**1. Introduction**

Heat integration has been a well-established energy saving technique for the chemical process industry since the global energy crisis in the 1970s [1]. There has also been extensive development of pinch analysis methodologies for industrial heat exchanger network (HEN) design focusing on minimisation of operating and capital costs [2]. The developed methodologies typically assume that process parameters such as supply/target temperatures and stream flowrates are fixed [3]. In practice, these process parameters may fluctuate due to plant start-ups/shut-downs, changes in feed or product demand as well as quality, changes in environmental conditions and other operational disturbances. The impact of these parameter changes influences energy related-decision making as a step for efficient energy management in the industry [4,5]. The extent to which a HEN is able to cope with disturbances is known as flexibility [3]. Previous works have included flexibility, safety, controllability and operability in the pre-design stage.

Marselle et al. [6] pioneered the study of operability considerations for HENs. They proposed a manual combination of several resilient designs with maximum energy efficiency under different worst-case scenarios. Hafizan et al. [7] proposed the controllability of HEN under uncertainty by having a large heat exchanger area. This method is able to recover maximum heat with minimum utility. The paper was also partly presented at the 13th SDEWES conference and proceedings. Linnhoff and Kotjabasakis [8] introduced the concept of downstream paths to identify disturbance propagation paths through HEN. Supply temperature and feed flowrate disturbances occurring at the feed stream of heat exchangers can affect the target temperatures of processes located downstream of the heat exchanger path. HEN modification, therefore, may need to be performed to reject the process disturbances.

Escobar et al. [9] introduced a computational framework for the synthesis of controllable and flexible HENs over a specified range of inlet temperatures and flow rate variations using a decentralised control system. This framework comprised two stages—the HEN design and the operability analysis and adjustment of control variables during operation in the presence of uncertain parameters. Hafizan et al. [10] developed a pinch analysis-based methodology, which considered both safety and operability aspects in HEN synthesis. The concept of downstream paths suggested by Linnhoff and Kotjabasakis [8] was used for the assessment of flexibility and structural controllability. Cuˇ ˇ cek and Kravanja [11] proposed a novel three-step methodology for HEN retrofit with fixed and flexible designs for large-scale total sites (TS). This method modified the HEN by forming profitable heat exchanger matches with improved utility consumption as well as by proposing intermediate utility production.

Most recent works have developed a multi-period formulation for the synthesis of flexible HENs. Isafiade and Short [12] proposed a three-step approach for improving the degree of flexibility of a multi-period HEN with unequal periods. However, this method is unable to cater for all the possible uncertainties of process parameters. Miranda et al. [13] recently proposed three sequential steps represented by linear programming (LP), multi-linear programming (MILP) and non-linear programming (NLP) for the synthesis of multi-period HEN. The same heat transfer can be operated under different operating conditions in the multi-period [13]. Kang and Liu [14] developed a three-step method for designing a flexible multi-period HEN when the disturbances of operating parameters occurred in sub-periods. The flexibility of nominal multi-period HEN is first determined and analysed prior to identifying the bottlenecks. As a next step, the design of flexible multi-period HEN is finalised by solving the sub-period debottlenecking model.

Several authors have considered the operability issues at the early stages of the process design. The need for this s widely accepted and has motivated the integration of process design and control (IPDC). Narraway and Perkins [15] and Walsh and Perkins [16] were the among the earliest to take into account the general mathematical programming techniques for the simultaneous design and control problem using dynamic process models. Recently, Abu Bakar et al. [17] introduced a new model-based IPDC of HEN which is decomposed into four hierarchical sequential stages. The proposed methodology recommends a solution that satisfies the design, control and economic criteria.

The optimal HEN with unclassified hot/cold process streams was discussed in the work of Kong et al. [18], Quirante et al. [19] and Onishi et al. [20]. All these works depend on the process operating conditions to finalise the classification of process streams. Kong et al. [18] presented mixed-integer nonlinear programming (MINLP) for the heat integration model which accounts for unclassified process streams and variable stream temperatures and flowrates. Quirante et al. [19] later extended the disjunctive model of the pinch location method proposed by Quirante et al. [21] and work by Kong et al. [18] for the simultaneous process optimisation and heat integration. This work is also extended for the isothermal process streams, multiple utilities and area estimation of HEN. The area estimation is done based on the vertical heat transfer between the hot and cold balanced composite curves. Onishi et al. [20] proposed an optimisation model to enhance the work and HENs energy efficiency and cost-effective synthesis considering the unclassified process streams. It combined the methods of mathematical programming and pinch location while adjusting the pressure and temperature of unclassified streams.

State-of-the-art studies on HEN flexibility, show that there are a few key limitations associated with the existing methods. In these previous works, the optimal design of HEN synthesis operated under uncertain operating parameters were considered with an appropriate strategy for control and operation. The control variables were assumed to be adjusted during the operation to improve the flexibility of HEN. However, several possible HEN configurations were needed for each of the scenarios in order to increase the flexibility and some exchanger area adjustment was required during the operation. Besides that, heuristics to guide heat exchanger sizing and bypass placement, and which can be applied in all cases have not been introduced. The understanding of how the temperature fluctuation in HEN affects the amount of heat recovery is still not clearly understood.

This work presents a methodology to manage temperature disturbances in HEN design for maximum heat recovery. The impact of the supply temperature fluctuations on utility consumption, heat exchanger sizing and bypass placement are studied to ensure the target temperatures of affected streams are achieved. At the same time, reducing the impact of the fluctuation on downstream heat exchangers and the immediately propagation of the disturbances to heaters or coolers is desired. Where possible, taking advantage of the disturbances for additional heat recovery is also desirable. The plus-minus principle for process changes are used and new heuristics are introduced to guide heat exchanger sizing and bypass placement. Linnhoff and Vredeveld [22] have introduced the plus-minus principle for visualising the impact of process modifications on the minimum utility target using the composite curves (CC). Chew et al. [23] applied the plus-minus principle for process modification aimed at maximising energy savings for total site heat integration (TSHI). This methodology enabled designers to identify the potential process changes to maximise energy recovery and reduce utility consumption. Song et al. [24] further implemented the plus-minus principle for inter-plant heat integration (IPHI) for case studies involving threshold problems. The proposed methodology provides a simple technique of rapidly assessing the effect of supply temperature (TS) fluctuations in heat recovery and utility reduction without the need for detailed process simulation.

#### **2. Methodology**

This section describes the methodology that was developed to manage supply temperature disturbances through modification of a conventional heat exchange network. By planning the right size for the heat exchangers, and by utilising the bypass streams, a HEN can be designed with the flexibility to cope with supply temperature disturbances. An illustrative case study of a HEN experiencing supply temperature disturbances on each process stream is used to demonstrate the applicability of the methodology. For the case study, disturbances are assumed to occur at all supply temperatures (TSH1, TSH2, TSH3, TSC1, TSC2 and TSC3) with a deviation of ±5 ◦C. The manipulated variables for process control include heat exchangers, bypasses and utility flowrates of coolers and heaters. The controlled variables are all the target temperatures (TtH1, TtH2, TtH3, TtC1, TtC2 and TtC3).

### *2.1. Step 1: Stream Data Extraction with Disturbances*

Table 1 shows the stream data which are used to illustrate the effect of disturbances on maximum energy recovery HEN. There are three hot streams (H1, H2 and H3) and three cold streams (C1, C2 and C3) involved in the process. The required data for the pinch study includes the supply temperature, Ts; target temperature, Tt; heat capacity flowrate, FCp; enthalpy, ΔH and the supply temperature fluctuation temperature range. The minimum temperature difference, ΔTmin is set as 10 ◦C.


**Table 1.** Stream data for nominal operation.

#### *2.2. Step 2: Perform Maximum Energy Recovery Targeting for the Nominal Case*

The maximum energy recovery (MER) targets are determined for the nominal case (without disturbances) by using pinch analysis targeting methods such as the problem table algorithm or composite curves by Linnhoff and Flower [25] or streams temperature vs enthalpy plot (STEP) by Wan Alwi and Manan [26]. The targeted minimum hot utility requirement QHmin is 450 MW and the minimum cold utility requirement QCmin is 180 MW. The hot pinch temperature, TPinch, hot is at 250 ◦C and the cold pinch temperature, TPinch, cold is at 240 ◦C. Figure 1 shows the composite curves of the nominal case.

**Figure 1.** Composite curves for the nominal case.
