A new methodology for simultaneous optimization of capital and operating cost targets in heat exchanger network design

A new approach has been developed for establishing cost-optimal targets for a heat exchanger network (HEN). We formulate a mixed-integer-linear-programming (MILP) transportation problem that simultaneously optimizes for heat exchanger units, heat exchange area and loads on each utility. Heat exchange matches are placed between each hot stream in each temperature interval and all cold streams in all the subsequent lower temperature intervals. The objective function is linear and minimizes the total annual cost of the HEN subject to heat balance constraints. The temperature intervals are generated with a temperature shift just greater than zero. Each temperature interval is small enough that we can linearize the log-mean temperature difference on each match while maintaining the accuracy. Flowrate continuity constraints are written on utility streams so that we could account for non-point utilities. Furthermore, constraints on heat exchange area that occur in retrofit scenarios are incorporated into the model. The solution of the optimization model provides the heat loads on each utility, in case of multiple hot and cold utilities, the heat load on every match pair, the heat exchange area target and the number of units target such that the total annual cost is minimum. Using these targets, it is straightforward to construct heat exchanger networks.     

基于夹点技术的航煤加氢换热网络优化

针对某航煤加氢装置现行换热网络夹点温差不合理导致能耗较大的现状,利用夹点技术对该装置换热网络进行分析、优化。在该装置实际工况下的夹点温差附近选取相应的夹点温差,计算出不同夹点温差对应换热网络的年总费用,得出年总费用最小的夹点温差,即最优夹点温差。在最优夹点温差的基础上生成新的换热网络,结果表明,节能效果显著。     

Heat integration retrofit analysis of a heat exchanger network of a fluid catalytic cracking plant

The impact of a process system on environmental pollution has both a local and global effect. The performance of the heat exchanger network (HEN) in a plant is an important aspect of energy conservation. Pinch technology and its recent extensions offer an effective and practical method for designing the HEN for new and retrofit projects.The fluid catalytic cracking (FCC) is a dominant process in oil refineries and there has been a sustained effort to improve the efficiency and yield of the unit over the years. Nevertheless, benefits and scope for improvement can still be found. The HEN of the FCC process considered here consists of a main column and a gas concentration section. Appropriate data were extracted from the existing network, using flowsheeting simulation. The stream data consists of 23 hot and 11 cold streams and cost and economic data required for the analysis were specified. The incremental area efficiency methodology was used for the targeting stage of the design and the design was carried out using the network pinch method consisting of both a diagnosis and optimisation stage. In the diagnosis stage promising designs were generated using UMIST developed sprint software. The generated design was then optimised to trade-off capital cost and energy savings. The design options were compared and evaluated and the retrofit design suggested.The existing hot utility consumption of the process was 46.055 MW with a ΔT_min of 24°C. The area efficiency of existing design was 0.805. The targeting stage using incremental area efficiency sets the minimum approach temperature at 11.5°C, thereby establishing the scope for potential energy savings. To achieve a practical project, the number of modifications is limited. The selected retrofit design has 8.955 MW saving – 74% of the whole scope. This corresponds to 27% utility cost savings with a payback period of 1.5 years. The modifications include addition of four heat exchanger units and repiping of one existing exchanger.     

Pinch locations at heat capacity flow-rate disturbances of streams for minimum utility cost heat exchanger networks

The work deals with heat exchanger network (HEN) targeting under heat capacity flow-rates of streams disturbances. In particular, the aim is to calculate all pinches that can exist in a HEN with utilities of minimum cost when stream heat capacity flow-rates (CPs) are allowed to change within given ranges. It is assumed that the disturbances are stochastic. The knowledge of pinches at certain as well uncertain data is of great importance in designing HENs. For instance, Pinch Technology is based on pinch phenomenon and its influence on HEN operation and design. In case of parameter disturbances, this is even more important since additional application in HEN’s control (see e.g. [1], [2]). It is worthnoting that in case of disturbances, pinches behave in very complex manner as it was shown in [1], [2], [3], [4], [5]. A rigorous approach has been developed for calculating all feasible locations of pinches that can occur in minimum utility cost of HENs operating at varying heat capacity flow-rates of process streams. The method is based on recursive solution of mixed-integer linear programming (MILP) optimisation model that requires quite moderate number of binary variables. Examples of method application and analysis of results are presented in the work.     

线性拟合换热网络性能与进口温度的关系

换热网络问题属于典型的混合整数非线性问题,有严重的非凸、非线性特性,且影响换热网络性能的因素众多.主要研究了换热网络进口温度与性能之间的关系.给定一换热网络固定结构,同时在固定面积的条件下,变动每股流体的进口温度,分析流体的进口温度与换热网络性能之间的关系,得出线性拟合的适用性.然后设计正交试验,拟合出性能与进口温度的线性模型,并验证该模型的准确性.最后根据拟合模型,从众多流股中优选冷、热流体组合成目标换热网络.     

基于最优夹点温差的换热网络优化设计

介绍了夹点技术基本原理及其在换热网络优化设计中的原则。利用ASPENPinch软件设计了一个有三股热股流、两股冷股流的换热网络，求得最优夹点温差是23．7℃，设计时取值23℃。夹点温差分别取10、23、30％进行换热网络初步优化设计，在相同换热器情况下，三者的总费用分别是44279、41931、42156美元／a。这证明采用最优夹点温差的换热网络经济性最好。     

Heuristic approach for heat exchanger networks

A systematic approach based on few heuristics for the synthesis of optimum heat exchanger networks has been developed. The approach, which is simple and easy to apply, consists of three sequential steps. In the first pre-analysis step, the optimum temperature approach is determined. In this step, a set of heuristic constraints are used to determine minimum utility requirements. In the second step, heat exchanger networks are generated using the H/H heuristic of matching hot and cold streams. In the third step, the initially generated networks evolve through loop breaking and energy relaxation to achieve the target of the minimum number of units. The effectiveness of the approach developed has been tested on a number of literature test problems ranging in size from four to ten streams and on an industrial case involving a recovery heat exchanger network around a topping tower. The approach produced simple network structures and improved energy recovery. The cost results obtained in this work agree favourably with optimal solutions reported in the literature.     

换热网络全局优化的多维峰谷轮换法

在峰谷轮换法的基础上提出了利用多维峰谷轮换法对以年综合费用最少为目标函数的无分流换热网络进行优化.在换热网络变量寻优过程中,首先将目标函数极小化得到一个局部极小值点,然后沿着多个方向进行变量搜索,找出最先跳出局部极小值点的变量组合,使得跳出局部极小值的搜索效率高于单变量的搜索效率,并可寻找到更好的换热网络结构,将极小化与跳出局部极小值点过程交替进行直至求得全局最优解.通过算例验证了该方法的可行性,且可找到比其它方法的优化结果更优的换热网络结构.     

Application of intensified heat transfer for the retrofit of heat exchanger network

A number of design methods have been proposed for the retrofit of heat exchanger networks (HEN) during the last three decades. Although considerable potential for energy savings can be identified from conventional retrofit approaches, the proposed solutions have rarely been adopted in practice, due to significant topology modifications required and resulting engineering complexities during implementation. The intensification of heat transfer for conventional shell-and-tube heat exchangers can eliminate the difficulties of implementing retrofit in HEN which are commonly restricted by topology, safety and maintenance constraints, and includes high capital costs for replacing equipment and pipelines. This paper presents a novel design approach to solve HEN retrofit problems based on heat transfer enhancement. A mathematical model has been developed to evaluate shell-and-tube heat exchanger performances, with which heat-transfer coefficients and pressure drops for both fluids in tube and shell sides are obtained. The developed models have been compared with the Bell-Delaware, simplified Tinker and Wills-Johnston methods and tested with the HTRI® and HEXTRAN® software packages. This demonstrates that the new model is much simpler but can give reliable results in most cases. For the debottlenecking of HEN, four heuristic rules are proposed to identify the most appropriate heat exchangers requiring heat transfer enhancements in the HEN. The application of this new design approach allows a significant improvement in energy recovery without fundamental structural modifications to the network.     

利用夹点技术优化蒸馏换热网络

介绍夹点技术设计的基本原理及设计原则,采用Aspen Hx-net软件,运用夹点技术对某炼油厂常压蒸馏装置换热网络进行优化分析,确定最优传热温差△Tmin、最小公用工程用量和夹点位置,并对换热网络进行了优化.装置运行情况表明,优化后的换热网络节能效果明显,装置投资回收期仅8个月.     

Studies on the retrofit of heat exchanger network based on the hybrid genetic algorithm

The retrofit of heat exchanger networks (HENs) is an important branch of investigation for systematic heat integration. The studies on the economical and efficient retrofit techniques are very important for the high energy-consumption enterprises to save energy, protect environment and improve their market competitiveness. Because the retrofit of HEN is an optimization problem normally solved by a mixed integer nonlinear program (MINLP) which requires enormous solution space, it is very difficult to solve it with the traditional optimization methods. In this paper, by the analysis of an existing heat exchanger network, the hybrid genetic algorithm is applied to obtain the optimal retrofitted HEN with full utilization of the existing heat exchangers and structures. Two examples are taken to show the better effect of the retrofit method with the optimal new heat exchangers and re-piping cost and energy saving.     

Simultaneous synthesis of flexible heat exchanger network

A framework is presented for generating flexible heat exchanger networks (HENs) over a specified range of variations in the flow rates and temperatures of the streams. The flexible HEN is synthesised using a combination of a multiperiod simultaneous MINLP model and search algorithms, where the total annual costs due to utility duties, exchanger areas and selection of matches are optimised. The simultaneous HEN synthesis allows the data to be distributed according to a probability distribution and it does not rely on the concept of pinch point. Both search algorithms involve a developed multiperiod NLP/LP model where utility costs are minimised. The proposed procedures are explained through an example including variations resulting in a network with variable splits and bypasses. This framework results in a HEN working under variations without losing stream temperature targets while keeping an economically optimal energy integration.     

Effect of maximum and minimum heat capacity rate on entropy generation in a heat exchanger

This paper presents a theoretical analysis of a heat exchanger with a negligible fluid flow pressure drop to determine whether it is better to operate the heat exchanger with the minimum or maximum heat capacity rate of the hot fluid from entropy generation point of view. Entropy generation numbers are derived for both cases, and the results show that they are identical, when the heat exchanger is running at a heat capacity ratio of 0.5 with heat exchanger effectiveness equaling 1. An entropy generation number ratio is defined for the first time, which has a maximum value at ε = 1/(1+R) for any inlet temperature ratio. When R equals 0.1, 0.5 and 0.9, the entropy generation number ratio receives a maximum value at an effectiveness equaling 0.91, 0.67 and 0.526, respectively. When R=0.9, the entropy generation number ratio is the same for all inlet temperature ratios at ε=0.8. The results show that the entropy generation number ratio is far from 1 depending on the inlet temperature ratio of the cold and hot fluid. The results are valid for parallel‐flow and counterflow heat exchangers. Copyright © 2010 John Wiley & Sons, Ltd.     

Thermal-economic multi-objective optimization of plate fin heat exchanger using genetic algorithm

Thermal modeling and optimal design of compact heat exchangers are presented in this paper. ε–NTU$\epsilon ''–''\mathit{NTU}$ method was applied to estimate the heat exchanger pressure drop and effectiveness. Fin pitch, fin height, fin offset length, cold stream flow length, no-flow length and hot stream flow length were considered as six design parameters. Fast and elitist non-dominated sorting genetic-algorithm (NSGA-II) was applied to obtain the maximum effectiveness and the minimum total annual cost (sum of investment and operation costs) as two objective functions. The results of optimal designs were a set of multiple optimum solutions, called ‘Pareto optimal solutions’. The sensitivity analysis of change in optimum effectiveness and total annual cost with change in design parameters of the plate fin heat exchanger was also performed and the results are reported. As a short cut for choosing the system optimal design parameters the correlations between two objectives and six decision variables with acceptable precision were presented using artificial neural network analysis.     

Optimization for a heat exchanger couple based on the minimum thermal resistance principle

Following the brief introduction to the concept of a physical quantity, entransy, the equivalent thermal resistance of a heat exchanger couple is defined based on the entransy dissipation. The minimum thermal resistance principle is applied to obtain the optimal heat capacity rate of the medium fluid and the optimal allocation of heat exchangers thermal conductance, which correspond to the maximum heat transfer rate in the heat exchanger couple. In addition, analytical expression for the optimal heat capacity rate of the medium fluid is derived, whose reciprocal equals the sum of the reciprocal of the individual heat capacity rate of the hot and cold fluids, just like the case of two electrical capacitors in series. Numerical results in the variation of the thermal resistance and the heat transfer rate with the medium fluid heat capacity rate or the thermal conductance allocation agree with the theoretical analyses. Finally, for comparison, the entropy generation rate is also calculated to obtain its relation with the thermal performance of the heat exchanger couple. The results show that there is no one-to-one correspondence of the minimum entropy generation rate and the maximum heat transfer rate. This indicates that the minimum entropy generation principle cannot be used for optimizing the heat exchanger couple.     

Loop breaking in heat exchanger networks by mathematical programming

In many cases heat exchanger network (HEN) designs require some changes aimed at reduction of units number. This is the case if a rule of division at pinches is applied in designing a HEN as e.g. in pinch analysis approaches. Matches at loops across pinches can be removed and the number of matches in a HEN goes down to the global minimum. Such elimination of units is commonly referred to as loop breaking.Several methods have been suggested for loop breaking. Existing approaches require iterative tedious computations. Moreover, since based on rules from insight into the problem they do not ensure optimal solutions.In this contribution we developed an approach that is based on mathematical programming. The aim is to minimise or to reduce number of units at the condition of minimum energy penalty. The optimisation model consists of relations determining HEN’s topology, heat and mass balances for each heat exchanger (including heaters and coolers) as well as splitters and mixers. Inequalities ensuring feasible heat exchange are included, too.In order to overcome difficulties with solving mixed-integer nonlinear (MINLP) optimisation problem we have decided to impose the condition of linearity for our model. Hence, goal function in optimisation does not account for total cost but the aim is to minimise number of matches and heat load of utilities. Furthermore, flow rates of streams have to be fixed. To relax constraint of fixed flow rates at splitters we have applied a concept of small superstructure that contains all types of arrangements for heat exchangers: parallel, serial and serial–parallel connections. This gives mean to simplify HEN’s topology by replacing parallel arrangement by serial one.Linear optimisation model developed by us accounts for inequality constraints for outlet streams temperatures. We applied EMAT value instead of HRAT. Some new matches can be inserted into a HEN by a designer to make topology changes possible.The optimisation model is of mixed-integer linear type and requires moderate number of binary variables. It can be easily extended in MINLP one that accounts for total cost. In this paper solutions for some literature examples are presented that proved validity of the approach and shows practical merits of the approach.     

较大规模换热器网络的一种综合优化方法

基于分级超结构换热器网络模型的特点，改进了计算温度分布的通用解方法，以遗传算法和模拟退火算法为主，以瞎子爬山优化算法以及一些特殊优化策略为辅，设计了相应的计算程序，它需要的计算机内存要比现有的其他方法小。实例证明，该方法可成功地应用于较大规模的换热器网络的优化，并得到比现有各种方法更优的结果。     

Paths combination for HENs retrofit

With the significant increase in fuel price, energy conservation projects should be reviewed and analyzed properly. Retrofit of heat exchanger networks (HENs) is among the common projects to reduce the plant operational cost. This paper introduced a new procedure using the path analysis approach for HEN retrofit. The developed procedure attempts at generating options for retrofit solution. These options are created by combining the available utility paths in HEN systematically. Instead of relying on a single path, the heat load could be shifted from HEN utilities using a set of paths simultaneously. To ensure feasible heat transfer between the hot and cold streams throughout, Exchanger Minimum Approach Temperature (EMAT) is maintained while shifting the heat load. The available exchangers’ pressure drop is considered in calculating the heat transfer coefficients. HEN devices are subjected to some additional area without any topological modification. In addition, the investment of such area could be recovered in a short span of time. The calculation of this approach encountered some iteration which has been overcome by mathematical programming. Demonstration example showed some options to be reasonable retrofit solutions. Energy savings ranged between $150 K and $450 K per year with payback time of less than 2 years were possible.     

Inverse problem and variation method to optimize cascade heat exchange network in central heating system

Urban heating in northern China accounts for 40％ of total building energy usage.In central heating systems,heat is often transfened from heat source to users by the heat network where several heat exchangers arc installed at heat source,substations and terminals respectively.For given overall heating capacity and heat source temperarure,increasing the terminal fluid temperature is an effective way to improve the thermal performance of such cascade heat exchange network for energy saving.In this paper,the mathematical optimization model of the cascade heat exchange network with three-stage heat exchangers in series is established.Aim at maximizing the cold fluid temperature for given hot fluid temperature and overall heating capacity,the optimal heat exchange area distribution and the medium fluids' flow rates are determined through inverse problem and variation method.The preliminary results show that the heat exchange areas should be distributed equally for each heat exchanger.It also indicates that in order to improve the thernmal performance of the whole system,more heat exchange areas should be allocated to the heat exchanger where flow rate difference between two fluids is relatively small.This work is important for guiding the optimization design of practical cascade heating systems.     

Applying multiple decomposition methods and optimization techniques for achieving optimal cost in mixed materials heat exchanger networks

The optimization of the total annual cost in heat exchanger networks has been one of the overarching goals when synthesizing these networks. Several methodologies and techniques have been developed to achieve optimal costs in mixed material heat exchanger networks. This paper demonstrates the application of two decomposition methodologies (total decomposition and partial decomposition) for typical cost rules. The objective function was defined as the optimization and minimization of the total annual cost in mixed materials heat exchanger network. Three optimization algorithms, hybrid genetic‐particle swarm optimization (GA‐PSO), shuffled frog leaping algorithm (SFLA) techniques, and ant colony optimization (ACO), were used to further optimize the total cost in mixed materials heat exchanger network. The results indicate that the total annual cost in partial decomposition method was smaller than that in full integration method and total decomposition method. The reduction of the total annual cost was about 27% for GA‐PSO algorithm, 24% for SFLA and 10% for ACO relative to the results reported in this work. In partial decomposition method, at least one mixed material of heat exchanger was used to reduce the hot and cold utility for decreasing the total annual cost. Partial decomposition method resulted in the highest reduction of the total annual cost compared with other methods. Percentage of difference of the total annual cost were 0.36%, 1.92%, and 5.05% for full integration, total decomposition, and partial decomposition methods, respectively, in comparison with the previous studies. Results have been compared with the results of other studies to demonstrate the accuracy of the applied algorithms.