Dynamics of a continuous stirred tank reactor for styrene polymerization initiated by a binary initiator mixture. II: Effect of viscosity dependent heat transfer coefficient

The dynamic behavior of the solution polymerization of styrene in a continuous stirred tank reactor is analyzed with a mixture of tert-butyl perbenzoate and benzoyl peroxide as an initiator system. In the modeling of the reactor, a viscosity dependent reactor wall heat transfer coefficient is used to account for the changing heat transfer efficiency as monomer conversion and polymer molecular weight increase. The steady state and bifurcation behaviors have been investigated with the reactor residence time, initiator feed composition, initiator concentration, feed solvent volume fraction, and coolant temperature as bifurcation parameters. Unlike the reactors with constant heat transfer coefficient, the present system exhibits relatively simple steady state and dynamic bifurcation behaviors. Oscillatory behavior is observed only when the solvent volume fraction in the feed exceeds 0.2. The dynamic simulation of the reactor also indicates that a feedback temperature controller may fail to maintain the reactor temperature when the heat transfer coefficient changes as a result of process disturbances.     

Dynamics of a CSTR for styrene polymerization initiated by a binary initiator system

The steady state and dynamic behavior of a continuous stirred tank reactor has been analyzed for free radical solution polymerization of styrene initiated by a mixture of two initiators having different thermal stabilities. From the steady state analysis of the reactor model with a mean residence time as a bifurcation parameter, four unique regions of steady state solutions are identified in an operating parameter space for a given initiator feed composition. A variety of complex bifurcation behavior such as multiple steady states, Hopf bifurcation and limit cycles have been observed and their stability characteristics have been analyzed. The effects of feed initiator composition and the concentration of the initiator in the feed stream on the reactor dynamics are also presented.     

Continuous emulsion polymerization of styrene in a single Couette–Taylor vortex flow reactor

The effect of the geometrical and operational parameters on the mixing characteristics of a Couette–Taylor vortex flow reactor (CTVFR) were investigated and were correlated with the same parameters by using the tank‐in‐series model. Continuous emulsion polymerization of styrene was conducted at 50°C in a CTVFR to clarify the effects on kinetic behavior and reactor performance of operational parameters such as rotational speed of inner cylinder (Taylor number), reactor mean residence time, and emulsifier and initiator concentrations in the feed streams. It was found that steady‐state monomer conversion and particle number could be freely varied only by varying the Taylor number. In order to explain the observed kinetic behavior of this polymerization system, a mathematical model was developed by combining the empirical correlation of the mixing characteristics of a CTVFR and a previously proposed kinetic model for the continuous emulsion polymerization of styrene in continuous stirred tank reactors connected in series (CSTRs). On the basis of these experimental results, it was concluded that a CTVFR is suitable for the first reactor (prereactor) of a continuous emulsion polymerization reactor system. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 1931–1942, 2001     

Experimental study and simulation of the polymerization of methyl methacrylate at high temperature in a continuous reactor

The bulk polymerization of MMA at high temperature (120–180°C) in a continuous pilot‐plant reactor has been studied. The polymerization is initiated by diterbutyle peroxide and the chain transfer agent is 1‐butanethiol. A simulation program has been developed to predict the steady state behavior of the reactor. The particular features of the kinetic at above‐T_g temperature are included in the model, especially the thermal initiation of the reation and the attenuation of the autoacceleration effect. For the flow and mixing model, the actual vessel cannot be approximated to a single ideal reactor because of its design and of the moderate agitation imposed by the high viscosity of the reacting fluid. A tanks in series model with a recycle stream between tanks is proposed to evaluate the backmixing caused by the special design of the agitator. The parameters of the model are determined with the help of the experimental residence time distribution measured on the reactor. The data collected on the actual reactor, i.e., operation, conversion, molecular weight, temperature, are compared to the calculated one. The agreement is satisfactory but the tendencies are slightly underestimated. The program is a tool to evaluate the effect of modifications of the design of the reactor or changes on the operation parameters like input rate, temperature, and agitation on its behavior. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 79: 2038–2051, 2001     

Mathematical model and analysis of PMMA solution processes

A mathematical model of reactors for the polymerization of methylmethacrylate (MMA) has been developed and analyzed in order to better understand the reactor dynamics and to determine conditions for improved operation. The exploration of the effect of heat transfer in an MMA polymerization reactor system has been conducted by the development of a detailed model. Two correlations for the overall heat transfer coefficient have been used to study the effect of heat transfer. The heat transfer coefficient estimated by an empirical correlation (Kravaris) is only a function of conversion. Due to its simplicity, it may not express very well the true heat transfer phenomena. But in Henderson’s correlation, it is related to the viscosity of the reaction mixture, which in turn depends on the reaction temperature and volume fraction of each species in the reactor. The steady state solutions of mass and energy balances in the reactor depend on the nature of the heat transfer correlation, as does the number of isola branches. Henderson’s correlation may be preferred to calculate the dynamics of the PMMA reactors. The addition of jacket dynamics to the system results in no isola solution branches and no Hopf bifurcations.     

气相法聚乙烯工艺冷凝态操作模式的稳定性和动态行为

气相法聚乙烯工艺冷凝态操作模式由于显著提高了循环气移热能力和反应器时空产率,已成为流化床乙烯聚合工艺的主流操作模式。建立了气相法聚乙烯工艺冷凝态操作模式的数学模型,包括流化床反应器模型,多级换热器模型和反应温度、压力以及循环气组成的控制模型。基于此,采用流程模拟方法,计算了系统在反应器温度采用闭环控制时的稳态解;根据系统对小扰动的动态响应特点,定性判断了反应器温度采用开环控制和闭环控制时聚合反应系统的稳定性;考察了系统对1-己烯分压和催化剂进料速率的阶跃响应特性。结果表明,反应器温度采用闭环控制时,聚合反应系统在所考察操作条件下均是稳定的,而采用开环控制时,解曲线被分叉点分割为稳定区域和不稳定区域。反应器温度对1-己烯分压阶跃变化的动态响应表明聚合反应系统存在长、短周期两类振荡,表明冷凝态操作模式下乙烯聚合反应过程是一个多控制回路耦合的复杂过程。     

Dynamics of a cascade of two continuous stirred tank polymerization reactors with a binary initiator mixture

The dynamic behavior of two continuous stirred tank reactors in series has been investigated for free radical solution polymerization of styrene with a binary mixture of two initiators having different thermal decomposition activities. For a wide range of initiator feed composition, both reactors exhibit quite complex nonlinear steady state and transient behavior. When the reactor residence time is used as a bifurcation parameter, the second reactor can have up to five steady states. For certain range of reactor operating conditions, bifurcations to various types of periodic solutions have been observed, such as Hopf bifurcation, isolas, period doubling, period-doubling cascade, and homoclinics. The effects of other reactor variables, such as total initiator concentration, coolant temperature, and reactor volume ratio on the reactor dynamics, are illustrated to show the complex dynamic behavior of the two-reactor system catalyzed by a mixture of t-butyl perbenzoate and benzoyl peroxide.     

On the influence of mixing on crystal precipitation processes—application of the segregated feed model

The segregated feed model (SFM), a compartmental mixing model, is used to predict the influence of mixing on crystal precipitation. In this method, the population balance is solved simultaneously with the mass balances using crystallisation kinetic, solubility and computational fluid dynamics (CFD) mixing data. Mean properties are calculated for the three different zones of the reactor (two feed zones and bulk zone). It is predicted that during continuous operation, the product particle size exhibits oscillating behaviour before reaching steady state after about ten residence times. In contrast, the second moment (surface area) sharply increases during the first residence time and remains constant thereafter.Different mixing conditions are modelled by varying the mesomixing and micromixing times, which can be regarded as convective and diffusive exchange parameters between the compartments of the reactor. The overall nucleation rate is found to strongly depend on the mixing conditions, as it depends in a highly non-linear manner on the level of supersaturation. In consequence, the nucleation rate varies over three orders of magnitude between ‘good’ and ‘poor’ mixing conditions. Using the SFM, the effect of different feed points, feed rates, feed tube diameters, energy dissipation rates, impeller types and vessel sizes on the nucleation rate and the particle size during crystal precipitation is illuminated. Predictions of the model compare favourably with batch and continuous experimental data for calcium oxalate.     

一氧化碳偶联反应器分岔行为

The bifurcation behavior of the CO coupling reactor was examined based on the one-dimensional pseudohomogeneous axial dispersion dynamic model. The method of finite difference was used for solving the boundary value problem; the continuation technique and the direct method were applied to determine the bifurcation diagram.The effects of dimensionless adiabatic temperature rise, Damkoehler number, activation energy, heat transfer coefficient and feed ratio on the bifurcation behavior were investigated. It was shown that there existed static bifurcation and the oscillations did not occur in the reactor. The result also revealed that the reactor exhibited at most 1-3-1 multiplilicity patterns within the range of practical possible parameters and the measures, such as weakening the axial dispersion of reactor, enhancing heat transfer, decreasing the concentration of ethyl nitrite, were efficient for avoiding the possible risk of multiple steady states.     

Thermal decomposition of 3,3,6,6,9,9-hexaethyl-1,2,4,5,7,8-hexaoxacyclononane in solution and its use in methyl methacrylate polymerization

The kinetics of the thermal decomposition reaction of diethylketone triperoxide (3,3,6,6,9,9-hexaethyl-1,2,4,5,7,8-hexaoxacyclononane, DEKTP) in ethylbenzene solution were studied in the temperature range of 120.0–150.0 °C and at an initial concentration range of 0.01–0.10 M. This peroxide was used as a new initiator in methyl methacrylate (MMA) polymerization process at high temperatures (110.0–140.0 °C) in ethylbenzene solution. The effects of initiator concentration and reaction temperature on the polymerization rate were investigated in detail. Thus, activation parameters of the solution polymerization process (ΔE _d* = 83.3 kJ mol⁻¹ and ΔE _p* − ΔE _t*/2 = 54.0 kJ mol⁻¹) will be obtained. DEKTP can effectively act as initiator in MMA polymerization and its performance is similar to that presented by a multifunctional initiator resulting in high-molecular weight polymethylmethacrylate with a high reaction rate.     

The bifurcation behavior of continuous free-radical solution loop polymerization reactors

The bifurcation behavior of continuous free-radical solution loop polymerization reactors is analyzed in this work. A mathematical model is developed in order to describe the impact of the recycling pump and other external reactor parts upon the process dynamics and stability. Stability analysis is performed using bifurcation theory and continuation methods. It is shown that under certain operational conditions as many as seven steady states are predicted for the loop polymerization reactor. Oscillatory behavior is observed for a wide range of process parameters and onset of oscillations is observed during the transition from operation without material recycling to operation with partial recirculation of the polymer solution. Besides, at certain constrained range of operation conditions, complex dynamics can be observed, including the onset of chaotic behavior. It is also shown that the thermal parameters of the reactor and recycling pump exert a profound effect upon the process stability. For this reason it is shown that oscillatory behavior is very unlikely to occur in actual industrial reactors.     

Low-density polyethylene vessel reactors: Part I: Steady state and dynamic modelling

By the use of a perfectly mixed model and an imperfectly mixed one for lowdensity polyethylene vessel reactors, we show that increases in the initiator consumption with polymerization temperature are due to mixing limitations at the initiator feed. With all its parameters independently estimated, the imperfectly mixed model provides an excellent agreement with experimental data for several initiators, feed flow rates and polymerization pressures. In the temperature region of industrial interest for each type of initiator, the open-loop reactor dynamics drastically change from open-loop unstable, at low temperatures, to open-loop stable at high polymerization temperatures.     

Kinetic investigations of acrylic–polyurethane composite latex

The effect of various reaction parameters on the rate of polymerization, R_p, and on the particle size and morphology of aqueous acrylic–polyurethane hybrid dispersions, prepared by semibatch emulsion polymerization, was investigated. The particles of polyurethane dispersion were used as seeds during the polymerization of acrylic component: methyl methacrylate (MMA), butyl acrylate (BA), and a mixture of MMA and BA with the ratio of 1:1. These emulsions were found to form structured polymer particles in aqueous media using scanning electron microscopy. The kinetics of the emulsion polymerization was studied on the basis of Wessling's model. The influence of emulsifier and initiator concentrations, including the monomer feed rates, R_m, on the rates of polymerization and on the properties of the resulting dispersions were studied. The number of particles and the particle size were also measured during the polymerization process. The final values were found to be independent of the concentration of the emulsifier, initiator and the monomer feed rate in monomer starved conditions. In the steady‐state conditions, during the seeded semibatch hybrid emulsion polymerization, the rate of polymerization and the monomer feed rate followed the Wessling relationship 1/R_p = 1/K + 1/R_m. The dispersions MMA/PU, BA/PU, and MMA/BA/PU have K values of 0.0441, 0.0419 and 0.0436 mol/min, respectively. The seeded BA/PU hybrid polymerization proceeded according to Smith‐Ewart Case I kinetics, while the MMA/PU hybrid emulsions demonstrate Case II of the Smith‐Ewart kinetic model. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 84: 2639–2649, 2002     

CONTROL OF A CONTINUOUS POLYMERIZATION REACTOR BY WIENER INPUT/OUTPUT DATA-BASED PREDICTIVE CONTROLLER WITH DIRECT INVERSE IDENTIFICATION

This article reports an experimental study for the identification and predictive control of a continuous methyl methacrylate (MMA) solution polymerization reactor. The Wiener model was introduced to identify the polymerization reactor in a more efficient manner than the conventional methods of Wiener model identification. In particular, the method of subspace identification was employed and the inverse of the nonlinear part was directly identified. The input variables in this work were the jacket inlet temperature and the feed flow rate, while the monomer conversion and the weight average molecular weight were selected as the output variables. On the basis of the identified model a Wiener-type input/output data-based predictive controller was designed and applied to the property control of polymer product in the continuous MMA polymerization reactor by conducting an on-line digital control experiment with online densitometer and viscometer. Despite the complex and nonlinear characteristics of the polymerization reactor, the proposed controller was found to perform satisfactorily for property control in the multiple-input multiple-output system with input constraints for both set-point tracking and disturbance rejection. This was also confirmed by simulation results.     

CONTROL OF A CONTINUOUS POLYMERIZATION REACTOR BY WIENER INPUT/OUTPUT DATA-BASED PREDICTIVE CONTROLLER WITH DIRECT INVERSE IDENTIFICATION

This article reports an experimental study for the identification and predictive control of a continuous methyl methacrylate (MMA) solution polymerization reactor. The Wiener model was introduced to identify the polymerization reactor in a more efficient manner than the conventional methods of Wiener model identification. In particular, the method of subspace identification was employed and the inverse of the nonlinear part was directly identified. The input variables in this work were the jacket inlet temperature and the feed flow rate, while the monomer conversion and the weight average molecular weight were selected as the output variables. On the basis of the identified model a Wiener-type input/output data-based predictive controller was designed and applied to the property control of polymer product in the continuous MMA polymerization reactor by conducting an on-line digital control experiment with online densitometer and viscometer. Despite the complex and nonlinear characteristics of the polymerization reactor, the proposed controller was found to perform satisfactorily for property control in the multiple-input multiple-output system with input constraints for both set-point tracking and disturbance rejection. This was also confirmed by simulation results.     

Non-linear bifurcation analysis of the living nitroxide-mediated radical polymerization of styrene in a CSTR

In this paper, the non-linear behavior of the styrene nitroxide-mediated radical polymerization (NMRP) taking place in a continuous stirred tank reactor (CSTR) is studied. The cooling water flow rate, feed stream temperature, cooling water feed temperature, monomer feed stream concentration and residence time were chosen as the bifurcation parameters. Typical hysteresis behavior was found for this reactor, making necessary the use of a control scheme to operate in potential regions of interest. Input multiplicities, as well as disjoint bifurcations and isola behavior were found, making the reactor to be prone to operability and control problems.     

Synthesis of nanosize poly(methyl methacrylate) microlatexes with high polymer content by a modified microemulsion polymerization

Summary Nanosize poly(methyl methacrylate) (PMMA) microlatexes with high PMMA/surfactant ratio have been successfully prepared by a modified microemulsion polymerization, i.e., continuous and slow addition of monomer (MMA) to the polymerizing MMA microemulsion with mild stirring. Number-average diameters of 33–46 nm with narrow polydispersity (D_v/D_n= 1.1) and polymer content of 6–24 wt% were achieved using low levels of surfactant (dodecyltrimethylammonium bromide, DTAB) — less than 1 wt% of the reaction mixture. Particle diameter depended on polymerization temperature, MMA content, and concentrations of initiator and surfactant. Larger particles wereformed when temperature was too high, initiator concentration was too high, or surfactant concentration was too low. Received: 24 February 1998/Accepted: 24 March 1998     

Experimental study and model simulation of a two-stage continuous polymerization process for polystyrene

Free radical solution polymerization of styrene in two stage polymerization process has been studied using a binary mixture of symmetrical bifunctional initiators. The continuous reactor system was composed of two reactor units; a prepolymerization reactor (e.g. stirred tank reactors) and a filled tubular reactor packed with static mixers. When the stirred tank reactor was used as a prepolymerizer, a feed stream to the filled tubular reactor was more viscous than the monomer/solvent mixture. It was of interest to investigate how the performance of the filled tubular reactor has been investigated by the feed of viscous prepolymer solution. A dynamic model of the continuous two stage polymerization process was presented by experimental data and model simulation. A reasonably good agreement between the model and the experimental data was obtained without using any adjustable parameters. The experimental results of the two stage polymerization were compared with the results without prepolymerization reactor. It was found that the addition of a prepolymerization reactor has almost no effect on the performance of the filled tubular reactor.     

Plasma-induced polymerization

Summary The plasma-induced bulk copolymerization of alphamethyl styrene (MS) with methyl methacrylate (MMA) and with acrylonitrile (AN) was studied at room temperature. The reactivity ratio values: MMA — MS r_MMA= 0.42 r_MS= 0.22 AN — MS r_AN = 0.03 r_MS= 0.14 as well as the configurational parameter = 0.21 for the first system indicate that both systems can be described by the simple terminal model, neglecting the depolymerization reactions.     

Polymerization of styrene in a continuous filled tubular reactor

Free radical solution polymerization of styrene has been studied using a binary mixture of symmetrical bifunctional initiators in a filled tubular reactor packed with static mixers. Owing to intensive radial mixing induced by the static mixers, a near plug flow pattern was obtained in the reactor with some axial dispersion effect. The axial mass dispersion coefficient was determined from the residence time distribution experiment and a dynamic axial dispersion model has been developed and solved to investigate steady state and transient behavior of the filled tubular reactor. With a solvent volume fraction of 0.3, the monomer conversion up to 70% was obtained without fouling problems in the temperature range 90 to 120°C. The experimental filled tubular reactor was operated under various reaction conditions and a reasonably good agreement between the model and the experimental data was obtained without using any adjustable parameters.