J. of Supercritical Fluids 54 (2010) 178–189 Contents lists available at ScienceDirect The Journal of Supercritical Fluids journal homepage: www.elsevier.com/locate/supflu Analysis of the kinetics of regeneration of bidispersed activated granular carbon, by supercritical carbon dioxide B. Bensebia a,b , A. Dahmani a , O. Bensebia a , D. Barth c,∗ a Laboratoire de Thermodynamique et de Modélisation Moléculaire, Faculté de Chimie, Université des Sciences et de la Technologie Houari Boumediene, BP 32, El Alia, Alger 16111, Algeria b Département de Génie des Procédés, Université Hassiba Ben Bouali de Chlef, BP 151, 02000-Chlef, Algeria c Laboratoire des Sciences du Génie Chimique, Nancy-Université, CNRS, 1 rue Grandville, BP 20451, F 54001-Nancy, France article info Article history: Received 21 October 2009 Received in revised form 15 April 2010 Accepted 17 April 2010 Keywords: Supercritical desorption Bidisperse solids Macropore diffusion Micropore diffusion abstract A desorption of m-xylene by supercritical CO 2 under different temperatures (40, 50 and 60 ◦ C) and pres- sures (80, 100 and 128 bar) has been modelled using the analytical solution expressing the desorption yield for bidisperse granular activated carbon. This solution is in the form of an infinite double series. The coefficients of which were calculated by solving the transcendental equation using the method of Newton–Raphson. Solutions of first and second order of this equation determine the coefficients of the analytical solution. The results of this modelling, including macropore and micropore diffusion, show very good concordancy between experimental and simulated data for all operating conditions, which confirms the appropriateness of this model for this type of adsorbent considered. Only the equilibrium adsorption constant “K C ” was used as adjustable parameter. The values of K C varied between 13.32 and 121.33 and the maximum average deviation between estimated and fitted values not exceeding 6.54%. On the other hand, it has been particularly highlighted for the experimental conditions studied, that the contribution of resistance due to external transfer and axial dispersion were negligible and that the resis- tance due to macropore diffusion was consistent and it was possible to reduce the time of desorption by reducing the size of the grain. © 2010 Published by Elsevier B.V. 1. Introduction Many potential applications have been proposed which involve desorption of solutes from solid using SCF solvents: these include activated carbon regeneration [1–7] using SC-CO 2 . To design large scale supercritical desorption process is necessary to understand in which way dynamic desorption is influenced by process vari- ables as mass transfer effects, equilibrium considerations but also the texture of the solid. The models developed [8–16] are gen- erally based on the differential mass balance equations for the different phases and different assumptions about the resistance to mass transfer and solute–solid, solute–solvent interactions. The common assumption in the above-cited models is the monodis- perse pore structure within the adsorbent particle. It has been demonstrated [17,18] that erroneous diffusivities may result if dif- fusion data in a bidisperse grain are analyzed as a monodisperse porous material. Then, to interpret accurately the transport phe- nomena in adsorbent with broad pore size distribution (such as ∗ Corresponding author. Tel.: +33 3 83 17 50 27; fax: +33 3 83 32 29 75. E-mail addresses: danielle.barth@ensic.nancy.fr, Danielle.Barth@eeigm.inpl-nancy.fr (D. Barth). activated carbon) the real porous structure must be taken into account [19]. It is generally accepted that microporous adsorbents, such as activated carbon, are bidisperse [20] and have both micropores as well as macropores. The description of transport processes in such bidisperse solids is difficult due to the complex and largely unknown nature of the pore network, and a variety of structural idealization have been proposed based on which approximate methods for diffusion and adsorption have been developed. The simplest and most popular of these idealizations considers the solid particle as comprising an aggregate of microporous spherical microparticles, with the inter-microparticles macropores provid- ing the channels for intragranular transport. The pore size of the micropores is of the order of molecular dimension, and there- fore, molecules of solute inside the micropore never escape the attraction potential of the pore walls. This means that molecules in the free form do not exist and only adsorbed molecules exist in the micropore. During the desorption process, these adsor- bate molecules diffuse (in the adsorbed state) under a gradient of concentration to reach the mouths of micropores where des- orption equilibrium with the fluid in the macropores takes place. These large macropores basically act as passage way for desorbed molecules to diffuse from the interior of the grain (macropores) to 0896-8446/$ – see front matter © 2010 Published by Elsevier B.V. doi:10.1016/j.supflu.2010.04.005