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.     

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.     

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.     

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。     

Analysis of an LDPE compact autoclave reactor by two-cell model with backflow

A two-cell model with backflow and heat exchange is developed to analyze the dynamics of an LDPE compact autoclave reactor. The backflow exists between the two mixing cells and represents the degree of mixing within the reactor. The performance of the reactor and the physical properties of the product polymer such as the number average molecular weight and the polydispersity are investigated under various operating conditions, especially when the initiator feed concentration is varied. Bifurcation diagrams are constructed by taking the initiator feed concentration as the bifuracation parameter and the dynamic feature in the feasible parameter ranges for operation are carefully examined. Indeed, various dynamic characteristics are observed by performing numerical analysis of the nonadiabatic system with the internal cooling device. As the rate of heat transfer increases, various multiplicity patterns and oscillatory behavior such as the limit cycle and the focus are found. The reactor behavior even undergoes period doubling and gradually gives rise to a chaotic behavior in certain ranges of the initiator feed concentration when the coolant temperature becomes low. The existence of chaos is examined by the phase plane plot and Poincaré map. Apparently, the monomer concentration can be substantially increased with proper heat removal and initiator supplement scheme. For this, however, the complex dynamic features must be taken into account in the reactor design.     

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.     

Analysis of a CFSTR with two consecutive reactions in transient states

The sensitivity of a chemical reactor is defined by the matrix which relates the steady state gain of output variables to unit step changes in input variables. This definition proves applicable to reactors with arbitrary residence time distributions. The sensitivity calculation is illustrated by treating a specific example. Three ordinary differential equations which govern (he transient behavior of a CFSTR with two consecutive reactions are numerically solved to demonstrate the parametric sensitivity and temperature runaway phenomena for some parameters such as the feed temperature, the feed concentration, the heat transfer coefficient and the wall temperature. The estimation of the regions of parametric sensitivity is briefly discussed.     

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.     

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.     

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.     

搅拌塔式反应器传热特性研究

分析了搅拌塔式反应器（ＳＣＲ）中多级冷却盘管隔板的传热特性,用稳态和非稳态的传热方法进行了实验研究。提出了同时考察拌雷诺数和轴向液流雷诺数影响的ＳＣＲ中多级冷却盘管隔板表面传热膜系数的关联式。研究结果表明,对于ＳＣＲ中冷却盘管隔板表面的传热膜系数,轴向液轩诺系数的影响与搅拌雷诺数的影响相比具有同等的重要性。     

Analysis of Steady‐State Temperature Profiles from a Laboratory Reactor by Means of a Process Simulator

A process simulator was used for the analysis of steady‐state results from a laboratory‐scale tubular reactor for the oxidation of carbon monoxide over a platinum catalyst. From a set of 14 steady‐state experiments, temperature profiles were simulated with two adjustable parameters recovered by optimizing the fit: k°, the pre‐exponential portion of the rate constant, and h_out, the outer wall heat transfer coefficient for the reactor tube. Simulation showed that despite elaborate insulation the reactor did not behave adiabatically. Simulation also predicted fairly well the magnitude of phenomena such as ignition, extinction, and rate hysteresis (caused by changes in feed temperatures or concentrations) but at temperatures below the experimental values.     

Dynamic modeling and simulations of the behavior of a fixed‐bed reactor‐exchanger used for CO2 methanation

A multidimensional heterogeneous and dynamic model of a fixed‐bed heat exchanger reactor used for CO₂ methanation has been developed in this work that is based on mass, energy and momentum balances in the gas phase and mass and energy balances for the catalyst phase. The dynamic behavior of this reactor is simulated for transient variations in inlet gas temperature, cooling temperature, gas inlet flow rate, and outlet pressure. Simulation results showed that wrong‐way behaviors can occur for any abrupt temperature changes. Conversely, temperature ramp changes enable to attenuate and even fade the wrong‐way behavior. Traveling hot spots appear only when the change of an operating condition shifts the reactor from an ignited steady state to a non‐ignited one. Inlet gas flow rate variations reveal overshoots and undershoots of the reactor maximum temperature. © 2017 American Institute of Chemical Engineers AIChE J, 64: 468–480, 2018     

Maximum production of methanol in a pilot-scale process

Mathematical models for both bench- and pilot-scale methanol synthesis reactors were developed by estimating the overall heat transfer coefficients due to different heat transfer characteristics, while the effectiveness factor was fixed because the same catalysts were used in both reactors. The overall heat transfer coefficient of a pilot-scale reactor was approximately twice that of a bench-scale reactor, while the estimate from the correlation reported for the heat transfer coefficient was 1.8-times higher, indicating that the values determined in the present study are effective. The model showed that the maximum methanol production rate of approximately 16 tons per day was achievable with peak temperature maintained below 250 °C in the open-loop case. Meanwhile, when the recycle was used to prevent the loss of unreacted gas, peak temperature and production rate decreased due to low CO and CO₂ fraction in the recycled stream at the same space velocity as the open-loop operation. Further analysis showed that, since the reaction was in the kinetic regime, the production rate could be maximized up to 18.7 tons per day by increasing the feed flowrate and inlet temperature despite thermodynamically exothermic reaction.     

Bifurcation Analysis of the Fluidized Bed Polyethylene Reactor with Internal Cooler

A mathematical model has been developed to simulate a gas‐phase ethylene polymerization reactor with internal cooler. The model was analyzed to determine the effects of reactor operating conditions on dynamics and stability. The reactor model employed assumed that both the gas and polymer phase in the reactor are well mixed. Comparing the present model to one with external heat exchanger confirms that, in either form, gas‐phase polyethylene reactors are prone to show unstable steady states, limit cycles and excursions toward unacceptably high temperature steady states. It was also observed that, with internal cooler, minor design changes in the cooler area available for heat transfer and in the inlet temperature of the coolant have a significant effect on the low stable steady state range of catalyst feed rates. With internal cooler, the suitable operating range increased with the increase in the area available for heat transfer. This effect is insignificant in the case of a reactor with external heat exchanger. Manipulating the reactor coolant inlet temperature and/or gas velocity can increase the stability range in the reactor with internal cooler as against one with external heat exchanger.     

Experimental studies of a consecutive—competitive reaction in steady state and forced periodic CSTRs

Experimental studies of diethyl adipate saponification in a CSTR show that forced cycling of feed composition produces significant yield increases in intermediate product relative to the optimal steady state operation, while forced temperature cycling has much less effect. Related experiments provide useful transient heat transfer data for this system. Reaction kinetics have been determined in water and in a 50% (v/v) isopropanol solvent.     

Dynamic Analysis of Thermal Behaviour of a Laboratory Reactor Using a Process Simulator

A process simulator was used to study dynamic results from a laboratory‐scale tubular reactor for the oxidation of carbon monoxide (CO) with oxygen over Pt/alumina catalyst. Passive response experiments were used to obtain lumped values of the heat capacity and the overall heat transfer coefficient. Temperature profile experiments were used to obtain the only adjustable kinetic parameter: k°, the pre‐exponential portion of the rate constant. Integral reactor phenomena were studied: step‐decreases in the feed temperature, step‐changes in feed concentration, and ignition of the reactor by pressure. Simulated results provided good agreement with experiments.     

Heat transfer coefficient in a high pressure tubular reactor for ethylene polymerization

Heat transfer in tubular reactors for the high pressure polymerization of ethylene is very complex, since these tubular reactors are usually divided into several zones that exhibit different flow patterns and critical fouling behavior. The correct estimation of the overall heat transfer coefficient along the reactor axial distance is a major issue when assessing the predictive capabilities of a mathematical model for the process. In general, previous models employed either constant heat transfer coefficients or the usual correlations for the Nusselt number. Neither of these two approaches is accurate enough to allow a correct prediction of the reactor behavior with respect to temperature profiles and product molecular properties. The present work performs a more comprehensive estimation of the heat transfer coefficient in these reactors. At a first stage the overall heat transfer coefficients were estimated by using approapriate energy balances and a good set of experimental data. Then, a predictive model was proposed for the overall heat transfer coefficient. All flow regimes, as well as fouling effects, were taken into account, and the parameter estimation was based on temperature profiles obtained from an industrial reactor. The temperature profiles, conversions, pressures and molecular properties calculated by means of the experimentally fitted heat transfer coefficients or with the predictive model showed good agreement with plant data.     

CFD analysis of hydrodynamic, heat transfer and reaction of three phase riser reactor

Catalytic cracking reaction and vaporization of gas oil droplets have significant effects on the gas solid mixture hydrodynamic and heat transfer phenomena in a fluid catalytic cracking (FCC) riser reactor. A three-dimensional computational fluid dynamic (CFD) model of the reactor has been developed considering three phase hydrodynamics, cracking reactions, heat and mass transfer as well as evaporation of the feed droplets into a gas solid flow. A hybrid Eulerian-Lagrangian method was applied to numerically simulate the vaporization of gas oil droplets and catalytic reactions in the gas-solid fluidized bed. The distributions of volume fraction of each phase, gas and catalyst velocities, gas and particle temperatures as well as gas oil vapor species were computed assuming six lump kinetic reactions in the gas phase. The developed model is capable of predicting coke formation and its effect on catalyst activity reduction. In this research, the catalyst deactivation coefficient was modeled as a function of catalyst particle residence time, in order to investigate the effects of catalyst deactivation on gas oil and gasoline concentrations along the reactor length. The simulation results showed that droplet vaporization and catalytic cracking reactions drastically impact riser hydrodynamics and heat transfer.