**3. Simulation and Optimisation of Heat Pumps**

A series of simulations and optimisations were performed by changing the inlet and outlet temperatures of the source and sink to study the performance of these different HP cycles in different scenarios. The settings of parameters and variables of the HP are shown in Table 1. ΔTmin denotes the specifications of the minimum allowed temperature differences of the heat exchangers. The pressure differences (ΔP) between the stream inlets and outlets of the heat exchangers in the HP are all 50 kPa. In the "Adjust" unit, the heat transfer duty of the heat exchanger Cold-side-HX is set to 10 MW by adjusting the flowrate of stream Source-in, which is the optimisation variable. The optimisation objective is to maximise the COP. Based on the simulation results, the application range of these three types of HPs is classified and can be predicted, mapping their suitability for the various process heat source and sink scenarios.


**Table 1.** Settings of parameters and variables.

<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.

The simulation results of the considered scenarios are shown in Figures 6 and 7. In Figure 6, the performance as a function of the temperature lifts expressed as the inlet and outlet temperature differences is evaluated. Figure 7 provides an evaluation of the COP as a function of the temperature lift expressed as ΔT1 and ΔT2.

**Figure 6.** COP of different heat pumps varies with ΔTin and ΔTout: (**a**) JCHP-Ar, (**b**) JCHP-CO2, (**c**) VCHP and (**d**) TCHP.

**Figure 7.** COP of different heat pumps varies with ΔT1 and ΔT2: (**a**) JCHP-Ar, (**b**) JCHP-CO2, (**c**) VCHP and (**d**) TCHP.

Case 1. COP modelled as a function of the temperature lift represented by ΔTin and ΔTout

The variation of COP of different HPs with ΔTin and ΔTout is shown in Figure 6. As can be seen from Figure 6a, when 0 ◦C < ΔTin < 30 ◦C and 30 ◦C < ΔTout < 80 ◦C, the COP of JCHP-Ar decreased with the increase of ΔTin, but did not change much with ΔTout. The COP of JCHP-CO2 decreased with the increase of ΔTin but did not change much with ΔTout, as Figure 6b illustrates. This indicates that, when the inlet temperature difference (ΔTin) between the heat source and sink is not significant, even if the outlet temperature difference (ΔTout) between the two is very large (such as ΔTout increasing to 80 ◦C), the COP of the actual JCHP is still very high. It can be seen that the JCHP is very suitable for processes where the ΔTout is massive, and ΔTin is small. The smaller ΔTin, the higher is the COP of JCHP.

When 0 ◦C < ΔTin < 30 ◦C and 30 ◦C < ΔTout < 80 ◦C, the COP of the evaluated VCHP decreased with the increase of ΔTout, but did not change much with ΔTin, as can be detected from Figure 6c. Therefore, when ΔTout between the source and sink is small, even if the ΔTin between the two is significant (the maximum ΔTin can only be equal to the ΔTout), the COP of the actual VCHP is higher. The observations imply that VCHP is very suitable for processes where the temperature difference (ΔT) between the heat source and sink is not large. The smaller ΔTout, the higher is the COP of VCHP.

The COP of the evaluated TCHP decreased with the increase of ΔTout and ΔTin when 0 ◦C < ΔTin < 30 ◦C and 30 ◦C < ΔTout < 80 ◦C, as can be detected from Figure 6d. The observations imply that the application scope of TCHP is relatively narrow. TCHP is very suitable for processes where the ΔTin is small and ΔTout < 40 ◦C.

The variation trend of TCHP is not very regular, and the performance contours are less noticeable. This is because TCHP is a transcritical cycle, and the thermophysical properties of CO2 in the supercritical state are nonlinear, as the substance does not behave like a gas or a liquid. This makes it necessary to model the HP behaviour also as a function of the other two temperature lift representations: ΔT1 and ΔT2, by analogy with heat exchanger temperature differences and the T–S diagrams of the HP cycles.

Case 2. COP modelled as a function of the temperature lift represented as ΔT1 and ΔT2

The change of COP of different HPs with ΔTin and ΔTout is studied by fixing the outlet temperature of sink Tsink-out to a certain level. In this study the Tsink-out is set as 50 ◦C. When Tsink-out is 50 ◦C, the change of COP of the different HPs with ΔT1 and ΔT2 is shown in Figure 7. It can be seen that the COP of JCHP-Ar decreased with the increase of ΔT1 and ΔT2. The COP of JCHP-CO2 first increased and then decreased with the increase of ΔT1 and ΔT2, featuring a maximum. The COP of VCHP and TCHP decreased with the increase of ΔT1, but did not change much with ΔT2.

It can be seen from Figure 7d that when the temperature difference ΔT1 is small, even if the temperature difference ΔT2 is large, the COP of the TCHP is higher. The TCHP is then very suitable for a small temperature rise ΔT1 (preferably ΔT1 ≤ 10 ◦C) combined with a large ΔT2 process.

In conclusion, the observations imply from Figures 6 and 7 that JCHP is very suitable for the process of steep T–H lines of the source and sink in GCC. VCHP suitable for selection when the slopes of the T–H lines of the source and sink have a relatively low gradient (closer to flat). TCHP suitable for selection when the slope of the T–H line of the source have a relatively low gradient (closer to flat) and steep T–H line of the sink in GCC.
