Supplementary Material Available. The Appendix will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (105 X 148 mm, 24X reduction, negatives) containing ail of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. C. 20036. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche, referring to code number PROC-74-124.
Literature Cited Bourne, D
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nag el,^., Thielen, B., Chem. lng. Tech., 44,416 (1972). Stichlmair,J., Thesis, TU Munich, 1971. Stichlmair,J., Mersmann, A , , Chem. lng. Tech., 4 3 , 2 2 (1971).
u. v., Thesis,ETH, Z u r i c h , '972.
Received for reuiew May 9, 1973 Accepted October 15, 1973
Mathematical Model of the Aluminum Oxide Rotary Kiln
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Andrzej Manitius, Ewa Kurcyusz, and Wieslaw Kawecki Institute of Automatics, Polytechnical School of Warsaw, 00-665 Warsaw, Poland
A steady-state model of the rotary kiln used for calcination of basic ammonium aluminum sulfate in production of aluminum oxide is described. Carrying away of solid particles by gas stream and chokes in the inner kiln wall are specific features of the kiln considered. The model consists of a set of ordinary differential equations describing reaction kinetics and mass and heat balances, a set of algebraic equations for space-depending parameters, and a set of two-point boundary conditions. An algorithm for a numerical solution of the model equations with two point boundary conditions is described along with a method for computation of the kiln with and without chokes. Computational results for the kiln with and without chokes are presented. and a comparison of computed and experimental data for a kiln with chokes is given.
1. Introduction
This paper describes a mathematical model of a rotary kiln which is used for calcination of basic ammonium aluminum sulfate in production of aluminum oxide. The model is designed for simulation of steady state of the kiln and for design purposes. It has been derived from mass and heat balance considerations and represents a rather large set of ordinary differential equations and algebraic formulas. Rotary kilns are often used in the chemical industry; however, the mathematical modeling of such plants still represents a difficult and incompletely solved problem. In addition, measurements of internal parameters of the kilns are very difficult to perform. In recent years some papers on the mathematical models of the rotary kilns appeared. Sass (1967) described a simulation of the heat transfer phenomena in a cement kiln. He has computed several temperature profiles which were close to gas temperatures measured at some points. Some discussion on his results also has been reported (Kaiser and Lane, 1968; Cribb and Langley, 1969). Sass's work did not contain a modeling of chemical reactions and mass transfer phenomena. Riffaud, e t al. (1970), described some interesting results of a hybrid simulation of both steady state and dynamic conditions of an aluminum oxide kiln; their discussion of model development is very concise, however, with few details. Spang (1972) described a simulation of both steady-state and dynamic responses of a cement kiln, but had no experimental data available to evaluate the quantitative aspects of the model accuracy. The present work differs from previous ones by several factors. In the kiln considered there are two phenomena which complicate significantly the mathematical model;
' Present address, Centre de recherches mathematiques, Universite de Montreal, Montreal 101, Canada
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Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 2, 1974
these are the carrying away of powder-like material by a hot gas stream, and the chokes in the inner wall. There is no burning zone in the kiln. The number of simplifying assumptions is relatively small compared to some of the other papers. In consequence equations are more complicated but all important coefficients are computed at each point of the kiln rather than assumed constant. Only steady-state conditions are simulated. Several measurements of the kiln parameters were performed thus enabling the authors to'evaluate the model performance. For the same kiln another type of model, based on the division of the kiln into several large zones, has been investigated and partially described by Manitius, et al. (1972).
2. Process Description and Assumptions The scheme of the kiln is shown in Figure 1. Heat is supplied to the kiln by a hot combustion gas, the combustion taking place in a separate chamber. The gas temperature is nearly 1300" at the "hot" end and nearly 700" a t the "cold" end of the kiln. The raw material, which is supplied to the cold end of the kiln, is basic ammonium aluminum sulfate (BAAS), a white powder with a particle size ranging between 20 and 100 F . A rather large part (20-5070) of the powder is carried away from the kiln by the gas stream and is recovered in separating facilities to be returned to the kiln. The existence of this phenomenon, called a carry over, is an essential feature of the kiln considered. The chemical formula of the BAAS assumed in the model is (NH4)2.0.3A1203-4S03.8H20. The powdered BAAS contains usually 15-20% moisture. The following subsequent transformations take place in the kiln: (a) drying; (b) liberation of two particles of H20 (at ca. 450"); (c) endothermic decomposition (at ca. 540") according to
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Figure 1. General scheme of the kiln installation.
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Figure 4. Cross section of the kiln.
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