Globally optimal synthesis of heat exchanger networks. Part I: Minimal networks

This article introduces the concept of minimal structure (MSTR) and presents an enumeration algorithm for the synthesis of heat exchanger networks based on MSTR. Minimal Structures refer to a class of heat exchanger networks featuring acyclic heat transfer networks without energy loops. The enumerations used are either exhaustive or smart with a stopping criterion. Without loss of generality we use the isothermal mixing Synheat model, that is, the method applies identically to other superstructures, with likely variations in the optimization models associated to each step. A conjecture is used to state that the algorithm renders solutions that are globally optimal. Literature examples are used to demonstrate the capabilities of the enumeration algorithm. Most of our solutions compare favorably with the best reported ones in literature, with exceptions where the reported solution is not minimal.     

Globally optimal synthesis of heat exchanger networks. Part III: Non-isothermal mixing in minimal and non-minimal networks

In this work, the enumeration algorithms presented in Parts I and II for the globally optimal synthesis of minimal and non-minimal heat exchanger networks are extended to consider non-isothermal mixing. New mathematical models, including non-isothermal mixing constraints, are proposed to target the bounds of energy consumption and the binding exchanger minimum approximation temperature. These models are solved using the algorithms, which involve solving systems of equations instead of mathematical programming. Three global optimization strategies are proposed to optimize each enumerated structure, involving the use of a global solver directly, or the use of a Golden Search based on energy consumption and a flowrate optimization model considering non-isothermal mixing. The flowrate optimization model is reformulated as a convex problem, which is solved by using nonlinear programming or a mathematical programming-free methodology, that is, solving Karush–Kuhn–Tucker equations. A new Global Optimum Search Algorithm is developed and examples are tested comparing different optimization strategies.     

Energy conservation in water allocation networks with negligible contaminant effects

A methodology to target the minimum energy requirement in water allocation networks where impurity concentrations do not play any significant role is proposed in this paper. The proposed methodology is mathematically rigorous and targets the minimum utility requirement satisfying the minimum approach temperature prior to the detailed design of both the water allocation network as well as the heat exchanger network. The proposed algorithm is presented through a tableau-based calculation procedure. A water allocation network design algorithm is proposed that guarantees the minimum energy targets obtained through the proposed energy recovery algorithm. The proposed methodology is also applied to inter-process heat integration between various water allocation networks.     

Multi-period design of heat exchanger networks

Heat exchanger networks are an integral part of chemical processes as they recover available heat and reduce utility consumption, thereby improving the overall economics of an industrial plant. This paper focuses on heat exchanger network design for multi-period operation wherein the operating conditions of a process may vary with time. A typical example is the hydrotreating process in petroleum refineries where the operators increase reactor temperature to compensate for catalyst deactivation. Superstructure based multi-period models for heat exchanger network design have been proposed previously employing deterministic optimisation algorithms, e.g. (0005 and 0180). Stochastic optimisation algorithms have also been applied for the design of flexible heat exchanger networks recently (0110 and 0115). The present work develops an optimisation approach using simulated annealing for design of heat exchanger networks for multi-period operation. A comparison of the new optimisation approach with previous deterministic optimisation based design approaches is presented to illustrate the utilisation of simulated annealing in design of optimal heat exchanger network configurations for multi-period operation.     

Evolutionary synthesis of heat-exchanger networks

An algorithmic-evolutionary approach for the synthesis of heat exchanger networks is proposed. This approach is based on searching and breaking all heat load loops in the initial network. The method can effectively minimize the number of heat transfer units in an existing network without increasing its utility consumption above the minimum thermodynamic requirement.     

基于热损失的换热网络夹点设计法

现行的换热网络目标方法,在进行换热网络价格估算时,未考虑热物流的热损失。在真实的设计中,换热器壳体保温后仍与环境温度相差较大,则其热损失不可忽略。文章提出了一个新的基于热损失的换热网络夹点设计法,该方法首先以综合费用最小为目标确定出最小温差,然后建立问题表格确定出夹点位置及最小公用工程消耗,最后再进行换热网络设计。文中采用某石油常减压换热网络系统为典型算例对该方法的前两步进行了分析研究,论证了该方法的必要性及可行性。结果表明:该方法与基本Linnhoff夹点技术法估算的投资费用有较大的差距之外,在一定的最小温差下,其与基本Linnhoff夹点技术法确定的夹点位置不同,公用工程消耗也有较大的差距。     

基于(火积)耗散热阻的换热器网络优化

基于(火积)耗散热阻的概念, 分析了换热器网络中的传热过程, 并结合变频泵的性能分析和管网的阻力分析, 建立了换热器网络中结构参数、运行参数和用户需求之间的直接联系, 完善了换热器网络优化的数学模型。在此基础上, 构建了基于(火积)耗散热阻换热器网络优化的方法。最后以一个典型的有变频水系统的换热器网络为例, 阐释了基于(火积)耗散热阻的换热器网络优化方法。研究结果表明, 在给定换热器网络中各换热器热导的情况下, 通过优化计算可以获得使换热器网络中总泵能耗最小的运行参数。在变工况运行的情况下, 随着换热器网络换热量的增大, 各变频泵的运行参数出现不同程度的增大, 增大的速度与工质的性质和管网的阻力特性等因素有关。     

Simultaneous MINLP synthesis of heat and power integrated heat exchanger networks

This paper describes the simultaneous MINLP synthesis of heat and power integrated heat exchanger networks. The objective of this work is to obtain feasible networks with optimal tradeoffs between investment, utility and power consumption caused by pressure drops in heat exchangers, and to use a detailed design model for exchangers in the synthesis in order to represent pressure drops and heat transfer coefficients as functions of exchanger design variables. In this way, the simultaneous synthesis of HEN and the detailed exchanger design become completely consistent and optimal.     

A monogenetic algorithm for optimal design of large-scale heat exchanger networks

The optimal design of large-scale heat exchanger networks is a quite difficult task not only due to its non-linear characteristics but also due to a great number of local optima in its solution space. An explicit analytical solution of stream temperatures for the superstructure heat exchanger networks was developed, which reduces number of decision variables significantly. Based on this solution, a mathematical model for synthesis of heat exchanger networks was formulated for searching the optimal configuration of a heat recovery system by a hybrid genetic algorithm. For large-scale heat exchanger networks, a monogenetic algorithm based on the optimization of sub-networks is proposed. In the first step of the optimization, the hybrid genetic algorithm is applied to the synthesis of the whole heat exchanger network for finding the functional groups (sub-networks) rather than the chromosomes (positions of the heat exchangers and splits of the streams) and genes (areas and heat capacity flow rates). Then the monogenetic algorithm for evolution of the functional groups is carried out to improve the HEN. This procedure was applied to examples taken from literature and better results were obtained.     

KIRCHHOFF'S LAW AND LOOP-BREAKING FOR THE DESIGN OF HEAT EXCHANGER NETWORKS

Traditional evolutionary methods for the synthesis of heat exchanger networks normally produce an initial network containing excess units when compared to the minimum units target. Subsequently, this network is simplified by energy relaxation. However, current methods fail to guarantee that the evolution follows a pathway ensuring that the minimum energy penalty is incurred. A new method to guide this evolution is presented. It is based on the application of Kirchhoff's Law to the network. This enables easy prediction of the actual energy penalties incurred by instituting different loop-breaking strategies. The minimum energy penalty may be discovered and the units to be removed to constitute an optimal solution readily identified. The precedence order for loop breaking in networks containing multiple loops can also be determined according to their respective energy penalties. The proposed algorithm enables the designer to undertake the loop-breaking phase of network design with confidence. The minimum energy path may be followed until a final network is discovered.     

Limitations in using Euler's formula in the design of heat exchanger networks with Pinch Technology

Pinch Technology developed by Linnhoff and other workers has been widely adopted and considered to be one of the most successful techniques in process energy integration. The number of heat exchanger units is one of the most important aspects in the problem and Euler's formula has been applied in correlating the number of units and loops in the network. However, planarity of a graph is required for the application of Euler's formula, a fact that has been ignored in previous literature. It is demonstrated in this paper that Euler's formula cannot always be applied in Pinch Technology, by presenting examples of non-planar graphs resulting from thermodynamically feasible heat exchanger networks.     

基于持续节能的换热网络缓释优化

针对给定的换热网络,应用在线控制来实现系统的持续节能,然而在换热网络运行的全生命周期内,需要考虑操作裕量和控制的自由度来保证系统的可持续性、经济性和安全性等。本文从工艺设计、控制系统设计的角度对换热网络的研究进展进行阐述分析,并在此基础上提出一种可持续节能和缓释裕量的控制方法,并利用相位轨迹求解优化的切换点以使控制变量的变化最小,实现在给定裕量的条件下合理利用裕量,进而实现系统的持续可控,并通过实例证明方法的有效性。     

Optimal operation of heat exchanger networks

The paper discusses optimal operation of a general heat exchanger network with given structure, heat exchanger areas and stream data including predefined disturbances. A formulation of the steady state optimization problem is developed, which is easily adapted to any heat exchanger network. Using this model periodically for optimization, the operating conditions that minimize utility cost are found. Setpoints are constant from one optimization to the next, and for implementing the optimal solution special attention is paid to the selection of controlled variables such that the operation is insensitive to uncertainties (unknown disturbances and model errors). This is the idea of self-optimizing control. In addition to heat exchanger networks, the proposed method may also be applied to other processes where the optimum lies at the intersection of constraints.     

改进的无分流换热器网络最优综合法

提出了不分流换热网络改进的同步最优综合混合整数非线性规则模型，通过引入处理带０－１整型变量的规则，提出了采用非线性规划求解换网络综合ＭＩＮＬＰ问题的方法，只需求解ＮＬＰ问题就可得到连续变量和０－１变量同步优化的网络结果。算例表明，该模型和方法是有效的。     

基于经济学观点确定换热网络传热温差

从分析和经济学的角度提出了确定换热网络最小传热温差的方法。在基于夹点技术温焓图的基础上,把冷、热公用工程物流的基本属性同工艺物流的组合曲线一起标示于温焓图上,组成平衡组合曲线。对平衡冷、热组合曲线进行分段积分,较精确地求取换热网络传热过程的损失。以损费用代替公用工程的能耗费用作为操作费用,确定经济目标函数,用以计算最佳的传热温差。该方法为合理地降低能源消耗指明了方向,同时揭示了能量在过程系统中演变和变化的本质。     

Interval based MINLP superstructure synthesis of combined heat and mass exchanger networks

An interval based superstructure approach for combining the synthesis of heat and mass exchanger networks is presented in this paper. The technique involves combining the interval based MINLP superstructure (IBMS) for the synthesis of heat exchanger networks (HENs) with that of mass exchanger networks (MENs). The two networks are made to interact through the lean stream in the mass exchange network. The new approach involves the use of the lean substream concept to explore potential mass exchange temperatures. An example which involves a one-lean stream mass exchange problem alongside regeneration and hot and cold utilities is presented.     

一种新的用于换热网络全局优化的强制进化随机游走算法

应用启发式方法在换热网络全局优化上的优点,提出了一种全新的强制进化随机游走算法（random walk algorithm with compulsive evolution,RWCE）,算法以目标函数减小为强制方向,通过各换热单元面积的随机扩大或缩小,同时实现了整型变量（换热单元数）和连续变量（换热单元面积）的同步优化。另外,算法能够以一定的概率选择接受差解,使其具备极强的跳出局部最优解的能力和全局搜索能力。算例验证表明,RWCE算法相比于其他启发式方法具有程序简单、更易实现、算法适应性及全局搜索能力更强的优点,使优化质量得到进一步提升。     

随机搜索算法在换热网络优化中的应用进展

随着对能源利用率要求的不断提高,换热网络的优化已引起了人们的高度重视。本文综述了国内外应用随机搜索算法处理换热网络优化问题的最新研究进展,分析了当前应用较多的4种随机搜索算法：遗传算法、模拟退火算法、粒子群算法、禁忌搜索算法。阐述了这些算法各自的优势和尚待改进的问题,指出将不同算法结合起来解决大规模的换热网络优化问题是今后的研究方向。     

换热网络的热流均匀性因子

提出并建立了能够评价换热网络换热效能的热流均匀性因子,在两个条件下对该因子进行验证和分析。首先,在相同结构上保持换热器单元总面积之和不变的条件下模拟计算,考察热流均匀性因子与总换热量之间的对应关系,并与温差均匀性因子进行比较;其次,在改变换热网络结构的条件下优化计算,考察各优化结构的热流均匀性因子与总换热量之间的对应关系。通过两个具体的换热网络实例验证该因子,结果表明：热流均匀性因子越小则对应的换热网络总体换热效能越好。由此说明本研究建立的换热网络的热流均匀性因子能够从总体上反应换热网络的换热效能,能够作为其换热效能的一种新的评价指标,并能为换热网络的综合及优化提供新的思路。     

Optimal cyclic cleaning scheduling in heat exchanger networks under fouling

This work addresses the problem of cyclic cleaning scheduling in heat exchanger networks (HENs). A salient characteristic of this problem is that the performance of each heat exchanger decreases with time which can then be restored to its initial state by performing cleaning operations. Due to the cyclic nature of the schedule, some operations may span successive cycles (wrap-around) which should be taken into account in the mathematical models. A tight mixed integer linear programming (MILP) model is proposed minimising cleaning cost and energy requirements. A complex heat exchanger network example is presented to illustrate the applicability of the proposed model.