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     

Optimization of grade transitions in polyethylene solution polymerization processes

This study considers the development of optimization models for grade transition of polyethylene solution polymerization processes. A detailed mathematical model is developed to capture the dynamics of the solution polymerization process. This includes time delay models for vapor and liquid recycle streams as well as a reduced, yet accurate, vapor‐liquid equilibrium (VLE) model derived from rigorous VLE calculations. Simultaneous dynamic optimization approach is applied to solve the optimization problem to reduce off‐spec production time and transition time. Two optimization formulations, single stage and multistage, are developed to deal with single‐value target and specification bands of product properties, respectively. The results show significant reductions in grade transition time and off‐spec production time. In addition, the multistage formulation designed for problems with specification bands outperforms its single stage counterpart. It minimizes transition time and off‐spec production directly, and leads to higher performance control profiles. © 2015 American Institute of Chemical Engineers AIChE J, 62: 1126–1142, 2016     

采用同步策略的化工动态优化求解(英文)

An approach of simultaneous strategies with two novel techniques is proposed to improve the solution accuracy of chemical dynamic optimization problems. The first technique is to handle constraints on control variables based on the finite-element collocation so as to control the approximation error for discrete optimal problems, where a set of control constraints at element knots are integrated with the procedure for optimization leading to a significant gain in the accuracy of the simultaneous strategies. The second technique is to make the mesh refinement more feasible and reliable by introducing length constraints and guideline in designing appropriate element length boundaries, so that the proposed approach becomes more efficient in adjusting elements to track optimal control profile breakpoints and ensure accurate state and control profiles. Four classic benchmarks of dynamic optimization problems are used as illustrations, and the proposed approach is compared with literature reports. The research results reveal that the proposed approach is preferable in improving the solution accuracy of chemical dynamic optimization problem.     

Optimization of grade transitions in polyethylene solution polymerization process under uncertainty

Model-based dynamic optimization is an effective tool for control and optimization of chemical processes, especially during transitions in operation. This study considers the dynamic optimization of grade transitions for a solution polymerization process. Here, a detailed dynamic model comprises the entire flowsheet and includes a method-of-moments reactor model to determine product properties, a simple yet accurate vapor–liquid equilibrium (VLE) model derived from rigorous calculations, and a variable time delay model for recycle streams. To solve the grade transition problem, both single stage and multistage optimization formulations have been developed to deal with specification bands of product properties.This dynamic optimization framework demonstrates significant performance improvements for grade transition problems. However, performance can deteriorate in the presence of uncertainties, disturbances and model mismatch. To deal with these uncertainties, this study applies robust optimization formulations through the incorporation of back-off constraints within the optimization problem. With back-off terms calculated from Monte Carlo simulations, the resulting robust optimization formulation can be solved with the same effort as the nominal dynamic optimization problem, and the resulting solution is shown to be robust under various uncertainty levels with minimal performance loss. Additional case studies show that our optimization approach extends naturally to different regularizations and multiple sources of uncertainty.     

Integrated Optimization Strategies for Dynamic Process Operations

Process systems engineering faces increasing demands and opportunities for better process modeling and optimization strategies, particularly in the area of dynamic operations. Modern optimization strategies for dynamic optimization trace their inception to the groundbreaking work Pontryagin and his coworkers, starting 60 years ago. Since then the application of large-scale non-linear programming strategies has extended their discoveries to deal with challenging real-world process optimization problems. This study discusses the evolution of dynamic optimization strategies and how they have impacted the optimal design and operation of chemical processes. We demonstrate the effectiveness of dynamic optimization on three case studies for real-world reactive processes. In the first case, we consider the optimal design of runaway reactors, where simulation models may lead to unbounded profiles for many choices of design and operating conditions. As a result, optimization based on repeated simulations typically fails, and a simultaneous, equationbased approach must be applied. Next we consider optimal operating policies for grade transitions in polymer processes. Modeled as an optimal control problem, we demonstrate how product specifications lead to multistage formulations that greatly improve process performance and reduce waste. Third, we consider an optimization strategy for the integration of scheduling and dynamic process operation for general continuous/batch processes. The method introduces a discrete time formulation for simultaneous optimization of scheduling and operating decisions. For all of these cases we provide a summary of directions and challenges for future integration of these tasks and extensions in optimization formulations and strategies.     

A novel analytical second-order sensitivity calculation approach using the finite element method for chemical engineering problems

This paper presents an effective orthogonal collocation approach to approximate dynamic optimization problems into nonlinear programming problems, where the resulting problems can then be usually solved by first-order sensitivity based algorithms. However, the results obtained fail to satisfy the timeliness and accuracy requirements of some dynamic optimization problems. A novel collocation approach with second-order sensitivity information is therefore first proposed to improve the efficiency of the method. The resulting nonlinear programming problem is obtained through the orthogonal collocation on finite element combined with a single shooting approach. Three benchmark optimal control problems are considered to demonstrate the performance of the presented approach. Comparisons among the proposed approach, the BFGS method, and other literature solutions are also carried out in detail. Numerical results validate the effectiveness of the proposed method and the time saving benefit.     

Optimal grade transition and selection of closed-loop controllers in a gas-phase olefin polymerization fluidized bed reactor

To satisfy the diverse product quality specifications required by the broad range of polyolefin applications, polymerization plants are forced to operate under frequent grade transition policies. Commonly, the optimal solution to this problem is based on the minimization of a suitable objective function defined in terms of the changeover time, product quality specifications, process safety constraints and the amount of off-spec polymer, using dynamic optimization methods. However, considering the great impact that a given control structure configuration can have on the process operability and product quality optimization, the time optimal grade transition problem needs to be solved in parallel with the optimal selection of the closed-loop control pairings between the controlled and manipulated variables. In the present study, a mixed integer dynamic optimization approach is applied to a catalytic gas-phase ethylene-1-butene copolymerization fluidized bed reactor (FBR) to calculate both the “best” closed-loop control configuration and the time optimal grade transition policies. The gPROMS/gOPT computational tools for modelling and dynamic optimization, and the GAMS/CPLEX MILP solver are employed for the solution of the combined optimization problem. Simulation results are presented showing the significant quality and economic benefits that can be achieved through the application of the proposed integrated approach to the optimal grade transition problem for a gas-phase polyolefin FBR.     

基于联立法的乙烯淤浆聚合牌号切换过程动态模拟

以乙烯淤浆聚合流程为研究对象,建立了包含动力学和热力学的动态机理模型,采用有限元正交配置法对控制变量和状态变量同步离散化,实现了全联立动态模拟。热力学物性计算采用Kriging函数估计,可适用于多个工况,最大误差不超过2%。利用Aspen Plus 5个牌号工况的数据,进行了模型稳态验证,并实现了牌号切换动态模拟,计算了平均分子量等质量指标,与Aspen Dynamic曲线吻合较好,为牌号切换的优化奠定了基础。     

Dynamic real‐time optimization with closed‐loop prediction

Process plants are operating in an increasingly global and dynamic environment, motivating the development of dynamic real‐time optimization (DRTO) systems to account for transient behavior in the determination of economically optimal operating policies. This article considers optimization of closed‐loop response dynamics at the DRTO level in a two‐layer architecture, with constrained model predictive control (MPC) applied at the regulatory control level. A simultaneous solution approach is applied to the multilevel DRTO optimization problem, in which the convex MPC optimization subproblems are replaced by their necessary and sufficient Karush–Kuhn–Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints. The performance of the closed‐loop DRTO strategy is compared to that of the open‐loop prediction counterpart through a multi‐part case study that considers linear dynamic systems with different characteristics. The performance of the proposed strategy is further demonstrated through application to a nonlinear polymerization reactor grade transition problem. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3896–3911, 2017     

Integrated scheduling and dynamic optimization of grade transitions for a continuous polymerization reactor

This paper presents a modeling and numerical solution method for an integrated grade transition and production scheduling problem for a continuous polymerization reactor. The optimal sequence of production stages and the transitions between them is supposed to be determined for producing a given number of polymer grades at certain amounts and quality specifications in the most economical way. The production schedule has to satisfy due dates for specific orders. This operational problem is cast into a mixed-integer dynamic optimization problem. Disjunctions and logical constraints are combined with a validated differential–algebraic model describing the polymer process during the production of a specific grade as well as along a transition between two different grades. The modeling and solution approach proposed by Oldenburg et al. [Oldenburg, J., Marquardt, W., Heinz D., & Leineweber, D. B. (2003)] is tailored to this problem class to provide an efficient solution technique. An industrial example process serves as an example to illustrate the modeling and solution techniques suggested.     

Addressing the control problem of algae growth in water reservoirs with advanced dynamic optimization approaches

In this work, we develop a lake eutrophication model to determine restoration policies for water quality improvement. This hybrid biogeochemical model has been formulated within a simultaneous dynamic optimization framework as an optimal control problem, whose solution provides limiting nutrient inflow profiles to the lake, as well as in-lake biomanipulation profiles. The water quality model comprises a set of partial differential algebraic equations in time and space, which result from dynamic mass balances on main phytoplankton groups, nutrients, dissolved oxygen and biochemical demand of oxygen. Spatial discretization has been performed in two layers. The simultaneous approach proceeds by discretizing control and state variables by collocation over finite elements and solving the large scale nonlinear program with an interior point method with successive quadratic programming techniques.     

带路径约束的聚烯烃牌号切换操作优化方法

产品多样化需求使得聚烯烃生产过程中经常需要进行牌号切换操作。以往关于牌号切换优化的研究大多只关心切换过程结束后聚合物质量指标是否达到目标牌号值,对过渡过程中质量指标及状态变量的波动情况缺少关注,而过程的波动会影响到最终产物的质量性质和操作平稳性。为此,本文以聚乙烯气相流化床反应器为对象,通过在牌号切换优化命题中加入关于熔融指数等的路径约束,防止过渡过程中的状态变量剧烈波动影响聚合物树脂质量。为求解此类带路径约束的动态优化问题,对常规的控制变量参数化方法进行了改进,通过求解微分代数方程(DAE方程)将路径约束转化为控制变量约束。仿真结果表明,加入路径约束可以有效避免牌号切换中变量的剧烈波动,增强过程平稳性。     

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。     

基于全局正交配置的非线性预测控制算法

针对非线性预测控制(NMPC)在线优化计算量大这一关键问题,提出一种基于全局正交配置的非线性预测控制算法。该算法以高阶插值正交多项式为基函数同时配置优化时域内的状态变量和控制变量,将连续动态优化问题转化为非线性规划问题(NLP)求解。全局正交配置可以使用较少的配置点而获得较高的逼近精度,这样即使NMPC使用很长的优化时域,离散化后得到的NLP问题的规模也比较小,能够有效地降低在线优化计算量。最后,以连续聚合反应过程为例验证了算法的有效性。     

Simultaneous process and control system design for grade transition in styrene polymerization

We present a comprehensive approach to the simultaneous design and control of a continuous stirred tank reactor (CSTR) for styrene solution polymerization that must be able to produce different polymer grades. The resulting tool allows simultaneous selection of the polymerization equipment, the multivariable feedforward-feedback controller's structure and tuning parameters, the steady states and the transition paths between them. For this purpose a multiobjective optimization is implemented to minimize the annualized reactor cost, the operating costs, the production of off-specification polymer and the transition time between steady states. Trade-offs between the sometimes conflicting objectives are dealt with by the optimization. Unlike many previous grade transition studies, steady states are not known a priori. The only known parameters are the target molecular weights to be produced at each steady state. We have analyzed three different scenarios, and propose practical criteria for selecting the most reasonable optimum when the solution is not unique.     

Study on Optimal Strategy of Grade Transition in Industrial Fluidized Bed Gas-Phase Polyethylene Production Process

A model of grade transition is presented for a commercialized fluidized bed gas-phase polyethylene production process. The quantity of off-specification product and the time of grade transition can be minimized by the optimization of operating variables, such as polymerization temperature, the ratio of hydrogen to ethylene, the ratio of co-monomer to ethylene, feed rate of catalyst, and bed level. A new performance index, the ratio of melt flow (MFR), is included in the objective function, for restraining the sharp adjustment of operation variables and narrowing the distribution of molecular weight of the resin. It is recommended that catalyst feed rate and bed level are decreased in order to reduce the grade transition time and the quantity of off-specification product. This optimization problem is solved by an algorithm of sequential quadratic programming (SQP) in MATLAB. There is considerable difference between the forward transition and reverse transition of grade with regard to the operating variab     

热集成精馏系统的动态优化策略研究

提出基于机理模型,以最小能耗为目标的热集成精馏系统的动态优化策略。SQP和正交配置的离散化方法实现动态优化的计算,仿真结果表明该方法的有效性。     

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     

连续聚合过程中产品牌号过渡的优化

以流化床乙烯气相聚合工艺为例建立了产品牌号切换模型 ,通过同时优化聚合温度、氢气和共聚单体的浓度、催化剂流率和料位高度等 5个操作变量的变化轨迹 ,使产品牌号的切换时间最短 ,过渡料数量最少 .研究表明 ,聚合温度、氢气和共聚单体的浓度对树脂性能指标的控制起主要作用 .为了减少过渡料的数量 ,一般均需降低催化剂流率和料位高度 .通过在目标函数中增加熔流比控制项可以抑制操作变量的剧烈调节 ,达到控制分子量分布的目的 .同时发现 ,产品牌号的正向和反向切换所得到的操作变量的最优轨迹很不相同 ,反映了系统的非线性