A reactive optimization strategy for the simultaneous planning,scheduling and control of short-period continuous reactors

The efficient and economic operation of processing systems ideally requires a simultaneous planning, scheduling and control framework. Even when the optimal simultaneous solution of this problem can result in large scale optimization problems, such a solution can represent economic advantages making feasible its computation using optimization decomposition and/or few operating scenarios. After reducing the complexity of the optimal simultaneous deterministic solution, it becomes feasible to take into account the effect of model and process uncertainties on the quality of the solution. In this work we consider those changes in product demands that take place once the process is already under continuous operation. Therefore, a reactive strategy is proposed to meet the new product demands. Based on an optimization formulation for handling the simultaneous planning, scheduling, and control problem of continuous reactors, we propose a heuristic strategy for dealing with unexpected events that may appear during operation of a plant. Such a strategy consists of the rescheduling of the products that remain to be manufactured after the given disturbance hits the process. Such reactive strategy for dealing with planning, scheduling and control problems under unforeseen events is tested using two continuous chemical reaction systems.     

Simultaneous mixed-integer dynamic optimization for integrated design and control

We consider strategies for integrated design and control through the robust and efficient solution of a mixed-integer dynamic optimization (MIDO) problem. The algorithm is based on the transformation of the MIDO problem into a mixed-integer nonlinear programming (MINLP) program. In this approach, both the manipulated and controlled variables are discretized using a simultaneous dynamic optimization approach. We also develop three MINLP formulations based on a nonconvex formulation, the conventional Big-M formulation and generalized disjunctive programming (GDP). In addition, we compare the outer approximation and NLP branch and bound algorithms on these formulations. This problem is applied to a system of two series connected continuous stirred tank reactors where a first-order reaction takes place. Our results demonstrate that the simultaneous MIDO approach is able to efficiently address the solution of the integrated design and control problem in a systematic way.     

A decomposition algorithm for simultaneous scheduling and control of CSP systems

We present a decomposition algorithm to perform simultaneous scheduling and control decisions in concentrated solar power (CSP) systems. Our algorithm is motivated by the need to determine optimal market participation strategies at multiple timescales. The decomposition scheme uses physical insights to create surrogate linear models that are embedded within a mixed‐integer linear scheduling layer to perform discrete (operational mode) decisions. The schedules are then validated for physical feasibility in a dynamic optimization layer that uses a continuous full‐resolution CSP model. The dynamic optimization layer updates the physical variables of the surrogate models to refine schedules. We demonstrate that performing this procedure recursively provides high‐quality solutions of the simultaneous scheduling and control problem. We exploit these capabilities to analyze different market participation strategies and to explore the influence of key design variables on revenue. Our results also indicate that using scheduling algorithms that neglect detailed dynamics significantly decreases market revenues. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2408–2417, 2018     

间歇化工过程热集成研究进展

间歇化工过程热集成问题的研究能够促进过程系统的可持续发展并且提高产业经济性和技术竞争力,顺应了化工发展大环境。本文介绍了以系统综合优化为目标的间歇化工过程热集成研究的发展现状,整理了早期研究的三大通用图解模型,并讨论和比较了在建模求解过程中常见算法。总结了当前研究的重点在换热网络设计优化、热储罐系统和考虑调度的热集成三个方面,并评述了与之相关的进展、瓶颈和研究意义。指出了热集成问题已成为当前间歇化工过程的研究热点,其中热集成和生产调度的协同优化十分必要,能够从系统全局的角度上给出优化方案。但由于间歇化工过程中存在较多的不确定性和约束条件,增加了热集成的研究难度,因此对间歇化工过程优化设计提出了更高的要求。     

Integrated scheduling and dynamic optimization of batch processes using state equipment networks

A systematic framework for the integration of short‐term scheduling and dynamic optimization (DO) of batch processes is described. The state equipment network (SEN) is used to represent a process system, where it decomposes the process into two basic kinds of entities: process materials and process units. Mathematical modeling based on the SEN framework invokes both logical disjunctions and operational dynamics; thus the integrated formulation leads to a mixed‐logic dynamic optimization (MLDO) problem. The integrated approach seeks to benefit the overall process performance by incorporating process dynamics into scheduling considerations. The solution procedure of an MLDO problem is also addressed in this article, where MLDO problems are translated into mixed‐integer nonlinear programs using the Big M reformulation and the simultaneous collocation method. Finally, through two case studies, we show advantages of the integrated approach over the conventional recipe‐based scheduling method. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

UNCERTAINTY AT BOTH DESIGN AND OPERATION STAGES

Process uncertainty is almost always an issue during the design of chemical processes (CP). In the open literature it has been shown that consideration of process uncertainties in optimal design necessitates the incorporation of process flexibility. Such an optimal design can presumably operate reliably in the presence of process and modeling uncertainty. Halemane and Grossmann (1983) introduced a feasibility function for evaluating CP flexibility. They also formulated a two-stage optimization problem for estimating the optimal design margins. These formulations, however, are based implicitly on the assumption that during the operation stage, uncertain parameters can be determined with enough precision. This assumption is rather restrictive and is often not met in practice. When available experimental information at the operation stage does not allow a more precise estimate of some of the uncertain parameters, new formulations of the flexibility condition and the optimization problem under uncertainty are needed. In this article, we propose such formulations, followed by some computational experiments.     

A nested online scheduling and nonlinear model predictive control framework for multi-product continuous systems

In the pursuit of integrated scheduling and control frameworks for chemical processes, it is important to develop accurate integrated models and computational strategies such that optimal decisions can be made in a dynamic environment. In this study, a recently developed switched system formulation that integrates scheduling and control decisions is extended to closed-loop operation embedded with nonlinear model predictive control (NMPC). The resulting framework is a nested online scheduling and control loop that allows to obtain fast and accurate solutions as no model reduction is needed and no integer variables are involved in the formulations. In the outer loop, the integrated model is solved to calculate an optimal product switching sequence such that the process economics is optimized, whereas in the inner loop, an NMPC implements the scheduling decisions. The proposed scheme was tested on two multi-product continuous systems. Unexpected large disturbances and rush orders were handled effectively.     

A multiobjective approach to design chemical plants with robust dynamic operability characteristics

In chemical plants, operability problems arise mainly due to poor process designs, inaccurate models and/or the control system designs that are unable to cope with process uncertainties. In this paper, a process design methodology is presented that addresses the issue of improving dynamic operability in the present of process uncertainty through appropriate design modifications. The multiobjective nature of the design problem is carefully exploited in the subsequent formulations and a nonlinear programming approach is taken for the simultaneous treatment of both steady-state and dynamic constraints.

Scope—Today, a chemical engineer faces the challenge of designing chemical plants that can operate safely, smoothly and profitably within a dynamic process environment. For a typical chemical plant, major contributions to such an environment originate from external disturbances such as variations in the feedstock quality, different product specifications and/or internal disturbances like catalyst poisoning and heat-exchanger fouling. To guarantee a flexible operation despite such upsets, traditionally, the procedure was either to oversize the equipment or to place large storage tanks between the processing units. Proposed design methods attempted to find optimal operating regimes for chemical plants while compensating for process uncertainty through empirical overdesign factors.

Studies concerned with the interplay between the process design and operation aspects have appeared recently [1, 2] and focused on achieving better controllability upon modifying the plant design, without explicitly considering process uncertainty. Nevertheless, maintaining satisfactory dynamic operability in an environment of uncertainty remained as a pressing issue and the need was raised quite frequently for a rigorous treatment of the topic [3].

The development of new analytical tools [4, 5] made it possible to consider dynamic operability at the process design stage and modify the plant design accordingly. In this paper, a methodology is presented, that systematically guides the designer towards process designs with better dynamic operability and economics, The problem is formulated within a multiobjective optimization framework and makes extensive use of singular-value decomposition and nonlinear semi-infinite programming techniques.

Conclusions and Significance—A multiobjective optimization problem is proposed for designing chemical processes with better dynamic operability characteristics. Robustness indices are used as the indicators of dynamic operability and placed as constraints within the optimization scheme. A semi-infinite nonlinear programming problem results due to the frequency-dependent nature of such constraints. A discretization procedure is suggested to handle the infinite number of constraints and an ellipsoid algorithm allows an interactive solution of the process design problem. A process consisting of three CSTRs is treated as an example, illustrating the potential of the methodology in solving design-related operability problems.     

Dynamic predictive scheduling of operational strategies for continuous processes using mixed-logic dynamic optimization

Industrial processes are usually operated in a highly dynamic environment, e.g. with time-varying market prizes, customer demand, technological development or up- and downstream processes. Due to these disturbances, the operational strategies comprising objectives and constraints are regularly adjusted to reflect a change in the environment in order to achieve or maintain optimal process performance. The related operational objectives need not only be of an economical nature, but can also include flexibility, risk or ecological objectives. In this paper, a novel methodology is presented for the modeling and dynamic predictive scheduling of operational strategies for continuous processes. Optimal control actions are computed on a moving horizon employing discrete-continuous modeling and mixed-logic dynamic optimization as introduced by Oldenburg et al. (2003). The approach is successfully demonstrated considering the operation of a wastewater treatment plant.     

Simultaneous mixed-integer dynamic optimization for environmentally benign electroplating

Hoist scheduling, especially cyclic hoist scheduling (CHS), is used to maximize the manufacturing productivity of electroplating processes. Water-reuse network design (WRND) for the electroplating rinsing system targets the optimal water allocation, such that fresh water consumption and wastewater generation are minimized. Currently, there is still a lack of studies on integrating CHS and WRND technologies for electroplating manufacturing. In this paper, a multi-objective mixed-integer dynamic optimization (MIDO) model has been developed to integrate CHS and WRND technologies for simultaneous consideration of productivity and water use efficiency for environmentally benign electroplating. The orthogonal collocation method on finite elements is employed to convert the MIDO problem into a mixed-integer nonlinear programming (MINLP) problem. The efficacy of the methodology is demonstrated by solving a real electroplating example. It demonstrates that the computational methods of production scheduling, process design, and dynamic optimization can be effectively integrated to create economic and environmental win-win situations for the electroplating industry.     

Release mechanism analysis of design margin for slowly-time-varying chemical processes

Slowly-time-varying characteristics are common in chemical processes, and the changes of slowly-time-varying parameters in an operating cycle gradually decrease the performance of chemical process. So, enough margins must be added for design variables during the phase of process design according to the possible worst-case influence of slowly-time-varying parameters. The design margins will be released gradually compensating the worse influence of slowly-time-varying parameters in an operating cycle. It can be called as a perfect operation that the operating point is on the boundary of process constraints when an operating cycle is ending. In this paper, the margin release mechanism of slowly-time-varying chemical processes is analyzed. Based on the universal dynamic model containing slowly-time-varying parameters, the full cycle operation optimization is solved by minimum principle of optimal control. It is found that the optimal margin release trajectory is related to the curve of slowly-time-varying parameter, ensuring that the optimal margin release is only dependent on the operating cycle. This mechanism is verified by the example of acetylene hydrogenation reactor. For slowly-time-varying chemical processes, the shorter the operating cycle is set, the faster the design margin is released, the higher temporary economic benefit is obtained; otherwise, the longer the operating cycle is set, the more integrated economic benefit is accomplished.     

慢时变化工过程裕量释放机制分析

化工过程普遍存在慢时变特性,在一个运行周期内慢时变参数的变化造成化工装置性能逐渐下降。为此,过程设计时需要按照慢时变参数可能的“最坏”影响对设计变量留出足够的设计裕量,在一个运行周期内通过操作逐渐释放,补偿慢时变参数的不利影响,且理想操作是保证到运行周期结束时化工装置性能恰好达到过程约束边界。本文对慢时变过程设计裕量的释放机制进行了分析,考虑含慢时变参数的全周期操作优化通用动态模型,通过最优控制的极小值原理求解该优化问题,建立了最优裕量释放轨迹和慢时变参数变化曲线之间的联系,从而证明最优裕量释放只与慢时变化工过程的运行周期有关。以乙炔加氢反应器为例验证了该裕量释放机制,对于慢时变化工过程,设定的运行周期越短,设计裕量释放越快,仅能获得较高的短期经济效益;反之,设定较长的运行周期,设计裕量缓慢释放,能获得更高的长期经济效益。     

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     

Advances in simultaneous strategies for dynamic process optimization

Following on the popularity of dynamic simulation for process systems, dynamic optimization has been identified as an important task for key process applications. In this study, we present an improved algorithm for simultaneous strategies for dynamic optimization. This approach addresses two important issues for dynamic optimization. First, an improved nonlinear programming strategy is developed based on interior point methods. This approach incorporates a novel filter-based line search method as well as preconditioned conjugate gradient method for computing search directions for control variables. This leads to a significant gain in algorithmic performance. On a dynamic optimization case study, we show that nonlinear programs (NLPs) with over 800,000 variables can be solved in less than 67 CPU minutes. Second, we address the problem of moving finite elements through an extension of the interior point strategy. With this strategy we develop a reliable and efficient algorithm to adjust elements to track optimal control profile breakpoints and to ensure accurate state and control profiles. This is demonstrated on a dynamic optimization for two distillation columns. Finally, these algorithmic improvements allow us to consider a broader set of problem formulations that require dynamic optimization methods. These topics and future trends are outlined in the last section.     

动态过程优化算法的计算量比较

A comparison of arithmetic operations of two dynamic process optimization approaches called quasi-sequential approach and reduced Sequential Quadratic Programming (rSQP) simultaneous approach with respect to equality constrained optimization problems is presented. Through the detail comparison of arithmetic operations, it is concluded that the average iteration number within differential algebraic equations (DAEs) integration of quasi-sequential approach could be regarded as a criterion. One formula is given to calculate the threshold value of average iteration number. If the average iteration number is less than the threshold value, quasi-sequential approach takes advantage of rSQP simultaneous approach which is more suitable contrarily. Two optimal control problems are given to demonstrate the usage of threshold value. For optimal control problems whose objective is to stay near desired operating point, the iteration number is usually small. Therefore, quasi-sequential approach seems more suitable for such problems.     

设计余量对运行优化和化学过程控制性能的影响简

Operation optimization is an effective method to explore potential economic benefits for existing plants. The m.aximum potential benefit from operationoptimization is determined by the distances between current operating point and process constraints, which is related to the margins of design variables. Because of various ciisturbances in chemical processes, some distances must be reserved for fluctuations of process variables and the optimum operating point is not on some process constraints. Thus the benefit of steady-state optimization can not be fully achied（ed while that of dynamic optimization can be really achieved. In this study, the steady-state optimizationand dynamic optimization are used, and the potential benefit-is divided into achievable benefit for profit and unachievable benefit for control. The fluid catalytic cracking unit （FCCU） is used for case study. With the analysis on how the margins of design variables influence the economic benefit and control performance, the bottlenecks of process design are found and appropriate control structure can be selected.     

化工过程运行系统的集成

提出了基于智能体方法的化工过程运行系统的集成策略.依据过程操作响应的时间尺度,把过程运行系统分成故障检测与诊断、模拟优化和调度3个子系统,分别建立相应的智能体模型.通过信息集成和任务集成实现化工过程运行系统的整体集成.报道了该集成方法对TE过程的案例应用.结果表明：基于智能体的方法能实现多个运行决策的全局协调和集成,达到过程运行系统整体优化的目标.     

Simultaneous mixed-integer dynamic scheduling of processes and their energy systems

Increasingly volatile electricity prices make simultaneous scheduling optimization desirable for production processes and their energy systems. Simultaneous scheduling needs to account for both process dynamics and binary on/off-decisions in the energy system leading to challenging mixed-integer dynamic optimization problems. We propose an efficient scheduling formulation consisting of three parts: a linear scale-bridging model for the closed-loop process output dynamics, a data-driven model for the process energy demand, and a mixed-integer linear model for the energy system. Process dynamics is discretized by collocation yielding a mixed-integer linear programming (MILP) formulation. We apply the scheduling method to three case studies: a multiproduct reactor, a single-product reactor, and a single-product distillation column, demonstrating the applicability to multiple input multiple output processes. For the first two case studies, we can compare our approach to nonlinear optimization and capture 82% and 95% of the improvement. The MILP formulation achieves optimization runtimes sufficiently fast for real-time scheduling.     

Integration of scheduling and control with online closed-loop implementation: Fast computational strategy and large-scale global optimization algorithm

In this paper, we propose a novel integration method to solve the scheduling problem and the control problem simultaneously. The integrated problem is formulated as a mixed-integer dynamic optimization (MIDO) problem which contains discrete variables in the scheduling problem and constraints of differential equations from the control problem. Because online implementation is crucial to deal with uncertainties and disturbances in operation and control of the production system, we develop a fast computational strategy to solve the integration problem efficiently and allow its online applications. In the proposed integration framework, we first generate a set of controller candidates offline for each possible transition, and then reformulate the integration problem as a simultaneous scheduling and controller selection problem. This is a mixed-integer nonlinear fractional programming problem with a non-convex nonlinear objective function and linear constraints. To solve the resulting large-scale problem within sufficiently short computational time for online implementation, we propose a global optimization method based on the model properties and the Dinkelbach's algorithm. The advantage of the proposed method is demonstrated through four case studies on an MMA polymer manufacturing process. The results show that the proposed integration framework achieves a lower cost rate than the conventional sequential method, because the proposed framework provides a better tradeoff between the conflicting factors in scheduling and control problems. Compared with the simultaneous approach based on the full discretization and reformulation of the MIDO problem, the proposed integration framework is computationally much more efficient, especially for large-scale cases. The proposed method addresses the challenges in the online implementation of the integrated scheduling and control decisions by globally optimizing the integrated problem in an efficient way. The results also show that the online solution is crucial to deal with the various uncertainties and disturbances in the production system.