MILP-based initialization strategies for the optimal design of water-using networks

The optimal design of water-using systems involves necessarily the exploitation of all possible water reuse and recycling alternatives. The general problem can be formulated as a non-convex nonlinear program (NLP), but due to the presence of bilinear terms, it may be difficult for local optimization solvers to attain global optimal solutions. To overcome this difficulty, this paper presents two mixed integer linear programming (MILP)-based procedures to generate a few structurally different starting points for the NLP. In both, the problem is decomposed into calculation stages by assuming that the water streams progress in series through the water-using units, with the binary variables selecting which unit belongs to a certain stage. Their main difference concerns the way fixed flowrate units are handled, either separately or in conjunction with a fixed load operation, since the former comprise a linear subsystem. The two algorithms are compared to a closely related LP-based method taken from the literature and to the one employed by the global optimization solver BARON. The results from a large set of example problems confirm their effectiveness in avoiding local solutions despite the small number of starting points. In contrast to the previous method they are easily scalable and, for some of the larger problems, could find better solutions than BARON with significantly fewer computational resources. The results have also shown that the option of tackling one unit at a time is the most favorable.     

用水系统的近优化运行及其操作窗口获取方法

针对用水系统优化设计和操作的可靠性问题,本文以用水过程进出口浓度为噪声因子、以近优化用水目标为控制因子,提出了用水系统近优化设计和操作的操作窗口分析方法及其实现步骤;建立了用水系统近优化操作参数获取的数学模型和搜索策略,并通过计算实例阐明了所提出方法的可行性。本文提出的分析方法为用水系统的近优化设计和操作可靠性的分析提供了理论分析基础。     

再生循环水系统引入再生过程后夹点位置

引入再生循环的最优水系统可以最大限度地节约新鲜水的用量和减少废水的排放,是当前节水技术研究的重点。用水系统引入再生过程后,极限供水线会发生变化,从而水系统夹点个数以及位置都可能会发生变化。运用前人总结出的再生循环过程最佳供水线的构造方法,分析影响引入再生过程后夹点位置变化的因素,发现引入再生过程前后夹点位置的变化情况与以下因素有关：极限复合曲线上的凹点位置以及凹向极限供水线的程度和最高浓度用水单元水流率与新鲜水流率的关系,并分析得出夹点位置的变化规律,从而为用水网络的分析和设计提供理论性的指导。     

含再生再利用的用水网络的优化设计

对单组分含再生再利用的用水系统,提出了一种基于序贯操作模型的整体优化设计方法。该方法分别针对单组分含再生再利用的用水网络设计可能存在的三种情况,以新鲜水和再生水用量最小为目标,给出了相应的设计策略,数学的表达是一个非线性规划。首先依据规则将操作对贫流的要求进行分段排序,并通过引入操作的质量交换分配系数αi,将各操作依据规则虚拟地分配为再生前过程和再生后过程,然后按操作序列逐级进行操作和操作水源之间的的优化匹配,建立含再生再利用的用水网络的序贯操作模型,最后将此综合问题归结为非线性规划问题来求解,从而完成用水过程的设计。给出了一个实例,计算结果表明本文方法是有效和简便易行的。     

Homotopy continuation enhanced branch and bound algorithms for strongly nonconvex mixed-integer nonlinear optimization

Large-scale strongly nonlinear and nonconvex mixed-integer nonlinear programming (MINLP) models frequently appear in optimization-based process synthesis, integration, intensification, and process control. However, they are usually difficult to solve by existing algorithms within acceptable time. In this study, we propose two robust homotopy continuation enhanced branch and bound (HCBB) algorithms (denoted as HCBB-FP and HCBB-RB) where the homotopy continuation method is employed to gradually approach the optimum of the NLP subproblem at a node from the solution at its parent node. A variable step length is adapted to effectively balance feasibility and computational efficiency. The computational results from solving four existing process synthesis problems demonstrate that the proposed HCBB algorithms can find the same optimal solution from different initial points, while the existing MINLP algorithms fail or find much worse solutions. In addition, HCBB-RB is superior to HCBB-FP due to much lower computational effort required for the same locally optimal solution.     

The Zymark BenchMatetrade mark. A compact, fully-automated solution-phase reaction work-up facility for multiple parallel synthesis

The rapid growth of multiple parallel synthesis in our laboratories has created a demand for a robust, easily accessed automated system for solution-phase reaction work-up, since the manual work-up of large numbers of small-scale reactions is both time-consuming and tedious, and is a rate limiting step in the generation of large numbers of compounds for test. Work-up in chemical organic synthesis consists of a series of post-reaction operations designed using differential chemical properties to remove excess reagent or starting material, reagent products and, where possible reaction by-products. Careful consideration of post-reaction operations as a clean-up step can obviate the requirement for purification. Generally, work-up can be resolved into four operations: filtration, solvent addition (dilution, trituration), washing and separation (partition) and it is the selection and ordering of these four basic operations that constitutes a chemical work-up. Following the proven success of centralized Zymate robotic systems in the compilation, execution and work-up of complex reaction sequences, a centralized chemical work-up service has been in operation for over 12 months. It now seemed prudent that the needs of multiple parallel synthesis would be better served by the development of a compact, automated system, capable of operating in a standard chemistry laboratory fume-hood. A Zymark BenchMate platform has been configured to perform the four basic operations of chemical solution work-up. A custom-built filtration station, incorporating an integrated tipping facility for the sample tube has also been developed. Compilation of each work-up is through a set of Visual Basic procedure screens, each dedicated to a particular work-up scenario. Methods are compiled at the chemist's own PC and transferred to the BenchMate via a diskette.     

分阶段线性规划法快速设计含有多种污染物的用水网络

针对含有多种污染物用水网络的设计问题,提出了一种新方法.该方法先基于各个用水过程的污染物最大出口浓度对过程排序,然后采用GAMS(general algebraic modeling system)语言建立线性规划模型,依次对序列中的每个过程的废水回用方案进行优化计算,以确定出其最小新鲜水用量和来自前驱的废水回用量.该方法虽然不能保证所得解的全局最优性,但它能快速地找到最优或近似最优解,而且方法简单.     

多杂质体系间歇过程用水网络优化

对多杂质体系完全间歇过程用水网络优化进行了研究,建立了用水网络超结构和非线性规划数学模型,利用中间储罐跨越时间约束,设置用水过程流量上下限以加速收敛。首先确定关键杂质,并将关键杂质浓度最大的水源直接排往废水,获得简化的用水网络超结构;其次,运用GAMS求解,得到最小新鲜水量、废水量、中间储罐数目及优化的用水网络结构。实例研究证明本文提出的方法可行,并能以较少周期获得优化的网络结构,同时可以减少中间储罐数目。     

Synthesis of Water Utilization System Using Concentration Interval Analysis Method （Ⅱ） Discontinuous Process

The first part of the series of this article proposed a systematic method for the synthesis of continuous water-using system involving both non-mass-transfer-based and mass-transfer-based operations.This article,by extending the method,proposes a time-dependent concentration interval analysis（CIA）method to solve the problems associated with the synthesis of discontinuous or batch water-using systems involving both non-mass-transfer-based and mass-transfer-based operation.This method can effectively identify the possibility of water reuse and the amount of water reused under time constraints for minimizing the consumption of freshwater in single or repeated batch/discontinuous water-using systems.Moreover,on the basis of the heuristic method adapted from concentration interval analysis method for the continuous process network design,the network design for the discontinuous or batch process can be obtained through the designs for every time interval.Case study illustrates that the method presented in this article can simultaneously minimize the freshwater consumption in single or repeated batch/discontinuous water system and can determine a preferable storage tank capacity for some problems.     

Optimal integrated energy systems design incorporating variable renewable energy sources

The effect of variability in renewable input sources on the optimal design and reliability of an integrated energy system designed for off-grid mining operation is investigated via a two-stage approach. Firstly, possible energy system designs are generated by solving a deterministic non-linear programming (NLP) optimization problem to minimize the capital cost for a number of input scenarios. Two measures of reliability, the loss of power supply probability (LPSP) and energy index of reliability (EIR), are then evaluated for each design based on the minimization of the external energy required to satisfy load demands under a variety of input conditions. Two case studies of mining operations located in regions with different degrees of variability are presented. The results show that the degree of variability has an impact on the design configuration, cost and performance, and highlights the limitations associated with deterministic decision making for high variability systems.     

反应器网络综合三分布参数通用模型

提出了一种应用于反应器网络综合的三分布参数通用模型 .3个分布参数分别是侧线进料、侧线循环和侧线采出参数 ,这些参数能影响反应器网络内部的浓度和停留时间分布 ,所以由它们构成的通用模型具有简捷有效的特点 .基于此模型可将反应器网络集成转化成一个优化问题 ,通过有限元正交配置将原来含有微分方程的优化模型转化为非线性优化问题 ,优化计算后得到最优分布参数 .从案例研究可以看出 ,侧线进料、循环和采出策略能较全面地反映在不同动力学和优化目标函数下的最优反应器网络特征 ,并进而简化为工业可行的反应器网络     

基于浓度间隔分析的用水系统集成(Ⅱ)不连续过程

The first part of the series of this article proposed a systematic method for the synthesis of continuous water-using system involving both non-mass-transfer-based and mass-transfer-based operations.This article,by ex- tending the method,proposes a time-dependent concentration interval analysis(CIA)method to solve the problems associated with the synthesis of discontinuous or batch water-using systems involving both non-mass-transfer-based and mass-transfer-based operation.This method can effectively identify the possibility of water reuse and the amount of water reused under time constraints for minimizing the consumption of freshwater in single or repeated batch/discontinuous water-using systems.Moreover,on the basis of the heuristic method adapted from concentra- tion interval analysis method for the continuous process network design,the network design for the discontinuous or batch process can be obtained through the designs for every time interval.Case study illustrates that the method presented in this article can simultaneously minimize the freshwater consumption in single or repeated batch/discontinuous water system and can determine a preferable storage tank capacity for some problems.     

Control Vector Parameterization‐Based Adaptive Invasive Weed Optimization for Dynamic Processes

A novel optimal approach named invasive weed optimization‐control vector parameterization (IWO‐CVP) for chemical dynamic optimization problems is proposed where CVP is used to transform the problem into a nonlinear programming (NLP) problem and an IWO algorithm is then applied to tackle the NLP problem. To improve efficiency, a new adaptive dispersion IWO‐based approach (ADIWO‐CVP) is further suggested to maintain the exploration ability of the algorithm throughout the entire searching procedure. Several classic chemical dynamic optimization problems are tested and detailed comparisons are carried out among ADIWO‐CVP, IWO‐CVP, and other methods. The research results demonstrate that ADIWO‐CVP not only is efficient, but also outperforms IWO‐CVP in terms of both accuracy and convergence speed.     

间歇用水系统中废水回用与集中再生处理的调度优化设计方法

针对间歇用水系统建立了废水回用与废水集中再生处理协调运行和调度优化的数学规划设计模型。在多周期运行条件下,以保证循环周期中水系统最优运行为目标,提出了消除不同操作周期下储罐中水量和浓度波动的多周期反算求解策略,并确定了多周期操作下优化的用水网络。通过单杂质间歇用水系统实例阐明了所提出方法的有效性,为具有废水集中再生处理的间歇用水系统从启动到稳定的多周期操作和设计提供依据。     

A bilevel NLP sensitivity‐based decomposition for dynamic optimization with moving finite elements

Optimal control has guided numerous applications in chemical engineering, and exact determination of optimal profiles is essential for operation of separation and reactive processes, and operating strategies and recipe generation for batch processes. Here, a simultaneous collocation formulation based on moving finite elements is developed for the solution of a class of optimal control problems. Novel features of the algorithm include the direct location of breakpoints for control profiles and a termination criterion based on a constant Hamiltonian profile. The algorithm is stabilized and performance is significantly improved by decomposing the overall nonlinear programming (NLP) formulation into an inner problem, which solves a fixed element simultaneous collocation problem, and an outer problem, which adjusts the finite elements based on several error criteria. This bilevel formulation is aided by a NLP solver (the interior point optimizer) for both problems as well as an NLP sensitivity component, which provides derivative information from the inner problem to the outer problem. This approach is demonstrated on 11 dynamic optimization problems drawn from the optimal control and chemical engineering literature. © 2014 American Institute of Chemical Engineers AIChE J, 60: 966–979, 2014     

具有中间水道的多杂质用水网络简化设计方法

与常规水网络相比,具有中间水道的水网络更有利于运行和控制。浓度势是作者最近提出的解决多杂质用水网络设计的新概念。在浓度势概念基础上提出了一种具有中间水道的多杂质用水网络设计新方法。该方法采用浓度势方法设计出初始水网络,并在此基础上初步确定各中间水道的结构及水量,然后根据浓度势从小到大的顺序依次由中间水道满足各用水过程,而各级中间水道的最终水量以能满足各级水阱需求来确定。该方法只需简单计算即可完成具有两级中间水道的水网络设计。对文献实例求解结果表明,所得结果与由数学规划法得出的结果接近。     

A COMBINED MILP AND LOGIC-BASED APPROACH TO THE SYNTHESIS OF OPERATING PROCEDURES FOR BATCH PLANTS

Synthesizing a set of operating procedures for the safe and efficient transient operation of chemical plants is a difficult problem owing to the enormous number of possible combinations of actions in a typical plant. In most current industrial plant design practice, there are no formal methods for systematically transforming process specifications into operating procedures for the plant operators and into sequence control instructions for the control computers. There is much scope for a formalized computer-based procedure synthesis methodology to assist the design engineer/plant operator with both the formulation and assessment of procedures off-line and, eventually, with the on-line problem of procedure synthesis in response to unexpected situations

A recently developed approach for operating procedure synthesis for multipurpose batch plants is considered. The modelling formalism used includes the separate definition of process operations, as State Task Networks, and of physical plant, at the level of detail of a piping and instrumentation diagram. In this paper, a subgoaling procedure is developed using the State Task Network representation which decomposes the procedure synthesis goals into simpler subgoals by means of an efficient Mixed Integer Linear Programming (MILP) technique. Detailed control sequences are then generated for each subgoal using a set of rules and algorithms specific for each type of subgoal. The procedure sequences thus generated are validated by simulation on a plant model with checking of physical and operational constraints at each new plant state. We have found that this hierarchical approach to the procedure synthesis problem greatly reduces the problem complexity

The usefulness of the general approach and of the subgoaling procedure in particular are demonstrated through a multiproduct batch plant example.     

New approach for scheduling crude oil operations

Scheduling of crude oil operations is crucial to petroleum refining, which includes determining the times and sequences of crude oil unloading, blending, and CDU feeding. In the last decades, many approaches have been proposed for solving this problem, but they either suffered from composition discrepancy [Lee et al. 1996. Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management. Industrial and Engineering Chemistry Research 35, 1630-1641; Jia et al., 2003. Refinery short-term scheduling using continuous time formulation: crude-oil operations. Industrial and Engineering Chemistry Research 42, 3085-3097; Jia and Ierapetritou, 2004. Efficient short-term scheduling of refinery operations based on a continuous time formulation. Computer and Chemical Engineering 28, 1001-1019] or led to infeasible solutions for some cases [Reddy et al., 2004a. Novel solution approach for optimizing crude oil operations. A.I.Ch.E. Journal 50(6), 1177-1197; 2004b. A new continuous-time formulation for scheduling crude oil operations. Chemical Engineering Science 59, 1325-1341]. In this paper, coastal and marine-access refineries with simplified workflow are considered. Unlike existing approaches, the new approach can avoid composition discrepancy without using iterative algorithm and find better solution effectively. In this approach, a new mixed integer non-linear programming (MINLP) formulation is set up for crude oil scheduling firstly, and then some heuristic rules collected from expert experience are proposed to linearize bilinear terms and prefix some binary variables in the MINLP model. Thus, crude oil scheduling can be expressed as a complete mixed integer linear programming (MILP) model with fewer binary variables. To illustrate the advantage of the new approach, four typical examples are solved with three models. The new model is compared with the most effective models (RKS(a) and RKS(b) models) presented by Reddy et al. [2004a. Novel solution approach for optimizing crude oil operations. A.I.Ch.E. Journal 50(6), 1177-1197; 2004b. A new continuous-time formulation for scheduling crude oil operations. Chemical Engineering Science 59, 1325-1341], which proves that the new approach is valid and feasible in most small-size and medium-size problems.