ISSN 0040-5795, Theoretical Foundations of Chemical Engineering, 2009, Vol. 43, No. 3, pp. 260–267. © Pleiades Publishing, Ltd., 2009. Original Russian Text © L.D. Asnin, K.Kachmarski, A.A. Fedorov, Yu.S. Chekryshkin, 2009, published in Teoreticheskie Osnovy Khimicheskoi Tekhnologii, 2009, Vol. 43, No. 3, pp. 276–283. 260 INTRODUCTION In recent decades, a considerable increase in interest of industrial adsorption technologies has been observed. The range of their use varies from the purifi- cation of industrial gases from undesirable impurities to the separation of gas mixtures with production of commercial large-tonnage products [1–3]. A modern approach to the design of adsorbers and the determina- tion of optimum technological conditions of their oper- ation assumes the capability of calculating the distribu- tion of the concentration of an adsorbate along the bed of an adsorbent at any time point for any experimental conditions. In research and engineering practice, there is frequently the inverse problem: determination of mass transfer coefficients from output curves of the adsorbate [2, 3]. Solving these problems is associated with the application of models of various complexities depending on the set objective and computational capa- bilities [3, 4]. The most general model should include all factors that affect mass transfer. In isothermal col- umn dynamics, four groups of factors associated with axial dispersion, external mass transfer, mass transfer inside adsorbent grains, and the kinetics of adsorp- tion/desorption are generally distinguished. Their con- sistent and strict account for single-component adsorp- tion leads to a set of two material balance equations (for the adsorbate in the mobile phase and inside the grain of the adsorbent) and two rate equations describing the kinetics of mass transfer from the flow into the pores of the adsorbent and the kinetics of adsorption–desorption on the walls of pores [5]. The use of the general model is associated with a number of difficulties of a compu- tational character [2, 6] and a need to know a large number of characteristics of the system, which are not always easy to determine experimentally or to calculate theoretically [7]. Therefore, various simplified models are more often used in practice. In chromatography, the mixed-diffusion model proposed by Morbidelli et al. [6, 8] enjoys widespread use. In this model, the internal structure of the grain of an adsorbent is neglected, using the concentrations of a substance in the gas and solid phases and , respectively, that are averaged over the volume of the grain. The balance equations in the mobile and solid phases are written as (1) (2) where the effective mass transfer coefficient is calcu- lated using the rule of the additivity of external- and internal-diffusion resistances 1/k eff = 1/k ext + 1/k int (k ext C p q ε e ∂ C ∂ t ------ u ∂ C ∂ x ------ + = ε e D ax ∂ 2 C ∂ x 2 -------- 1 ε e – ( ) k eff a V C C p – ( ) , – ε p ∂C p ∂ t --------- 1 ε p – ( ) ∂ q ∂ t ----- + k eff a V C C p – ( ) , = Description of the Dynamics of Vapor Adsorption in a Fixed Bed of an Adsorbent Using Various Approximations of the Mixed-Diffusion Model L. D. Asnin a , K. Kachmarski b , A. A. Fedorov a , and Yu. S. Chekryshkin a a Institute of Technical Chemistry, Ural Branch of the Russian Academy of Sciences, ul. Lenina 13, Perm, 614000 Russia b Zheshuv University of Technology, Zheshuv, Poland e-mail: asninld@mail.ru Received March 24, 2008 Abstract—The use of the mixed-diffusion model for calculating the dynamics of adsorption of the vapors of volatile organic compounds in a fixed bed of a porous adsorbent is considered. The V 2 O 5 /Al 2 O 3 system is used as an example. It is shown that a simplified version of the mixed-diffusion model in which the influence of axial dispersion is neglected and the establishment of equilibrium on the external boundary of a grain is assumed gives distorted knowledge of the real dynamics of the process. The complete mixed-diffusion model adequately reflects the influence of the contributions of axial dispersion and external and internal mass transfer in the smearing of the sorption front, but diversions from the assumptions of the model that manifest themselves in the concentration dependence of an apparent internal-diffusion coefficient are also observed in this case. The considerable advantage of the model is that using a single-fitting parameter allows experimental data to be approximated with a satisfactory accuracy. DOI: 10.1134/S004057950903004X