Heat Exchanger Network Synthesis Problem Research Articles

Intelligent search strategy applied in heat exchanger network synthesis

Heat exchanger network (HEN) synthesis has been acknowledged as an effective design technique to achieve significant energy savings in a wide range of industrial and engineering applications. In this regard, heuristic methods have been demonstrated as a powerful means to solve the HEN synthesis problem. However, because the new structure is generated at random, the structures that can effectively make the objective cost descend are limited in comparison to the entire evolutionary process. In addition, such heuristic methods are usually time-consuming processes. In this work, an intelligent search strategy is proposed to increase the efficiency of heuristic methods. Based on the defined objective cost, this strategy could rapidly and effectively find a route that could satisfy cost minimization. It can also achieve further evolution aimed at highlighting potential structures. The proposed search strategy can increase the ability of searching and reduce time consumption. Considering the random walk algorithm with compulsive evolution as an example, the principle and impact of intelligent search were clearly demonstrated. Furthermore, applying the intelligent search strategy to the random walk algorithm with compulsive evolution to some cases in the existing literature was found to yield better solutions.

Flexible heat integration system in first-/second-generation ethanol production via screening pinch-based method and multiperiod model

In sugarcane biorefineries, energy integration plays a fundamental role regarding by-product destination and final sales profitability. In biorefineries, the by-product of the sugar/ethanol production process – sugarcane bagasse – can be burned in boilers to produce steam to supply the thermal demands of the plant. Normally, the quantity of bagasse from the plant exceeds the quantity necessary for supplying the energy requirements of the plant. This surplus can be used for either (i) additional electricity production and selling to the grid or (ii) second-generation (2G) ethanol production. To maximize profit, the plant should be flexible to produce either electricity or 2G ethanol according to the current market prices of these products. In this work, an approach is presented for designing a flexible heat exchanger network (HEN) based on a multiperiod synthesis. It involves assessing probabilities of occurrence for different bagasse use scenarios. These values are obtained from a pinch-based approach for screening optimal heat integration in a range of ethanol/electricity prices. A multiperiod HEN synthesis problem is then solved with variable flow rates. Results show that maximum bagasse diverted to 2G ethanol production is increased from 66% to 77% with the new HEN compared to the original design considered.

An analytical model to study the dynamic response of heat exchanger network

An analytical model for the heat exchanger network (HEN) has been proposed in this work to study the dynamic performance of HEN in the design stage. The model relies on the Laplace transform to obtain the system outlet temperature function when facing operational changeover. Equipped with the decomposition strategy and pathway analysis, the model can reach the system outlet temperature function in the time domain in an easy way and free of the numerical difficulty concern caused by the inverse Laplace transform process that may occur toward complicated expressions. The potential bias of the model has been illustrated both in static and dynamic aspects by changing the operational conditions of a heat exchanger. The analytical model has been applied in a four streams HEN synthesis problem to investigate the trade-off result between the economic cost and the response time. Moreover, the comparison with the simulation result toward selected HENs has shown that the proposed model may act as a pre-selection tool to predict the dynamic performance of various HENs during the design stage.

Multiple-solution heat exchanger network synthesis using P-HENS solver

Analysis on the alternative designs on top of the optimal network has proven valuable and meaningful for the decision-makers in determining the most suitable options which fulfill a wide range of objective functions. On the basis of an extension of the P-graph framework, a procedure was developed previously for multiple-solution heat exchanger network (HEN) synthesis. This procedure is capable of generating the n-best HENs depending on predefined structural constraints, for example, the maximum number of heat exchangers used for the entire system, the maximum number of sequential heat exchangers on each stream, the maximum number of stream splittings per stream. Since the choice of a parameter influences the effect of other parameters on the result, it is difficult to find the proper set of parameters for the solver that result in all plausible solutions to the original problem. Naturally, this issue emerges in any HEN synthesis problem, its systematic treatment is essential. The purpose of the current work was to develop a heuristic framework for determining the most reasonable parameters of the HEN generation algorithm and guiding the designer through the optimization process. The outcome of this study not only benefits the researchers and industrial practitioners of this field but may also be extended for educational purposes.

Node dynamic adaptive non-structural model for efficient synthesis of heat exchanger networks

Balancing the trade-off between structural diversity (solution space) and optimization efficiency is an urgent challenge in the modeling and global optimization of heat exchanger network synthesis problems. This paper presents a node dynamic adaptive non-structural model without stream splitting to enhance optimization efficiency under the premise of ensuring an adequate solution space. The node-based non-structural stream matching mechanism can be used to make the solution space scalable and achieve the efficacy of multi-stage stage-wise superstructure with a finite number of nodes. Two node dynamic adaptive strategies (uniformly distributed and random) are established to periodically adjust the number of nodes in process streams and the node distribution of existing heat exchanger units, thereby preventing a decrease in computational efficiency due to an excess number of preset nodes while still satisfying the solution space requirements. The node dynamic adaptive non-structural model is optimized using the random walk algorithm with compulsive evolution. The proposed method was applied to four well-known heat exchanger network case studies. High-quality solutions were obtained, and they are more economical than most of the optimal results previously reported in the literature. These results demonstrate the enhanced computational efficiency and applicability of the proposed synthesis method based on a node dynamic adaptive non-structural model for efficiently solving large-scale heat exchanger network synthesis problems.

Investigation of loops and paths as optimization tools for total annual cost in heat exchanger networks

This research investigates the effectiveness of loops and paths as embedded in a modified pinch package (Aspen Energy Analyzer), that comprises a blend of traditional pinch technique with mathematical programming, in simultaneous optimization of total annual cost (TAC) in heat exchanger network synthesis (HENS). It uses composite curves, grand composites curves, supertargeting and looping system just as in pinch, as well as linear programming and mixed integer linear programming (MILP) in the design of HENs. The tool was adopted in solving some literature problems that had earlier been solved using pinch and mathematical programming techniques. The results obtained compared well with those of various authors that used different techniques as shown in the tables of cost comparison in this paper. The loop and path optimization technique adopted in this research obtained the least TAC in four out of five problems solved in this paper. This shows that loop and path optimization as available in a software-combining pinch and mathematical programming can be more effective than various other methods that have been adopted in the literature. It further demonstrated that no particular technique can return the lowest TAC for all HENS problems.

A New Nodes-Based Model for Optimization of Heat Exchanger Network Synthesis

Searching the global optimal value in heat exchanger network synthesis (HENS) becomes more difficult along with the increasing scale of cases. In structural optimization model, such as stage-wise superstructure, solution domain can be enlarged by adding the stages of network, which would involve multiple integer and continuous variables in optimization and result in a decreasing computational efficiency. Thus, a new nodes-based model with stream splits is proposed, which can promote the quality of result and decrease time consumption at the same time. The characteristic of this model is that it changes the matching mode of heat exchangers by setting the number of nodes on streams to quantify the positions of heat exchangers. The proposed nodes-based model has more flexibility in generating and eliminating the heat exchangers and strong ductility in exploring the solution domain. The random walk with compulsive evolution is modified for enhancing its searching ability and applying modified random walk algorithm with compulsive evolution (RWCE) into the new proposed model. The obtained results of Case 1, Case 2 and Case 3 are superior to those reported in the literature, which decreases 106 USD·a−1, 1253 USD·a−1, 23 444 USD·a−1, respectively, verifying the robust effectiveness of this new model in solving HENS problem.

Heat exchanger network synthesis with detailed exchanger designs: Part 1. A discretized differential algebraic equation model for shell and tube heat exchanger design

AbstractA new method for the detailed design of shell and tube heat exchangers is presented through the formulation of coupled differential heat equations, along with algebraic equations for design variables. Heat exchanger design components (tube passes, baffles, and shells) are used to discretize the differential equations and are solved simultaneously with the algebraic design equations. The coupled differential algebraic equation (DAE) system is suitable for numerical optimization as it replaces the nonsmooth log mean temperature difference (LMTD) term. Discrete decisions regarding the number of shells, fluid allocation, tube sizes, and number of baffles are determined by solving an LMTD‐based method iteratively. The resulting heat exchanger topology is then used to discretize the detailed DAE model, which is solved as a nonlinear programming model to obtain the detailed exchanger design by minimizing an economic objective function through varying the tube length. The DAE model also provides the stream temperature profiles inside the exchanger simultaneously with the detailed design. It is observed that the DAE model results are almost equal to the LMTD‐based design model for one‐shell heat exchangers with constant stream properties but shows significant differences when streams properties are allowed to vary with temperature or the number of shells are increased. The accuracy of the solutions and the required computational costs show that the model is well suited for solving heat exchanger network synthesis problems combined with detailed exchanger designs, which is demonstrated in Part 2 of the paper.

A novel two-step synthesis method with weakening strategy for solving large-scale heat exchanger networks

Efficiently solving large-scale heat exchanger network (HEN) synthesis problems remains a challenging task mainly due to the presence of discontinuity caused by integer variables as well as nonlinearity of the objective cost function. This paper focuses on efficiently solving large-scale HEN synthesis problems based on a chessboard presentation with no splits, and aims to achieve globally near-optimal solutions by using a two-step synthesis method along with a weakening strategy for fixed investment costs that is conducive to bypass the discontinuity. The first step is to generate the most promising network structure by using an improved cuckoo search algorithm to optimize integer and continuous variables simultaneously. In the second step, a cuckoo search algorithm is utilized to directly optimize the heat exchanger area of the optimal structure obtained in the first step. Meanwhile, fixed-cost weakening strategies are applied in the above two steps for improving the optimization efficiency. The proposed method has been tested on several HEN cases, and two of which, namely the 20- and 39-stream problems, are presented in this paper. For these two cases, although the solutions obtained do not contain stream splits, their total annual costs are close to best solutions with stream splits and lower than those best solutions with no-splits reported in the literature, and their chessboard network configurations are clear and simple. Based on these results, the developed method demonstrates the applicability to handle large-scale HEN problems, and is also useful for guiding the grassroots or retrofit design of large-scale HENs or other engineering process syntheses with less cost and less pollution.

A Nodes-Based Non-Structural Model Considering a Series Structure for Heat Exchanger Network Synthesis

The aim of heat exchanger network synthesis is to design a cost-effective network configuration with the maximum energy recovery. Therefore, a nodes-based non-structural model considering a series structure (NNM) is proposed. The proposed model utilizes a simple principle based on setting the nodes on streams such that to achieve optimization of a heat exchanger network synthesis (HENS) problem. The proposed model uses several nodes to quantify the possible positions of heat exchangers so that the matching between hot and cold streams is random and free. Besides the stream splits, heat exchangers with series structures are introduced in the proposed model. The heuristic algorithm used to solve NNM model is a random walk algorithm with compulsive evolution. The proposed model is used to solve four scale cases of a HENS problem, the results show that the costs obtained by NNM model can be respectively lower 3226 $/a(Case 1), 11,056 $/a(Case 2), 2463 $/a(Case 3), 527 $/a(Case 4) than the best costs listed in literature.

Optimal heat exchanger network synthesis based on improved cuckoo search via Lévy flights

Heat exchanger network synthesis (HENS) is still a challenging task for minimizing the Total Annual Cost (TAC). In this work, a Cuckoo Search Algorithm (CSA) is introduced to solve the NonLinear Programming (NLP) problem of the fixed heat exchanger network design to determine the optimal heat load distribution, which can help improve the heat load configurations of previously found optimum configurations. The improved CSA (ICSA) is used to solve the Mixed Integer NonLinear Programming (MINLP) problem for optimal HENS, which can simultaneously optimize continuous and integer variables, and the proposed stream arrangement strategy aims to optimize the stream match search space by lowering the stage demands, i.e. reducing the number of independent variables, which is a promising means for an easier solution of large and medium sized HENS problems. Four large and medium sized benchmark cases have been investigated, obtaining no-splits results with lower TAC in a shorter computational time. In addition, a special feature from case 3 and 4 is analyzed, which is useful in order to achieve a lower TAC by using modified Stage-Wise Superstructure (SWS) models with flexible utility placement.

A Novel Approach for Linearization of a MINLP Stage-Wise Superstructure Formulation

Mathematical programming using superstructure formulations has been used for cost efficient heat exchanger network synthesis (HENS) for about three decades now and significant improvements have been achieved since then. One major problem is the combinatorial nature of the underlying superstructure formulations which means that the mathematical complexity of the HENS problem scales exponentially with problem size. In this paper a novel approach using convex linear approximations is presented for simultaneous HENS. The linearization is carried out prior to optimization and the original Mixed Integer Non-Linear Programming (MINLP) problem is reformulated into a Mixed Integer Linear Programming (MILP) problem. For the linearized problem a global optimum can be obtained much faster compared to the original MINLP formulation. For all presented case-studies feasible solutions could be obtained, which compare well with results from other authors.

A Systematic Comparison of Stagewise/Interval-Based Superstructure Approaches for the Optimal Synthesis of Heat Exchange Networks

This article describes a study in which the various stagewise and interval-based superstructures for the mixed integer non-linear programming (MINLP) optimisation of heat exchanger networks were systematically compared, using exactly the same basis. The effect of using different logarithmic mean temperature difference (LMTD) approximations on the Total Annual Cost of the network and the network structure were examined. The accuracy of the approximations was also analyzed over a wide range of temperature difference ratios. It is concluded that the best approximation, which is the Underwood-Chen approximation, should be used in future mathematical optimisation of Heat Exchanger Network Synthesis problems.

An efficient method based on the uniformity principle for synthesis of large-scale heat exchanger networks

The optimal design of large-scale heat exchanger networks is a difficult task due to the inherent non-linear characteristics and the combinatorial nature of heat exchangers. To solve large-scale heat exchanger network synthesis (HENS) problems, two dimensionless uniformity factors to describe the heat exchanger network (HEN) uniformity in terms of the temperature difference and the accuracy of process stream grouping are deduced. Additionally, a novel algorithm that combines deterministic and stochastic optimizations to obtain an optimal sub-network with a suitable heat load for a given group of streams is proposed, and is named the Powell particle swarm optimization (PPSO). As a result, the synthesis of large-scale heat exchanger networks is divided into two corresponding sub-parts, namely, the grouping of process streams and the optimization of sub-networks. This approach reduces the computational complexity and increases the efficiency of the proposed method. The robustness and effectiveness of the proposed method are demonstrated by solving a large-scale HENS problem involving 39 process streams, and the results obtained are better than those previously published in the literature.

Synthesis of multi-period heat exchanger networks based on features of sub-period durations

In this work, a representative sub-period method is proposed for synthesis of multi-period heat exchanger networks (HENs). For the multi-period HENs with a large number and significantly different durations of sub-periods, the sub-period with the longest duration is taken as the representative sub-period. The cost-effective HEN structure in this representative sub-period can be obtained by solving the single-period HEN synthesis problems, and the operational parameters are then optimized to meet the requirements of other non-representative sub-periods on the fixed HEN structure achieved by the former step. In particular, for synthesis of multi-period of HENs with similar durations of sub-periods, a simplified model method is also proposed. In this method, the multi-period HENs are finalized by introducing the commonly shared heat exchangers in the multi-period HENs model. Both of the proposed methods avoid directly solving the multi-period HEN model, and hence the computational loads are reduced. An industrial case study for the synthesis of multi-period HENs is carried out to illustrate the procedure of the proposed methods. The effectiveness and advantages of the proposed methods are demonstrated by the comparison with the results obtained by the methods in literature. The effects of period duration on the cost-effectiveness of the multi-period HENs are discussed and highlighted.

Simultaneous Heat Exchanger Network Synthesis Involving Nonisothermal Mixing Streams with Temperature-Dependent Heat Capacity

Heat exchanger network synthesis (HENS) is faced with the dilemma of substantial nonisothermal mixing and nonconstant thermal properties of streams against the higher computational efficiency required to solve mathematical programming models with a large amount of variables and high nonlinearity. In this work, by replacing the conventional binary variable in a HENS model, a nonlinear approximation term is developed to indicate the existence of a heat exchanger so as to reduce the amount of variables and constraint as well as enhance the model’s computational efficiency. With this approximation, a new HENS model was formulated considering simultaneously nonisothermal mixing and temperature-dependent heat capacity flow rate. All the variables of the model are stated with clear upper and lower bounds. A 10-stream (5 hot process streams and 5 cold process streams) benchmark HENS problem is solved by the developed model. The results show that the proposed model can generate a better cost-optimal heat exchanger...

Efficient algorithm for simultaneous synthesis of heat exchanger networks

The mathematical programming based simultaneous approaches for heat exchanger network synthesis (HENS) result in large, complex, non-convex mixed-integer nonlinear programming (MINLP) models, for which finding even a feasible solution is a challenge. We propose a tailor-made search strategy that repeatedly revives the outer approximation (OA) algorithm of Viswanathan and Grossmann (1990), which in its original form is mostly ineffective for solving large HENS problems. We propose three smaller and simpler perturbations of the master problem in the OA algorithm by prioritizing, fixing, eliminating, or limiting exchangers in various ways to avoid premature termination. Our approach needs no feasible starting point, and solves much faster and better than some commercial MINLP solvers. We illustrate the application of our strategy with two recent HENS models on seven literature examples with up to 39 process streams. The algorithm solves them very efficiently and obtains solutions as good or better than those reported in the literature. Its robustness and effectiveness are exemplified by a large literature problem involving 39 process streams, where it obtains a 0.32% better solution than the best reported in the literature via a genetic algorithm.

Simultaneous synthesis of heat exchanger network with the non-isothermal mixing

Optimization of heat exchanger network is attributed to improving the process industrial energy utilization ratio. Energy consumption reduction plays an important role in the low-carbon economic development. Several synthesis approaches for heat exchanger network have been proposed and extended during the last three decades. With the evolution of the computer technology, the simultaneous synthesis method via mathematic programming attracts a great deal of attention worldwide. However, some difficulties still need to be overcome, for instance, model simplification and computational complexity. In this work, the simultaneous stage-wise synthesis model without the assumption of isothermal mixing is presented and implemented using effective initialization strategies and a novel two-level algorithm. Three case studies illustrated the better performance of the initialization strategies and two-level algorithm for heat exchanger network synthesis problems, considering non-isothermal mixing.

Bilevel heat exchanger network synthesis with an interactive multi-objective optimization method

Heat exchanger network synthesis (HENS) has been an active research area for more than 40 years because well-designed heat exchanger networks enable heat recovery in process industries in an energy- and cost-efficient manner. Due to ever increasing global competition and need to decrease the harmful effects done on the environment, there still is a continuous need to improve the heat exchanger networks and their synthesizing methods. In this work we present a HENS method that combines an interactive multi-objective optimization method with a simultaneous bilevel HENS method, where the bilevel part of the method is based on grouping of process streams and building aggregate streams from the grouped streams. This is done in order to solve medium-sized industrial HENS problems efficiently with good final solutions. The combined method provides an opportunity to solve HENS problems efficiently also regarding computing effort and at the same time optimizing all the objectives of HENS simultaneously and in a genuine multi-objective manner without using weighting factors. This enables the designer or decision maker to be in charge of the design procedure and guide the search into areas that the decision maker is most interested in. Two examples are solved with the proposed method. The purpose of the first example is to help in illustrating the steps in the overall method. The second example is obtained from the literature.

A hybrid optimization strategy for simultaneous synthesis of heat exchanger network

The heat exchanger network synthesis problem often leads to large-scale non-convex mixed integer nonlinear programming formulations that contain many discrete and continuous variables, as well as nonlinear objective function or nonlinear constraints. In this paper, a novel method consisting of genetic algorithm and particle swarm optimization algorithm is proposed for simultaneous synthesis problem of heat exchanger networks. The simultaneous synthesis problem is solved in the following two levels: in the upper level, the network structures are generated randomly and reproduced using genetic algorithm; and in the lower level, heat load of units and stream-split heat flows are optimized through particle swarm optimization algorithm. The proposed approach is tested on four benchmark problems, and the obtained solutions are compared with those published in previous literature. The results of this study prove that the presented method is effective in obtaining the approximate optimal network with minimum total annual cost as performance index.