AN IMPROVED MODEL FOR TEMPERATURE AND CONVERSION PROFILES IN TUBULAR HIGH PRESSURE POLYETHYLENE REACTORS

An earlier computer model for tubular high pressure polyethylene reactors is extended to take into account two radical generating sources, in addition to an injected initiator: a long-lived intermediate, possibly generated from the interaction of ethylene with trace amounts of oxygen, and the ethylene itself undergoing thermal polymerization. The first of these reactions can account for the smoothing of the temperature profile near the peak temperature, attributed by Lee to initiator and radical carryover; the second, whose inclusion is justified by experiments recently performed by Buback, can account for the explosive decomposition of ethylene known to occur in LDPE reactors if the temperature is allowed to exceed about 350°C, and it also can contribute significantly to polymer production at very high temperatures. The contribution of both reactions must be evaluated quantitatively, if reliable heat transfer coefficients are to be obtained from experiment.     

NUMERICAL SOLUTION OF UNSTEADY CONVECTIVE DIFFUSION WITH CHEMICAL REACTION IN TIME DEPENDENT FLOWS

An earlier computer model for tubular high pressure polyethylene reactors is extended to take into account two radical generating sources, in addition to an injected initiator: a long-lived intermediate, possibly generated from the interaction of ethylene with trace amounts of oxygen, and the ethylene itself undergoing thermal polymerization. The first of these reactions can account for the smoothing of the temperature profile near the peak temperature, attributed by Lee to initiator and radical carryover; the second, whose inclusion is justified by experiments recently performed by Buback, can account for the explosive decomposition of ethylene known to occur in LDPE reactors if the temperature is allowed to exceed about 350°C, and it also can contribute significantly to polymer production at very high temperatures. The contribution of both reactions must be evaluated quantitatively, if reliable heat transfer coefficients are to be obtained from experiment.     

High pressure polymerization of ethylene and rheological behavior of polyethylene product

A mathematical model of the high pressure polymerization of ethylene in tubular reactors was tested with experimental data obtained from an industrial size tubular reactor. Series of experiments involving changes in operating conditions were carried out, and process data and polyethylene samples were collected. The collected samples were characterized for their molecular weight distributions and various rheological material functions involving shear and extensional flows. The findings of the model were compared against the generated process data and the molecular weight distributions of the samples. The determined rheological behavior exhibited strong dependence on the primary characteristics of the resins. Overall, this study should introduce a better understanding of the interactions between high pressure reaction conditions and the primary properties of polyethylene, including moments of molecular weight distribution and extent of branching on one hand and the interrelationships between primary properties and the rheological behavior of the high pressure polyethylene product on the other hand.     

Dynamic modeling of multizone,multifeed high-pressure LDPE autoclaves

A comprehensive mathematical model is developed to simulate the dynamic behavior of multizone, multifeed high-pressure ethylene polymerization autoclaves. To describe the complex flow patterns occurring in low-density polyethylene (LDPE) autoclaves, a user-specified multisegment, multirecycle model representation of the actual multizone reactor is established. A general reaction mechanism is employed to represent the kinetics of ethylene polymerization. Dynamic mass, molar species, and energy balances are derived to predict the polymerization rate, monomer conversion, molecular weight developments (e.g., M_n, M_w, long- and short-chain branching), and temperature profile with respect to time and spatial position in the reactor. Detailed results on the start-up and grade transition of a four-zone autoclave reactor are presented and the effects of the macromixing parameters (e.g., number of segments per reaction zone and the total and side external recycle ratios) on the dynamic behavior of the reactor are investigated. It is shown that the model macromixing parameters can significantly affect the initiator consumption rate in a reaction zone. The present model is capable of predicting accurately the dynamic behavior of LDPE autoclaves and, thus, can be employed in the design, optimization, and control of these reactors. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 73: 2327–2348, 1999     

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.     

Modeling of branching density and branching distribution in low-density polyethylene polymerization

Low-density polyethylene (ldPE) is a general purpose polymer with various applications. By this reason, many publications can be found on the ldPE polymerization modeling. However, scission reaction and branching distribution are only recently considered in the modeling studies due to difficulties in measurement and computation of scission effect and branchings of polymer. Our previous papers [Kim, D.M., et al., 2004. Molecular weight distribution modeling in low-density polyethylene polymerization; impact of scission mechanisms in the case of CSTR. Chemical Engineering Science 59, 699-718; Kim, D.M., Iedema, P.D., 2004. Molecular weight distribution modeling in low-density polyethylene polymerization; impact of scission mechanisms in the case of a tubular reactor. Chemical Engineering Science, submitted for publication] are concerned with the scission reaction during ldPE polymerization and its effect on molecular weight distribution (MWD) of ldPE for various reactor types. Here we consider branching distributions as a function of chain length for CSTR and tubular reactor processes. To simultaneously deal with chain length and branching distributions, the concept of pseudo-distributions is used, meaning that branching distributions are described by their main moments. The computation results are compared with properties of ldPE samples from a CSTR and a tubular reactor. Number and weight average branchings and branching density increase as chain length increases until the longest chain length. The concentrations of long chain branching (LCB) are close to those of first branching moment in both CSTR and tubular reactor systems. The branching dispersity, a measure for the width of the branching distribution at a certain chain length, has the highest value at shorter chain length and then monotonously decreases approaching to 1.0 as chain length increases. Excellent agreements in branching dispersities between calculation with branching moments and prediction with assumption of binomial distribution for a tubular reactor and CSTR processes show that the branching distribution follows a binomial distribution for both processes.     

Prediction of the molecular and polymer solution properties of LDPE in a high-pressure tubular reactor using a novel Monte Carlo approach

In the present work, a novel kinetic/topology Monte Carlo algorithm is developed for the prediction of molecular, topological and solution properties of highly branched low-density polyethylene (LDPE), produced in a high-pressure multi-zonal tubular reactor. It is shown that the combined kinetic/topology MC algorithm can provide comprehensive information regarding the distributed molecular and topological properties of LDPE (i.e., molecular weight distribution, short- and long-chain branching distributions, joint molecular weight-long chain branching distribution, branching order distribution, seniority/priority distributions, etc.) The molecular/topological results obtained from the MC algorithm are then introduced into a random-walk molecular simulator to calculate the solution properties of LDPE (i.e., the mean radius of gyration, R_g, and the branching factor, g) in terms of the chain length of the branched polyethylene. The validity of the commonly applied approximation regarding the random scission of highly branched polymer chains is assessed by a direct comparison of the average molecular properties of LDPE (i.e., number and weight average molecular weights), calculated by the combined kinetic/topology MC algorithm, with the respective predictions obtained by the commonly applied method of moments (MOM). Through this comparison it is demonstrated that the ambiguous implementation of the random scission reaction in the MOM formulation can result in erroneous predictions of the weight average molecular weight and MWD of LDPE. Finally, the effects of two key process parameters, namely, the polymerization temperature profile and the solvent concentration, on the molecular, topological and polymer solution properties of LDPE produced in a multi-zonal tubular reactor are investigated.     

Modeling of ethylene polymerization with difunctional initiators in tubular reactors

The severe thermodynamic conditions of the high‐pressure ethylene polymerization process hinder ethylene from going to full conversion. One remedy to improve the monomer conversion is to make effective use of difunctional peroxides. Multifunctional peroxides can accelerate the polymerization rate, produce branching, and modify the rheological properties of molten polymers. This article proposes a kinetic model based on a postulated reaction mechanism for ethylene polymerization initiated by difunctional initiators in a high‐pressure tubular reactor. Three peroxides suitable for ethylene polymerization were compared for their effectiveness. Compared to dioctanoyl peroxide, the two difunctional peroxides considered performed much better for the higher temperature regions of the reactor and gave ethylene conversions nearly twice as high for only half of the initial amount of dioctanoyl. They also generated low‐density polyethylene polymer with a broader molecular weight distribution and longer chain branching. These two important polymer characteristics can influence the end‐product rheological properties. Injecting fresh ethylene at different points along the reactor improved the conversion and produced more branched polymer. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

管式法LDPE产品浊度影响因素及改进措施

通过在管式法低密度聚乙烯装置上控制反应压力和各反应区压降、调整反应温度器分布、合理设定引发剂注入压力、优化反应器流量分配和比例控制、调整添加剂用量等,降低了树脂薄膜制品的浊度值。提高了膜制品的光学性能,改进了高档膜料树脂的质量,其中控制引发剂注入压力比对应点反应压力高25MPa,反应器流量分配调整为正面进料为41．8％,第一侧流为28．7％,第二侧流为29．5％。     

Analysis of an industrial continuous slurry reactor for ethylene-butene copolymerization

This work presents the analysis of a slurry polymerization stirred tank reactor for the production of high-density polyethylene. A coordination mechanism is adopted including initiation, propagation, first order deactivation, hydrogen transfer, ethylene transfer, transfer to co-catalyst and β-hydride elimination. Two site types are considered each one with its own kinetic constants. A non-uniform solid phase is considered and in the particle there is a radial distribution of chemical species such as the living and dead polymer chains. In this sense, a general local balance is proposed, providing state equations for the moments of chain length distribution and for the active site concentrations that are treated together with all others modeling scales. The multigrain model approach was adopted, combined with a simulation strategy applying orthogonal collocation. The simulation procedure handles all the equations simultaneously and the model is capable of predicting the behavior of operation variables and variables associated with the polymer properties.     

High pressure tubular reactors for ethylene polymerization optimization aspects

Optimal policies for operation of high pressure tubular reactors for ethylene polymerization are presented. The work is based on a previously developed model, allowing accurate representation of different configurations and operation conditions of industrial relevance. Several policies based on temperature and initiator concentration as control parameters are evaluated and compared.     

Modeling of ethylene copolymerization in nonisothermal high‐pressure reactors using bifunctional initiators

Enhancing the performance of high‐pressure LDPE process is valuable for polymer industry. However, the severe thermodynamics requirement of high pressure and temperature hinders the reaction process from getting simultaneously high monomer conversion and polymer molecular weights. Bifunctional peroxides used as initiators can boost the polymerization rate and alter rheological polymer properties. This article proposes a new kinetics model of ethylene/butyl acrylate copolymerization with bifunctional initiators in a high‐pressure nonisothermal tubular reactor. Model predictions are compared with available data. A SQP optimization scheme is employed to determine a suitable wall temperature for each zone along the nonisothermal tubular reactor. In comparison with the monofunctional TBPPI peroxide, a lower amount of the bifunctional DHBPPI peroxide is needed to get a higher conversion in shorter residence time, but at the expense of higher thermal energy. The results also showed that polymers produced with bifunctional peroxides are significantly more branched. POLYM. ENG. SCI., 59:74–85, 2019. © 2018 Society of Plastics Engineers     

环管反应器内传热过程的数值模拟

为了对环管反应器内传热规律进行研究,在Euler-Euler双流体动量传递模型和环管反应器聚合传质模型的基础上,考虑了环管反应器内传热过程,建立了环管反应器传热数学模型,对工业烯烃聚合环管反应器内流动、传热和传质及聚合反应过程进行了研究。反应器内浆液温度的模拟值与工业现场值吻合,说明所建立的环管反应器传热数学模型是有效的。模拟结果表明,环管反应器温度与物料浓度存在不均匀分布。在上升段,温度分布呈中心对称,在弯管段不再呈中心对称,下降段的温度因弯管段的不均匀分布而不再呈中心对称分布;随着浆液入口速度或入口固体颗粒相体积分数的增加,环管反应器上升直管段,弯管段以及下降直管段温度降低;管壁冷却水温度不同,对环管反应器内冷却能力也不同,在反应器内相同的释放热量情况下,冷却水温度越低,对反应器内物料的冷却能力就越强。     

Modeling and optimization of a high-pressure ethylene polymerization reactor using gPROMS

A gPROMS implementation of a comprehensive steady-state model of the high-pressure polymerization of ethylene in a tubular reactor is presented. Model outputs along the reactor length include the complete molecular weight distribution and branching indexes, as well as monomer conversion, average molecular weights, reactants’ compositions, and reactor temperature and pressure. A detailed calculation of physical and transport properties, such as the reaction mixture density, heat-transfer capacity, viscosity and global heat-transfer coefficient is also included. The reactor model is included in an optimization framework that is used to determine the best operating conditions for producing a polymer with tailor-made molecular structure in terms of the complete molecular weight distribution, branching and polydispersity.     

Study of Ethylene Polymerization Under Single Liquid Phase and Vapor‐Liquid Phase Conditions in a Continuous‐Flow Tubular Reactor

The feasibility of using continuous‐flow tubular reactors (CFTR) as an efficient research tool for polymerization reactions is investigated. This is a continuation of the extensive effort that had been made at Dow in recent years to set up and employ an electro‐thermal microreactor (an ohmically‐heated CFTR), which resulted in several internal and external publications and a US Patent. The main focus of this work is to investigate the effect of operating conditions and flow composition, mainly the number of existing phases, on the molecular weight of the polymer. A series of polymerization experiments were performed in single‐phase (liquid) and two‐phase (vapor‐liquid) flow regimes. In single‐phase polymerization, the ethylene concentration falls continuously along the length of the reactor. This will have a significant effect on the kinetics of polymerization, particularly the molecular weight of the produced polymer. A key advantage of operating in the two‐phase region is that an almost constant ethylene concentration is maintained along the length of the reactor. In effect, the vapor phase serves as a reservoir that replenishes the ethylene consumed in the liquid phase by polymerization. The molecular weight data show that this assumption is valid provided that the rate of mass transfer is significantly higher than the rate of the polymerization reaction.     

Dynamic prediction of the bivariate molecular weight-copolymer composition distribution using sectional-grid and stochastic numerical methods

In the present study, a two-dimensional fixed pivot technique (2-D FPT) and an efficient Monte Carlo (MC) algorithm are described for the calculation of the bivariate molecular weight-copolymer composition (MW-CC) distribution in batch free-radical copolymerization reactors. A comprehensive free-volume model is employed to describe the variation of termination and propagation rate constants as well as the variation of the initiator efficiency with respect to the monomer conversion. Simulations are carried out, under different reactor conditions, to calculate the individual monomer conversions, the leading moments of the ‘live’ and ‘dead’ polymer chain length distributions as well as the dynamic evolution of the distributed molecular properties (i.e., molecular weight distribution (MWD), copolymer composition distribution (CCD) and joint MW-CC distribution). The validity of the numerical calculations is examined via a direct comparison of the simulation results, obtained by the two numerical methods, with experimental data on the styrene-methyl methacrylate batch free-radical copolymerization. Additional comparisons between the 2-D FPT and the MC methods are carried out for different polymerization conditions. It is clearly shown that both numerical methods are capable of predicting the distributed molecular and copolymer properties, with high accuracy, up to very high monomer conversions. It is also shown that the proposed dynamic MC algorithm is less computationally demanding than the 2-D FPT.     

Modeling of “living” free‐radical polymerization processes. I. Batch,semibatch, and continuous tank reactors

A comprehensive mathematical model is developed for “living” free‐radical polymerization carried out in tank reactors and provides a tool for the study of process development and design issues. The model is validated using experimental data for nitroxide‐mediated styrene polymerization and atom transfer radical copolymerization of styrene and n‐butyl acrylate. Simulations show that the presence of reversible capping reactions between growing and dormant polymer chains should boost initiation efficiency when using free nitroxide in conjunction with conventional initiator and also increase the effectiveness of thermal initiation. A study shows the effects of the value of the capping equilibrium constant and capping reaction rate constants for both nitroxide‐mediated styrene polymerization (using alkoxyamine as polymer chain seeds) and atom transfer radical polymerization of n‐butyl acrylate (using methyl 2‐bromopropionate as chain extension seeds). Also the effect of introducing additional conventional initiator into atom transfer radical polymerization of n‐butyl acrylate is studied. It is found that the characteristics of long chain growth are determined by the fast exchange of radicals between growing and dormant polymer chains. Polymerization results in batch, semibatch, and a series of continuous tank reactors are analyzed. The simulations also show that a semibatch reactor is most flexible for the preparation of polymers with controlled architecture. For continuous tank reactors, the residence time distribution has a significant effect on the development of chain architecture. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 1630–1662, 2002     

Highly efficient reversible addition–fragmentation chain‐transfer polymerization in ethanol/water via flow chemistry

Utilization of a flow reactor under high pressure allows highly efficient polymer synthesis via reversible addition–fragmentation chain‐transfer (RAFT ) polymerization in an aqueous system. Compared with the batch reaction, the flow reactor allows the RAFT polymerization to be performed in a high‐efficiency manner at the same temperature. The adjustable pressure of the system allows further elevation of the reaction temperature and hence faster polymerization. Other reaction parameters, such as flow rate and initiator concentration, were also well studied to tune the monomer conversion and the molar mass dispersity (?) of the obtained polymers. Gel permeation chromatography, nuclear magnetic resonance (NMR), and Fourier transform infrared spectroscopies (FTIR) were utilized to monitor the polymerization process. With the initiator concentration of 0.15 mmol L^?1, polymerization of poly(ethylene glycol) methyl ether methacrylate with monomer conversion of 52% at 100 °C under 73 bar can be achieved within 40 min with narrow molar mass dispersity (D) ? (<1.25). The strategy developed here provides a method to produce well‐defined polymers via RAFT polymerization with high efficiency in a continuous manner. © 2017 Society of Chemical Industry