Simulation and optimization of the continuous tower process for styrene polymerization

The continuous tower process, a popular industrial process for the manufacture of polystyrene, was simulated and optimized. A kinetic model for the thermal polymerization of styrene, which takes into account the Trommsdorff effect and the volume change accompanying the reaction, was developed. This was used to formulate model equations for the continuous flow stirred tank reactor (CSTR) and plug flow reactor (several sections) in the tower process. The model can predict monomer conversion, number‐ and weight‐average molecular weights, polydispersity index (PDI), and temperature at various locations in the unit, under specified operating conditions. Multiobjective optimization of this process was also carried out, for which an adaptation of a genetic algorithm (GA) was used. The two objectives were maximization of the final monomer conversion and minimization of the PDI of the product. The conversion in the CSTR was constrained to lie within a desired range, and polymer having a specified value of the number‐average molecular weight was to be produced. The optimal solution was a unique point (no Pareto sets were obtained). The optimal solutions indicated that the tower process is operated under near‐optimal conditions. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 775–788, 2004     

A numerical study on the effects of acidic catalyst on the polymerization of nylon-6

The effects of acetic acid on the polymerization characteristics of nylon-6 are investigated in a reactor model that consists of a continuous flow stirred tank reactor (CSTR) and a tubular reactor connected in series. Mathematical models for the CSTR and the tubular reactor have been established and solved by numerical methods. In the CSTR, the monomer conversion and the molecular weights are increased as the feed acetic acid concentration is increased. In the tubular reactor, the acid acts as both a catalyst and a modifier for the polymerization reaction. The effects of the feed acetic acid content on the zeroth, first and second moments and the polydispersity index of the polymer have been discussed.     

FBR for catalytic propylene polymerization: Controlled mixing and reactor modeling

Particle mixing and segregation have been studied in a small-scale fluidized-bed reactor (FBR) under pressure. The solids mixing is relatively faster than the residence time of catalyst particles in the case of a polymerization process, but smaller particles accumulate in the upper zone. Semibatch propylene polymerization experiments showed that the vertical temperature gradients are caused mainly by catalyst segregation. At low gas velocities, segregation and mixing can differ under reacting conditions compared to nonreacting conditions due to particle–particle interactions. Catalyst concentration gradients caused by incomplete mixing are strengthened remarkably by the exothermic reaction even at low polymerization rates. These observations do not represent an industrial situation. The FBR has therefore been equipped with a draft tube and cone to control vertical solids mixing. The internal solids circulation rate is a nonlinear function of the gas velocity. Strongly reduced segregation, elutriation, and entrainment observed were compared to experiments without a draft tube. Temperature profiles observed during polymerization can be controlled by the solids circulation rate. Hydrogen injections led to an instantaneously increased polymerization rate, probably due to the reactivation of dormant sites. Irreversible deactivation rates of dormant and active sites seem to be the same. Moreover, hydrogen appeared to be very effective for widening the molecular-weight distribution. A compartment model developed describes the temperature profile in the reactor and related molecular-weight distribution of the polymer.     

基于动态优化和反馈控制的聚合反应过程牌号切换策略

针对单反应器多牌号聚合物生产过程, 提出一种结合动态优化和反馈控制的牌号切换策略。以实验室规模的连续搅拌釜式反应器中苯乙烯聚合牌号切换为对象, 以原料消耗最少为优化目标, 利用迭代动态规划求得切换过程中反应条件和产品性能指标的优化轨迹。引入针对反应温度的路径约束, 使优化后的切换轨迹更易跟踪实现, 防止过渡过程中变量的剧烈波动。仿真结果表明, 这一切换策略可以显著减少牌号切换过渡时间及过渡过程中原料的消耗量, 并能够有效克服进料温度变化的干扰。     

CLOSED-LOOP CONTROL OF A SEEDED CONTINUOUS EMULSION POLYMERIZATION REACTOR SYSTEM

A reactor configuration for continuous emulsion polymerization is proposed consisting of a plug flow reactor followed by a train of CSTR's. Monomer conversion is controlled by manipulating the quantity of water and monomer which are allowed to bypass the plug flow reactor and enter the first CSTR directly. A multivariate pole-placement adaptive controller is used to implement the controls. Simulation results indicate good control of both conversion and particle size. Open-loop experimental results indicate the effectiveness of the plug flow reactor for eliminating the oscillations sometimes found in CSTR emulsion polymerization.     

Anionic polymerization of styrene: The search for an industrial process

Anionic polymerizations were carried out in the laboratory using a CSTR reactor design and conditions typical of current commercial mass polystyrene plants. Polystyrene having excellent color and polydispersity was produced. Polymer quality, styrene conversion, and molecular weight control were all linked to use of polymerization feed of consistently high purity and polymerization in the 90–110°C temperature range. The results of this study clearly show that high quality polystyrene can be made utilizing anionic polymerization chemistry in existing well mixed mass polystyrene reactors of the CSTR design. The key to the successful practice of this technology is the ability to produce consistently high purity polymerization feed.     

Multiple steady states,viscosity, and high conversion in continuous free-radical polymerization

Using existing literature data on the rate of a bulk polymerization of styrene in a batch reaction carried to high conversion, it is mathematically demonstrated that there is a clear possibility of the existence of multiple steady states induced by viscosity effects in isothermal continuous stirred tank reactors. In solutions of high viscosity, the rate of free-radical polymerization increases with conversion, reaching a peak at very high viscosity, then falling off rapidly. Given this sort of behavior, it is demonstrated mathematically that steady-state mass balance solutions are possible at three levels of conversion. The lower and higher steady states are stable while the middle steady-state condition is shown to be necessarily unstable. This multiplicity of steady states with its particular problems of stability is analogous to the much studied phenomena of temperature stability. It is closely related to the problems of concentration stability characteristic of autocatalytic and heterogeneous catalytic reactions. This multiple steady-state problem is qualitatively discussed in relation to reactor stability, control, and optimization.     

Periodic control of continuous stirred tank reactors—II Cases of a nonisothermal single reactor

The optimal periodic control of a single nonisothermal CSTR in which a single reaction, a parallel reaction or a consecutive reaction is taking place is studied. Both the feed rate and the heat transfer between the reactor content and the immersed coil are periodically controlled. Utility consumption and conversion of the raw material into the waste are included in the performance index together with conversion into the desired product. The results indicate a respectable improvement in the reactor performance.     

Optimization of polymer synthesis through distributed control of polymerization conditions

An optimal control methodology is applied to the goal of lowering polydispersity while increasing conversion in polymerization reactions. An illustration using initiator, heat, and monomer flux control profiles for free‐radical polymerization of styrene in a plug flow reactor is provided and compared with available experimental data. The design calculations use a kinetic model that includes the gel effect. The reactor designs show that distributed initiator, heat, and monomer fluxes along the length of the reactor lower the polydispersity of the styrene polymers and increase conversion for a given reaction time. The monomer flux maintains a nearly constant monomer concentration in the reactor. The initiator and heat fluxes are highly correlated. The temperature rises as a result the heat flux; but the initiator flux results in a lower initiator concentration relative to the initiator cofeed case. At a reaction time of 120 min, a conversion of 44% and a polydispersity of 1.73 have been achieved. The theoretical designs, although not proven to be globally optimal, are of high quality. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2922–2928, 2002     

工业聚合反应装置 Ⅳ．乳液聚合反应器（上）

比较了乳液聚合用间歇聚合釜和连续搅拌釜式反应器操作中的反应工程特性，并根据这些特性介绍了间歇式和连续式乳液聚合反应器，除釜式外还有环管式和脉冲填料塔等新型反应器，同时还相应讨论了乳液聚合过程反应热的撤除以及传热设备。     

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.     

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.     

聚合与混合

以化学反应工程观点对聚合物制造过程进行工程分析。着重阐述了聚合过程中粘度变化对物系传热传质状态和反应动力学的影响,以及对聚合反应器性能,以至对聚合物产品性能的影响。针对增粘过程的搅拌,异粘流体的调匀、粘稠物系的微观混合和非均相体系的产品粒度分布这4类典型的聚合过程课题,分析了各自的混合规律、提出了改进聚合反应器性能,提高产品质量的控制因素及其控制对策。     

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.     

Multiobjective dynamic optimization of batch free radical polymerization process catalyzed by mixed initiator systems

The optimal control policies for batch free radical polymerization of styrene catalyzed by a binary mixture of monofunctional initiators have been determined using a multiobjective dynamic optimization technique. The process objectives considered in the optimization include monomer conversion, polymer molecular weight, initiator residue level, and total reaction time. It is illustrated through model simulations and experiments that the performance of the batch polymerization process can be improved significantly through the use of optimal initiator mixture and polymerization temperature programming. This paper also illustrates how the multiobjection optimization technique can be used effectively to solve complex polymerization reactor optimization problems with detailed reaction models.     

聚乙交酯的合成

利用搅拌反应釜合成了聚乙交酯(PGA);应用红外光谱、核磁共振等对聚合物的结构进行了表征; 研究了PGA聚合过程中特性粘数、单体转化率、聚合物的热稳定性等的变化。结果表明:聚合物转化率和聚合物特性粘数的变化趋势相同,反应开始阶段变化较慢,随后加快,最后趋于平缓。聚合时间为105 min时, 聚合物的特性粘数达到最大为1．0 dL／g,单体的转化率为99．0％,随着特性粘数的增加,聚合物的热稳定性提高;PGA的流变性能受相对分子质量影响显著,没有反应完全的试样仍具有聚合活性。     

Application of experimental non-linear control based on generic algorithm to a polymerization reactor

The dynamics of free radical polymerization of styrene and on-line control of temperature in a cooling jacketed batch polymerization reactor is investigated. The benzoyl peroxide initiator is introduced into the reactor once at the beginning of the reaction to obtain the desired monomer conversion and the desired average chain length in a minimum reaction time. The optimal constant set temperature, which is generally realized in industrial applications, and the set profile are used as two different optimal operating conditions. The temperature control of the polymerization reactor is achieved experimentally and theoretically. The control of nonlinear systems has progressed considerably, and various nonlinear process model based control techniques have appeared in the literature. The problem is how to tune the controller in order to obtain comparable closed loop responses. Generic model control (GMC) is applied and the performance of the control results are compared with the previously published control results.     

甲基丙烯酸甲酯本体聚合中物性参数的测定及关联

甲基丙烯酸甲酯(MMA)本体聚合过程中比热容、黏度和导热系数等物性参数是影响聚合动力学和体系传热的重要因素.研究了聚合转化率和温度对MMA本体聚合体系密度、比热容、黏度和导热系数的变化,发现随着转化率增大,体系比热容减小,密度、黏度和导热系数增大,并存在黏度发生突变的临界转化率;随着体系温度增大,密度和导热系数减小,比热容和黏度突变对应的临界转化率增大.建立了能描述各物性参数随转化率(聚合物浓度)和温度变化的数学关联式,计算值和实验值吻合较好,建立的各关联式能较好地预测MMA本体聚合中的物性的变化,可为聚合配方及传热的设计提供基础.     

Integration of CFD and polymerization for an industrial scale cis-polybutadiene reactor

A computational fluid dynamics (CFD) approach, coupled with anionic polymerization kinetics, was used to investigate the solution polymerization in a 12?m³ industrial scale cis-polybutadiene reactor. The kinetic model with double catalytic active sites was integrated with CFD by a user-defined function. The coupled model was successfully validated by the plant data and then used to investigate the key operating variables. Also, predictions of CFD model were compared with those of continuous stirred tank reactor (CSTR) model. Although the reaction mixture is well mixed in the middle and at the top of the reactor, there exists a poor mixing feeding zone at the bottom, which leads to serious deviations from the ideal CSTR. The polymerization process with nonideal mixing is very sensitive to the inlet temperature and the feeding rate. Enhancing the mixing performance in the feeding zone could be an effective way to improve the product quality.     

Precipitation polymerization of acrylic acid: Kinetics,viscosity and heat transfer

The free-radical precipitation polymerization of acrylic acid in toluene was studied in an isothermal reaction calorimeter. The polymerization shows an autocatalytic behaviour of the rate of polymerization typical for precipitation polymerizations. The rate of polymerization with respect to conversion can be modeled by taking the volume fraction of the precipitated polymer into consideration. The viscosity of the reaction mixture increases with increasing volume fraction of precipitated polymer. The viscosity runs through a maximum at high conversion. The final viscosity decrease is probably due to shear stress caused aggregation phenomena of the polymer particles. A model is discussed which can describe the increase and decrease of viscosity of the system. By means of reaction calorimetry it is possible to determine the reaction-sided heat transfer coefficient during polymerization. The comparison of the experimentally determined temperature course of the reaction mixture and the temperature course calculated with a coupled model of the polymerization and the calorimeter shows that the heat-transfer characteristic changes instantaneously during a small conversion interval at the very beginning of the polymerization.