SEPARATIONS Scale-up of the Solid-Liquid Extraction Using Characteristic Function Technique E. Simeonov,* I. Seikova, I. Pentchev, and A. Mintchev Department of Chemical Engineering, University of Chemical Technology and Metallurgy, 8, St. Kliment Ohridski Boulevard, Sofia, 1756 Bulgaria A scale-up methodology based on the characteristic function approximation for the mass-transfer rate is proposed that provides a reliable and inexpensive method for designing and controlling an extraction apparatus. The characteristic function is derived in terms of the usual kinetic and equilibrium parameters. An analytical expression for the overall resistance to mass transfer is also obtained, providing a linearly variable mass-transfer resistance during the extraction. Experimental data for the kinetics of extraction in a laboratory-scale batch extractor from four solid-liquid systems are presented and discussed in relation to the theory. The calculation procedure is applied to estimate the extraction times in a continuous-action apparatus corresponding to an assigned extraction yield. The calculation results are also supported by experiments in a pilot screw extractor. Introduction Leaching of useful compounds from vegetable materi- als is a complex diffusion-dominated process, whose characteristics give rise to a number of difficulties, methodological as well as mathematical. Usually two approaches have been used for the design and control of extraction plants. The classical modeling approach requires the simultaneous solution of the coupled dif- ferential mass balances in the column for the solid and liquid phase.s 1 A number of analytical and numerical solutions have been developed that involve specific assumptions as a function of the system being investigated. In the usual case, to describe the solute flux inside a single particle, the pore diffusion model 2-4 or its approximation by linear driving force models 5-7 has been adopted. Such equilibrium models 8-11 assume that a local equilibrium is established at the interface with the solid phase and incorporate the internal resistance through a solid- phase mass-transfer coefficient. A large number of adjustable parameters in the numerical solutions, in- corporating both equilibrium and kinetic effects, as well as a lack of accurate data for a complex vegetable structure in most cases limit the applicability of the classical modeling for process design purposes. Another approach is based on the analysis of reliable experimental data for system behavior from an existing plant and then proceeds to the scale-up of the designed apparatus under comparable conditions. Such an ap- proach is represented by the characteristic function technique. 12,13 This technique has been evaluated on the basis of the experimental data for the kinetics of the process (which are usually obtained in a periodically stirred vessel), which contains implicit factors that influence the rate of the process. The primary objective of the present study is to improve the predictive capabilities of the characteristic function and to provide an extension of the extraction rate at different process scales. In addition, guidelines are presented on how such functions can be used for sizing and controlling the extraction apparatus, par- ticularly when the type of extracted material is being changed. The application of the method is illustrated by experiments for different extraction systems of practical interest, performed in a closed-batch ap- paratus, i.e., for systems in a continuous-action screw extractor. Experimental Section Extraction Kinetics under Periodic Conditions in a Stirred Vessel. Four extraction systems were investigated to demonstrate the applicability of the design methodology under a wide range of experimental conditions: In system I. (Geranium macrorhizum L.- water), tannins were extracted as a valuable solute. The tannin concentration was measured by the modified Loewental method 14 by titration with KMnO 4 in the presence of indigo carmine and sulfonic acid. In system II (Amorpha fruticosa L.-petroleum ether), where the solid phase contains isoflavanoids, the liquid-phase concentration was determined by weighing (precision ) 10 -3 g) the extracts after the solvent had been evaporated in a drying unit at T ) 50 °C. In system III ( Silibum marianum L.-methanol), the silimarin (car- sil) concentration in the liquid phase was measured spectrophotometrically. Finally, in system IV (Lavan- dula vera L.-petroleum ether), lavender flowers were extracted with previously distilled water vapor. The analyses of the contents of the extracted substances in * To whom correspondence should be addressed. Tel.: +3592 626405. E-mail:evgeni@uctm.edu. 4903 Ind. Eng. Chem. Res. 2004, 43, 4903-4907 10.1021/ie030650m CCC: $27.50 © 2004 American Chemical Society Published on Web 06/30/2004