Heat Exchanger Network Problem Research Articles

An anti-greedy random walk algorithm for heat exchanger network synthesis

Heat exchanger network (HEN) synthesis is a vibrant research field in process system engineering, with substantial contributions to energy conservation and emissions reduction initiatives. The optimal design of a heat exchanger network is not an easy task due to the abundance of local optima in the solution space caused by the non-linear, non-convex, and discontinuous nature of the problem. Generally, several heuristic algorithms employ a greedy evolutionary mechanism, optimize through greedily accepting the decrease in the objective function, and converge to obtain the optimal solution. The Random Walk algorithm has a simple evolutionary mechanism, is prone to mutation, and exhibits high flexibility. However, the algorithm's inherent persistent greediness in searching restrict the scope of the search. Thus, this paper proposes an anti-greedy concept based on the Random Walk method to serve as the basis of a new synthesis approach called the Anti-greedy Random Walk algorithm. Two strategies are proposed in the algorithm, which broaden the solution domain by slowing down rapid unit reduction and accepting imperfect solutions, respectively. One strategy is to thoroughly search for the integer and continuous variables of the HEN problem by covering a much larger search space. Another is to escape the local extrema and move forward to discover more possibilities. Quantitative data demonstrates the algorithm's ability to avoid the local extrema and enhance the search effectiveness. Three different scales of classical cases are used in this work and the obtained results are superior to the published ones.

Combining reinforcement learning with mathematical programming: An approach for optimal design of heat exchanger networks

Heat integration is important for energy saving in the process industry. It is linked to the persistently challenging task of optimal design of heat exchanger networks (HEN). Due to the inherent highly nonconvex nonlinear and combinatorial nature of the HEN problem, it is not easy to find solutions of high quality for large scale problems. Reinforcement learning (RL) method which learns strategies through ongoing exploration and exploitation, reveal advantages in such area. However, due to the complexity of the HEN design problem, the RL method for HEN should be dedicated and designed. A hybrid strategy combining RL with mathematical programming is proposed to take better advantage of both methods. An insightful state representation of HEN structure as well as a customized reward function are introduced. A Q-learning algorithm is applied to update the HEN structure using the ϵ-greedy strategy. Better results are obtained from three literature cases of different scales.

Retrofit heat exchanger network optimization via graph-theoretical approach: Pinch-bounded N-best solutions allows positional swapping

Retrofit heat exchanger network (HEN) optimization is a fundamentally unique problem which requires the consideration of existing structures, compared to grassroots design problems. The optimization of retrofit HENs is particularly difficult due to the integration of both existing and newly acquired equipment. The re-routing of existing equipment can lead to various network topologies, increasing the complexity of considerations. In this work, we exploit the P-graph framework to solve retrofit HEN problems, guaranteeing to find the topology of optimal solutions within the constrained space of the HEN retrofit problem. The P-graph framework has additional advantages that allows topologically-efficient search space, simplifies additional unit placement, considers unit positional swapping (re-sequencing and re-piping within search constraints), considers stream splitting, and n-best solution visualization. The pinch minimum utility constraint also provides a bound for the maximum number of modifications in the HEN, significantly reducing search space. The proposed P-graph-based approach is demonstrated using a real refinery case study to show its capability in obtaining the topology of the optimal HEN, highlighting the economic and energy benefits. Further extensions to other retrofit process integration problems (e.g. retrofit water network, hydrogen network etc.) will be enabled via the proposed P-graph approach.

Matrix Non-Structural Model and Its Application in Heat Exchanger Network without Stream Split

Heat integration by a heat exchanger network (HEN) is an important topic in chemical process system synthesis. From the perspective of optimization, the simultaneous synthesis of HEN belongs to a mixed-integer and nonlinear programming problem. Both the stage-wise superstructure (SWS) model and the chessboard model are the most widely adopted and belong to structural models, in which a framework is assumed for stream matching, and the global optimal solution outside its feasible domain may be defined by the framework. A node-wise non-structural model (NW-NSM) is proposed to find more universal stream matching options, but it requires a mass of structural variables and extra multiple correction strategies. The aim of this paper is to develop a novel matrix non-structural model (M-NSM) for HEN without stream splits from the perspectives of global optimization methods and superstructure models. In the proposed M-NSM, the heat exchanger position order is quantized by matrix elements at each stream, and a HEN structure is initialized by the random generation of matrix elements. An approach for solving HEN problems based on a matrix real-coded genetic algorithm is employed in this model. The results show that M-NSM provides more flexibility to expand the search region for feasible solutions with higher efficiency than previous models.

An improved Levenberg–Marquardt method for nonsmooth equations with application to multi-stream heat exchangers

Systems of nonsmooth equations are very useful in the study of nonlinear complementarity problems, variational inequality problems, bilevel programming problems, and arise in the mathematical modeling of many problems in chemical processing, mechanics and engineering. In this paper, we introduce a hybrid method for solving systems of nonsmooth equations, which combines the idea of Levenberg–Marquardt–type methods with bundle techniques, while avoiding the hypothesis of differentiability of the least squares merit function. Some numerical results comparing the proposed method with LP-Newton method indicate that the improved Levenberg–Marquardt algorithm works quite well in practice. As an application of the proposed algorithm, we consider the multi-stream heat exchanger network problem, where a heat exchange network must be designed to meet a specified exit temperature for a given set of streams.

Optimization of the Total Annual Cost in Heat Exchanger Networks with Multiple Utilities

This research work was focused on optimizing heat exchanger network problems from literature involving multiple utilities with the objective function of minimizing the Total Annual Costs of the designed networks. This was achieved through the use of pinch methodology on Aspen Pinch software, Version 11.1. Supertargeting was used to obtain the minimum temperature difference for two case studies and the networks were designed on Grid Diagrams. The design of the networks was focused on the energy-capital costs tradeoffs, preventing the use of extra heat exchanger units to reduce energy costs at the expense of capital costs. This paid off as the networks designed in this research obtained the lowest total annual costs (TACs) when compared with the results obtained by other researchers on the case studies under review.

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.

Modeling and optimization of inter-plant indirect heat exchanger networks by a difference evolutionary algorithm

Inter-plant indirect heat integration via intermediate fluid circuit is an efficient energy-saving and heat recovery method, but traditional optimization methods, such as sequential synthesis, may not provide the best solutions. This paper addresses a multi-plant indirect heat exchanger network problem using a two-layer simultaneous synthesis method. To reduce the nonlinear constraints in the simultaneous heat exchanger network model, the outer layer uses a differential evolution algorithm to determine the temperatures of the intermediate fluid, while the inner layer uses a deterministic method to obtain the heat capacity flow rate of the intermediate fluid and the heat exchanger network configuration. Optimization was performed to minimize the total annualized cost, as the sum of utility cost, heat exchanger cost, pump cost, and pipe cost. The differential evolution algorithm in the outer layer improved the simultaneous synthesis efficiency in the inner MINLP model and also provided better results in the case studies.

Flexibility Analysis of Heat Exchanger Network Retrofit Designs using Monte Carlo Simulation

The aim of this paper is to use Monte Carlo Simulation (MCS) to conduct an analysis of the flexibility and controllability of retrofitted Heat Exchanger Network (HEN) designs. Historical plant data is often uncertain and variable but is an important tool for understanding the real-time operation of a HEN. MCS uses these uncertainties to give an analysis of the retrofitted HENs, and it can be used in a more detailed analysis of the controllability and flexibility. Using Monte Carlo Simulation, inflexibility has been defined as the probability of a HEN to fail to meet temperature targets within defined tolerances. Inflexibility can be used as a tool to guide the retrofit analysis of a HEN. A retrofit HEN design should improve the flexibility of the network without compromising on the expected energy savings. The proposed method is demonstrated using a four-stream HEN problem. The inflexibility of the network was shown to be improved with bypass control and optimal allocation of retrofit area and the proposed method succeeds in augmenting the retrofit design method so that cost-effective, flexible retrofit HENs can be identified.

A Simple Method for Finding Optimal Paths of Hot and Cold Streams inside Shell and Tube Heat Exchangers to Reduce Pumping Cost in Heat Exchanger Network Problems

In this paper, a simple method is presented for the synthesis and retrofit of heat exchanger networks (HENs) by considering pressure drop as well as finding proper path of streams inside heat exchangers (HEs) to reduce the pumping cost of network. Generally, HEN problems lead to MINLP models which have convergence difficulties due to the existence of both continuous and integer variables. In this study, instead of solving these variables simultaneously, a combination of Genetic Algorithm (GA) with Quasi Linear Programming (QLP) and Integer Linear Programming (ILP) was used for solving the problem. GA was used to find optimal HENs structure and streams paths, whereas continuous variables were solved by QLP. For the retrofit of HENs, a modified ILP model was used. Results show that the proposed method has the ability to reduce the cost of annual pumping due to considering optimal paths for streams in the HEs compared to the literature.

Comparison of Graphical Tools for Targeting and Retrofit of Heat Exchanger Networks

Depleting fossil and water resources, increasing environmental concerns and energy prices provide the impetus to continually improve heat integration in existing process plants. Four new graphical tools with potential to guide Heat Exchanger Network (HEN) design and retrofit are reported in literatures since 2010. These tools include Stream Temperature vs Enthalpy Plot (STEP) and HEat Allocation and Targeting (HEAT) for simultaneously targeting and design of a HEN, Energy Transfer Diagram (ETD) to capture the flowrate of heat transferred from the heating utilities to the environment through each heat-exchanger and process units as a function of temperature, Heat Exchanger Load Diagram (HELD) to identify heat-exchanger configuration. All these graphical tools are concisely explained and applied to guide the design and retrofit of a HEN problem. Compared with the traditional Composite Curve (CC) and Grid Diagram (GD), the advantages and disadvantages of each tool are compared and summarized. Suggestions to make a choice are provided.

Non-structural model of heat exchanger network: Modeling and optimization

Simultaneous synthesis of heat exchanger network (HEN) is an indispensable strategy to improve energy efficiency and realize high techno-economic performances. The structural models that involve a stage-wise superstructure have some limitations concerning the global optimization for the HEN, including the flexibility of configurations and computational efficiency of synthesis methods. Therefore, a novel non-structural model (NSM) is proposed in this work for the simultaneous synthesis of the HEN. Firstly, the concept of a non-structural HEN configuration is described based on an analysis of the drawbacks of structural models. Then, the mathematical formulation of the NSM is provided. Finally, a general implementation method is proposed to realize the simultaneous synthesis of an NSM-based HEN and make it a feasible synthesis method. Six medium and large scale case studies are used to demonstrate the flexibility of configurations in the proposed model and its performance concerning the global optimization of HEN synthesis using a random walk algorithm with compulsive evolution. The combination of the NSM and the heuristic method has led to better optimal solutions than those that exclude the stream splits as published in previous works, achieving high quality and efficiency in the synthesis of HEN problems.

Identifying optimal thermodynamic paths in work and heat exchange network synthesis

The process synthesis problem referred to as work and heat exchange networks (WHENs) is an extension of the classical heat exchanger networks problem considering only temperature and heat. In WHENs, additional properties are pressure and work, and strong interactions exist between temperature, pressure, work, and heat. The actual sequence of heating, cooling, compression, and expansion for pressure changing streams (PCs) will affect the shape of the composite and grand composite curves, the Pinch point, and the thermal utility demands. Even stream identities (hot or cold) will sometimes change. The identification of the optimal thermodynamic path from supply to target state for PCs becomes a primary and fundamental task in WHENs. An MINLP model has been developed based on an extension of the Duran–Grossmann model (that can handle variable temperatures) to also consider changing stream identities. Three reformulations of the extended Duran–Grossmann model have been developed and tested for two examples. © 2018 American Institute of Chemical Engineers AIChE J, 65: 549–561, 2019

Application of the Microsoft Excel Solver tool in the solution of optimization problems of heat exchanger network systems

Optimization of heat exchanger networks (HENS) is a field of interest in Chemical Engineering. The aim is to use the residual heat of process streams to raise the temperature of other process streams which are cold, thus minimizing the use of hot and cold utilities. The usual way to deal with this task is to pose a linear programming problem according to a transshipment model in order to minimize either the general services consumptions or the number of hot and cold stream matchings required. This optimization is subjected to several restrictions given by the energy balances corresponding to each heat exchange.The high number of variables and equations obliges the use of specific software to solve these problems, e.g. GAMS (General Algebraic Modelling System). However, this software is not intuitive and requires a long time of training and a certain level of practice for the students to adequately use it.This work describes the use of Microsoft Excel-Solver for the sequential solving of HENS optimization problems according to the transshipment model. Solver is a much simpler, intuitive and easily available tool for the students who, besides, usually learn how to use it in the first years of their degree, in Informatics or similar subjects. Thus, it is not necessary to spend extra time in the teaching of the software, time that may be devoted to other contents.This paper presents an example of HENS problem proposed in the subject Simulation and Optimization of Chemical Processes corresponding to the Joint Master in Chemical Engineering of the Rey Juan Carlos University and the Autónoma University of Madrid and solved by the students using Excel-Solver.

Area Targeting of Heat Exchanger Network (Hen) Using a Modified Pinch Technique

Aspen Hysys version 8.6 which is a modified pinch tool was used to minimize the area of two heat exchanger networks problem and the results obtained were compared with those of other methods used by researchers that have solved the same problems. Stream data adopted from previous research work comprising the inlet and outlet temperatures, heat capacity flow rate, and specific heat capacity were imputed and solved for minimum area using the principle of modified pinch technology embedded in the Aspen Hysys software.The minimum approach temperature, composite curve, grand composite curve and the grid diagram representation are all series of steps employed in the methodology to achieve minimal area targeting using the Aspen Hysys. The problems solved in this research compared well with those of other researchers and even obtained a smaller exchanger area when compared with the non-linear programming technique (NLP). For instance, an area of 22.17m2 was obtained in the first example as against 29.84m2 obtained by the non-linear programming techniques, resulting in a percentage difference of 25.7%. Also in the second example solved in this research, an area of 106.4m2 was obtained against 188.9m2obtained with the NLP technique which gives a percentage difference of 43.67%.The overall assessment of the results on area targeting on these problems using Aspen Hysys points to the fact that the traditional pinch technique can still obtain results that are as good as those obtained using mathematical programming techniques in heat exchanger networks (HENs).

Two-step MILP/MINLP approach for the synthesis of large-scale HENs

Although different methodologies for the synthesis of heat exchanger network (HEN) problems have been introduced in the last forty years, there are still significant challenges to be addressed, such as solving large-scale problems. This study focuses on synthesizing large-scale HENs using mathematical programming to achieve near globally optimal solutions based on a two-step MILP/MINLP approach. In the first step a mixed-integer linear programming (MILP) model, TransHEN, is used that obtains a globally optimal solution at selected ΔTmin. By utilisation of this model, the most promising matches are selected based on feasibility and viability. The second step entails using the matches selected in the TransHEN of Step 1 in a mixed-integer nonlinear programming (MINLP) model, HENsyn, using a reduced superstructure, to generate a feasible HEN. This study presents also a simultaneous Total Site synthesis with direct heat transfer between processes, and is the first step in the wider project of synthesising an entire Total Site with direct and indirect heat transfer; and is the first step in the wider scope of synthesising an entire Total Site with direct and indirect heat transfer; however, in order to attain this goal, a tool capable of an appropriately handling large number of streams is required. The newly developed procedure has been tested on several case studies, two of which are presented in this paper. For Case study 1 the results obtained lie within the range of best solutions obtained by other authors. Case study 2, consisting of 173 process stream and involving multiple hot utilities, shows the applicability of the developed method to handle large-scale HEN problems.

Synthesis of a multipass heat exchanger network based on life cycle energy saving

A method was described in this paper for the synthesis of a multipass heat exchanger network (HEN) based on minimization of the life cycle accumulative total cost. Considering the fouling resistance will be increased with the running of HEN, the overdesign was always optimized to minimize the total cost. A superstructure model was used in the proposed method to optimize multipass HEN. Fouling and heat transfer coefficients were used in different operating periods. Since the fouling resistance was increased slowly with running time, the life cycle running period was decomposed into several running intervals, and the corresponding heat transfer area was optimized for each heat exchanger. Then, the accumulative total cost was calculated and compared in different operating intervals to obtain the optimal design. Since the fouling resistance was varied with the running of HEN, the optimal HEN results were changed in correspondence to different accumulative total costs. Consequently, the optimal heat transfer area was obtained based on the minimization of the life cycle accumulative total cost. To show the reliability of this approach, it was applied to synthesize a HEN problem taken from open literature, and results were compared to those predicted from published methods. By comparisons of these results, the accumulative total cost for HEN based on life cycle energy saving is the most profitable one. The results demonstrated that it is necessary to consider the HEN optimization in different operating intervals and compare the corresponding accumulative total cost in order to realize the life cycle energy saving.

A new algorithm using front prediction and NSGA-II for solving two and three-objective optimization problems

In this paper, a new hybrid algorithm (FP–NSGA-II) is proposed by combining the fast and elitist non-dominated sorting genetic algorithm-II (NSGA-II) with a simple front prediction algorithm. Due to the significant computational time of evaluating objective functions in real life engineering problems, the aim of this hybrid approach is to better approximate the Pareto front of difficult constrained and unconstrained problems while keeping the computational cost similar to NSGA-II. FP–NSGA-II is similar to the original NSGA-II but generates better offsprings. This is achieved by using a prediction operator which utilizes the direction in the decision variable space between each solution in the first front and the nearest neighbour solution in the second front, in order to extrapolate future chromosomes. This enables the addition of solutions that are closer to the true Pareto front into the new generation. To assess the performance of the proposed approach, eight benchmark two-objective test problems and four three-objective test problems are used to compare FP–NSGA-II with NSGA-II. In addition, a three-objective heat exchanger network problem is examined to show the potential application of FP–NSGA-II in real-life problems. Results indicate that the FP–NSGA-II improves upon the performance of NSGA-II for a variety of benchmark test problems exhibiting different characteristics. In addition, a similar front prediction algorithm could also be easily integrated with other evolutionary algorithms to enhance its performance.

Synthesis of multipass heat exchanger network with the optimal number of shells and tubes based on pinch technology

Many methods have been proposed for the synthesis of multipass heat exchanger network (HEN). Considering that both parallel and countercurrent flows are involved in the multipass HEN, temperature difference correction factor FT is commonly used. However, the correction factor FT is always obtained by trial and error iterations, which are difficult to compute. On the other hand, the threshold value for multipass heat exchanger design and multipass HEN synthesis may change with the operating conditions although a rule of thumb for correction factor FT is given to avoid temperature cross. This paper introduces a new approach for optimal heat exchanger network synthesis based on pinch technology considering multipass heat exchangers. For this purpose, the relationships between the number of passes for shells and tubes, and pinch character are analyzed by using modified composite curves. Then, the minimum temperature difference (ΔTmin) and the number of shells and tubes are optimized based on pinch technology. The proposed methodology allows for proper handling of the trade-offs involving energy consumption, number of units and passes for shells and tubes, and network area to provide a network with the minimum total annual cost. To show the reliability of this approach it is used to synthesis two heat exchanger network problems taken from open literature and results are compared to that predicted from published methods.

Floating pinch method for utility targeting in heat exchanger network (HEN)

Most of the established methods for utility targeting in a heat exchanger network (HEN) are mainly focusing on fixed stream conditions, where the flow rate, heat capacity, supply and target temperatures are fixed. However, in the process industries, the stream conditions (flow rates and temperatures) are not fixed. Therefore, the established HEN targeting methods cannot be directly applied to locate the hot and cold utility targets for HEN problem with varying flow rates and temperatures. To address this issue, a revised floating pinch method which uses binary variables to parameterise the stream locations on the composite curves, is presented in this work to identify the minimum utilities targets. The revised method simplify the earlier version of floating pinch method presented by Duran and Grossmann (1986) by avoiding the non-differentiability in the mathematical program. Two cases, one with fixed parameters while another with temperature-dependent properties and varying operating parameters are solved to illustrate the revised model.