用伪并行遗传/模拟退火算法进行多流股换热器网络综合的研究

The multi-stream heat exchanger network synthesis (HENS) problem can be formulated as a mixed integer nonlinear programming model according to Yee et al. Its nonconvexity nature leads to existence of more than one optimum and computational difficulty for traditional algorithms to find the global optimum. Compared with deterministic algorithms, evolutionary computation provides a promising approach to tackle this problem. In this paper, a mathematical model of multi-stream heat exchangers network synthesis problem is setup. Different from the assumption of isothermal mixing of stream splits and thus linearity constraints of Yee et al., non-isothermal mixing is supported. As a consequence, nonlinear constraints are resulted and nonconvexity of the objective function is added. To solve the mathematical model, an algorithm named GA/SA (parallel genetic/simulated annealing algorithm) is detailed for application to the multi-stream heat exchanger network synthesis problem. The performance of the proposed approach is demonstrated with three examples and the obtained solutions indicate the presented approach is effective for multi-stream HENS.     

A systematic approach for synthesizing a low-temperature distillation system

In this paper, by combining a stochastic optimization method with a refrigeration shaft work targeting method, an approach for the synthesis of a heat integrated complex distillation system in a low-temperature process is presented. The synthesis problem is formulated as a mixed-integer nonlinear programming (MINLP) problem, which is solved by simulated annealing algorithm under a random procedure to explore the optimal operating parameters and the distillation sequence structure. The shaft work targeting method is used to evaluate the minimum energy cost of the corresponding separation system during the optimization without any need for a detailed design for the heat exchanger network (HEN) and the refrigeration system (RS). The method presented in the paper can dramatical y reduce the scale and complexity of the problem. A case study of ethylene cold-end separation is used to il ustrate the application of the approach. Compared with the original industrial scheme, the result is encouraging.     

考虑操作分解的热集成用水网络设计

This article deals with the design of energy efficient water utilization systems allowing operation split. Practical features such as operating flexibility and capital cost have made the number of sub operations an important parameter of the problem. By treating the direct and indirect heat transfers separately, target freshwater and energy consumption as well as the operation split conditions are first obtained. Subsequently, a mixed integer non-linear programming （MINLP） model is established for the design of water network and the heat exchanger network （HEN）. The proposed systematic approach is limited to a single contaminant. Example from literature is used to illustrate the applicability of the approach.     

Synthesis of Heat Integrated Complex Distillation Systems via Stochastic Optimization Approaches

This paper addresses the application of stochastic optimization approaches to the synthesis of heat integrated complex distillation system, which is characterized by large-scale combinatorial feature. Conventional and complex columns, thermally coupled (linked) side strippers and side rectifiers as well as heat integration between the different columns are simultaneously considered. The problem is formulated as an MINLP (mixed-integer nonlinear programming) problem. A simulated annealing algorithm is proposed to deal with the MINLP problem and a shortcut method is applied to evaluate all required design parameters as well as the total cost function. Two illustrating examples are presented.     

热集成复杂精馏流程综合的随机最优化方法

This paper addresses the application of stochastic optimization approaches to the synthesis of heat integrated complex distillation system, which is characterized by large-scale combinatorial feature. Conventional and complex columns, thermally coupled (linked) side strippers and side rectifiers as well as heat integration between the different columns axe simultaneously considered. The problem is formulated as an MINLP (mixed-integer nonlinear programming) problem. A simulated annealing algorithm is proposed to deal with the MINLP problem and a shortcut method is applied to evaluate all required design paxameters as well as the total cost function. Two illustrating examples are presented.     

柔性换热网络综合与清洗计划同步优化(英文)

A novel methodology is presented for simultaneously optimizing synthesis and cleaning schedule of flexible heat exchanger network (HEN) by genetic/simulated annealing algorithms (GA/SA). Through taking into account the effect of fouling process on optimal network topology, a preliminary network structure possessing twofold oversynthesis is obtained by means of pseudo-temperature enthalpy (T-H) diagram approach prior to simultaneous optimization. Thus, the computational complexity of this problem classified as NP (Non-deterministic Polynomial)-complete can be significantly reduced. The promising matches resulting from preliminary synthesis stage are further optimized in parallel with their heat exchange areas and cleaning schedule. In addition, a novel continuous time representation is introduced to subdivide the given time horizon into several variable-size intervals according to operating periods of heat exchangers, and then flexible HEN synthesis can be implemented in dynamic manner. A numerical example is provided to demonstrate that the presented strategy is feasible to decrease the total annual cost (TAC) and further improve network flexibility, but even more important, it may be applied to solve large-scale flexible HEN synthesis problems.     

反置式间歇蒸馏塔的设计程序(Ⅰ)多组分理想物系

Inverted batch distillation column(stripper) is opposed to a conventional batch distillation column(rectifier). It has a storage vessel at the top and products leave the column at the bottom. The batch stripper is favourable to separate mixtures with a small amount of light components by removing the heavy components as bottom products. In this paper, we are presenting a shortcut procedure based on our earlier work for design and simulation of the inverted batch distillation column, which is equivalent to the Fenske-Underwood-Gilliland procedure for continuous distillation. Given a separation task, we propose to compute the minimum number of stages(Nbmin) and the minimum reboil ratio(Rbmin) required in a batch stripper,which are the stages and reboil ratio required in a hypothetical inverted batch distillation column operating in total reboil ratio or having an infinite number of stages,respectively. Then, it is shown that the performance of inverted batch columns with a finite number of stages and reboil ratios could be correlated in Gilliland coordinates with the minimum stages Nbmln and the minimum reboil ratio Rbmin.     

质量交换网络集成的状态空间法

State space approach is an effective method to mass-exchange network (MEN) synthesis. By decomposing the network into two interactive parts, a distribution network and a process operator, the synthesis problem can be formulated into a mixed integer nonlinear programming (MINLP) model. In this article, a generalized state space model based on typical MEN is established and verified in two cases. A new asymmetrical operator and cost index are also adopted to speed up the solution process. The results demonstrate the efficiency of the proposed approach.     

基于流股虚拟温度综合大规模多流股换热器网络

Effective temperature level of stream, namely stream pseudo temperature, is determined by its actual temperature and heat transfer temperature difference contribution value. Heat transfer temperature difference contribution value of a stream depends on its heat transfer film coefficient, cost per unit heat transfer area, actual temperature, and so on. In the determination of the suitable heat transfer temperature difference contribution values of the stream, the total annual cost of multistream heat exchanger network （MSHEN） is regarded as an objective function, and genetic/simulated annealing algorithm （GA/SA） is adopted for optimizing the heat transfer temperature difference contribution values of the stream. The stream pseudo temperatures are subsequently obtained. On the basis of stream pseudo temperature, optimized MSHEN can be attained by the temperature-enthalpy （T-H） diagram method. This approach is characterized with fewer decision variables and higher feasibility of solutions. The calculation efficiency of GA/SA can be remarkably enhanced by this approach and more probability is shown in searching the global optimum solution. Hence this approach is presented for solving industrial-sized MSHEN which is difficult to deal by traditional algorithm. Moreover, in the optimization of stream heat transfer temperature difference contribution values, the effects of the stream temperature, the heat transfer film coefficient, and the construction material of heat exchangers are considered, therefore this approach can be used to optimize and design heat exchanger network （HEN） with unequal heat transfer film coefficients and different of construction materials. The performance of the proposed approach has been demonstrated with three examples and the obtained solutions are compared with those available in literatures. The results show that the large-scale MSHEN synthesis problems can be solved to obtain good solutions with the modest computational effort.     

Minimizing investment cost for multi-period heat exchanger network retrofit by matching heat transfer areas with different strategies

Multi-period heat exchanger network (HEN) retrofit is usually performed by targeting and matching heat trans-fer areas. In this paper, based on the reverse order matching method we proposed previously, three strategies of matching heat transfer areas are proposed to minimize the investment cost for the retrofit of HEN in multi-period, in which replacement of heat exchangers, addition of heat exchangers and addition of heat transfer areas are performed. We demonstrate the procedures through three scenarios, including maximum number of substituted heat exchangers after retrofit, minimum additional heat transfer areas in the retrofitted HEN, and minimum investment cost for retrofit. The strategies are extended to a single period HEN retrofit problem. The results of multi-period and single period HEN retrofit problems indicate the effectiveness of the strategies. More-over, these results are better than those reported in literature. The strategies are simple and easy to implement, which are of great benefit to large-scale HEN retrofit in practice.     

多流股换热器网络综合方法在原油预热系统中的应用

以原油常减压蒸馏装置原油预热网络为研究对象,进行了多流股换热器网络的实例综合. 基于超结构物理模型建立了改进的多流股换热器网络综合数学模型,提出将该网络综合问题由混合整数非线性规划问题转化为简单的非线性规划问题的求解策略,并利用改进的遗传/模拟退火新算法进行了原油预热网络的综合. 与Hextran软件的综合结果以及现场换热网络的对比表明,本模型和求解策略可以应用于工业规模的多流股换热器网络综合,有可能取得较好的经济效益.     

Simultaneous MINLP synthesis of heat exchanger networks comprising different exchanger types

This paper describes the simultaneous MINLP synthesis of heat integrated heat exchanger networks comprising different heat exchanger types. The stage-wise superstructure of heat exchanger networks (HEN) by Yee and Grossmann (Comput. Chem. Eng. 14 (1990) p. 1165) is extended to alternative exchanger types. The selection of the types is modeled by disjunctions based on operating limitations and the required heat transfer area. Since different types of heat exchangers involve different design geometries, which influences the inlet and outlet temperatures of heat exchangers, additional constraints are specified to provide a feasible temperature distribution in HEN. The consideration of different exchanger types drastically increases the combinatorics, size and computation effort needed to solve the problem. The integer-infeasible path MINLP approach has been applied to perform an efficient initialization scheme and to halve CPU times for solving MILP master problem of the modified OA/ER algorithm. A special multilevel MINLP procedure in reduced integer space has been proposed to solve medium size HEN problems (20 streams) comprising 10³ and more binary variables.     

用于热集成精馏序列综合的改进模拟退火算法

提出一个用于多组分热集成精馏系统综合问题的改进模拟退火算法.将优化问题表示为混合整数非线性规划（MINLP）问题,将算法设计同研究问题的特征相结合,运用本文方法可在同一退火策略下实现流程结构和操作参数的同步优化,并能达到计算精度和计算速度的更好均衡.通过对大规模算例（产品数≥10）的计算表明,该方法对求解此类问题非常有效.     

换热器网络设备面积与清洗时序同步优化

表面结垢会严重影响换热器的传热效率,定期清洗是解决该问题的主要方式.针对以往换热器网络清洗时序优化方法中用于决策的整型变量较多而难以求解的问题,提出以换热器清洗的最大允许污垢热阻为优化变量,取代表示换热器是否清洗的二进制变量,将混合整数非线性规划问题转化成非线性规划问题,能够有效地减小问题规模,降低求解难度.优化过程中兼顾换热器网络的设计型与操作型问题,采用遗传/模拟退火算法同步优化换热器的面积与清洗时序.将该方法用于一个实例,所得年度总费用与文献基本一致,验证了该方法的有效性.     

Shell and tube heat exchanger design using mixed‐integer linear programming

The design of heat exchangers, especially shell and tube heat exchangers was originally proposed as a trial and error procedure where guesses of the heat transfer coefficient were made and then verified after the design was finished. This traditional approach is highly dependent of the experience of a skilled engineer and it usually results in oversizing. Later, optimization techniques were proposed for the automatic generation of the best design alternative. Among these methods, there are heuristic and stochastic approaches as well as mathematical programming. In all cases, the models are mixed integer non‐linear and non‐convex. In the case of mathematical programming solution procedures, all the solution approaches were likely to be trapped in a local optimum solution, unless global optimization is used. In addition, it is very well‐known that local solvers need good initial values or sometimes they do not even find a feasible solution. In this article, we propose to use a robust mixed integer global optimization procedure to obtain the optimal design. Our model is linear thanks to the use of standardized and discrete geometric values of the heat exchanger main mechanical components and a reformulation of integer nonlinear expressions without losing any rigor. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1907–1922, 2017     

A computerized and integrated approach for heat exchanger network design in multipurpose batch plants

Significant savings in the utility cost of batch plants can be obtained by heat integration. In this study, an integrated mathematical programming approach is developed for the determination of the cost optimal heat exchanger network for multipurpose batch chemical plants. A single step, interactive computer program (BatcHEN) which is developed for the determination of the campaigns (i.e. the set of products which can be produced simultaneously), the heat exchange areas of all possible heat exchangers in the campaigns and finally the heat exchanger network are all discussed. A matrix search algorithm is used for the determination of the campaigns. Heat exchange areas for the possible heat exchangers are found by solving a nonlinear optimization model with a grid search algorithm. Finally the heat exchanger network optimization is modeled as a mixed integer linear programming problem and then solved by the modeling and optimization software GAMS/XA.     

Heat‐integrated distillation columns: Vapor recompression or internal heat integration?

Internally, heat‐integrated distillation columns (HIDiC) and vapor recompression (VRC) constitute alternative design options to provide sustainable distillation processes. However, the design is often based on heuristic rules or the experience of the designer, as no systematic methodology driven by economics has been established so far. The increased complexity of heat‐integrated columns can hardly be dealt with using simulation studies but rather calls for a systematic design procedure. A new design methodology is presented here; it builds on a superstructure, mixed‐integer minimization of total annualized cost of operation and rigorous thermodynamic modeling. Optimal VRC and HIDiC designs are identified for the separation of binary, multicomponent, and nonideal mixtures and benchmarked against conventional distillation column designs. A small number of intermediate heat exchangers is optimal for these HIDiC configurations, eventually reducing to a single heat exchanger similar to VRC. Therefore, VRC designs are often more cost efficient due to simpler equipment. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Synthesis of heat exchanger networks with nonisothermal phase changes

Most literature on the synthesis of heat exchanger networks via mathematical programming methods has dealt with phase changes by assuming nearly isothermal conditions. Many multicomponent phase changes of practical interest (e.g., those in sub‐ambient processes) occur over ranges of temperatures and exhibit nonlinear temperature‐enthalpy relations (T‐H curve). In such cases, isothermal approximations may lead to inferior or unacceptable networks. In this article, we propose a mixed‐integer nonlinear programming formulation and a solution algorithm to incorporate nonisothermal phase changes in heat exchanger network synthesis. We approximate the nonlinear T‐H curves via empirical cubic correlations, and propose a procedure to ensure minimum temperature approach at all points in the exchangers. Our approach successfully solves two industry examples and shows promise for significant cost reductions when compared with existing processes. © 2009 American Institute of Chemical Engineers AIChE J, 2009