Elsevier

Chemical Engineering Science

Volume 227, 14 December 2020, 115924
Chemical Engineering Science

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

https://doi.org/10.1016/j.ces.2020.115924Get rights and content

Highlights

  • A simultaneous multi-plant indirect heat exchanger network model was proposed.

  • Using DE to search for the temperatures of the two ends in the intermediate fluids circuit.

  • Deterministic method and heuristic algorithm were combined.

  • Connection cost and pump related cost were involved.

Abstract

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.

Introduction

Heat exchanger networks (HENs) are widely applied to energy recovery in the chemical industry to decrease energy consumption and improve economy (Klemeš and Kravanja, 2013). Most HEN synthesis contributions can be classified as either sequential or simultaneous methods (Furman and Sahinidis, 2002). Sequential synthesis methods divide the HEN into several subproblems to reduce the computational requirements. One example is pinch analysis (PA) proposed by Linnhoff and Flower (Linnhoff and Flower, 1978, Linnhoff and Flower, 1978), which includes the problem table algorithm and grid diagram that can greatly improve the practicality of HEN optimization. Well-known graphical tools such as composite curves (CC) (Linnhoff, 1989), grand composite curves (GCC) (Linnhoff, 1989) and site utility grand composite curves (SUGCC) (Klemeš et al., 1997) provide a thermodynamics-based systemic view of the HEN system. The pinch design method (Linnhoff and Hindmarsh, 1983) starts the design from the pinch and gradually moves away to generate HENs with lower utilities costs and fewer heat transfer units. The transshipment model is another widely used sequential HEN synthesis method. In 1986, Papoulias and Grossmann (Papoulias and Grossmann, 1983, Papoulias and Grossmann, 1983, Papoulias and Grossmann, 1983) proposed a transshipment model to minimize the total annualized cost (TAC), using linear programming (LP) and mixed integer linear programming (MILP). The HEN synthesis was performed in three steps; (i) minimizing utility cost, (ii) decreasing the number of units, and (iii) designing and optimizing a HEN with minimum TAC based on the targets from (i) and (ii) (Floudas et al., 1986). These models may only provide an approximated optimal solution due to sequential synthesis; however, the simultaneous optimization of HEN may provide better structures after synchronously applying various cost indicators and environmental factors. Therefore, Yee et al. (Yee and Grossmann, 1990, Yee et al., 1990) introduced a stage-wise superstructure model that included most of the heat transfer matches that may exist between streams, and its versatility made it the most widely used HEN synthesis model.

In recent years, with the rapid development of economics, chemical industry parks have gradually emerged, and HENs can potentially recover more heat via multi-plant heat integration. Linnhoff and Eastwood (1997) first proposed the concept of multi-plant heat integration in 1987 and used pinch technology to establish energy targets for waste heat integration between plants. More researchers have recently shown interest in inter-plant heat integration. Wang et al. (2015) first discussed three basic connection patterns (direct, indirect, and hybrid) for waste heat integration among three plants. The direct method integrates heat between plants by directly using process streams to provide a larger heat recovery due to smaller temperature differences during heat transfer. Cheng et al. (2014) applied sequential synthesis to construct multi-plant direct heat integration; however, this HEN model requires heavy investment in pipelines and may bring greater risks due to unplanned shutdowns of other plants because a shutdown in one plant may have a significant negative effect on its partners (Chew et al., 2013).

Heat integration across plants has been considered impractical for various reasons (Rodera and Bagajewicz, 1999), including the fear that continuous operation in one plant may be interrupted by other plants. If an accident leads to the unplanned shutdown of one plant, another plant may have to use an alternative HEN to reach its target temperatures. The indirect heat integration can prevent this type of risk and enable a more operable multi-plant HEN.

Wang et al. (2015) combined the direct and indirect heat integration methods to build a HEN superstructure suitable for multi-plant conditions. To maximize the cost savings of plants, Bagajewicz and Rodera (Bagajewicz and Rodera, 2000) introduced a strategy to determine the minimum number of intermediate fluid circuits and developed a MILP model to determine the optimal position of the intermediate fluid circuits. Stijepovic and Linke (2011) considered distance factors across plants and focused on the optimization of waste energy at industrial parks. Chang et al. (2015) merged graphical methods based on PA with mathematical programming to obtain a generalized MINLP model with a minimum TAC value, considering many factors, such as capital costs of heat exchangers, pumps and pipes, as well as operating cost of pump delivery and energy loss during transportation. To prevent the algorithm from falling into a local solution during optimization, a convex reconstruction and piecewise relaxation method (Chang et al., 2016) was applied to redefine the MINLP model that synchronously demonstrated intra- and inter-plant heat integration as a convex problem to ease calculation intensity. Based on PA, Chang et al. (Chang et al., 2017) found that thermal oil has better heat recovery efficiency than steam. They established a mixed integer nonlinear programming (MINLP) model that contains both intra-plant and inter-plant heat exchangers to optimize TAC using thermal oil as the intermediate fluid. Bade and Bandyopadhyay (2014) proposed a LP model to minimize the heat flow rate of thermal oil. Tarighaleslami et al. (2017) presented a unified total site heat integration (TSHI) targeting method that addressed isothermal (steam) and non-isothermal (hot water) utilities. Song et al. (Song et al., 2017, Song et al., 2017) split the large-scale indirect HEN synthesis into smaller sub-problems by adopting a search algorithm based on PA to maximize the heat recovery potential in the entire HEN. Later, it was shown that (Song et al., 2018) that the parallel connection pattern for inter-plant heat integration (IPHI) presented the maximum inter-plant heat recovery potential and greater flexibility. Chang et al. (2018) added Nash equilibrium (Nash, 1951) constraints to the sequential synthesis of multi-plant indirect HEN, and indicated that the plant with higher operational risk should have a larger cost-sharing ratio. Pan et al. (2018) proposed a simultaneous optimization model of multi-plant indirect HEN. An Alopex-based evolutionary algorithm (AEA) was used to optimize the model and minimize the TAC, and simultaneously obtained the heat capacity flow rate of the intermediate stream, the temperature at both ends, and the optimal structure of the HEN. Hong et al. (2019) applied the transshipment model to an intermediate fluid circuit, where the temperatures of the process streams were used to estimate the upper and lower temperature limits at both ends of the intermediate fluid based on unknown intermediate fluid temperatures. Liu et al. (2020) proposed an optimization-based method to automatically select and arrange multiple intermediate fluids for a single plant in their indirect heat integration. Multi-period designs under different operating conditions were considered.

The above research describes the procedure of multi-plant indirect heat integration development and provides important guidance for future studies. However, the simultaneous synthesis of multi-plant indirect HEN is intrinsically flawed because current MINLP models contain many nonlinear constraints, making it difficult to use them to solve problems. Since the MINLP model must simultaneously consider multiple factors, such as utilities, heat exchangers, and pipelines, there are three unknown parameters in the intermediate fluid circuit, including the cold-end temperature, hot-end temperature, and the heat capacity flow rate. Solving the problem without simplification is difficult, and it is easy to end up with a local optimal solution. In response to this problem, Laukkanen et al. (2012) assumed that the temperatures of the cold and hot ends of the intermediate fluid circuit were the same, which allowed the use of a large heat capacity flow rate to reduce optimization difficulties. Chang et al. (2017) used different heat capacity flow rates in the intermediate fluid circuit to iteratively solve the MINLP model to determine the lowest TAC and its corresponding heat capacity flow rate. Pan et al. (2018) proposed a method of 'clamping' the temperatures at both ends of the intermediate fluid by setting the hot-end and cold-end temperatures to their limiting values and then gradually reducing the possible range to determine the temperature at both ends. Based on the simplification of the simultaneous synthesis model, this study proposes a two-layer optimization method for multi-plant indirect heat integration. A differential evolution (DE) algorithm is applied to determine the temperatures of both ends of the intermediate fluid in the outer layer. Then, a deterministic method is applied to optimize a MINLP model in the inner layer to determine the configuration and TAC of the HEN based on the temperatures obtained in the outer layer. Through the iterative calculation of inner and outer layers, the optimal HEN is determined. The remainder of the paper is organized as follows. Section 2 introduces the specific structure of the simultaneous optimal indirect HEN model and its constraints. Section 3 provides the DE algorithm used to identify the temperatures of intermediate fluid. In Section 4, three examples are presented to prove the feasibility of the proposed model. Finally, conclusions are provided in Section 5.

Section snippets

Parallel indirect heat integration superstructure model

Indirect heat transfer is a heat integration method that uses intermediate fluids to circulate heat among plants. The plant that releases heat into the intermediate fluid is called the heat source plant, and the one that absorbs heat from the intermediate fluid is called the heat sink plant. PA (Linnhoff, 1989) can be used to determine heat source plants with surplus heat and heat sink plants with heat demand. The total heat capacity of the intermediate fluid in all heat source plants equals

The application of the DE algorithm in the indirect HEN synthesis

In 1997, Storn and Price proposed the DE algorithm (Storn and Price, 1997). The fitness function of the DE algorithm should be the TAC value of the indirect HEN model. Each time, the optimized temperatures of the two ends of the intermediate fluid are sent to the MINLP model of the inner layer to generate the HEN configuration and obtain the optimal TAC. Then, the TAC obtained using the corresponding temperatures of the two ends is returned to the outside DE algorithm to determine the

Case studies

The proposed method was used to code the DE algorithm in MATLAB, and the MINLP model of the indirect HEN was obtained using the solver DICOPT (Grossmann et al., 2002) in GAMS 24.0 (Brook et al., 1988). The intersection between MATLAB and GAMS depends on using the gdx file as an interface. For example, the wgdx command in MATLAB can write the temperatures of the two ends of the intermediate fluid on the gdx file to help GAMS generate the structure with the optimal TAC value. Similarly, the rgdx

Conclusions

A simultaneous synthesis method for multi-plant indirect heat integration that considers tradeoffs among the heat exchanger, utility, and pipeline costs is proposed. To obtain the best HEN, a two-layer optimization process is designed. A DE algorithm is applied in the outer layer to identify the two end-temperatures of the intermediate fluid circuit. Based on the two-end temperatures, a MINLP model in the inner layer can be optimized to obtain the HEN configurations and TAC values. The TAC

CRediT authorship contribution statement

Yitong Tian: Methodology, Software, Writing - review & editing. Yuhui Jin: Conceptualization, Software, Formal analysis, Data curation. Shaojun Li: Resources, Supervision, Project administration, Funding acquisition.

Declaration of Competing Interest

The authors declared that there is no conflict of interest.

Acknowledgments

The authors of this paper appreciate the National Natural Science Foundation of China (under Project No. 21406064) and the Fundamental Research Funds for the Central Universities under Grant 222201717006 for their financial support. Many thanks to the anonymous reviewers for their careful work, thoughtful suggestions, and detailed comments on language that have helped improve this paper substantially.

References (43)

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