Approximate solutions have been obtained for the equations of nonstationary mass transfer in packed-column apparatuses, and a method has been proposed to calculate them under the conditions of laminar motion of a liquid phase and displacement of a gas. On the basis of the nonstationary-mass-transfer equations, a problem of control of packed-column apparatuses has been solved. The solutions of the equations have been obtained in the form of an expansion of functions in a trigonometric series; formulas to determine the values of terms in the series have been presented. Initial conditions for the equations of nonstationary mass transfer are equations of a stationary process. Exact and approximate solutions for the stationary-mass-transfer equations have been obtained based on which an algorithm has been proposed for designing packed-column apparatuses. A calculation of the process of absorption of an acetone vapor from air by water has been carried out. Plots of the control and of the concentration change in controlling and with different perturbations have been presented.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. M. Olevskii, Film Heat- and Mass-Transfer Equipment [in Russian], Khimiya, Moscow (1988).
M. I. Farakhov, A. G. Laptev, and M. M. Basharov, Modernizing mass-exchange apparatuses by new packings in chemical engineering, Teor. Osn. Khim. Tekhnol., 49, No. 3, 247–252 (2015).
A. M. Kagan, L. A. Yudina, and A. S. Pushnov, Active surface of elements of irregular heat- and mass-transfer packings, Teor. Osn. Khim. Tekhnol., 46, No. 2, 199–206 (2012).
L. S. Gordeev, A. I. Kozlov, M. B. Glebov, and N. V. Khitrov, Investigation of the use of high-porosity cellular materials in packed rectification columns, Teor. Osn. Khim. Tekhnol., 43, No. 5, 567–574 (2009).
S. V. Alekseenko, D. M. Markovich, A. R. Evseev, A. V. Bobylev, B. V. Tarasov, and V. M. Karsten, Experimental investigation of the distribution of a liquid in a column with structural packings, Teor. Osn. Khim. Tekhnol., 41, No. 4, 442–448 (2007).
A. G. Kasatkin, Basic Processes and Apparatuses of Chemical Technology [in Russian], Khimiya, Moscow (1973).
V. M. Ramm, Absorption of Gases [in Russian], Khimiya, Moscow (1976).
V. I. Elizarov, R. R. Shavaleev, E. S. Titova, and A. R. Safarov, Mathematical model of mass transfer in packed columns, Vestn. Kazansk. Tekhnol. Univ., 18, No. 22, 134–136 (2015).
R. R. Shavaleev, V. V. Elizarov, and V. D. Elizarov, Mathematical modeling of stationary mass transfer in packed-column apparatuses, Vestn. Kazansk. Tekhnol. Univ., 20, No. 5, 109–113 (2017).
B. V. Devyatov, N. D. Demidenko, and V. A. Okhorzin, The Dynamics of Distributed Processes in Technological Apparatuses, Distributed Monitoring, and Control [in Russian], Krasnoyarskoe Knizhnoe Izd., Krasnoyarsk (1976).
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1972).
A. A. Samarskii and E. S. Nikolaev, Methods for Solving Grid Equations [in Russian], Nauka, Moscow (1978).
V. V. Kafarov, Principles of Mass Transfer [in Russian], Vysshaya Shkola, Moscow (1972).
K. F. Pavlov, P. G. Romankov, and A. A. Noskov, Examples and Problems on the Course of Processes and Apparatuses of Chemical Technology: A Manual for Graduate Students [in Russian], Khimiya, Leningrad (1987).
S. G. D′yakonov, V. I. Elizarov, and A. G. Laptev, Theoretical Foundations and Modeling of the Processes of Separation of Substances [in Russian], Izd. Kazansk. Univ., Kazan (1993).
S. G. D′yakonov, V. V. Elizarov, and V. I. Elizarov, Theoretical Foundations of Designing Chemical-Technology Apparatuses on the Basis of Conjugate Physical and Mathematical Modeling [in Russian], KGTU, Kazan (2009).
L. D. Pevzner, The Theory of Control Systems [in Russian], Lan’, St. Petersburg (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 92, No. 4, pp. 906–916, July–August, 2019.
Rights and permissions
About this article
Cite this article
Elizarov, D.V., Shavaleev, R.R. & Elizarov, V.V. Nonstationary Mass Transfer and Controlling the Process During the Laminar Motion of a Liquid in Packed-Column Apparatuses. J Eng Phys Thermophy 92, 877–888 (2019). https://doi.org/10.1007/s10891-019-01999-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10891-019-01999-3