半间歇聚合反应分子量分布周期操作的迭代学习控制

通过对半间歇聚合反应的引发剂进料实施周期操作,研究了这类操作方式对聚合物分子量分布的影响。研究结果显示,周期操作能改善聚合反应过程,对分子量分布有明显的加宽作用。对性能指标进行改进,以引发剂周期进料的占空比为控制变量,采用基于粒子群优化的迭代学习算法,对分子量分布进行了优化控制。仿真分析表明,在实际对象和模型存在不匹配的情况下,运用迭代粒子群算法,控制输入随着批次学习的进行而逐渐趋于最优解,聚合反应的分子量分布则不断逼近希望的分子量分布。实验结果验证了以周期操作方式对半间歇聚合过程分子量分布进行迭代优化控制的可行性。     

On-line multi-variable predictive control of molar mass and particle size distributions in free-radical emulsion copolymerization

A multi-variable model predictive control (MPC) was formulated to solve control problems associated with a combination of regulation and targeting desired set-points. We investigated the simultaneous control of key polymer properties: the particle size (PSD) and molecular weight distribution (MWD) by manipulating the flow rates of the monomers (styrene, MMA), surfactant, initiator and the temperature of the reactor. A multi-input-multi-output (MIMO) formulation was constructed for the constrained optimal control problem to maximize the width of the PSD (with M_n at a constant set-point), and to maximize the average molar mass. The strategy developed within a gPROMS-API-DCS environment allowed real-time implementation of model-based control of the process. The optimal control problem was implemented via an interface to a dynamic optimization code. Major improvements in process operation and polymer property control resulted on the implementation of our multi-variable MPC algorithm. The manipulation of the four flow rates and the temperature increased the degree of freedom in the system and achieved tighter PSD and MWD control. The on-line performance of MPC for MWD and PSD control was found to be satisfactory.     

Optimal flowsheet configuration of a polymerization process with embedded molecular weight distributions

We consider the optimal reactor network synthesis of a polymerization process with detailed molecular weight distributions (MWDs). Based on an industrial high‐density polyethylene (HDPE) slurry process model including an embedded MWD, a fully connected process superstructure of continuous stirred tank reactors (CSTRs) is established through the introduction of splitters. Using this generalized superstructure as a basis, two nonlinear programming (NLP) problem formulations, which simultaneously maximize the monomer conversion and minimize the deviation between the calculated and target MWDs, are developed by applying multiobjective optimization (MO) methods. Different optimal flowsheet configurations are generated by systematically manipulating a set of continuous decision variables. Several case studies that consider different specifications on MWD are conducted to illustrate the effectiveness and efficiency of the proposed synthesis approach. Numerical results show that the optimal flowsheet configurations overcome the limitations of conventional reactor network structures and help to increase reactor productivity at the desired product quality. © 2015 American Institute of Chemical Engineers AIChE J, 62: 131–145, 2016     

Optimal operation of ethylene polymerization reactors for tailored molecular weight distribution

This work presents a comprehensive steady‐state model of the high‐pressure ethylene polymerization in a tubular reactor able to calculate the complete molecular weight distribution (MWD). For this purpose, the probability generating function technique is employed. The model is included in an optimization framework, which is used to determine optimal reactor designs and operating conditions for producing a polymer with tailored MWD. Two application examples are presented. The first one involves maximization of conversion to obtain a given MWD, typical of industrial operation. Excellent agreement between the resulting MWD and the target one is achieved with a conversion about 5% higher than the ones commonly reported for this type of reactor. The second example consists in finding the design and operating conditions necessary to produce a polymer with a bimodal MWD. The optimal design for this case involves a split of the initiator, monomer, and modifier feeds between the main stream and two lateral injections. To the best of our knowledge, this is the first work dealing with the optimization of this process in which a tailored shape for the MWD is included. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

Model based control of a liquid swelling constrained batch reactor subject to recipe uncertainties

This work presents the application of nonlinear model predictive control (NMPC) to a simulated industrial batch reactor subject to safety constraint due to reactor level swelling, which can occur with relatively fast dynamics. Uncertainties in the implementation of recipes in batch process operation are of significant industrial relevance. The paper describes a novel control-relevant formulation of the excessive liquid rise problem for a two-phase batch reactor subject to recipe uncertainties. The control simulations are carried out using a dedicated NMPC and optimization software toolbox OptCon which implements efficient numerical algorithms. The open-loop optimal control problem is computed using the multiple-shooting technique and the arising nonlinear programming problem is solved using a sequential quadratic programming (SQP) algorithm tailored for large-scale problems, based on the freeware optimization environment HQP. The fast response of the NMPC controller is guaranteed by the initial value embedding and real-time iteration technologies. It is concluded that the OptCon implementation allows small sampling times and the controller is able to maintain safe and optimal operation conditions, with good control performance despite significant uncertainties in the implementation of the batch recipe.     

Reactor modeling and recipe optimization of polyether polyol processes: Polypropylene glycol

The reactor modeling and recipe optimization of conventional semibatch polyether polyol processes, in particular for the polymerization of propylene oxide to make polypropylene glycol, is addressed. A rigorous mathematical reactor model is first developed to describe the dynamic behavior of the polymerization process based on first‐principles including the mass and population balances, reaction kinetics, and vapor‐liquid equilibria. Next, the obtained differential algebraic model is reformulated by applying a nullspace projection method that results in an equivalent dynamic system with better computational performance. The reactor model is validated against plant data by adjusting model parameters. A dynamic optimization problem is then formulated to optimize the process recipe, where the batch processing time is minimized, given a target product molecular weight as well as other requirements on product quality and process safety. The dynamic optimization problem is translated into a nonlinear program using the simultaneous collocation strategy and further solved with the interior point method to obtain the optimal control profiles. The case study result shows a good match between the model prediction and real plant data, and the optimization approach is able to significantly reduce the batch time by 47%, which indicates great potential for industrial applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2515–2529, 2013     

Dynamic optimization for grade transition processes using orthogonal collocation on molecular weight distribution

To meet the demands of a competitive market, an industrial plant often produces several grades of polymer product through the same process in an economical way. As molecular weight distribution (MWD) is a crucial quality index of polymers, dynamic optimization for grade transition based on MWD is highly important, but challenging. This study considers the development of optimization models for MWD-based grade transition. An MWD reconstruction method using orthogonal collocation in two dimensions is developed to capture the dynamic feature of MWD in time and the distributive feature in chain length. The simultaneous collocation approach is adopted to discretize the model. Two optimization formulations are proposed to describe minimizing the transition time as well as off-spec production. Both formulations inherit the advantages of the simultaneous collocation approach. The numerical results show that the proposed methods can efficiently solve the grade transition problem with MWD specification, and obtain high performance control profiles to reduce the production cost. © 2019 American Institute of Chemical Engineers AIChE J, 65: 1198–1210, 2019     

A novel strategy for dynamic optimization of grade transition processes based on molecular weight distribution

To achieve different end‐use properties of polymers, an industrial plant must produce several grades of the product through the same process under different operating conditions. As molecular weight distribution (MWD) is a crucial quality index of polymers, grade transition based on MWD is of great importance. Dynamic optimization of the grade transition process using MWD is a challenging task because of its large‐scale nature. After analyzing the relationships among state variables during polymerization, a novel method is proposed to conduct the optimal grade transition using dynamic optimization with a small‐scale moment model, combined with a steady‐state calculation of the MWD. By avoiding expensive computation in dealing with dynamic MWD optimization, this technique greatly reduces the computational complexity of the process optimization. The theoretical equivalence of this simplification is also proved. Finally, an industrial high‐density polyethylene slurry process is presented to demonstrate the efficiency and accuracy of the proposed strategy. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2498–2512, 2014     

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.     

Dynamic optimization of the methylmethacrylate cell‐cast process for plastic sheet production

Traditionally, the methylmethacrylate (MMA) polymerization reaction process for plastic sheet production has been carried out using warming baths. However, it has been observed that the manufactured polymer tends to feature poor homogeneity characteristics measured in terms of properties like molecular weight distribution. Nonhomogeneous polymer properties should be avoided because they give rise to a product with undesired wide quality characteristics. To improve homogeneity properties force‐circulated warm air reactors have been proposed, such reactors are normally operated under isothermal air temperature conditions. However, we demonstrate that dynamic optimal warming temperature profiles lead to a polymer sheet with better homogeneity characteristics, especially when compared against simple isothermal operating policies. In this work, the dynamic optimization of a heating and polymerization reaction process for plastic sheet production in a force‐circulated warm air reactor is addressed. The optimization formulation is based on the dynamic representation of the two‐directional heating and reaction process taking place within the system, and includes kinetic equations for the bulk free radical polymerization reactions of MMA. The mathematical model is cast as a time dependent partial differential equation (PDE) system, the optimal heating profile calculation turns out to be a dynamic optimization problem embedded in a distributed parameter system. A simultaneous optimization approach is selected to solve the dynamic optimization problem. Trough full discretization of all decision variables, a nonlinear programming (NLP) model is obtained and solved by using the IPOPT optimization solver. The results are presented about the dynamic optimization for two plastic sheets of different thickness and compared them against simple operating policies. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Computation of near-optimal control policies for free-radical polymerization reactors

A polymer is characterized by the average degree of polymerization and the molecular weight distribution. Approximate optimization of temperature control, or catalyst feed rate control, or both are performed to attain not only the desired average degree of polymerization but also the desired molecular weight distribution. This near-optimal policy, which is a function of time only for a batch polymerization reactor, is first expressed by a polynomial, and the coefficients of the polynomial are estimated by a pattern search technique. This coefficient's estimation method coupled with a nonlinear search technique was found to be suitable for solving this type of our optimization problem involving complex chemical kinetics.     

The influence of reactor type and operating conditions on the molecular weight distribution in vinyl acetate polymerization

The vinyl acetate polymerization system was investigated with respect to the breadth of the molecular weight distribution (MWD) in batch, continuous segregated, and continuous micromixed reactors. Models were developed employing a complex kinetic scheme including polymer transfer and terminal double bond polymerization, without neglecting initiation and termination steps. Inclusion of a gel effect for terminal double bond polymerization gave better agreement with experimental molecular weight data in suspension polymerization. Simulation results showed the MWD order in the three reactor types is not fixed, but a function of reactant concentrations and the importance of chain branching. In some cases changing the initiator type and concentration will change the MWD order.     

考虑初始操作温度影响的间歇放热反应系统动态柔性分析

It is shown in this article that by changing the initial operation condition of the batch processes, the dynamic performance of the system can be varied largely, especially for the initial operational temperature of the exothermic reaction. The initial operation condition is often ignored in the designing batch processes for flexibility against disturbances or parameter variations. When the initial condition is not rigid as in the case of a batch reactor, where the initial reaction temperature is quite arbitrary, optimization can also be applied to determine the ＂best＂ initial condition to use. Problems for dynamic flexibility analysis of exothermic reaction including initial temperature and process operation can be formulated as dynamic optimization problems. Formulations are derived when the initial conditions are considered or not. When the initial conditions are considered, the initial condition can be transferred into control variables in the first optimal step. The solution of the dynamic optimization is on the basis of Rugge-Kutta integration algorithm and decomposition search algorithm. This method, as illustrated and tested with two highly nonlinear process problems, enables the determination of the optimal level. The dynamic performance is improved by the proposed method in the two exothermic reaction examples.     

Molecular weight distribution in low-density polyethylene polymerization; impact of scission mechanisms in the case of a tubular reactor

It has been shown that scission kinetics strongly affects the molecular weight distribution (MWD) of low-density polyethylene (ldPE) in a continuous stirred tank reactor (CSTR). The present paper focuses on the effects of different chemical scission mechanisms, linear and topological scission, as well as mechanical scission on MWD in batch and tubular reactors. In contrast to the CSTR, a batch reactor MWD does not show bimodalities or long tails. The tubular reactor was modeled as an industrially representative system with four initiator injection points and a proper ‘cocktail’ of different initiators. Calculated MWD was compared to one experimentally determined with SEC-MALLS for a commercial tubular product and fair agreement was found. Typically, these MWDs are broad, but not bimodal. Sensitivity studies were performed as to scission kinetics and the effect of chain transfer agent (CTA). Both batch and tubular reactor were observed to be less sensitive to scission kinetics than a CSTR. In addition, alternative CTA injection strategies (downstream positions) were tested. These showed interesting behavior leading to very broad and bimodal MWD. The model allows following the MWD broadening along the tube. We conclude that batch and tubular ldPE reactors lead to completely different MWD behavior than a CSTR and that it is possible to manipulate it to a great extent.     

基于GSA-LSTM动态结构特征提取的间歇过程监测方法

间歇过程监测对于保证批次生产过程的稳定运行具有重要意义。传统过程监测方法难以提取间歇过程数据特有的非线性结构和动态时变特征。为此,提出了一种融合图采样聚合网络和长短期记忆网络(GSA-LSTM)的典型相关分析方法用于间歇过程在线监测。首先,利用K近邻方法将批次过程数据转化为图结构形式,利用图采样聚合网络(GraphSAGE)提取数据内部的结构特征,然后利用长短期记忆网络(LSTM)提取数据的非线性动态特征,通过权重系数将结构特征和动态特征融合得到更具有代表性的间歇过程数据特征。进一步地,利用典型相关分析方法对残差建立监测模型。最后将所提方法应用于数值例子和注塑过程监测,结果分析验证了所提方法的有效性。     

基于GSA-LSTM动态结构特征提取的间歇过程监测方法

间歇过程监测对于保证批次生产过程的稳定运行具有重要意义。传统过程监测方法难以提取间歇过程数据特有的非线性结构和动态时变特征。为此,提出了一种融合图采样聚合网络和长短期记忆网络(GSA-LSTM)的典型相关分析方法用于间歇过程在线监测。首先,利用K近邻方法将批次过程数据转化为图结构形式,利用图采样聚合网络(GraphSAGE)提取数据内部的结构特征,然后利用长短期记忆网络(LSTM)提取数据的非线性动态特征,通过权重系数将结构特征和动态特征融合得到更具有代表性的间歇过程数据特征。进一步地,利用典型相关分析方法对残差建立监测模型。最后将所提方法应用于数值例子和注塑过程监测,结果分析验证了所提方法的有效性。     

PTFE间歇聚合反应过程变周期动态经济优化控制

聚四氟乙烯(PTFE)间歇聚合生产模式可满足小批量、多用途以及高质量产品的市场需求。针对PTFE聚合过程存在强非线性和大时滞特性,提出了一种基于自由终端的动态经济优化控制方法。首先,将生产周期作为一个自由度纳入优化变量建立动态经济优化问题,采用改进控制变量参数化方法,控制输入被离散为可变长度的片状序列,便可将动态经济优化问题转换为非线性规划(NLP)问题;然后,采用基于梯度下降的内点罚函数法求解NLP问题,通过变周期预测时域的滚动优化控制方法优化控制输入和终端时间;最后将提出的变周期动态经济优化控制与传统PI控制、非线性模型预测控制进行对比测试分析,仿真结果表明本方法单位经济效益更高,生产周期更短,突显了间歇生产的灵活性。     

PTFE间歇聚合反应过程变周期动态经济优化控制

聚四氟乙烯(PTFE)间歇聚合生产模式可满足小批量、多用途以及高质量产品的市场需求。针对PTFE聚合过程存在强非线性和大时滞特性,提出了一种基于自由终端的动态经济优化控制方法。首先,将生产周期作为一个自由度纳入优化变量建立动态经济优化问题,采用改进控制变量参数化方法,控制输入被离散为可变长度的片状序列,便可将动态经济优化问题转换为非线性规划(NLP)问题;然后,采用基于梯度下降的内点罚函数法求解NLP问题,通过变周期预测时域的滚动优化控制方法优化控制输入和终端时间;最后将提出的变周期动态经济优化控制与传统PI控制、非线性模型预测控制进行对比测试分析,仿真结果表明本方法单位经济效益更高,生产周期更短,突显了间歇生产的灵活性。     

An optimization study on the pyrolysis of polystyrene in a batch reactor

The pyrolysis process of polystyrene (PS) has been investigated to find optimal temperature profiles which minimize the reaction time and the reaction energy required for a given conversion in a batch reactor. Assuming that the fragmentation of PS in pyrolysis is described by the mechanism of random and/or specific degradations, we used a continuous kinetic model for solving three moment equations to determine the transient change of molecular weight distributions (MWD) of the polymers. We then converted this independent-variable minimization problem using a coordinate transformation to a dependent-variable minimization problem that yields the optimal temperature profiles as its solution. The optimization results obtained in this study encompass the cases of different objective functions which cover minimum reaction time, minimum energy consumed, or any combination of these. It has turned out that maintaining the reaction temperature constant at an optimal level is the best solution in this optimization problem. An economic cost function also has been introduced as the third objective function to be minimized in addition to the reaction time and the reaction energy. This new function can serve as a convenient measure to judge the performance of the pyrolysis process minimizing the involved cost.     

Control of molecular weight distribution and tensile strength in a free radical styrene polymerization process

A new method is presented for modeling and controlling polymer molecular weight distribution (MWD) and tensile strength in a batch suspension polymerization of styrene. The molecular weight distribution is modeled by computing the weight fraction of the polymer in different chain length intervals. Tensile strength is then related to the modeled molecular weight distribution using a correlation available in the literature and based on the concept of a threshold molecular weight. This method enables the design of operating conditions for a batch suspension polymerization reactor, which will theoretically yield amorphous polystyrene with a desired tensile strength. Two numerical examples are presented to illustrate the feasibility of the proposed method. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 1017–1026, 1998