## Appendix A Absorption Chiller Modeling  
This appendix is devoted to presenting the modeling of the absorption chiller in this work. Figure 11 depicts the examined absorption chiller, which is a single-effect absorption machine operating with a LiBr-H\({}_{2}\)O working pair. This system has an internal heat exchanger in order to have higher performance. The evaporator is the device that is coupled to the CO\({}_{2}\) refrigeration system and the subcooling is performed with this device. The generator is the device that needs the heat input from an external heat source, while the condenser and the absorber reject heat to the environment. Below, the main mathematical modeling of the absorption is given. More details can be found in [42; 43; 44] about this modeling.  
Firstly, it has to be said that the subcooling in the CO\({}_{2}\) cycle is produced by the absorption chiller evaporator. So, it can be written:  
\[\mathrm{Q_{e,ach}}=\mathrm{m_{r}}\cdot\left(\mathrm{h_{j}}-\mathrm{h_{i}}\right) \tag{11}\]  
The energy balance in the generator can be written as below:  
\[\mathrm{Q_{g}}=\mathrm{m_{r}}\cdot\mathrm{h_{g}}+\mathrm{m_{str}}\cdot\mathrm{ h_{d}}-\mathrm{m_{w}}\cdot\mathrm{h_{c}} \tag{12}\]  
The energy balance in the absorber can be written as below:  
\[\mathrm{Q_{a}}=\mathrm{m_{r}}\cdot\mathrm{h_{j}}+\mathrm{m_{str}}\cdot\mathrm{ h_{f}}-\mathrm{m_{w}}\cdot\mathrm{h_{a}} \tag{13}\]  
The energy balance in the condenser can be written as below:  
\[\mathrm{Q_{con}}=\mathrm{m_{r}}\cdot\left(\mathrm{h_{h}}-\mathrm{h_{g}}\right) \tag{14}\]The heat exchanger effectiveness (\(\eta_{\text{hex}}\)) is defined as below:  
\[\eta_{\text{hex}}=\frac{\text{h}_{\text{d}}-\text{h}_{\text{e}}}{\text{h}_{\text{ d}}-\text{h}_{\text{b}}} \tag{10}\]  
It has to be said that this definition gives slightly higher heat transfer rates compared to the definition with the respective temperatures.  
The energy balance in the heat exchanger can be written as below:  
\[\text{m}_{\text{w}}\cdot(\text{h}_{\text{c}}-\text{h}_{\text{b}})=\text{m}_{ \text{str}}\cdot(\text{h}_{\text{d}}-\text{h}_{\text{e}}) \tag{11}\]  
The work input in the circulation pump is neglected, so it can be written:  
\[\text{h}_{\text{b}}=\text{h}_{\text{a}} \tag{12}\]  
The enthalpy is conserved in the throttling valves, so it can be written:  
\[\text{h}_{\text{f}}=\text{h}_{\text{e}} \tag{13}\]  
\[\text{h}_{\text{i}}=\text{h}_{\text{h}} \tag{14}\]  
The temperature levels in the absorber and the condenser are assumed to be the same:  
\[\text{T}_{\text{con}}=\text{T}_{\text{a}} \tag{15}\]  
At this point, it has to be said that the temperature (\(\text{T}_{\text{a}}\)) is the saturation temperature of the weak solution at the low pressure inside the absorber.  
The total mass flow rate balance in the generator can be written as below:  
\[\text{m}_{\text{w}}=\text{m}_{\text{str}}+\text{m}_{\text{r}} \tag{16}\]  
The mass flow rate balance about the LiBr substance in the generator can be written as below:  
\[\text{X}_{\text{w}}\cdot\text{m}_{\text{w}}=\text{X}_{\text{str}}\cdot\text{ m}_{\text{str}} \tag{17}\]  
Moreover, it has to be said that the state point \"j\" is assumed to be saturated vapor, while the state point \"h\" to be saturated liquid.