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Process Engineering and Chemical Plant Design 2011 Process Engineering and Chemical Plant Design 2011 Editors: Günter Wozny and Łukasz Hady Universitätsverlag der TU Berlin Berlin 2011 Editors: Günter Wozny and Łukasz Hady Fachgebiet Dynamik und Betrieb Technischer Anlagen Technische Universität Berlin Sekretariat KWT 9 Straße des 17. Juni 135 D-10623 Berlin http://www.dbta.tu-berlin.de Umschlaggestaltung: Łukasz Hady Umschlagfoto: Gasbehandlungsanlage zur Kokerei- gasentschwefelung, Uhde GmbH ISBN 978-3-7983-2361-2 (Druckausgabe) ISBN 978-3-7983-2362-9 (Online-Version) Berlin 2011 * Gedruckt auf säurefreiem alterungsbeständigem Papier Druck/ Printing: Endformat, Ges. für gute Druckerzeugnisse mbH Köpenicker Str. 187-188, 10997 Berlin Vertrieb/ Publisher: Universitätsverlag der TU Berlin Universitätsbibliothek Fasanenstr. 88 (im VOLKSWAGEN-Haus) D-10623 Berlin Tel.: (030)314-76131; Fax.: (030)314-76133 E-Mail: [email protected] http://www.univerlag.tu-berlin.de 18th International Conference Process Engineering and Chemical Plant Design Günter Wozny and Łukasz Hady, Editors Copyright © 2011, Berlin Institute of Technology. All rights reserved. P R E A M B L E The 18th International conference in “Process Engineering and Chemical Plant Design” is taking place in Berlin from september 19th to september 23rd 2011. We are pleased with the successful collaboration which is the result of a meanwhile 30 years continual international cooperation between the Cracow University of Technology and the Berlin Institute of Technology. This relationship has also been intensified by student exchange programs and international transfer of knowledge between the participating universities during the last years. This book contains the abstracts of all contributions and lectures which are presented by the miscellaneous participants within the scope of the conference. Different topics are addressed, concerning industrial problems as well as forward-looking questions and fundamental investigation of special phenomena for the chemical and the power generation industry. Thereby special attention is paid to fundamental research of complex correlations, modelling and simulation, process control and operation, sustainable and efficient energy generation as well as troubleshooting and problems within the operation and control of chemical processes. We want to appreciate all participants individually, especially our partners from Cracow University of Technology and also from the Warsaw and the West Pomeranian University of Technology. Special thanks go to the office for foreign relations (ABZ) and the DAAD for their financial support. All contributions have been peer-reviewed. Therefore we also want to thank the reviewers for their work. The authors are responsible for the contents of their articles. 18th International Conference Process Engineering and Chemical Plant Design Günter Wozny and Łukasz Hady, Editors Copyright © 2011, Berlin Institute of Technology. All rights reserved. BARBARA TAL-FIGIEL* SOLID-LIQUID EXTRACTION FROM PLANTS WITH A BIDISPERSE POROUS STRUCTURE – EXPERIMENTAL KINETICS AND MODELLING Abstract This paper deals with the mathematical model of extraction from a capillary porous particle with bidisperse structure. Capillary porous particles with bidisperse structure, possessing capillaries of two, strongly different sizes, occur frequently in nature and technology. Neglecting the polydispersity of capillary sizes in capillary porous particles makes the obtained results less accurate and prevents elucidation of some physical mechanisms of substance transfer inside the particles. The bidisperse model of a capillary porous particle is analytically the simplest variant of the polydisperse model, which makes it possible to reveal fundamental aspects of mass transfer in real polydisperse particles. The mathematical planar model of extraction process from the particle can be described by the following set of equations: the diffusion equation for the porous body and the convective diffusion equation for the transport channel, with initial and boundary conditions for these equations, and the velocity profile in the transport channel. To solve the set of equations the grid and finite element methods were used. A numerical analysis of the model demonstrates that, for liquid extraction of a desired substance from the particle, there exists an optimum range of oscillation frequencies of the liquid in large pores. Results of numerical simulations are presented together with the criterial equation for calculating the effective diffusion coefficient, obtained in the course of processing these results. The experiments consisted of different types of liquid-solid extraction of active ingredients from plants. Keywords: solid-liquid extraction, bidisperse porous model. *Institute of Chemical and Process Engineering, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland. Solid-liquid extraction from plants with a bidisperse porous structure 3 1. Introduction Mathematical models of extraction processes, that are different from conventional diffusion models [1-4], were proposed recently. The reason for this is the need to make the description of the process more realistic, in particular, to improve the way in which the structure of a porous solid, from which the target component has to be extracted, is taken into account. New models take into consideration the bidispersed structure of a porous material and the presence of convective motion in large pores [5-9]. Convective mass transfer is taken into account within the diffusion models both by introducing coefficients of effective diffusion and by directly introducing the convective term [5,6]. The model is proposed for the process of extraction from a semi-infinite solid containing two types of pores: large pores that extend to the surface and small pores that are connected to large pores. Effective transport coefficients in two types of pores are assumed to be different. Theoretical results are compared with experimental data related to the kinetics of the extraction of the target components from plant materials obtained in apparatuses with an intensive hydrodynamic mode (mixing, ultrasounds). In this model, it is shown that the mass flux at the boundary of a semi-infinite solid with the branched system of pores at each time point t>0 is greater than that for a system, in which there are no branches from the main channel. The processing of experimental data on the kinetics of the extraction of active substances from plants has shown that the process is equally well described by both the model of extraction from a porous solid with semi-infinite transport pores and the model of extraction from a solid with the pores of a finite length. The problem of studying the regularities of solvent extraction from porous media is a matter of concern, because this process is widely used in the industry, especially in the extraction of medicinal components from plants. The pore space in actual media can have a very complicated structure (fig.1). There are pores with variable diameter, branched pores, isolated cavities, and the like. Therefore, the behavior of the diffusion process in such media can be much different from that in a single pore. Fig. 1. Structure of plant material Conventional methods for extracting active substances from plants are, as a rule, ineffective, since they do not ensure a sufficient degree of depletion of plants and are characterized by a long duration and nonproductive expenditures of input energy. At the same time, a constant increase in the volumes of production dictates a necessity for 4 B. Tal-Figiel development of new intensive extraction methods and apparatuses for their implementation. 2. Mass transfer model The model of solid-liquid extraction [5], depicted on fig.2, was used. A solution of the desired component from the porous body, is largely transported through small capillaries which branch off in large pores, either dead-end or through. It is assumed, that there is no liquid motion in the capillaries and active substance is transported there by molecular diffusion. However external-pressure pulses of some amplitude can induce liquid oscillations in large pores because of compression of the gas contained in capillaries [9]. Figure 2. Planar model of a particle with bidisperse structure; 1) porous block, 2) transport channel Thus, large pores can be regarded as transport channels where active substance is transferred by convection. Compared to molecular diffusion, convection can ensure a rate of solute extraction from particle, that is many times higher. Assuming, that the diffusion coefficient DM is independent of the active substance concentration, this process can be described by the following set of equations: diffusion equation for the porous body: ∂∂CC2 11=−D , (1) ∂τ M ∂y2 where: C1 is the active substance concentration in the porous block, 2 -1 DM – molecular diffusion coefficient [m s ], τ – time [s], and the convective diffusion equation for the transport channel 22 ∂∂CC22⎛⎞ ∂∂ CC 22 +=−+uDM ⎜⎟22, (2) ∂∂τ xxy⎝⎠ ∂∂ where: C2 – the active substance concentration in the transport channel, u – the longitudal (along the x-axis) fluid velocity. The initial and boundary conditions for these equations are the following: Cx,y,110212()τ ==0C,0xL,hyhh; ≤≤ <≤+ (3) Solid-liquid extraction from plants with a bidisperse porous structure 5 Cx,y,2202()τ ==0 C ,0 ≤≤ x L,0 <≤ y h ; (4) Cx,yh,2212()==τ Cx,yh,( =τ); (5) qx,yh,1222( ==τ) qx,yh,( =τ); (6) Cx0,y,22()====τ CxL,y,( τ) C, 202 0 << y h; (7) qx,yh112(
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