Pergamon Comput er s t hem. Engng Vol.22, Suppl., pp. S95-S102, 1998 0 1998 Published by Elsevier Science Ltd.All rights reserved Printed in Great Britain PII: SOO9?3-1354(98)00042-8 0098-1354/98 $19.00 + 0.00 Application and Validation of the Pseudo-Kinetic Rate Constant Method to High Pressure LDPE Tubular Reactors A. Baltsas, E. Papadopoulos, and C. Kiparissides Department of Chemical Engineering and Chemical Process Engineering Research Institute, Aristotle University of Thessaloniki, P.O. Box 472, Thessaloniki, Greece Abstract The present study is concerned with the application of the pseudo-kinetic rate constant method to high pressure LDPE tubular reactors. The utilization of multiple monomers is of profound importance to the polymer manufacturing industry since it leads to the production of an unlimited number of polymer types with a wide range of properties. However, by increasing the number of comonomers the kinetic rate expressions describing the appearance / disappearance of the various molar species become fairly complex. In order to simplify the kinetic treatment of the resulting expressions, the pseudo-kinetic rate constant method can be employed, in combination with the method of moments, to model the multicomponent free-radical polymerization of ethylene in a high pressure tubular reactor. 0 1998 Published by Elsevier Science Ltd. All rights reserved. Keywords: pseudo-kinetic rate constant method, tubular reactors, polyethylene, free-radical copolymerization Introduction Low Density Polyethylene (LDPE) and its copolymers are commonly produced in high-pressure autoclaves and tubular reactors. A high-pressure LDPE tubular reactor consists of a spiral wrapped metallic pipe with a large length to diameter ratio and a total length ranging from 500 to 1500m. The heat of reaction is partially removed through the reactor wall by a heat transfer fluid resulting in a non- isothermal reactor operation. A commercial reactor can have multiple reaction and cooling zones and includes a number of initiators, monomers and solvents feed points. To describe the complex free radical kinetics of multicomponent ethylene polymerization a fairly general reaction mechanism can be employed (Kiparissides et. al., 1993, 1996). The mechanism includes initiator decomposition, chain initiation and propagation reactions, chain transfer to monomer, solvent and polymer, intramolecular transfer and p-scission of set- and tert-radicals, as well as termination reactions. Based on the postulated kinetic scheme, the reactor design equations can be derived, using the pseudo-kinetic rate constant method to describe the chain length developments in a high-pressure LDPE tubular reactor. The tubular reactor model includes energy, momentum and mass balances for all reacting species and is supported by the physical transport and thermodynamic properties equations. Although a great number of papers have been published on the modeling of homo- and copolymerizations, only a limited number of articles s9.5 have been appeared in the literature describing multicomponent polymerizations (Tobita et al., 1988, 1991, Zabinsky et al., 1992). The assumptions involved in modeling multicomponent polymerizations, using the pseudo-kinetic rate constant method, have been validated by Xie et. al. (1993) and Storti et al. (1989) for linear and branched polymers. The Pseudo-Kinetic Rate Constant Method A fairly general kinetic mechanism describing the free-radical copolymerization of ethylene is given in Table 1. The subscripts p and q denote the number of units of monomer 1 and monomer 2 chemically bound in the copolymer chain. The superscript “i” denotes the monomer type on which the active center is located. To simplify the mathematical model equations, the pseudo-kinetic rate constant method can be applied to describe molecular weight developments in multicomponent free-radical polymerization of ethylene in a high-pressure tubular reactor. According to the original developments of Hamielec and MacGregor (1983), the pseudo-kinetic rate constants can be defined as in Table 2 for the free- radical multicomponent polymerization of ethylene. The pseudo-kinetic rate constants are expressed in terms of the rate constants of the pertinent elementary reactions, weighted by the mole fractions of the free monomers or/and the mole fractions of the various macroradicals in the reaction mixture.