W. Harmon Ray

The dynamic behavior of continuous polymerization reactors—I: Isothermal solution polymerization in a CSTR

Abstract A mathematical model having no adjustable parameters is developed and compared with both dynamic and steady-states” in the neighborhood of unstable middle steady states is thought to be due to a combination of methacrylate with ethyl acetate solvent, in a CSTR, was shown to have ignition and hysteresis behavior characteristic of multiple steady states for sufficiently low solvent concentrations. The observation of “pseudosteady-states” in the neighborhood of unstable middle steady states is thought to be due to a combination of kinetic and hydrodynamic mechanisms.

The Bifurcation Behavior of Tubular Reactors.

Abstract Methods for studying the bifurcation behavior of tubular reactors have been developed. This involves the application of static and Hopf bifurcation theory for PDEs and the very precise determination of steady state profiles. Practical computational methods for carrying out this analysis are discussed in some detail. For the special case of a first order, irreversible reaction in a tubular reactor with axial dispersion, the bifurcation behavior is classified and summarized in parameter space plots. In particular the influence of the Lewis and Peclet numbers is investigated. It is shown that oscillations due to interaction of dispersion and reaction effects should not exist in fixed bed reactors and moreover, should only occur in very short “empty” tubular reactors. The parameter study not only brings together previously published examples of multiple and periodic solutions but also reveals a hitherto undiscovered wealth of bifurcation structures. Sixteen of these structures, which come about by combinations of as many as four bifurcations to multiple steady states and four bifurcations to periodic solutions, are illustrated with numerical examples. Although the analysis is based on the pseudohomogeneous axial dispersion model, it can readily be applied to other reaction diffusion equations such as the general two phase models for fixed bed reactors.

THE DYNAMIC BEHAVIOUR OF FLUIDIZED BED REACTORS FOR SOLID CATALYZED GAS PHASE OLEFIN POLYMERIZATION

Abstract The dynamic behaviour of fluidized bed reactors for ethylene and propylene polymerization is studied through detailed modelling and simulation. Both static and Hopf bifurcation behaviour is observed and can lead to temperature runaway if special care is not taken in start-up and in normal operation. A feedback control scheme can be used to control transients, but it is limited by recycle gas cooling capacity.

Identification and control of distributed parameter systems by means of the singular value decomposition

Abstract In this paper the basic properties of the singular value decomposition (SVD) for integral equation models of distributed parameter systems (DPS) are presented in the context of process identification and model-based control. In addition, new methods of analysis and computation are described in which SVD-based techniques are used to provide a practical solution for the DPS identification and control problem. Once developed, these novel procedures are applied to a class of linear DPS which are conventionally described by parabolic partial differential equation (PDE) models. An alternative integral equation representation for these processes is used to provide a general and readily identifiable pseudomodal input/output model for a wide variety of such DPS, including both spatially self-adjoint (diffusive) and non-self-adjoint (convective/diffusive) systems It is demonstrated that this SVD-based internal equation model of DPS is a sound and convenient basis for pseudo-modal feedback control system designs. A later paper will extend these methods to allow for model-predictive controller designs and nonlinear DPS

Modelling of the liquid phase polymerization of olefins in loop reactors

Abstract In this work a new model for the polymerization of olefins in a loop reactor is presented. The reactor is modelled as two tubular reactors interconnected. In contrast to the traditional equivalent CSTR approach, this model allows important effects such as recycle rate, axial dispersion and heat transfer to be investigated. Some simulation results are presented.

Dynamic PLS modelling for process control

Abstract A modification of the Partial Least-Squares (PLS) modelling procedure is presented which permits incorporation of a dynamic transformation into the standard algebraic form of this model. This makes it possible to use the resulting dynamic PLS model for control system design by employing precompensators and postcompensators constructed from the input and output loading matrices and basing the controller for the compensated plant on the dynamic inner relation of the modified PLS model.

Nonlinear dynamics found in polymerization processes — a review

Each year more than a hundred million tons of polymer are produced worldwide in a variety of polymerization processes. Most of the polymerization reactions involved are highly exothermic so that very interesting and troublesome nonlinear dynamics arise routinely in these processes. In this paper, the key reaction parameters are examined for a variety of important polymers and examples are provided illustrating the steady state multiplicity, sustained oscillations, and traveling waves which can arise in industrial reactors. Among the reactors discussed are stirred tanks, loops, and fluidized beds. Some of the effects of imperfect mixing will also be demonstrated by examples.

Control of systems described by population balance equations—I. Controllability analysis

Abstract The controllability of systems described by population balance equations through the use of lumped manipulated variables is addressed. A comprehensive model is first presented and then simplified in order to make some general results possible. More detailed analysis is undertaken for several specific systems: human population dynamics, emulsion polymerization, and crystallization. These encouraging controllability results for particulate processes suggest that the application of appropriate control stategies for the control of the particle size distribution through the manipulation of feed concentrations could be successful in practical situations.

Polymerization Reactor Control

The principal difficulties in achieving good control of polymerization reactors are related to inadequate on-line measurement, a lack of understanding of the dynamics of the process, the highly sensitive and nonlinear behavior of these reactors, and the lack of well-developed techniques for the control of nonlinear processes. Some illustrations of these problems and a discussion of potential techniques for overcoming some of these difficulties is provided.

Control of systems described by population balance equations. II: Emulsion polymerization with constrained control action

The control of unstable continuous stirred tank reactors for emulsion polymerization is addressed. Despite reported failures in past attempts to control reactor oscillations, recent controllability results (in Part I of this series) provided encouragement to carry out this study. A comprehensive nonlinear model is used for the simulations. SISO controllers coupling a wide range of manipulated and output variables are tested. The tuning of the controller parameters is accomplished through an extension to unstable systems of a relay input technique by Astrom and Hagglund (1983, Proceedings IFAC Workshop on Adaptive Control, San Francisco). Several controllers are successful in eliminating the open-loop sustained oscillations in methylmethacrylate emulsion polymerization. Suggestions are made about which of the successful control strategies may be most readily applied to operating reactors and which may require yet unavailable measurement technology.