基于随机优化的热耦合复杂精馏系统的综合(Ⅰ)模型化方法

基于随机型最优化策略,针对包含简单塔、带有侧线蒸出及侧线汽提塔的复杂塔、全热耦合（或Petlyuk）塔的热耦合复杂精馏塔系统的综合问题,提出一种模型化方法.针对热耦合复杂精馏流程系统所需塔段数目以及冷凝器和再沸器数目的不确定性,提出了一种分解求解策略,将原问题分解成一系列具有不同塔段数的子问题分别求解;针对流程结构的优化提出一种流程结构的编码表达法,该方法将问题的分离序列结构和热耦合方式分别用两组编码表示,对分离序列的编码采用了数据结构理论中的二叉树排序方法,使流程结构的描述变得更加简便;最后以预分馏塔组分回收率及回流比为连续变量,建立了热耦合复杂精馏系统优化的[JP+1]混合整数非线性规划（MINLP）模型,该模型用改进的模拟退火算法求解,可同时得到优化的流程结构和操作参数.     

Multistream heat exchangers: Equation‐oriented modeling and flowsheet optimization

Multistream heat exchangers (MHEXs), typically of the plate‐fin or spiral‐wound type, are a key enabler of heat integration in cryogenic processes. Equation‐oriented modeling of MHEXs for flowsheet optimization purposes is challenging, especially when streams undergo phase transformations. Boolean variables are typically used to capture the effect of phase changes, adding considerable difficulty to solving the flowsheet optimization problem. A novel optimization‐oriented MHEX modeling approach that uses a pseudo‐transient approach to rapidly compute stream temperatures without requiring Boolean variables is presented. The model also computes an approximate required heat exchange area to determine the optimal tradeoff between operating and capital expenses. Subsequently, this model is seamlessly integrated in a previously‐introduced pseudo‐transient process modeling and flowsheet optimization framework. Our developments are illustrated with two optimal design case studies, an MHEX representative of air separation operation and a natural gas liquefaction process. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1856–1866, 2015     

A novel stochastic optimization method to efficiently synthesize large-scale nonsharp distillation systems

This study presents a novel stochastic optimization method for the efficient synthesis of large-scale nonsharp distillation systems, where heat integration and thermal coupling can be involved simultaneously. A new binary tree encoding method was developed to represent distillation sequences with no limits on the number of middle components in nonsharp splits to ensure a complete solution space. Thermally coupled structures were defined by 0–1 binary variables. Evolutionary rules were developed to generate neighboring distillation configurations randomly. Finally, an optimization framework was proposed, where simulated annealing (SA) algorithm was used to optimize distillation configurations; for a certain distillation configuration randomly generated by SA, its continuous variables were optimized using particle swarm optimization algorithm. Four cases—including the synthesis of six- and seven-component nonsharp heat integrated and thermally coupled distillation sequences—were studied to demonstrate that the proposed method was efficient and could obtain optimal and valuable suboptimal solutions with high probabilities.     

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.     

面向热集成耦合的精馏过程集成控制与优化

针对具有塔底产品和进料换热热集成的精馏过程，通过机理分析和基于流程模拟软件的仿真分析，说明了再沸热负荷与塔底液位、进料温度等变量的耦合关系，提出了一种面向热集成耦合的集成控制和优化策略，使用再沸热负荷对原料的焓值变化进行补偿，并兼顾塔底液位，保证产品质量合格。集成策略在实际装置上进行了应用研究，解决了塔底产品流量与再沸热负荷之间的协调控制问题。     

Optimization of sub-ambient separation systems with embedded cubic equation of state thermodynamic models and complementarity constraints

A previously developed equation-based flowsheet optimization framework is extended and applied to design sub-ambient separation systems for oxy-fired coal power systems with carbon capture. Unlike most commercial flowsheet design and optimization tools, the proposed methods use exact derivatives and large-scale nonlinear programming algorithms to solve large flowsheet design problems with many degrees of freedom, including the simultaneous design of air separation units (ASUs) and their accompanying multistream heat exchangers. Emphasis is placed on additional model improvements regarding thermodynamic calculations. In order to maintain differentiability, complementarity constraints are used to model switches, including vanishing and reappearing phases. Nevertheless, these complementarity constraints may construct trivial phase equilibrium solutions, and a procedure based on embedded bubble and dew points calculations is proposed to avoid them. Furthermore, additional complementarity constraints for the cubic equation of state model are proposed to ensure correct phase identification in the supercritical region. Finally, the efficacy of these new models are demonstrated by optimization of the CO₂ processing unit and compression train for an oxy-fired power plant.     

Simultaneous process synthesis,heat, power,and water integration of thermochemical hybrid biomass,coal, and natural gas facilities

A comprehensive wastewater network is introduced into a thermochemical based process superstructure that will convert biomass, coal, and natural gas to liquid (CBGTL) transportation fuels. The mixed-integer nonlinear optimization (MINLP) model includes simultaneous heat, power, and water integration that utilizes heat engines to recover electricity from waste heat and several treatment units to process and recycle wastewater. A total of 108 case studies are analyzed which consist of combinations of six coal feedstocks, three biomass feedstocks, three plant capacities, and two process superstructures. This study discusses important process topological differences between the case studies and illustrates each component of the process synthesis framework using the two medium-sized capacity case studies that have low-volatile bituminous coal and biomass feedstocks.     

A new approach to thermal integration of distillation sequences

This paper describes a new approach for synthesizing thermally integrated distillation sequences. There are two key developments in this research. First, the overall flowsheet is optimized simultaneously as opposed to the traditional technique of optimizing each tower sequentially followed by heat integration. Second, maximum energy recovery techniques are used to estimate the total energy requirements of the thermally integrated network, eliminating the need to synthesize a heat exchanger network on each function evaluation in the optimization routine. A frequently reported five component light alkane system (Rathore's Problem) was used to illustrate this approach. Optimized process flowsheets, energy savings and a comparison with literature values are presented.     

Equation‐oriented simulation and optimization of process flowsheets incorporating detailed spiral‐wound multistream heat exchanger models

Multiple chemical processes rely on multistream heat exchangers (MHEXs) for heat integration, particularly at cryogenic temperatures. Owing to their geometric complexity, the detailed design of MHEXs is typically iterative: the exchanger geometric parameters are selected to match process specifications resulting from a flowsheet optimization step; then, the flowsheet is reoptimized with the predictions of the MHEX model, and these steps are repeated until a convergence criterion is met. This paper presents a novel framework that allows—for the first time, to our knowledge—for the simultaneous optimization of the process flowsheet and the detailed MHEX design. Focusing on spiral‐wound MHEXs, we develop an equation‐oriented exchanger model using industry‐accepted heat transfer and pressure drop correlations for single‐phase and multiphase streams. We embed this model in our previously developed pseudo‐transient equation‐oriented process simulation and optimization framework. We demonstrate our approach on an industrial case study, the PRICO^® natural gas liquefaction process. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3778–3789, 2017     

Global optimization of multiphase flow networks using spline surrogate models

A general modelling framework for optimization of multiphase flow networks with discrete decision variables is presented. The framework is expressed with the graph and special attention is given to the convexity properties of the mathematical programming formulation that follows. Nonlinear pressure and temperature relations are modelled using multivariate splines, resulting in a mixed-integer nonlinear programming (MINLP) formulation with spline constraints. A global solution method is devised by combining the framework with a spline-compatible MINLP solver, recently presented in the literature. The solver is able to globally solve the nonconvex optimization problems. The new solution method is benchmarked with several local optimization methods on a set of three realistic subsea production optimization cases provided by the oil company BP.     

考虑中间换热器的能量集成精馏序列合成

针对考虑中间换热器（IHE）的精馏序列合成问题,提出基于随机优化策略的能量集成非清晰精馏序列（IHE-HIDSs）合成方法。通过对精馏序列分离任务合并处引入二元0/1变量表示是否存在IHE,以精馏序列的年总成本（TAC）为优化目标,建立了该合成问题的隐式混合整数非线性规划模型（MINLP）,通过模拟退火和粒子群优化（SA-PSO）混合随机优化算法进行求解。为验证在精馏序列合成中同时考虑IHE的必要性以及所提出合成方法的有效性,对五组分醇类混合物和五组分烷烃类混合物两个算例的精馏序列合成问题进行了研究。结果表明,相比同时考虑热耦合和能量集成的精馏序列,IHE-HIDS具有更低的TAC。此外,所提出的方法可以在合理的计算时间内以高概率获得多个分离序列方案。     

Equation‐oriented optimization of process flowsheets with dividing‐wall columns

We present a new modeling approach for dividing‐wall columns (DWCs) that is amenable to equation‐oriented flowsheet simulation and optimization. The material, equilibrium, summation, and heat (MESH) equations describing a DWC are highly coupled and nonlinear, making DWC‐based process flowsheets challenging to simulate. Design optimization poses further challenges, typically requiring integer variables to select the number of column stages. To address these difficulties, we represent DWCs as networks of pseudo‐transient (differential‐algebraic) subunit models. We show that these networks have the same steady‐state solution as the original (algebraic) MESH equations, but present significant numerical benefits. We then embed these models in a previously developed pseudo‐transient flowsheet modeling and optimization framework. We further reformulate the models to require only continuous decision variables when selecting the optimal number of stages during design optimization. To illustrate these concepts, we discuss the DWC‐based intensification of the dimethyl ether process. © 2015 American Institute of Chemical Engineers AIChE J, 62: 704–716, 2016     

Evolutionary thermodynamic synthesis of zeotropic distillation sequences

The objective of this paper is to present a new evolutionary strategy for the synthesis of simple and complex distillation sequences. The initial flowsheet is the reversible multicomponent distillation scheme, which includes as the thermodynamically optimum superstructure many of the possible separation configurations. Assumptions with respect to ideal boiling behaviour or constant molar overflow are not required, but azeotropic systems are excluded. The computation time requirement is extremely low, because only flash-type calculations and no rigorous column simulations are involved. In this approach columns and heat exchangers are successively removed from the initial flowsheet by using thermodynamic information on splits. In this way not only simple sequences, but also sidestream withdrawals, sidestream strippers and sidestream enrichers can be created. The evolutionary strategy and the underlying modification criteria will be illustrated by several examples. Some comments on common heuristic rules and heat-integration possibilities are made in conclusion.     

The effects of feed splitting and heat integration in classical arrangements on cost minimization in separation of ternary mixture

Multi-component separation by distillation is known as a conventional method in chemical processes. In this study the effects of feed splitting on three classical arrangements (with and without heat integration) were investigated in order to reduce the total annual cost (TAC). Ternery mixture separation (propane, butane and pentane) by distillation was selected as a case study. An optimization problem was defined based on the effective parameters affecting the total annual cost. Optimum values for decision variables were calculated by applying the genetic algorithm. Calculation results showed that the heat integration procedure in the feed splitting method reduced the TAC significantly. It was also indicated that the prefractionator arrangement with heat integration resulted in the greatest decrease in the total annual cost.     

Formulating the optimization problem when using sequential quadratic programming applied to a simple LNG process

Sequential quadratic programming (SQP) may be very efficient compared with other techniques for the optimization of simple processes for the liquefaction of natural gas (LNG), and can be combined with process evaluation using commercial flowsheet simulators. However, the level of success is dependent on the formulation of the problem. In this work, effects of varying different aspects of the optimization problem formulation is investigated, such as variable selection, formulae for the estimation of derivatives, initial values, variable bounds, and formulation of constraints. Especially the formulation of the constraint for the temperature difference between the hot and cold composite curve is essential. The commonly used minimum temperature difference constraint should generally not be employed in gradient based optimization. Recommendations regarding optimization of simple LNG processes using SQP and flowsheet simulators are provided.     

SIMOP: Efficient reactive distillation optimization using stochastic optimizers

A methodology to improve the efficiency of stochastic methods applied to the optimization of chemical processes with a large number of equality constraints is presented. The methodology is based on two steps: (a) the optimization of the simulation step, which involves the optimum choice of design variables and subsystems to be simultaneously solved; (b) the optimization of the nonlinear programming (NLP) problem using stochastic methods. For the first step a flexible tool (SIMOP) is used, whereby different numerical procedures can be easily obtained, taking into account the problem formulation and specific characteristics, the need for specific initialization schemes and the efficient solution of systems of nonlinear equations. This methodology was applied to the optimization of a reactive distillation process for the production of ethylene glycol. Due to the complexity of the mathematical model, several different numerical procedures were generated, and their influence on the computational burden and on the reliability and accuracy of the optimization to reach the global optimum were studied. The results obtained suggest that in addition to the choice of design variables, the structure of subsystems associated to numerical procedures has a considerable impact on the performance of the optimizers.     

Deterministic global flowsheet optimization: Between equation-oriented and sequential-modular methods

Flowsheet optimization problems often exhibit multiple (suboptimal) local solutions. However, deterministic global optimization can get prohibitively expensive with increasing flowsheet size and has been mostly restricted to equation-oriented flowsheet models. In this work, we demonstrate how a reduced-space formulation for global optimization (a hybrid between equation-oriented and sequential-modular methods) can be applied to flash calculations as well as a process flowsheet combining flash units, reaction, and recycling, and investigate the influence of model formulation on solution time. Both for flash units using ideal or nonideal thermodynamics as well as for the flowsheet, the reduced-space formulation can be solved over an order of magnitude faster than a fully equation-oriented formulation. This demonstrates the potential of the approach even for flowsheets with implicit unit operations. However, the results also highlight the importance of identifying suitable model formulations at the unit operation level as well as the flowsheet level. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1022–1034, 2019     

Decentralized Control System Design for a Ternary Reactive Distillation with Inert Using Mixed Integer Optimization

Inferential control of ternary reactive distillation with inert is controversially discussed in recent literature. For further clarification, a systematic study based on mixed integer dynamic optimization is presented. Special emphasis is placed on robustness with respect to various disturbances arising in practice. This gives rise to a stochastic problem formulation which is extended step by step. Through this, significant improvements can be achieved and it is concluded that inferential control of ternary reactive distillation with inert is feasible.     

全流程卷式反渗透海水淡化系统操作优化

在对反渗透海水淡化系统流程和实际应用分析的基础上,提出了一种旨在降低总体操作费用的全流程反渗透海水淡化系统优化方法。首先根据系统变参数特点并充分利用蓄水池的缓冲能力,建立了反渗透过程机理模型、蓄水池动态过程模型以及变参数方程模型,实现了整个流程的方程描述。然后根据工艺流程和操作过程费用组成情况建立了总的操作费用模型,得到了全流程单位产水费用指标。在此基础上建立了以总体操作费用最低为目标、以开放方程描述的各模型方程为约束、以设备和产品质量限制为边界的优化命题,采用联立求解技术将该微分代数方程组成的优化（DAOP）问题转化为NLP问题后进行求解。最后对某海水淡化系统进行了实例研究。优化求解结果不仅表明本优化方法可以大幅降低实际操作费用,而且通过求解还可得到各种变参数条件下最优操作费用组成,以及实现费用最低的最优操作压力和流量变化曲线。本研究对优化海水淡化系统操作、降低总体操作费用具有重要意义。     

Simultaneous synthesis of distillation sequences in overall process schemes using an improved minlp approach

This paper describes the synthesis of distillation sequences simultaneously with the synthesis of other process subsystems. An improved MINLP approach is proposed for the synthesis of complex problems. The improvements were made on three major MINLP levels. By postulating the superstructures we propose to use smaller and more compact superstructures of the distillation sequences included in the flowsheet superstructure rather than the usual tree and network representations. In the modelling step a higher degree of simultaneity has been accomplished by the use of simultaneous models of the distillation column and aggregated models of other process units. To facilitate the optimization phase the modified OA/ER algorithm [Kravanja and Grossmann, Ind. Engng. Chem. Res.26, 1869–1880 (1994)], implemented in the computerized synthesizer PROSYN-MINLP, has been used to reduce the effect of nonconvexities. Also, a special initialization and linearization scheme for simultaneous synthesis of HEN has been proposed. The improved method is illustrated by the synthesis of the separation subsystem followed by the simultaneous synthesis of the heat integrated separation system and its heat exchanger network (HEN). Finally, the optimization of the overall process and the simultaneous synthesis of its distillation system and heat integrated HEN is presented.