Numerous articles (particularly those of synthetic material such as plastics and rubber) are produced by a respective chemical process, namely polymerization. Each such chemical process/polymerization involves a complex chemical reaction brought about in a reactor or network of reactors and ancillary equipment (e.g., distillation towers, dryers, extruders, etc.) Typically, the chemical process and polymer manufacturing systems (i.e., reactors and ancillary equipment) are expressed in terms of formulas or equations for purposes of modeling or simulating the chemical process/polymer manufacturing system.
The demands on simulation models for polymerization reactor processes and polymer manufacturing systems in general is growing due to advanced technology for polymerization catalysts such as metallocene catalysts. There is a rapidly growing need for simulation models to calculate full distributions of composition, molecular weight and long chain branching. This presents serious problems related to information transfer efficiency for both steady-state and dynamic simulations of polymer reactor systems which are part of a larger polymer manufacturing system.
Commonly the population balance equations of the subject polymer manufacturing system are solved by mathematically integrating either solving for species or solving for moments of distribution. The solution of the very large sets of algebraic and ordinary differential equations which comprise the population balance equations appears impossible even with the largest and fastest computers available today. Another problem which presents itself is the need to transfer concentration data of the very large number of polymer species (perhaps as many as 10.sup.5) through the network of polymer reactors and other process units in the polymer manufacturing system.
An efficient simulation strategy which gives high information transfer efficiency employs the method of using moments of the distribution (called the "method of moments") to calculate average polymer properties. (See U.S. Pat. No. 5,687,090, issued Nov. 11, 1997 to assignee of the present invention). Although the strategy satisfies many demands of polymer process simulators, it has one weakness which cannot be overcome without a complete change in polymer process/reactor modeling strategy. When polymer distributions in composition, molecular weight and long chain branching are complex (having a shoulder or bimodal, for example), these distributions cannot be accurately constructed (or reconstructed) given the moments of these distributions. In fact, the process of constructing complex distributions given moments (as many as one wishes) leads to multiple solutions and possible large errors.
In contrast to the method of moments, instantaneous property methods have been studied in isolated incidences. W. H. Stockmayer in J.Chem.Phys. 13:199 (1945) derives and discloses a useful analytical expression for bivariate distribution of properties (e.g., polymer chain chemical composition and molecular weight) for dead polymer chains produced instantaneously. However, he does not address or contemplate the use of such instantaneous property measures to track distribution of polymer properties (such as composition, molecular weight and long chain branching) through polymer reactor networks for modeling/simulation of reactor networks or polymer manufacturing systems.
A. H. Abdel-Alim and A. E. Hamielec in the J. Applied Polym. Sci., 16, 783 (1972) show the use of instantaneous property methods as applied to the batch polymerization of vinyl chloride. This paper was referred to in a text by J. A. Biesenberger and D. H. Sebastian, entitled "Principles of Polymerization Engineering," Wiley-Interscience, New York, (1983) in which instantaneous property methods were discussed.
A. E. Hamielec's research associates and Ph.D. students dominated the use of instantaneous property methods and these applications have all been for single batch polymerization reactors. Some of these publications include:
S. T. Balke and A. E. Hamielec, "Free Radical Polymerization of Methyl Methacrylate to High Conversions," J. Applied Polym. Sci., 17:905 (1973).
L. H. Garcia-Rubio and A. E. Hamielec, "Bulk Polymerization of Acrylonitrile-Model Development," J. Applied Polym. Sci., 23:1413 (1979).
C. J. Kim and A. E. Hamielec, "Polymerization of Acrylamide with Diffusion-Controlled Termination," Polymer, 25:845 (1984).
O. Chiantore and A. E. Hamielec, "Thermal Polymerization of p-Methyl Styrene at High Conversions and Temperatures," Polymer, 26:608 (1985).
D. Bhattacharya and A. E. Hamielec, "Bulk Thermal Copolymerization of Styrene/p-Methyl Styrene," Polymer, 27:611 (1986).
K. M. Jones et al., "An Investigation of the Kinetics of Copolymerization of Methyl Methacrylate/p-Methyl Styrene," Polymer, 27: 602 (1986).
T. M. Yaraskavitch et al., "An Investigation of the Kinetics of Copolymerization of p-Methyl Styrene-Acrylonitrile," Polymer, 28:489 (1987).
S. Zhu and A. E. Hamielec, "Chain Length Dependent Termination for Free-Radical Polymerization," Macromolecules, 22:3093 (1989). This paper is notable for its generalization of the Schulz-Flory and Stockmayer's distributions to account for chain-length dependent termination for free-radical polymerization.
S. Thomas et al., "Free-Radical Polymerization--An Elegant Method of Solving the Population Balance Equations with Chain Transfer to Polymer" Polymer Reaction Engineering, 5:183 (1997). This reference is notable for the first attempt to use instantaneous property methods with long chain branching and tracking distributions of molecular weight and long chain branching in a batch reactor.
"Predici" a simulation of polyreaction kinetics product by CiT GmbH is marketed as providing the computation of complete molecular weight distribution of polymers in a process simulator/modeler. This product is an example of the method where population balance equations are solved as differential equations. See "The Simulation of Molecular Weight Distributions in Polyreaction Kinetics by Discrete Galerkin Methods," Macromol. Theory Simul., 5:393-416 (1996).
Thus, to date, process modeling of polymer manufacturing systems remains computationally complex, inaccurate and inefficient or otherwise problematic.