defined as its main parameter. Based on the experimental curve, an assumption is made about the possible form of the cell model of adsorption process and mathematical processing of this curve is performed. The obtained values of model parameters have been calculated, the experimental data have been normalized by the trapezoidal method and the model has been tested for adequacy. The process of exchange of ions with the same charge, which takes place between the adsorbent and the adsorbate in exactly equivalent proportions in order to soften the water intended for the production of soft and alcoholic beverages, wine materials, is studied, as the taste of these products improves with the reduction of magnesium, copper and iron ions. Problems of mathematical modeling of adsorption processes in inhomogeneous media and methods of constructing mathematical problems of such models require further study and have the prospect of further research
Keywords
adsorption; mathematical model; thermal processes; cell model; trapezoid method; MathCAD
References
[1] T. G. Myersa, and M. G. Hennessy, "Mathematical modelling of carbon capture in a packed column by adsorption", Applied Energy, vol. 278, Nov. 15, 2020. doi: 10.1016/j.apenergy.2020.115565.
[2] E. Igberase, and P. O. Osifo, "Mathematical modelling and simulation of packed bed column for the efficient adsorption of Cu (II) ions using modified bio-polymeric material", Journal of Environmental Chemical Engineering, no. 7 (3), 2019.
[3] Amirhossein Ghorbani1, Ramin Karimzadeh, and Masoud Mofarahi, "Mathematical modeling of fixed bed adsorption: breakthrough curve", Department of chemical engineering, Tarbiat Modares University, Tehran, Iran, 2018. doi: 10.22059/JCHPE.2018.255078.1226.
[4] M. Askari, and H. Adibi, "Numerical solution of advection-diffusion equation using meshless method of lines", Iranian Journal of Science and Technology, Transactions A: Science, vol. 41, no. 2, pp. 457-464, 2017.
[5] M. P. Lenyuk, "Mathematical modeling of adsorption mass transfer with spectral parameter for inhomogeneous n-interface cylindrical bounded microporous media with a cavity", Visnyk Ternopilskoho derzhavnoho tekhnichnoho universytetu, vol. 9, no. 4, pp. 147-148, 2014 [in Ukrainian].
[6] M. R. Petryk, "Mathematical modeling of nonlinear dynamic problems of adsorption and diffusion for a fixed layer of adsorbent", Integral transformations and their application to boundary value problems: coll. of sci. papers, iss. 5, pp. 201-215. Kyiv: In-t matematyky NANU, 2000 [in Ukrainian].
[7] I. A. Burtnaya, and D. V. Litvinenko, "Mathematical model of the pervaporation process for binary mixtures", Vostochno-Evropeyskiy zhurnal peredovykh tekhnologiy, vol. 2, no. 4 (50), pp. 8-11, 2011. [Online]. Available: http://journals.uran.ua/eejet/article/view/1766 /1662 [in Russian].
[8] I. V. Sergienko, V. V. Skopetsky, and V. S. Deineka, Mathematical modeling and study of processes in inhomogeneous media. Кyiv, Ukraine: Naukova dumka, 2001 [in Russian]..
[9] P. N’Gokoli-Kekele, M. A. Spiringuel-Huet, and J. Fraissard, "An analitical study of molecular transport in zeolite bed", Adsorption (Kluwer), no. 8, p. 35-44, 2002.
[10] V. V. Kuzmin et al., Mathematical modeling of technological processes of assembly and mechanical processing of mechanical engineering products: textbook for universities. Moscow, Russia: Vysshaya shkola, 2008 [in Russian].
[11] B. Ya. Sovetov, and S. A. Yakovlev, Modeling of systems: textbook for universities, 3rd ed., revised and suppl. Moscow, Russia: Vysshaya shkola, 2001 [in Russian].
[12] A. N. Ostrikov et al., Processes and devices of food production, book 1. St. Petersburg, Russia: Giord, 2007 [in Russian].
[13] A. M. Poperechny, O. I. Cherevko, V. B. Garkusha, and N.V. Kirpychenko, Processes and apparatus of food production: textbook, A. M. Poperechny, Ed. Кyiv, Ukraine: Tsentr uchbovoi literatury, 2007 [in Ukrainian].
[14] V. P. Dyakonov et al., New information technologies: textbook, V. P. Dyakonov, Ed. Moscow, Russia: SOLON-Press, 2005 [in Russian].
[15] V. G. Dulov, and V. A. Tsibarov, Mathematical modeling in modern natural science: textbook, V. G. Dulov, Ed. St. Petersburg, Russia: Izd-vo St. Petersb. un-ta, 2001 [in Russian].