Estimation of Kinetic Parameters in Transition-Metal-Catalyzed Gas-Phase Olefin Copolymerization Processes Kyu Yong Choi,* Shihua Tang, and Ashuraj Sirohi Department of Chemical Engineering, University of Maryland, College Park, Maryland 20742 The estimation of kinetic parameters is a critical part of developing a process model for industrial polymerization processes. In transition-metal-catalyzed gas-phase olefin copolymerization processes, polymer density is a strong function of the amount of higher R-olefin comonomers incorporated into the polymer. For the calculation of copolymer composition with a process model, propagation rate constants, which vary from one catalyst system to another, must be known. In this paper, several computational methods applicable to batch, semibatch, and continuous reactors are presented to estimate the propagation rate constants and reactivity ratios in gas- phase olefin copolymerization processes. 1. Introduction In recent years, the polyolefin industry has experi- enced a revolutionary progress in catalyst and process technology. New and improved catalysts (e.g., single- site catalysts, metallocenes) are claimed to offer in- creased polymer productivity and more precise control of polymer properties. New end-use markets have also been developed to capitalize the development of new polyolefins that have distinct differences in their physi- cal, mechanical, and rheological properties from con- ventional polyolefins. As the competition among poly- olefin manufacturers becomes intense, it is crucial to shorten the new process development time for full commercialization of new process technology and to improve the existing polymerization processes. In industrial polyolefin processes, many different types of catalysts are used in continuous liquid slurry, solution, and gas-phase polymerization reactors to diversify the product grade slate. Since polyolefins are produced in large quantities in continuous reactors, it is desirable to optimize the production schedule and effectivly control the grade transition dynamics to minimize the production of off-specification products. One of the ways to improve the design and operation of a polymerization process is to develop an improved quantitative understanding of the process characteris- tics and use it to devise better operating strategies. A mathematical process model based on the fundamental reaction chemistry and physics of polymerization is a useful tool for such purposes. In developing a heterogeneous copolymerization proc- ess model, a kinetic scheme is first devised for a given catalyst and then modeling equations are derived. A typical polymerization process model consists of mass balances, energy balances, and a set of equations such as molecular weight moments to compute polymer molecular weight averages. The most important and often a very difficult task is to determine the relevant kinetic parameters for the process model. Given a specific polymerization catalyst, one may conduct labo- ratory experiments at different reaction conditions to obtain the kinetic data required for the process model. It is also not uncommon in practice that catalysts are tested directly on a large-scale pilot or a commercial plant. The main objective of this paper is to present analytical methods to estimate the copolymerization propagation rate constants and reactivity ratios for transition-metal-catalyzed olefin copolymerization proc- esses. 2. Estimation of Copolymerization Rate Constants In gas-phase olefin polymerization processes, control- ling the polymer property parameters such as copolymer composition and molecular weight averages is of par- ticular importance. It is because copolymer density and melt index, which are two of the most important property measures used by polymer manufacturers, depend on these parameters. To control the comonomer content in the polymer, the reactivity of active transi- tion-metal sites toward both monomer and comonomer should be known and gas-phase composition must also be controlled accordingly. Let us consider the chain propagation reactions for a binary copolymerization system represented by where P*(Q*) represents the growing polymer chain with M 1 (M 2 ) monomer linked to a transition-metal site. Although some transition-metal catalysts for olefin polymerization may have multiple active sites of differ- ent catalytic reactivity, let us assume that only one type of active site is present. To calculate the polymerization rate (or polymer productivity), copolymer composition, and polymer molecular weight averages, not only co- polymerization reactivity ratios (r 1 ) k 11 /k 12 , r 2 ) k 22 / k 21 ) but also four propagation rate constants must be known. The most commonly used method to determine the reactivity ratios in a homogeneous binary copolymeri- zation system is to utilize the Mayo-Lewis equation: * To whom correspondence should be addressed (e-mail: choi@eng.umd.edu). P* + M 1 9 8 k 11 P* (1.1) P* + M 2 9 8 k 12 Q* (1.2) Q* + M 1 9 8 k 21 P* (1.3) Q* + M 2 9 8 k 22 Q* (1.4) dM 2 dM 1 ) M 2 M 1 [ M 1 + r 2 M 2 r 1 M 1 + M 2 ] (2) 1095 Ind. Eng. Chem. Res. 1997, 36, 1095-1102 S0888-5885(96)00363-6 CCC: $14.00 © 1997 American Chemical Society