**1. Introduction**

Heat recovery has been regarded as a major measure to increase energy efficiency in process systems engineering. It can also help to reduce the environmental burden by reducing waste heat emission. Heat exchanger network (HEN) retrofit is an effective way to utilise heat from process streams and to minimise the energy consumption [1]. In the industrial application of HEN retrofit, different types of heat exchangers have their working temperature ranges and costs. The type of heat exchanger should be wisely selected for different usages and applications to ensure the heat exchangers can work under certain conditions with a relatively economic investment cost.

In the HEN retrofit problem, there are generally three approaches, i.e., Pinch Analysis (PA), mathematical programming, and a combined method [2]. The first work of PA was developed by Linnhoff and Flower [3]. Following their innovation, many PA-based graphical methods were proposed for HEN retrofits such as the Retrofit Thermodynamic Diagram (RTD) [4], Stream Temperature vs. Enthalpy Plot (STEP) [5], Temperature Driving Force (TDF) [6], and Energy Transfer Diagram (ETD) [7], which are widely used in the retrofit applications. Some extended methods and applications based on the above studies were reported. Lai et al. [8] proposed a combined STEP and heat exchanger area versus enthalpy (A vs. H) plot to customise a retrofit design toward a desired investment payback period. Kamel et al. [9] applied TDF on an existing HEN in an Egyptian refinery to improve energy saving with minor structural modifications. Lal et al. [10] modified the ETD and proposed a heat surplus-deficit table for the HEN retrofit to achieve energy saving.

RTD has been a particularly useful graphical visual tool. It can display the driving force around the heat exchanger and heat capacity flow rate graphically. Yong et al. [11] modified the RTD and proposed a Shifted Retrofit Thermodynamic Diagram (SRTD). In SRTD, the hot streams are shifted by subtracting the minimum allowed temperature difference (ΔTmin), and then the feasibility of implementing a heat exchanger can be visually seen by connecting both lower and higher temperature sides of hot and cold streams. If the slope of the connecting lines is negative, then it illustrates that the heat exchanger implementing plan violates the Pinch Rule. SRTD was later extended to the Shifted Retrofit Thermodynamic Grid Diagram (SRTGD) by Yong et al. [12]. It uses a dashed line to indicate the location of the Process Pinch. By applying this diagram, pinches can be detected, and the retrofit plan can be determined easier.

Apart from these graphical methods for HEN retrofit, mathematical programming has also been used in the retrofit design. Pan et al. [13] developed mixed-integer linear programming (MILP)-based iterative method for HEN retrofit. Their method fixed the logarithmic mean temperature difference (LMTD) in the original problem and executed two iteration loops to achieve certain energy-saving or net present value. Zhang and Rangaiah [14] applied integrated differential evolution to solve the HEN retrofit problem in one step. Onishi et al. [15] proposed a mathematical programming model for HEN retrofit, considering the pressure recovery of process streams to enhance heat integration. Pavão et al. [16] proposed an extended superstructure model and a corresponding meta-heuristic solution approach for the HEN retrofit problem. Wang et al. [17] developed a mathematical model based on the structure of the SRTGD and a two-stage method. In the first stage, the mathematical model was solved to obtain the topology of the HEN, with the aim of minimising utility and investment costs. While in the second stage, a particle swarm optimisation (PSO) algorithm was applied to adjust the inlet and outlet temperatures of each heat exchanger to achieve the goal of minimising the payback period based on the obtained topology from the first stage. This method considers the cost of utility and investment. It makes the retrofit design based on SRTGD more effective.

In the HEN retrofit process, achieving energy saving is one important task; another issue is to ensure the selected heat exchanger type can satisfy the heat transfer requirement between streams and has a relatively lower cost. Different types of heat exchangers such as shell and tube, double-pipe, compact plate, and spiral tube have their working temperature ranges and capital costs. These issues should be considered in the retrofit design process to determine an economic plan. Soršak and Kravanja [18] proposed a mixed-integer nonlinear programming (MINLP) model for HEN synthesis and modelled the selection of heat exchanger types. Fieg et al. [19] developed a hybrid genetic algorithm for HEN design. The investment and utility costs were calculated separately in a user subroutine to consider the specificity of heat exchangers. Sun et al. [20] presented the Stream Temperature vs. Enthalpy Plot Supertargeting (STEPS) method to optimise the cost of HEN. In their proposed step-by-step method, the heat exchanger types are considered and the capital cost is calculated. These previous papers considered the selection of heat exchanger types for the synthesis problem, the HEN retrofit with the consideration of heat exchanger types requires study. A method should be developed to consider both insights of thermodynamic and suitable heat exchanger type selection for HEN retrofit for potential industrial implementation.

The capital cost is the main criterion used to determine the selected heat exchanger type. Rathjens and Fieg [21] proposed a MINLP model and a genetic algorithm coupled with a deterministic local optimisation approach for HEN synthesis. In their model, the cost functions for each connection of heat source and sink are considered to make solutions more efficient. Aguitoni et al. [22] proposed a combined simulated annealing and differential evolution algorithm to minimise the sum of heat exchanger investment and energy cost. Kang and Liu [23] proposed three strategies to minimise the investment cost for the multi-period HEN retrofit. Ayotte-Sauvé et al. [24] proposed a stepwise approach for HEN retrofit to minimise the investment costs for new and retrofit heat exchangers as well as utility costs. Nemet et al. [25] proposed an MINLP model for the optimal design of HEN, considering the lifetime cost.

There are several advantages of using SRTGD as a visualisation tool in the HEN retrofit applications. It can identify the Process Pinch through the diagram. It is easy to check whether the retrofit plan violates the Pinch Rule [26], and to find if there is still potential for more heat recovery. It also shows the temperature range of each heat exchanger for hot and cold streams, which is a benefit that can be used in the heat exchanger type selection. However, there is still a need to develop a tool that can be used to help designers to select suitable types of heat exchangers visually. This tool should be easy to master and can show insights into network design.

To solve the above-mentioned issue, an SRTGD with the shifted temperature ranges of heat exchangers (SRTGD-STR) is developed as an effective tool for determining the retrofit plan of HENs and selecting feasible and cost-minimised heat exchanger types. The structure of the paper is organised as follows: Section 2 presents the detailed method of utilising this proposed visualisation tool to increase heat recovery and debottleneck an existing process. An illustrative example of how to implement this method is studied. Section 3 demonstrates a case study of the SRTGD-STR to show its effectiveness, and Section 4 presents the conclusion.
