4.1.2. Case 2: Raw Milk Processing into Dairy Products

The stream data are taken from Wallerand et al. [36], as shown in the Appendix A (Table A1). The ΔTmin of the process is 4 ◦C. As can be seen from the GCC in Figure 9, the Pinch Temperature of this process is 66.9 ◦C. The hot utility required is 2.34 MW and the cold utility required is 0.94 MW. It is assumed that the heat duty of the heat exchanger at the source side is fixed 0.71 MW. Both the process heat source and the sink undergo a phase transition. The source needs to be condensed, and the sink needs to be heated and evaporated. The pressure differences of the heat exchangers on the source side and sink sides are both set 0 kPa. The setting range of independent variables and optimisation results of HP integration into a dairy product process are shown in Table 4.


**Table 4.** Variable settings and optimisation results of a dairy product with an integrated heat pump.

<sup>1</sup> P2: The outlet pressure of the compressor in the HP cycle, MPa. <sup>2</sup> P5: The outlet pressure of the expander or expansion valve in the HP cycle, MPa. <sup>3</sup> R: The compression ratio of the compressor.

The GCC of the dairy products process integrated with different types of HPs is shown in Figure 9. As can be seen from Table 4, the four HPs (JCHP-Ar, JCHP-CO2, VCHP, and TCHP) can save 43%, 39%, 33%, and 78% of the hot utility by improving the waste heat quality of the process. The ranking of the HP COPs is VCHP > JCHP-CO2 > JCHP-Ar > TCHP when integrating with the dairy products process.

The reason can be seen in Figure 9. The ΔTin and the ΔTout between the source and the sink are both too small (1.5 ◦C). The slopes of both the source and sink in the GCC plot are too small (flat). As the working fluid of the JCHP remains a gas across the whole HP cycle, the ΔT between the inlet and the outlet of the working fluid in the JCHP varies significantly in the heat exchange with source or sink. The slope of the working fluid is relatively large in the GCC, as shown in Figure 9a,b. As the working fluid of the VCHP is evaporated during heat exchange with the source and is condensed during heat exchange with the sink, the ΔT between inlet and outlet of the working fluid in the VCHP does not change in the heat exchange with the source or sink. The slope of the working fluid is small in the GCC, as shown in Figure 9c. The working fluid of TCHP is evaporated during exchanging heat with the source, whereas it is a supercritical fluid during the heat transfer to the sink. Therefore, the slope of the working fluid is small in the heat exchange with the source in the GCC, while the slope of the working fluid is steep in the heat exchange with sink in GCC, as shown in Figure 9d. In this case, the average temperature between the working fluid and the source/sink in VCHP is small, so the energy loss of the heat exchangers is lower, the heat exchange efficiency is higher and affects COP positively. Although the average temperature between working fluid and source/sink in JCHP and TCHP is large, so the energy loss is higher, the heat exchange efficiency is smaller, and affects negatively to the COP. The performance of JCHP and TCHP are both weak. In addition, the outlet pressure of the compressor in TCHP is too high (17.54 MPa). This means high-pressure requirements for equipment of TCHP, with very high equipment investment costs. The TCHP economy is weak. This process is more suitable for Heat Integration with VCHP, which is consistent with the conclusion of Section 3. It can be seen that the method proposed in this study is feasible and effective.

**Figure 9.** GCC of case 2 with integration options using (**a**) JCHP-Ar, (**b**) JCHP-CO2, (**c**) VCHP and (**d**) TCHP.
