Particle size distribution in olefin continuous stirred-bed polymerization reactors

The control of polymer particle size and PSD is of industrial importance. Very fine particles pack poorly, thereby limiting reactor capacity, and present a dust explosion hazard. In olefin polymerization, a particle size distribution (PSD) in the polymerization reactor has been derived using population balances. Three reasonable reaction mechanisms for Ziegler-Natta catalysts, i.e., a simple reaction model, an active site reduction model, and a two sites model, have been used to derive the average number of active sites. It was observed that the PSD depends not only on residence time, but also on the reaction mechanism. It was also found that multiple active sites change the PSD slightly. The PSD, however, does not depend on initial catalyst volume.     

Particle size distribution and its effect on the olefin polymer reactor dynamics over olefin polymerization catalysts with multiple active sites

Mass and energy balances in a reactor have been derived to study the effect of particle size distribution for multiple active site catalyst systems on the reactor dynamics. It was found that multiple active sites in a Ziegler-Natta catalyst affect neither the reactor dynamics nor the particle size distribution, as opposed to a system which uses single site catalysts. It was discovered that a simple reaction model with a single type of active site dominant adequately explains the reactor dynamics and the particle size distributions for a continuous stirred-bed reactor for polymerization of propylene over a Ziegler-Natta catalyst.     

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.     

Coupling of CFD with PBM for a pilot-plant tubular loop polymerization reactor

A computational fluid dynamics model, coupled with population balance model (CFD–PBM), was developed to describe the liquid–solid two-phase flow in a pilot-plant tubular loop propylene polymerization reactor. The model combines the advantage of CFD to calculate the entire flow field and that of PBM to calculate the particle size distribution (PSD). Particle growth, aggregation and breakage were taken into account to describe the evolution of the PSD. The model was first validated by comparing simulation results with the classical calculated data. Furthermore, four cases studies, involving particle aggregation, particle breakage, particle growth or involving particle growth, breakage and aggregation, were designed to identify the model. The entire flow behavior and PSD in the tubular loop reactor, i.e. PSD, solid holdup and liquid phase velocity distribution, were also obtained numerically. The results showed that the model is effective in describing the entire flow behavior and in tracking the evolution of the PSD.     

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.     

Spinning wheel powder feeding device — fundamentals and applications

A spinning wheel powder feeding system has been developed as a conveying mechanism to feed fine particle aggregates on a laboratory scale. An example of a use of this conveying mechanism is with a transport tube reactor, since the reactor only provides a few seconds residence time to react the powder. Methods to shear the powder mechanically, as opposed to using a high gas velocity, are developed as to not reduce the available residence time in the reactor. The objective is to feed a powder at the smallest particle aggregate size possible rather than a large particle aggregate size generated by an upstream feeding device, and to achieve such dispersion using minimized gas flow. Statistical results show that the spinning wheel alone is able to reduce the mean aggregate size of the Particle Size Distribution (PSD) and when a minimal amount of gas is added to the system the PSD is reduced further. In addition, a fundamental model employing a discrete particle aggregate breakage equation combined with a Monte Carlo method has shown that the spinning wheel feeding system is able to consistently reduce particle aggregate size.     

Study of Some Variables Affecting Particle Size and Particle Size Distribution of Suspension Polymerization of Methyl Methacrylate

A laboratory reactor was designed and constructed to study the effect of both speed of agitation and a concentration of suspension stabilizer on particle size and particle size distribution during the suspension polymerization of methyl methacrylate. It was concluded that the average particle size of the prepared polymer powder is directly proportional to the speed of agitation and is inversely proportional to the stabilizer concentration. New empirical equations correlating the average particle size and the particle size distribution (PSD) were derived from the study.     

A CFD‐PBM‐PMLM integrated model for the gas–solid flow fields in fluidized bed polymerization reactors

Although the use of computational fluid dynamics (CFD) model coupled with population balance (CFD‐PBM) is becoming a common approach for simulating gas–solid flows in polydisperse fluidized bed polymerization reactors, a number of issues still remain. One major issue is the absence of modeling the growth of a single polymeric particle. In this work a polymeric multilayer model (PMLM) was applied to describe the growth of a single particle under the intraparticle transfer limitations. The PMLM was solved together with a PBM (i.e. PBM‐PMLM) to predict the dynamic evolution of particle size distribution (PSD). In addition, a CFD model based on the Eulerian‐Eulerian two‐fluid model, coupled with PBM‐PMLM (CFD‐PBM‐PMLM), has been implemented to describe the gas–solid flow field in fluidized bed polymerization reactors. The CFD‐PBM‐PMLM model has been validated by comparing simulation results with some classical experimental data. Five cases including fluid dynamics coupled purely continuous PSD, pure particle growth, pure particle aggregation, pure particle breakage, and flow dynamics coupled with all the above factors were carried out to examine the model. The results showed that the CFD‐PBM‐PMLM model describes well the behavior of the gas–solid flow fields in polydisperse fluidized bed polymerization reactors. The results also showed that the intraparticle mass transfer limitation is an important factor in affecting the reactor flow fields. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1717–1732, 2012     

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。     

State multiplicity in PFR-separator-recycle polymerization systems

This article explores the non-linear behaviour of isothermal and non-isothermal plug-flow reactor (PFR)-separator-recycle systems, with reference to radical polymerization. The steady-state behaviour of six reaction systems of increasing complexity, from one-reactant first-order reaction to chain-growth polymerization, is investigated. In PFR-separator-recycle systems feasible steady states exist only if the reactor volume exceeds a critical value. For one-reaction systems, one stable steady state is born at a transcritical bifurcation. In case of consecutive-reaction systems, including polymerization, a fold bifurcation can lead to two feasible steady states. The transcritical bifurcation is destroyed when two reactants are involved. In addition, the thermal effects also introduce state multiplicity. When multiple steady states exist, the instability of the low-conversion branch sets a lower limit on the conversion achievable at a stable operating point. A low-density polyethylene process is presented as a real plant example.The results obtained in this study are similar to CSTR-separator-recycle systems. This suggests that the behaviour is dictated by the chemical reaction and flowsheet structure, rather than by the reactor type.     

Control of particle size distribution for the synthesis of small particle size high solids content latexes

A polymerization process to synthesize bimodal latexes with maximum particle diameters below 350 nm and solids content above 65 wt% has been developed.The process is based on an iterative strategy to determine the optimal particle size distribution that gives the maximum packing factor for a given range of particle sizes and at a given solids content. The calculated optimal bimodal PSD was experimentally obtained in a seeded semi-continuous emulsion polymerization reaction as follows: in the first step, a polymer seed latex was loaded in the reactor and grown, under monomer starved conditions, until a given particle size. At this point a fraction of the same seed was added to the reactor and the feed was continued until the desired particle size distribution and solids content were achieved. The point at which the seed was added again to the reactor and the amount of seed required were determined by the iterative strategy and depended on the competitive growth rate ratio of large and small particles that is an input for the iterative strategy.Implementation of the solution obtained from the iterative strategy, and for the first time in the open literature, led to the production of a coagulum free and stable bimodal latex with 70 wt% of solids content and particle sizes below 350 nm.     

Dynamic modelling of the continuous emulsion polymerization of vinyl chloride

A dynamic model for the continuous emulsion polymerization of vinyl chloride (VCM) in a train of stirred tank reactors has been developed. This model can predict monomer conversion, polymer particle size distribution (PSD), molecular weight distribution and long and short chain branching frequencies under non-steady reactor operation during startup, reactor switching and during unstable operation when conversion and polymer and polymer particle properties oscillate with time. The model has been used to design a flexible reactor train configuration which operates in a stable mode and can produce latexes with a wide range of properties including a bimodal polymer particle size distribution.     

Integrated run-to-run and on-line model-based control of particle size distribution for a semi-batch precipitation reactor

The dynamics of particle size distribution (PSD) in a precipitation process are represented by a population balance (PB) and related differential–algebraic equations. The control of PSD is studied by using a closed-form solution of the PB. Batch-to-batch control and on-line single batch control strategies are investigated for controlling a semi-batch reactor. A systematic integration of the two strategies is shown to have a complementary effect on the control performance.     

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     

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.     

An Approach for Achieving Unstable Convergence for Non‐Isothermal CSTRs

The nonlinearity introduced by the temperature variation in the non‐isothermal continuous stirred tank reactor (CSTR) exhibits concentration multiplicity for certain parameter ranges. The dynamics of reactor temperature under these conditions would be very difficult to observe and maintain. In this work, a novel algorithm is proposed to stabilize the system by designing a cascade of CSTRs that are capable of achieving this inaccessible steady state. Optimization of reactors parameters is performed in an iterative manner to achieve this solution. For a first‐order reaction rate, this method was successful in achieving the inaccessible steady state temperature of 312.5 K using three CSTRs cascades. The suggested algorithm is presented both graphically as well as using computational optimization techniques. The transient simulation studies using the above three CSTRs showed that the unstable steady state is achieved. The newly designed cascade meets the design criteria and achieves the locally unstable steady state temperature to a high degree of accuracy.     

Inferential closed‐loop control of particle size and molecular weight distribution in emulsion polymerization of styrene

In this work, simultaneous inferential control of particle size distribution (PSD) and molecular weight distribution (MWD) in a semi‐batch emulsion polymerization reactor of styrene has been addressed. Using a comprehensive dynamic model for PSD and MWD predictions and performing a sensitivity analysis, it has been revealed that free surfactant and chain transfer agent (CTA) concentrations in the reactor are the most suitable candidates for inferential control of PSD and MWD, respectively. To control concentrations of these species in the reactor, their inlet feed flow rates are used as manipulated variables. It is assumed that the concentration of CTA is measured infrequently and therefore an open‐looped observer, based on the reaction calorimetry, has been designed to estimate the CTA concentration. The infrequent measurements of CTA concentration are used to correct its estimation. As the online measuring of the ionic free surfactant concentration is also difficult, solution conductivity which is a good indication of free surfactant concentration is used for control purposes. Simulation results show that the performance of the proposed control scheme is satisfactory even in the presence of model mismatch. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

Calculation of the particle size distribution in suspension polymerization using a compartment-mixing model

A modelling strategy for effective estimation of the particle size distribution (PSD) in suspension polymerization is presented. The strategy consists of coupling a population balance equation (PBE) and a compartment-mixing (CM) model to account for the non-homogeneous mixing in the tank reactor. The values for the rate of energy dissipation of each compartment are estimated from Computational Fluid Dynamics (CFD) calculations and experimental reports on systems with the same agitator and geometric characteristics. Model predictions using the CM model are compared with predictions that assume homogeneous mixing and experimental data on PSD from styrene and divinylbenzene pilot-plant suspension polymerization reactors of 1 and 5 L with Rushton and PBT impellers.     

EFFECTS OF HYDROCARBON LIQUID FEED IN POLYETHYLENE POLYMERIZATION PROCESS ON PARTICLE SURFACE TEMPERATURE

In the fluidized bed gas phase polymerization of polyethylene (PE), the heat generated by the exothermic polymerization process is dissipated into the gas mixture flowing past the polymer particles. The polymer particle temperature is determined by the extent of convective heat transfer and other mechanisms of heat removal. In addition to the heat removal by convective heat transfer, liquid hydrocarbon (HC) is often injected into the reactor to further remove heat by evaporation but without partaking in the reaction. The effects of adding this liquid HC on the particle surface temperature have been investigated numerically by means of a one-dimensional polar model. Results indicate that the primary mechanism for removal of the heat of polymerization from the particles is by means of convective heat transfer to the bulk gas, which amounts to 99.5% removal of total heat of polymerization. The PE particle temperature rises only by 1–2°C above the surrounding bed gas mixture. The addition of liquid HC to the feed, however, has a pronounced effect on controlling the reactor gas temperature as most of this liquid is evaporated to the gaseous phase before it reaches the polymer particles. To state it clearly, heat of polymerization is transferred from the particles to the reactor bulk gas predominantly by convection, and part of this heat is subsequently absorbed by evaporation of the fresh liquid HC in the feed. Comparison with a detailed computational fluid dynamic (CFD) model of polymerization in a generic gas phase reactor has also been conducted. The results confirm that the particle temperature rise above the reactor gas temperature is consistent with the one-dimensional model. However, local gas temperature variations are present in the reactor due to the unsteady gas-solid hydrodynamics. Hence, there are some zones that are a few degrees hotter/colder than the bulk reactor temperature with corresponding increase/decrease in particle temperature in these zones.