Article
Simultaneous synthesis of sub and above-ambient heat exchanger networks including expansion process based on an enhanced superstructure model

https://doi.org/10.1016/j.cjche.2020.02.026Get rights and content

Abstract

Synthesis of heat exchanger networks including expansion process is a complex task due to the involvement of both heat and work. A stream that expands through expanders can produce work and cold load, while expansion through valves barely affects heat integration. In addition, expansion through expanders at higher temperature produces more work, but consumes more hot utility. Therefore, there is a need to weigh work production and heat consumption. To this end, an enhanced stage-wise superstructure is proposed that involves synchronous optimization of expander/valve placement and heat integration for each pressure-change sub-stream in stages. A mixed-integer nonlinear programming (MINLP) model is established for synthesizing sub and above-ambient heat exchanger networks with multi-stream expansion, which explicitly considers the optimized selection of end-heaters and end-coolers to adjust temperature requirement. Our proposed method can commendably achieve the optimal selection of expanders and valves in a bid for minimizing exergy consumption and total annual cost. Four example studies are conducted with two distinct objective function (minimization of exergy consumption and total annual cost, respectively) to illustrate the feasibility and efficacy of the proposed method.

Introduction

The well-established heat integration strategies have made significant advances in academic research and industrial application for energy conservation and efficiency improvement. Numerous researchers have investigated thermodynamic and mathematical programming methodologies [[1], [2], [3], [4]] for optimal design of heat exchanger networks (HENs), since pinch analysis [5] was proven to be an efficient method for promoting thermal integration. Yang et al. [6] proposed the temperature-enthalpy and Grand Composite Curves for analyzing heat recovery. The FTS process applies both conventional and advanced exergy analyses to achieve maximum energy and exergy savings [7]. In addition to heat integration, the integration of work, another form of energy frequently available in chemical plants, takes the dominating responsibility for considerable energy savings and carbon emissions reduction when coping with pressure manipulation [8]. The fundamental importance of work integration through work exchanger network (WEN) synthesis has attracted extensive interest in the past few years.

Inspired by HEN synthesis, the notion of WEN was originally introduced by Huang and Fan [9]. As a pioneering contribution, they proposed heuristic rules and feasible matching conditions to facilitate WEN design, which boosted the development of more efficient integration methods and mechanical energy recovery strategies. Liu et al. [10] proposed a graphical integrating approach to identify feasible matches for direct WEN only operated under isothermal condition, which is upgraded by Zhuang et al. [11] using a novel diagram method suitable for any operation. Subsequently, Rankouhi and Huang [12] introduced a thermodynamic modeling and analysis approach to predict the maximum recoverable mechanical energy prior to network design. Subsequently, Zhuang et al. [13,14] successively put forward an improved transshipment model and superstructure-based model to further optimize placement of work-transfer devices. In addition, Razib et al. [15] formulated a MINLP model to achieve indirect WEN design. Nevertheless, the above studies did not consider heat integration. Actually, the temperature, pressure, heat and work of process streams are interacting. Compression expends less work at lower temperature and expansion produces more work at higher temperature, whilst the stream temperature will also be changed after compression and expansion, thus affecting the demand for heating and cooling utility. In addition, the properties of the stream (hot or cold) may change with pressure manipulations and the position of the pinch points may move so that conventional pinch analysis is not applicable. Therefore, it is inevitable to focus on simultaneously harnessing thermal and mechanical energy from process streams related to compression/expansion and heating/cooling requirement.

Since simultaneous integration of work and heat is a complicated issue, the basic insights into interactive effect of temperature and pressure on heat and work have been developed increasingly. Townsend and Linnhoff [16] proposed the criteria for appropriate placement of heat engines and heat pumps into heat exchanger networks. Afterwards, an Extended Pinch Analysis and Design (ExPAnD) method was developed by Aspelund et al. [17] for compression and expansion optimization in HEN based on heuristic rules. Gundersen et al. [18] specified that both compression and expansion should start at the pinch temperature. Based on this, a set of thermodynamic viewpoints were provided by Fu and Gundersen [[19], [20], [21]] to appropriately integrate compressors and/or expanders into sub and above-ambient HEN on the basis of the grand composite curves (GCCs) aiming at the minimum exergy consumption. These above-mentioned studies are based on thermodynamic insights, not considering economic aspects.

As the cold and hot identities of streams are uncertain due to the pressure manipulation, it is necessary to pre-specify the pressure manipulation and heat exchange route of hot and cold streams to determine the potential heat transfer. The strategy is proposed by Wechsung et al. and a mathematical model is developed to minimize external utility based on ExPAnD [22]. Onishi et al. [23] presented mathematical formulations for the HEN synthesis with pressure manipulation, using the pre-defined pressure manipulation routes. Afterwards, a superstructure-based model is introduced for the optimal synthesis of work and heat exchanger networks. They highlighted the importance for appropriate heat integration between pressure manipulation stages to significantly enhance mechanical energy recovery, thus reducing capital and operational expenses [24]. Huang and Karimi [25] further considered constant-pressure streams for heat integration and perform an optimized selection of end-heaters and end-coolers. Later, Zhuang et al. [26] proposed a step-wise method for direct WEN and HEN synthesis. Optimization-based frameworks for WHEN synthesis developed so far are based on deterministic approaches and commercial solver implementations. Recently, Pavão et al. [27] presented a novel alternative framework based on a matrix-based implementation fit for the use of a meta-heuristic solution approach. Moreover, a novel simulation-based meta-heuristic optimization approach is proposed by Hamedi for WHENS [28]. As a consequence, simultaneous optimization approaches have been explored to achieve cost savings through WHEN synthesis, due to the fact that temperature changes arising from work transfer are able to be exploited for heat integration whilst HEN design may adjust temperature to facilitate work integration.

The thermal identity of process streams is known on all above-mentioned approaches. However, it is difficult to clearly distinguish between hot and cold stream due to the highly variable temperature of the stream in industrial process. To address WHEN design with identity changes of process streams, Nair et al. [29] proposed a generalized framework for integrating heat and work simultaneously based on the strategies that do not pre-classify streams identity. Onishi et al. [30] introduced a mathematical programming model combined with pinch location method to optimize work and heat integration without classified streams. Afterwards, an extended Duran–Grossmann model is developed by Yu et al. [31] to identify optimal thermodynamic paths among pressure change streams firstly and then perform traditional HEN synthesis. However, it is difficult to address economic performance and the selection of valves and expanders is not considered during expansion.

Despite successful advances in WHEN synthesis, the previous superstructures mainly consist of two distinct networks exclusively for work integration and heat integration respectively. In that sense, heat exchange and work exchange cannot concurrently occur in one sub-stream, which may lead to omitting the optimal WHEN configuration. The deficiency is preliminarily overcome by Yu et al. [31], but it does not achieve synchronous integration of work and heat and the optimal selection of valves and expanders is also not considered during expansion. Additionally, for N2 Brdyton cycle in oxy-combustion process and membrane separation of CO2/N2 in post-combustion process, only expansion is included and large energy saving potential is demonstrated by expansion optimization and heat integration [32]. Both valves and expanders have the same effect on pressure reduction, but their cost and action principle are quite different. Therefore, both thermodynamic analysis and economic evaluation should be considered, which was not fully considered in previous studies.

To surpass the previous limitation, an enhanced stage-wise superstructure is proposed that involves synchronous optimization of expanders/valves placement and heat integration for each pressure-change sub-stream in stages. A MINLP model is established that explicitly considers non-isothermal mixing in each stage and enables the optimized selection end-heaters and end-coolers to adjust temperature requirement. It can successfully design sub and above-ambient heat exchanger networks with multi-stream expansion, in a bid for minimizing exergy consumption and total annualized cost. Four case studies are performed to assess the methodological efficacy and the enhanced thermodynamic feasibility and cost-efficiency of our model.

Section snippets

Problem Statement

The HEN synthesis with appropriate expansion equipment (expanders and valves) placement is achieved by coupling the expansion optimization and heat exchange identification for each sub-stream in an enhanced superstructure-based model, aiming at minimum exergy consumption and minimum total annualized cost (TAC) respectively, which can be stated as follows.

The set of streams is provided with known supply state (pressure, temperature, heat capacity flowrate) and target state (pressure,

Enhanced Stage-wise Superstructure

Different form the current model for work and heat integration exclusively performed in two distinct networks (HEN and WEN), an enhanced stage-wise superstructure is established that involves synchronous optimization of valves/expanders placement and heat integration for each pressure-change sub-stream in stages, as shown in Fig. 1. All intermediate temperatures and the inlet temperature of expansion equipment are decision variables, so appropriate placement of valves/expanders is a key issue.

Mathematical Model

The MINLP model is formulated by combining HEN synthesis with expansion optimization, where the mathematical formulations for HEN design are derived from Yee and Grossmann [33]. Thus, more detailed comments are chiefly devoted to addressing model additions and the modifications because of integrating expanders/valves into HEN. The following sets are defined for the development of the mathematical model:

  • H = {ii = 1, 2…, I, hot streams}

  • C = {j, j´│j, j´ = 1, 2…, J, cold streams}

  • PH = {ii = 1, 2…,

Example Studies

In this article, four examples are used to illustrate the efficacy and feasibility of our superstructure-based model. Example 1 and Example 2 selected from open literatures integrate expanders/valves into sub-ambient and above-ambient heat exchanger networks, respectively. Example 3 and Example 4 include two streams with expansion process at sub and above-ambient conditions. Firstly, this paper aims at HEN synthesis combined with optimal expanders/valves placement with the objective of minimum

Conclusions

A new MINLP model is formulated to synchronous optimization of expanders/valves placement and heat exchanger networks synthesis based on an enhanced stage-wise superstructure, which considers thermodynamic analysis (minimum exergy consumption) and economic evaluation (minimum total annualized cost). Secondly, the enhanced superstructure involves heat exchange and expanders/valves placement for pressure-change sub-streams in each stage, which is independent of rigorously thermodynamic route

Nomenclature

    A

    heat transfer area

    CO

    price of electricity

    dt

    approximation temperature between cold and hot streams

    dtcu

    approximation temperature between pressure-change streams and cooling utility

    dthu

    approximation temperature between cold streams and heating utility

    E

    exergy consumption

    Eqcu

    exergy consumption of cooling utility

    Eqhu

    exergy consumption of heating utility

    EW

    exergy consumption of expansion

    F

    heat capacity flowrate of stream

    Fe

    heat capacity flowrates of sub-stream through the valve

    Fv

    heat capacity flowrates

Superscripts

    after

    expanders after sub-stream heat exchangers

    before

    expanders before sub-stream heat exchangers

Subscripts

    CU

    cooling utility

    exp

    expansion

    he

    heat exchange

    HU

    heating utility

    i

    hot streams

    j, j´

    cold streams

    k

    stages

    Nk

    last stage

Acknowledgements

The authors would like to gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (No. 21776035) and China Postdoctoral Science Foundation (No. 2019TQ0045).

References (35)

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