**3. Final Sizing and Bypass Design for MER HEN with Disturbance on TS**

The heuristics proposed are applied for designing a HEN that is flexible to disturbances. Analysis of the effect of disturbances on each stream in the HEN is summarised in Table 3. It is shown that disturbances can cause either positive or negative impacts on the QH and QC of HEN. The bypass fraction is determined based on the heuristics proposed. Figure 17 shows the final HEN with the bypass placed. Each stream applied different heuristics according to the scenario described previously.

**Figure 17.** Overall HEN with bypass placement.


Analysisofbypassand utility requirementsofHENdesign.

> **Table 3.**

#### **4. Case Studies**

.

Illustrative case studies extracted from the literature are used to verify the applicability and accuracy of the proposed methodology for optimal HEN synthesis, considering the uncertainties at the supply temperature.

#### *Case Study 1*

The first example is based on a methanol synthesis process adapted from Kijevˇcanin et al. [29]. The Case Study 1 has ΔTmin of 20 ◦C. The pinch temperature is at 357.2 ◦C. The minimum heating requirement (QH,min) is 1953.88 kW while the minimum cooling requirement (QC,min) is 3463.53 kW. Expected variations of ±10 ◦C in the inlet temperature of streams H1 and C3 are assumed to vary from their nominal values. The case study consists of eight hot streams and three cold streams as shown in Table 4. Four scenarios involving the variations of the inlet temperatures between streams H1 and C3 are observed (Table 5).


**Table 4.** Stream data of Case Study 1 [29].

**Table 5.** Uncertain parameters for the considered inlet temperatures.


All the scenarios are applied in designing a HEN with the nominal HE area (previous work) and the maximum HE area (this work). Figure 18 shows the HEN at the nominal condition with the bypass placement but with different HE area and bypass fraction.

Analysis of the effect of disturbances on streams H1 and C3 for the nominal HE area (previous work) is shown in Table 6 while the maximum HE area (this work) is shown in Table 7. It is observed that the duty of HE2 increased to 319.70 kW when the supply temperature of hot stream H1 located across or above the pinch increased. This decreased the duty of hot utility HU2 to 181.80 kW. However, if the HE2 area is maintained at the nominal size, the duty of hot utility is also maintained at the nominal value. On the other hand, the duty of HE2 for both works decreased to 227.70 kW when the supply temperature of hot stream H1 is decreased. This led to an increase of hot utility HU2 to 273.80 kW in both works. For the cold stream C3 located below the pinch, it is observed that the duty of HE5 decreased to 186.60 kW when the supply temperature is increased for both works. Both designs

required large HU2 utility loads to cope with the deficit enthalpy of HE5. On the contrary, the duty of HE5 can be increased to 256.60 kW, at the maximum HE area when the supply temperature of C3 decreased. Consequently, the minimum cold utility for CU2 can be obtained.

**Figure 18.** Overall HEN with bypass placement for Case Study 1.

The impact of the changes on the economics for the cases of nominal HE area and maximum HE area were analysed by comparing the annualised capital and utility costs for both HEN using Equation (5) [30]. The basic rule to target for cost-effective minimum utilities is to maximise the use of higher temperature cold utilities and lower temperature hot utilities. The type of utilities suggested based on temperature interval is shown in Table 8. The rates for the utilities refer to Sun et al. [31].

$$\text{Annualised capital cost} = \text{Annualised factor} \times \left(1300 + 1000 \text{ A}^{0.83}\right) \tag{5}$$

where the annualised factor is 0.298.

Table 9 compares the heat recovery and economic performance of HEN with nominal HE area and maximum HE area for all the scenarios. Results of this study show that the new heuristics can guide the user to manage temperature disturbances in HEN design for maximum heat recovery with minimum total costs. Although this work has a high annualised capital cost due to larger HE area compared to the previous work, the annualised total costs for scenarios A, B and C is still much cheaper than the previous work. For scenario D, the total annualised cost is 0.16% higher due to the large HE area, but the utility load remains the same.







Cold utility

Hot utility (kW)

Total disturbed HE area (m2)

Annualised

Annualised

Annualised

 total cost (\$/y)

 utility cost (\$/y)

 99,685.86

 105,391.78

 112,728.50

 118,434.42

 98.409.62

 104,115.54

 114,004.74

 119,710.66

85,366.98

91,268.68

 111,452.25

 117,353.95

 82,814.49

 88,716.19

 114,004.74

 119,906.44

 capital cost (\$/y)

 227.80

 273.80

 227.80

> 77.774

 5705.92

 273.80

181.80

 273.80

 181.80

82.186

5901.70


 **D**

 273.80

#### **5. Case Study 2**

In this case study, the proposed methodology is applied to solve an illustrative example with three hot streams and three cold streams. The data used for this case study are adapted from the work of Escobar et al. [9]. The nominal data for the problem is listed in Table 10. The expected variations in the inlet temperatures are assumed ±10 K with ΔTmin of 10 K. In contrast to Escobar et al. [9], the nominal configuration of HEN is maintained. The maximum heat exchanger area approach is applied to increase the flexibility of HEN due to the uncertainty of operating conditions. The uncertain parameters considered in the design are given in Table 11.


**Table 10.** Stream data of Case Study 2 [9].

Exchanger capital cost (\$/y) = 8333.3 + 641.7 Area (m2)

Annualisation factor = 0.2/y

Cost of cooling utility = 60.576 (\$ /kW·y)

Cost of heating utility = 171.428 (\$/kW·y)

**Table 11.** Uncertain parameters for the points considered.


Initially, the MER for the nominal case (without disturbances) is determined by using pinch analysis targeting methods. For this case study, the nominal condition corresponds to the first iteration. By using the same (nominal) HEN configuration, in order for the target temperature to be achieved, the enthalpy for the cold streams is required to be increased while the enthalpy for the hot streams is decreased. Thus, the utility consumption (cold utility) can be reduced. At the same time, the area of the heat exchangers is required to be at the maximum size for the HEN design to be feasible. Figure 19 shows the HEN at the nominal condition with the bypass placement. On the other hand, Escobar et al. [9] suggested two different HEN designs for each iteration as the nominal design is not feasible for the variations up to 10 K in the inlet temperatures. The steps where the critical point is added to the nominal conditions and the multi-period optimisation problem needs to be repeated until the flexibility is accomplished. The new HEN configuration is designed with high flexibility. The TAC is comprised of the annualised utility cost and annualised capital cost. The TAC of this work for the first iteration is much higher than the previous work as the same HEN design with maximum heat exchanger area is applied. However, the TAC for this work with the consideration of uncertainty is \$25,986.93/y, comprising \$3028.80/y associated with operating expenses (utility consumption) and \$22,958.13/y to capital investment. This work gives 4%/y lower TAC compared to the work of Escobar et al. [9]. Although it has a higher capital cost, the utility consumption is reduced. This method is able to give positive effects even though the HEN has uncertain operating parameters, as it provides better utility usage and would be a good approach for considering a reduction in the

environmental impact associated with the use of fossil-based energy sources. The results of this work and those of Escobar et al. [9] are compared in Table 12.

**Figure 19.** Overall HEN with bypass placement for Case Study 2.


**Table 12.** Comparison results of HEN total annual cost for Case Study 2.

#### **6. Conclusions**

Heat exchanger network configuration can influence disturbance propagation and process behaviour, as well as limit process controllability and operability. A systematic methodology has been developed in this work to manage temperature disturbances and make a heat exchanger network more flexible and operable toward achieving the maximum heat recovery. The method considers the impact of supply temperature fluctuations on utility consumption, heat exchanger sizing and bypass placement. The maximum energy recovery targets are determined for the nominal case (without disturbances) by using pinch analysis targeting methods. The steps to manage the fluctuating supply temperature in the heat exchanger network to achieve target temperature and maximum energy recovery are defined in three stages: (1) the effect of increasing or decreasing supply temperature on the hot and cold streams energy requirement; (2) the fundamental theory of the plus-minus principle; (3) the effect of TS fluctuation on utilities based on the plus-minus principle. From all these steps, key observations were made and new heuristics based on the plus-minus principle of pinch analysis have been introduced for heat exchanger network design in maximising utility savings. The heuristics were applied by simulating various scenarios of disturbances occurring in the process streams of the heat exchanger network. Guidelines on the sizing of heat exchangers and bypass locations and fractions have also been proposed. The grid diagram and temperature vs enthalpy plot were used to illustrate the effect of changes in design and operating parameters. This approach involves a trade-off between the utility cost and capital cost of the affected heat exchangers. Application of the method on two case studies showed that the configuration of the heat exchanger network is maintained for all the scenarios. In addition, the exchanger areas are designed at the maximum size with a bypass to handle

the most critical uncertainty of operating conditions while minimising the utility usage. It showed that this method improved the annualised utility cost by up to 89%. Previous works in the literature required the exchanger area adjustment during the operation and have several heat exchanger network configurations for each scenario. Nevertheless, in industry, the configuration and area should be fixed during the operation even with unforeseen uncertainty. The modification of heat exchanger network design during the operation will be costly. This work is beneficial as it has a reduced utility usage and a higher capital cost.

Major novelties introduced by this work include:


However, overdesign factors could affect the annualised capital cost of heat exchanger networks. Future research should also include the probability of disturbances occurring in the heat exchanger network. This probability may influence the requirement of the maximum heat exchanger size in the design as well as the total annualised cost.

**Author Contributions:** Conceptualisation, S.R.W.A.; Methodology, A.M.H., S.R.W.A.; Validation, A.M.H.; Formal analysis, A.M.H., S.R.W.A.; Writing—original draft preparation, A.M.H.; writing—review and editing, S.R.W.A., Z.A.M., J.J.K.; supervision, S.R.W.A., Z.A.M., J.J.K., M.K.A.H.

**Acknowledgments:** The authors thank Universiti Teknologi Malaysia (UTM) for providing research funds for this project under Vote Number Q.J130000.3509.05G96, Q.J130000.2509.19H34, the Fundamental Research Grant Scheme under Ministry of Education with Vote Number R.J130000.7809.4F918 and from the EC project for Sustainable Process Integration Laboratory-SPIL (Project No. CZ.02.1.01/0.0/0.0/15\_003/0000456) funded by Czech Republic Operational Program Research and Development, Education, Priority 1: Strengthening capacity for quality research in collaboration agreement with Universiti Teknologi Malaysia (UTM).

**Conflicts of Interest:** The authors declare no conflict of interest.
