**3. Case Study**

A case study is used to illustrate the proposed method for HEN retrofit, considering heat exchanger types. The data is obtained from Ref. [11], and the target temperature of heat exchanger E3 is modified from 370 ◦C to 410 ◦C for a better illustration of the method. The case has one cold stream and six hot streams. The cold stream is heated by six heat exchangers connecting other streams. The ΔTmin of this HEN is designed as 10 ◦C. The stream data for the case study are listed in Table 5.


**Table 5.** Data pertaining to the existing HEN in the case study.

Note: *TS* is the supply temperature, (◦C); *TT* is the target temperature, (◦C); *CP* is the heat capacity flow rate, (kW/ ◦C); and *h* is the heat transfer coefficient, (kW/m2· ◦C).

Figure 7 shows the SRTGD-STR of the existing HEN. The temperatures of hot streams are shifted. According to this figure, two potential cold utilities can be removed or their power reduced. For cold utility C1, a vertical dotted line on the left side of stream 1 denotes the lowest cold stream temperature at 30 ◦C. Any hot stream segments spanning to the left of this vertical line can only be cooled by using

a cold utility. Cold utility C2 has the potential to be removed as cold stream S1 can still receive the heat from stream 4.

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**Figure 7.** SRTGD-STR of the existing HEN for the case study.

If the heat of stream 4 is fully used for heat recovery and the sequence of the heat exchangers in the existing HEN is not changed, then this retrofit plan would be infeasible, as shown in the red circle marked in Figure 8. The slopes of links between these two heat exchangers are negative. Re-piping and re-sequencing are needed to utilise the heat. By re-piping heat exchangers E4 and E5 between E2 and E3, the retrofit plan is feasible. The results are shown in Figure 9.

**Figure 8.** SRTGD-STR if the sequences of heat exchangers are not changed for the case study.

**Figure 9.** SRTGD-STR if one heat exchanger is added for the case study.

In this retrofit plan, the cold utility C2 is replaced by a heat exchanger to transfer heat from hot stream S4 to cold stream S1. The sequences of heat exchanger E3, E4, and E5 are changed to not violate the Pinch Rule. This reduces the 270 kW of utility used in this HEN.

In this retrofit process, the heat exchanger types are not considered. However, the capital cost of heat exchangers could also influence the retrofit plan optimisation. For the temperature range of this new heat exchanger N1, there are several choices, i.e., using shell and tube, double-pipe, or plate and frame heat exchangers. The selection of heat exchanger types should also be based on the normal area range of heat exchangers. The feasible and cheapest types should be selected.

As can be observed from Figure 7, the temperature range of cold utility C2 crosses over the temperature boundary of the spiral tube, which indicates another option, implementing two new heat exchangers for heat recovery. Another retrofit plan is illustrated in Figure 10 based on SRTGD-STR considering this possibility. In this plan, heat exchangers E4 and E5 on the cold stream S1 are still moved to the left side of E3, and two new heat, N1 and N2, are implemented between E5 and E3 on S1.

Under these circumstances, there are several choices about the heat exchanger types. The following four combinations can be selected, both shell and tube heat exchangers, both double-pipe heat exchangers, both plate and frame heat exchangers, or one double-pipe and one spiral tube. All these retrofit plans are listed in Table 6, and their capital costs are calculated according to equations provided in Section 2.3.

The results (Table 6) show that the feasible and cheapest retrofit plan is using two double-pipe heat exchangers for heat recovery. Its capital cost is 19.9 k\$. The utility cost saving of all these seven solutions is the same. An additional 270 kW of heat can be recovered by the new heat exchangers, which saves 10.7% of the maximum potential for heat recovery (2,520 kW) of this HEN. Although solution 2 has the minimum capital cost, its heat transfer area is 27.9 m2. It is higher than the normal area range of the double-pipe heat exchanger, which makes this plan infeasible. The plan implementing two plate and frame heat exchangers has the highest cost. For a relatively small heat transfer area, the double-pipe heat exchanger is the most recommended as it has an advantage in the cost. For a larger heat transfer area, the most economical option could be the shell-and-tube heat exchanger.

**Figure 10.** SRTGD-STR if two heat exchangers are added for this case study.


**Table 6.** Comparison of the results for the case study.

Note: S&T refers to the shell and tube heat exchanger, D-P refers to the double-pipe heat exchanger, S-T refers to the spiral tube heat exchanger, P&F refers to the plate and frame heat exchanger.
