Parametric sensitivity of chain polymerization reactors exhibiting the trommsdorff effect

The recently developed mathematical technique for studying the parametric sensitivity of reactors is extended to include chain polymerization systems exhibiting the gel and glass effects, as well as physical property variations. The sensitivities of the two temperature maxima with respect to various parameters are computed. It is found that, for a sample system, poly(methyl methacrylate), all the sensitivities of the gel effect induced temperature peak attain their maxima at the same conditions—this leads to a generalized temperature sensitivity constraint applicable to reactor design or operation. This sensitivity boundary is associated with high conversions and high molecular weights. The analysis shows that the dimensionless propagation activation energy, ?_p, and the dimensionless initiation activation energy, ?_d, are the two most important parameters governing the system performance. Sensitivities of the gel effect-induced number average chain length peak with respect to various parameters are also obtained. Again, all of these chain length sensitivities show maxima at the same condition, leading to the concept of a generalized chain length sensitivity criterion of constraint. Most importantly, the temperature and chain length sensitivity boundaries are virtually identical.     

Parametric sensitivity in fixed-bed reactors

Parametric sensitivity in fixed-bed reactors has been analysed by previous workers using the quasihomogeneous model [i.e. for the kinetic regime only]. In the present paper a general treatment is proposed in which transport limitations are also considered. It is shown that the critical inlet partial pressure is strongly dependent on the transport processes. Based on the analysis presented, four regimes of fixed-bed reactor operation are postulated and conditions are stated to identify the regime in which a given system would operate. These conditions are applied to some industrially important reactions to show that the regimes represent realistic systems. Procedures are developed to obtain the critical inlet partial pressure for systems lying in the various postulated regimes. Illustrative examples are then solved to demonstrate the procedures developed in the text. The correctness of the procedures is established by comparing the values of the critical inlet partial pressure obtained from the present analysis with those obtained from numerical solution.     

Scaleup factors of tubular emulsion polymerization reactors

This paper examines the important dimensionless numbers that control emulsion polymerization in a tubular reactor. It was found that the activation energy of polymerization was of major importance, while the role of monomer diffusion was not very significant. By selecting certain combinations of the dimensionless numbers, changes occurring during scaleup from a small tubular diameter to a larger diameter can be approximated.     

Free-radical polymerization of methyl methacrylate in tubular reactors

Mathematical modeling and experimental studies of the freeradical polymerization of methylmethacrylate in tubular reactors have been performed to ascertain the operating constraints, reactor behavior, and product quality of this process. This paper focuses on reactions at a temperature below the glass transition of poly(methyl methacrylate). This class of experiments is here referred to as low-temperature runs, in contrast to above-Tg polymerization. Reactor temperature and conversion histories of these low-temperature experiments are successfully described by a rheokinetic model, incorporating both detailed considerations of velocity profile development in the reactor and conversion-dependent kinetics. The limitations of this process are discussed in light of the complex fluid flow and heat transfer problems encountered in the system.     

Parametric sensitivity of the ignition process to mass transfer in adiabatic tubular reactors with exothermic heterogeneous reactions

The alternative effects of reaction kinetics, mass, heat and momentum transport on mass conversion by chemical reactions are examined theoretically for a reacot tube with laminar flow. The reaction enthalpy is considered. A heterogeneous reaction between several gaseous components takes place at the inner surface of this reactor tube. Strongly exothermic reactions lead to self-acceleration of the reaction, unless reaction enthalpy is removed through the tube wall. Under certain conditions, there will be a sudden change from mass transfer controlled by the reaction to that controlled by diffusion. This phenomenon is known as ignition of the reaction. The effect of ignition and its sensitivity to reaction enthalpy, thermal conductivity and diffusivity of the fluid as well as activation energy of the first order heterogeneous wall reaction are investigated by a numerical solution of the transport equations. Axial conduction of heat and mass is neglected both in the fluid and in the tube wall. Non-stoichiometric wall reactions of first order, with temperature dependent reaction rates and equilibrium constants, are considered. The results are presented in graphical form, as plots of the local mass flux at the reacting wall as functions of the dimensionless tube length.     

Simulation of nylon 6 polymerization in tubular reactors with recycle

In the hydrolytic polymerization of ?-caprolactam, the ring opening of the monomer is much slower than the polyaddition reaction. Hence, the mixing of aminocaproic acid to the feed results in a faster conversion of the monomer. Industrially, this fact is exploited by using a recycle stream. An isothermal plug flow reactor (PFR) with a recycle is simulated in this study, using two techniques: the method of successive substitutions and Wegstein's method. It is found that, under certain operating conditions, the use of a recycle stream gives higher monomer conversions and lower cyclic dimer concentrations than either a PFR or a homogeneous continuous-flow stirred-tank reactor (HCSTR), with the degree of polymerization almost the same as that obtained in an HCSTR, and thus offers a considerable advantage. However, when a recycle reactor is coupled with a subsequent flashing operation and a finishing reactor, these advantages are considerably reduced.     

High pressure tubular reactors for ethylene polymerization optimization aspects

Optimal policies for operation of high pressure tubular reactors for ethylene polymerization are presented. The work is based on a previously developed model, allowing accurate representation of different configurations and operation conditions of industrial relevance. Several policies based on temperature and initiator concentration as control parameters are evaluated and compared.     

Bulk polymerization in tubular reactors I. Experimental observations on fouling

Conditions under which fouling (polymer deposition) occurs in tubular polymerization reactors were studied using bulk methyl methacrylate polymerizations at 70°. It was demonstrated that reactor orientation and flow direction have a significant effect on fouling behaviour. Natural convection becomes increasingly important as concentration gradients in the reactor increase. Using the optimum reactor configuration determined in the first part of the study, a feasible operating region for the reactor was established, thereby permitting selection of conditions which will prevent reactor fouling.     

Use of neural networks for modeling of olefin polymerization in high pressure tubular reactors

Neural network computing is one of the fastest growing fields of artificial intelligence due to its ability to “learn” nonlinear relationships. This article presents the approach of back propagation neural networks for modeling of free radical polymerization in high pressure tubular reactors. Industrial data were used to train the network for prediction of the temperature profile along the reactor, as well as polymer properties such as density, melt flow index, and molecular weight averages. Comparisons were made between the neural network and mechanistic model predictions published in the literature. Results showed the promising capability of a neural network as an alternative approach to model polymeric systems. © 1994 John Wiley & Sons, Inc.     

Optimal location of measurements in tubular reactors

The optimal location of temperature measurements along the length of a non-adiabatic tubular reactor in which a first-order exothermic reaction is occu     

Axial diffusion in isothermal tubular flow reactors

Numerical solutions are presented for differential equations representing the isothermal steady flow tubular reactors with varied degrees of backmixing of the reactants in the axial direction and with reactions with order other than zero and first.     

Thermal stability of polymerization reactors

Temperature rises which occur in the early stages of polymerization in batch reactors are discussed. Comparisons between experimental results and a reactor model shows that realistic predictions of temperature rises can be made when the model allows for changes in density and specific heat of the reaction fluid. In the case of styrene polymerization, the neglect of density and specific heat changes leads to the prediction of large temperature increases, which are not found in practice. When allowance for these changes in physical properties is made, agreement between theoretical prediction and experimental results is good.     

Dispersion models of unsteady tubular reactors

Axial dispersion in time-variable laminar flow in a tubular reactor is analyzed using an exact procedure for the case of a homogenous first-order reaction. For the first time since the Taylor Dispersion model was originally introduced for the modeling of reactors, its validity is examined over a wide range of the reaction rate parameter by comparison against an exact analysis. It is shown that a constant coefficient dispersion model can be obtained from first principles for large values of time only for initial distribution problems; however, this simple approximate model also is reasonably good for describing concentration distributions for the present inlet distribution problem for slow reactions and for axial locations sufficiently far away from the inlet. For rapid reactions, while the dispersion model is inaccurate in describing axial concentration distributions, it is surprisingly good for predicting the reactor length required for complete conversion. In contrast to the conclusion of a recent article, it will be shown that the dispersion coefficient is independent of the reaction rate constant.     

The bifurcation behavior of tubular reactors

Methods for studying the bifurcation behavior of tubular reactors have been developed. This involves the application of static and Hopf bifurcation theory for PDE's 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.     

CFD simulation of gas-liquid contacting in tubular reactors

Gas-liquid contacting in tubular reactors was simulated using an Eulerian-Eulerian CFD approach in which accurate interphase momentum closure relations are incorporated, bubble-induced turbulence is accounted for, and population balance equations are used to describe bubble breakage and coalescence. The ability of two breakup kernels (Luo, H., Svendsen, H.F., 1996. Theoretical model for drop and bubble breakup in turbulent dispersions. A.I.Ch.E. Journal 42, 1225-1233; Lehr, F., Millies, M., Mewes, D., 2002. Bubble size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443) and three coalescence kernels (Prince, M.J., Blanch, H.W., 1990. Bubble coalescence and breakup in air sparged bubble columns. A.I.Ch.E. Journal 36, 1485-1499; Luo, H., 1993. Coalescence, breakup and liquid recirculation in bubble column reactors. Ph.D. Thesis, Norwegian University of Science and Technology, Trondheim; Lehr, F., Millies, M., Mewes, D., 2002. Bubble size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443) to accurately predict several flow parameters in pipe flow was tested.Good agreement between simulation and experimental results (radial profiles of gas holdup, turbulence intensity, and local Sauter bubble diameter) was achieved without the use of empirically derived relationships (such as Drift flux) by adjusting a single parameter which accounts for the deviation in the coalescence behaviour of tap water from that of pure water. The approach adopted in this investigation may thus be applicable to more complex hydrodynamic situations such as those encountered in mechanically agitated tanks and the need for extensive experimental testing may be replaced by single measurement of the effect interfacial properties have on coalescence rates.     

Analysis of condensation polymerization reactors. III. Continuous reactors

The kinetic model for polycondensation reactions has been derived and techniques for validating the model have been described in Parts I and II of this work. This paper is concerned with using the results of Part I and II for the analysis and design of continuous polycondensation reactors.     

Analysis of condensation polymerization reactors. II. Batch reactors

The kinetic model for polycondensation reactions was developed in Part I of this work. This kinetic model is now to be utilized as a framework for the analysis of batch experiments.     

Measurement and control of polymerization reactors

The measurement and control of polymerization reactors is very challenging due to the complexity of the physical mechanisms and polymerization kinetics. In these reactors many important variables, which are related to end-use polymer properties, cannot be measured on-line or can only be measured at low sampling frequencies. Furthermore, end-use polymer properties are related to the entire molecular weight, copolymer composition, sequence length, and branching distributions. This paper surveys the instrumentation technologies, which are of particular interest in polymerization reactors with emphasis on, for example, measurement of viscosity, composition, molecular weight, and particle size. This paper presents a hierarchical approach to the control system design and reviews traditional regulatory techniques as well as advanced control strategies for batch, semibatch, and continuous reactors. These approaches are illustrated by focusing on the control of a commercial multiproduct continuous emulsion polymerization reactor. Finally, the paper captures some of the trends in the polymer industry, which may impact future development in measurement and reactor control.