W. H. Ray

On the dynamic behavior of continuous stirred tank reactors

Abstract The types of dynamic behavior possible for a single first order reaction carried out in a stirred tank reaction are classified according to values of the parameters and plots in parameter space used to define the various possibilites. Analytic criteria are developed which predict the existence and stability character of limit cycles as a function of the system parameters. The types of dynamic behavior predicted are illustrated by numerical computation of the temperature and concentration trajectories. Several kinds of new jump phenomena for this problem are observed and explained in terms of the parameter space plots. The theory and analysis methods can be easily generalized to other types of reaction systems.

The classification of the dynamic behavior of continuous stirred tank reactors—influence of reactor residence time

Abstract The dynamic behavior of the continuous stirred tank reactor is analysed and classified for a variable reactor residence time. Although earlier work, treating the bifurcation to limit cycles and steady states with changing Damkohler number, yields a complete description of the problem, the evolution of multiple steady states and limit cycles is much more bizarre as the reactor residence time varies. In addition, it is the reactor residence time which is most easily varied experimentally so that the present results are more readily compared with experiment. Plots are given to show the influence of system parameters on the reactor behavior.

The dynamic behavior of continuous polymerization reactors—II Nonisothermal solution homopolymerization and copolymerization in a CSTR

Abstract The possible types of dynamic behavior have been determined for a CSTR in which bulk or solution free radical polymerization is carried out. To illustrate the methodology, the expected behavior of reactors for vinyl acetate or methylmethacrylate homopolymerization and vinyl acetate-methylmethacrylate copolymerization has been explicitly determined. The monomer feed ratios, solvent concentrations, and reactor cooling capacity which allow multiple steady states and limit cycles have been carefully mapped.

Reactor residence time distribution effects on the multistage polymerization of olefins—I. Basic principles and illustrative examples, polypropylene

Abstract Many polyolefins are produced by catalyzed olefin polymerization over solid catalysts. A variety of processes are currently in use including loop, continuous-stirred tank, horizontal stirred bed and fluidized-bed technologies. In each of these continuous processes, the reactor residence time distribution is unique and affects the resulting distribution of polymer properties. In this paper we present a population balance modeling approach for modeling multistage olefin polymerization processes using catalyst residence time as the main coordinate. The catalyst may possess a broad particle size distribution and contain multiple active sites with a comprehensive kinetic scheme involving multiple monomers. Diffusion limitations during reaction may also be a consideration. A variety of reactor systems can be modeled each with unique residence time distributions and having different internal and external residence time distribution. In addition, the modeling allows the consideration of particle size selection effects within the process. These effects are implemented in a model of a fluidized-bed reactor. The population balance model is illustrated with examples of propylene polymerization in the four major commercial processes listed above, with a high activity TiCl 4 MgCl 2 catalyst. Comparisons of total production capacity, catalyst yield distribution, polymer particle size and porosity distribution are made. It is found that significant differences exist between the different industrial processes. It is also found that the performance of the fluidized-bed reactor is highly sensitive to fluidization conditions, particle size selection effects and the catalyst particle size distribution. Differences in product quality are discussed and issues such as fines generation and particle sticking are addressed.

Some recent applications of distributed parameter systems theory-A survey

A survey of some recent applications of distributed parameter systems theory is presented. The practical areas discussed range from process control problems in an industrial plant to the identification, monitoring and control of air and water quality in our environment. Some new, promising areas of application are discussed along with suggestions for future research emphasis.

The dynamic behavior of continuous solution polymerization reactors. IV: Dynamic stability and bifurcation analysis of an experimental reactor

Abstract The dynamic behavior of the solution polymerization of vinyl acetate in a CSTR is analyzed. Preliminary experimental results showing the presence of limit cycles for this class of reactors are presented and a detailed bifurcation analysis of a mathematical model of the laboratory scale reactor is carried out using numerical continuation techniques. The method relies on the continuation of the loci of four types of special points in two parameters. This enables the classification of parameter space into regions where qualitatively different steady-state and dynamic phenomena are observed. These phenomena include S-shaped, isola- and mushroom-type multiplicities, as well as various periodic bifurcations. The combination of steady-state and period bifurcations result in a wide variety of possible structures. A new type of bifurcation diagram, not previously observed, has been found in parameter space. Detailed experimental evidence on the presence of limit cycles for this class of reactors will be presented in subsequent parts of this series.

On the dynamic behaviour of a class of homogeneous continuous stirred tank polymerization reactors

Abstract The steady state and dynamic behaviour of two typical vinyl polymerizations (polymethylmethacrylate and polystyrene with AIBN) carried out in a CSTR has been analyzed. Both the cases of constant and dynamically varying initiator concentration were treated for a wide range of reactor operating conditions. The results show that multiple steady states are possible even under isothermal conditions, but only unstable limit cycles appear possible for the systems studied.

The dynamic behaviour of continuous polymerization reactors—III: An experimental study of multiple steady states in solution polymerization

Abstract A study involving small scale reactor experiments coupled with detailed non-isothermal reactor modelling has been carried out shows that ‘isoia” ty

The dynamic behavior of continuous polymerization reactors—VI. Complex dynamics in full-scale reactors

Abstract The dynamic behavior of the solution polymerization of vinyl acetate in a continuous stirred tank reactor was analyzed in a previous study. Modelling results and experimental verification confirmed the existence of limit-cycle attractors for a laboratory—scale reactor. In the present work, the model is modified slightly to represent the behavior of full-scale industrial reactors. Results of a detailed bifurcation analysis indicate the existence of more regions in parameter space than for the earlier analysis. Complex structures are analyzed in detail. Examples include multiple stable periodic orbits, isolas of periodic solutions, nonhomogeneous periodic oscillations and cascading period doublings leading to chaos.

Kinetic study of gas phase olefin polymerization with a TiCl4/MgCl2 catalyst I. Effect of polymerization conditions

This study focuses on the kinetics of ethylene/propylene (homo/co)poly-merization reactions using a high activity TiCl 4 /MgCl 2 /AlEt 3 catalyst. The reactor system is a gas phase reactor equipped with an on-line composition control scheme. As such, important kinetic data such as the instantaneous reaction rate of each monomer is readily obtained. In the investigation, experiments are performed to study the effects of comonomer composition variations, temperature variations, hydrogen concentration variations, and variations in the Al/Ti ratio. It is observed that the ethylene and propylene instantaneous reaction rates show a rather peculiar pattern with the appearance of a second peak. Our work linked the existence of this peak to the Al/Ti ratio used. A theory based on the oxidation state change is proposed. This theory is also used to explain the effects of temperature changes and hydrogen concentration changes on the system. A variety of analytical techniques are employed to study the polymer properties and evidence is provided to support the existence of polymer partial melting at relatively high reaction temperatures. The resulting diffusion limitation is believed to be partially responsible for the observed activity decrease at such elevated temperatures.