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.     

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。     

Free‐radical solution polymerization of styrene in a tubular reactor—effects of recycling

The styrene free‐radical solution polymerization reaction in a tubular loop reactor is studied here both experimentally and through simulation. An attempt is made to compare the performances of tubular loop reactors when the recycle ratio is varied, based on steady‐state and dynamic responses and on the quality of the polymer produced at different conditions. It is shown here that steady‐state responses of loop reactors and traditional tubular reactors are very similar as far as the quality of the polymer obtained is concerned. Therefore, the recycle ratio cannot be used as a fundamental operation parameter for grade transitions at plant site. However, it is also shown that the recycling of polymer material is very important to accelerate the attainment of the final steady‐state in tubular reactor configurations, because recirculation of material homogenizes the distorted radial profiles of the axial flow velocities.     

Phase behavior analysis for industrial polymerization reactors

The production of polymer is a very important sector in the chemical processing industry as demand for polymeric materials increases, and these polymerization processes exhibit nonlinear dynamics posing difficulties on process operation and control. It is desirable to understand the relationship between open‐loop controllability and process conditions. The phase behavior that is an open‐loop indicator of the controllability for the methyl methacrylate and propylene polymerization reactor over the entire feasible operating region is determined, and the influences of design/operating parameters and model uncertainties on this inherent characteristic at the design stage are analyzed. Based on zero dynamics and singularity theory, directly in the nonlinear setting, a methodology for the preliminary analysis of the phase behavior over the whole feasible operating region is presented and applied into the above two reactors. The above research results demonstrate that to modify certain parameters in certain direction would improve the controllability and are expected to provide helpful guidelines for improving plant and control system design. This is desirable because it allows identification of the cause of the limitation to give an indication where to modify the design. © 2010 American Institute of Chemical Engineers AIChE J, 57: 2795–2807, 2011     

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.     

The mixing effect on the free radical MMA solution polymerization

Mathematical models of reactors for the polymerization of methylmethacrylate (MMA) have been developed and analyzed to elucidate reactor dynamics and to determine conditions for improved operation. The effects of mixing and heat transfer in an MMA polymerization reactor system have been explored by the development of an imperfect mixing model. To model imperfect mixing in polymerization, a reactor configuration using two tanks in parallel was used. Bifurcation diagrams developed using numerical analysis of the model have been drawn with two variable parameters, an exchange ratio, σ, and a volume ratio, κ. We use feed and coolant temperatures as bifurcation parameters. If variable parameters are small, the lower solution branch of the steady state solutions is quite different from that of a simple model that assumes perfect macro-mixing as bifurcation parameters change. If σ increases (κ=0.1, σ=1.0), the shape of a steady state solution curve differs significantly from that of a simple model as the feed temperature decreases.     

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.     

Numerical simulation of liquid-solid two-phase flow in a tubular loop polymerization reactor

Understanding hydrodynamics of tubular loop reactors is crucial in proper scale-up and design of these reactors. Computational fluid dynamics (CFD) models have shown promise in gaining this understanding. In this paper, a three-dimensional (3D) CFD model, using a Eulerian-Eulerian two-fluid model incorporating the kinetic theory of granular flow, was developed to describe the steady-state liquid-solid two-phase flow in a tubular loop propylene polymerization reactor composing of loop and axial flow pump. Corresponding simulations were carried out in the commercial CFD code Fluent. The entire flow field in the loop reactor was calculated by the model. The predicted pressure gradient data were found to agree well with the classical calculated data. Furthermore, the model was used to investigate the influences of the circulation flow velocity and the sold particle size on the solid hold-up. The simulation results showed that the solid hold-up has a relatively uniform distribution in the loop reactor at small particles in volume and high-circulation flow velocities.     

Use of bifurcation analysis for development of nonlinear models for control applications

Nonlinear system identification poses challenging questions because a closed general theory is not available for this field. Particularly, nonlinear models based on neural networks (NN) may present incompatible general dynamic process behavior, leading to improper closed-loop responses, even when they allow for satisfactory one step ahead prediction of process dynamics, as required by traditional validation methods. It is shown here that performing detailed bifurcation and stability analysis may be very helpful for the adequate development and implementation of nonlinear models and model based controllers. The study of many parameters that are defined a priori during the training of the NN shows that the spurious dynamic behavior is related mostly to the use of incomplete data sets during the learning process. This is an indication that, for each kind of process, the number, range and distribution of the data points in the operation region of interest are of paramount importance for proper training of the nonlinear model. Strategies to improve the quality of the training procedure are provided and analyzed both theoretically and experimentally, using the solution polymerization of styrene in a tubular reactor as a case study.     

Dynamic behavior of a continuous autothermal isobutylene polymerization reactor

Industrial autothermal cationic isobutylene polymerization reactors may present very complex dynamic behavior and difficult operation. A mathemathical model was developed to describe the operation of an autothermal solution industrial reactor, and some possible sources of complex dynamical behavior were analyzed. The results obtained indicate that the most probable source of the complex behavior observed industrially is the existence of adventitious impurities in the feeed stream. The effects caused by the presence of adventitious impurities on process operation and product properties were investigated for both polymerization and oligomerization. In the first case, impurities influence the reactor productivity but do not change the polymer quality. In the oligomerization, both the polymer quality and the reactor productivity are seriously affected by the existence of impurities in the feed stream. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 1403–1413, 1997     

Bifurcation control and eigenstructure assignment in continuous solution polymerization of vinyl acetate☆

The major difficulty in achieving good performance of industrial polymerization reactors lies in the lack of under-standing of their nonlinear dynamics and the lack of wel-developed techniques for the control of nonlinear pro-cesses, which are usually accompanied with bifurcation phenomenon. This work aims at investigating the nonlinear behavior of the parameterized nonlinear system of vinyl acetate polymerization and further modifying the bifurcation characteristics of this process via a washout filter-aid control er, with all the original steady state equilibria preserved. Advantages and possible extensions of the proposed methodology are discussed to provide scientific guide for further controller design and operation improvement.     

Effect of Polymer Particle Size and Inlet Gas Temperature on Industrial Fluidized Bed Polyethylene Reactors

Static and dynamic bifurcation behaviors dominate the operation of fluidized bed catalytic reactors for the production of polyethylene (UNIPOL Process) and have important implications on the safe operating temperature and polyethylene production rate. The investigations show that the multiplicity of the steady state phenomenon covers a wide range of parameters together with the phenomenon of periodic oscillations with sharply changing amplitudes with a change of the chosen bifurcation parameter. In some cases, the periodic branches terminate through periodic limit point (PLPs), while in other cases it terminates homoclinically. A detailed parameteric investigation using two-parameter continuation diagrams for the loci of static and Hopf bifurcation points as well as one parameter bifurcation diagrams shows that it is possible to increase the productivity of the unit considerably without exceeding the constraints of the polymer melting point. Gas feed temperature, catalyst feed rate, and polymer particle size distribution are important operating parameters in polyethylene fluidized bed reactors. Gas velocity plays a significant role in keeping the fluidized bed bubbling in addition to the fact that it acts as a cooling media by removing excess heat generated from the polymerization reaction. The kinetic behavior of the catalyst and effect of reactor temperature on product properties require, in some cases, operating just below the softening point of the polymer which requires a suitable controller to avoid polymer melting.     

新型连续乳液聚合反应器

介绍了4种主要连续乳液聚合反应器的研究新进展,包括连续搅拌釜式反应器、连续环管式反应器、脉冲填料塔式反应器及库爱特-泰勒旋流式反应器。提出了连续乳液聚合反应器的发展方向。     

Die maximal durchmischte Zwillingsschlaufe. Ein erweitertes Schlaufenmodell für isotherme,homogene reaktionen

The total range of reactor performance, that is between the PFR and the whole reactor volume being a stagnant zone, may be represented by the three parameter twin loop model. The two basic assumptions made in the model—plug-flow with no longitudinal mixing in each loop, as well as immediate mixing of the two recycling streams and the inflow on the molecular scale (maximum mixedness)—are fairly well achieved in large-scale reactors. Consequently, such reactors are easy to calculate without scale-up problems. At constant mean residence time the three parameters—total recycle number, partial recycle number, ratio of recycle times—can be varied independently. Thus, the twin loop is rather adaptable and easy to control.     

稀土异戊橡胶聚合工艺分析

从稀土异戊二烯聚合反应动力学出发,以2万t/a异戊橡胶生产装置为例,对其聚合单元首釜进行热稳定性分析,发现缩短原料在第一聚合釜内的停留时间,能够降低第一聚合釜的转化率,可以有效地提高第一聚合釜的热稳定性;对不同形式的搅拌器对釜内物料的返混效果进行了比较,采用内外反向双螺带聚合釜,釜内温度梯度小,催化剂浓度和活性均匀,避免了局部温度和催化剂浓度过高;优化第一与第二聚合釜之间管线走向,可以在一定程度缓解首釜至二釜之间管线挂胶的情况。     

New Integrated Catalytic Membrane Processes for Enhanced Propylene and Polypropylene Production

Newly reported integrated processes are discussed for aliphatic (paraffin) hydrocarbon dehydrogenation into olefins and subsequent polymerization into polyolefins (e.g., propane to propylene to polypropylene, ethane to ethylene to polyethylene). Catalytic dehydrogenation membrane reactors (permreactors) made by inorganic or metal membranes are employed in conjunction with fluid bed polymerization reactors using coordination catalysts. The catalytic propane dehydrogenation is considered as a sample reaction in order to design an integrated process of enhanced propylene polymerization. Related kinetic experimental data of the propane dehydrogenation in a fixed bed type catalytic reactor is reviewed which indicates the molecular range of the produced C₁-C₃ hydrocarbons. Experimental membrane reactor conversion and yield data are also reviewed. Experimental data were obtained with catalytic membrane reactors using the same catalyst as the non-membrane reactor. Developed models are discussed in terms of the operation of the reactors through computational simulation, by varying key reactor and reaction parameters. The data show that it is effective for catalytic permreactors to provide streams of olefins to successive polymerization reactors for the end production of polyolefins (i.e., polypropylene, polyethylene) in homopolymer or copolymer form. Improved technical, economic, and environmental benefits are discussed from the implementation of these processes.     

Control of a chaotic polymerization reactor: A neural network based model predictive approach

Continuous polymerization processes may be very sensitive to small changes of the operation conditions. Continuous VA (vinyl acetate) solution homopolymerization reactors may present multiple steady-states and oscillatory behavior. A predictive control scheme that uses an internal model of the process is employed to stabilize such reactors and make them less sensitive to disturbances while subject to “hard” control action constraints. An ANN (artificial neural network) is used as the internal model, leading to fairly good predictions of the reactor behavior, including its multiplicities. The performance of the resulting control algorithm is compared to that of a “well-tuned” conventional proportional-integral-derivative (PID) controller.     

苯乙烯连续搅拌釜式本体聚合工业过程模拟

采用了机理分析建模法对苯乙烯工业本体预聚过程进行了模型化研究，并通过对流体在反应器中混合模式的分析，表明预聚釜可视作全混流（CSRT）反应器模型，此外对热聚合机理中的引发级数和终止反应进行了考察，利用预聚釜的工业数据确立了三分子引发，同时考虑偶合和歧化终止以及向溶剂链转移的反应机理模型，并选取了合适的动力学参数，然后利用工业装置采集的数据进行了模拟，从宏观转化率，平均分子量和微观分子量分布两个方面对模型进行了验证，模拟结果和工业数据符合得较好，该模型方程不仅能模拟稳态，非稳态预聚过程，同时也为装置开发新产品，改造扩建，优化操作方案等提供了理论基础。     

Dynamics of continuous isobutylene cationic polymerizations

Polyisobutylene can be produced in either continuous cationic precipitation or solution polymerization reactors. It is known that the open-loop behavior of polymerization reactors may be very complex and may lead to oscillatory behavior, which is usually caused by thermal positive feedback (due to the large heats of reaction of polymerization reactions) and high viscosity effects (such as the gel effect in radical polymerization reactors and the decrease of heat transfer coefficients at high polymer concentrations). Oscillatory behavior may be observed in industrial isobutylene reactors, and it is intended to know whether these oscillations are inherent to the kinetic mechanism. Based on published experimental data, mathematical models are developed for both solution and precipitation processes. Steady-state solutions are calculated and steady-state stability is analyzed. Dynamic simulations and stability results reveal that only single stable steady-state solutions are possible for such reactors at usual operation conditions, which means that oscillatory behavior is not intrinsic to the reaction mechanism. © 1996 Wiley & Sons, Inc.     

Einfluss der Wechselwirkung von Reaktion und Fluiddynamik auf das Verhalten von Strahlschlaufenreaktoren

Jet loop reactors are used as apparatus to facilitate chemical or biological reactions. This type of apparatus is characterized by an internal circulation flow, essentially driven by the injection of liquid. The nozzle can also be used to inject and disperse gas. The internal fluid dynamics and thus the reactor behavior is significantly determined by the introduced momentum and by the internal gas distribution. To describe the mutual influence of a gas-consuming reaction and the internal fluid dynamics, a simplified model based on a momentum balance and a material balance was used. From the exemplary calculations, a critical range for non-selective reactions and for fluid dynamic stability is given.