## 2 Thermodynamic Design and Optimization
### Optimization Results  
The results of the design parametric analysis are shown in this section. For each supply pressure scenario, the best corresponding modified layout is presented, along with the set of parameters resulting from the optimization. The main difference in the cycle layout regards the secondary compression line C2, which can vary its configuration depending on the pressure ratio that needs to realize. Both the cases with the JT valve and with the turbo-expander are considered, in order to quantify the advantage in adopting an expansion device to produce mechanical power. The resulting layouts are reported in Figure 2a-d, relative to the supply pressure scenarios HPN, MHPN, MLPN and LPN, respectively. The high supply pressure (Figure 2a) concerns the main pipelines of the NG distribution network. It presents the advantage of reducing the pressure ratio operated by the primary compression line, thus decreasing the corresponding compression work. At the same time, the pressure difference between the storage pressure and the supply pressure results very high, increasing pressure ratio and power required by the secondary compressor line. The latter is also more complex, involving two stages of cooling (inter and after-cooler). The optimized layout for a supply pressure equal to 30 bar (Figure 2b) hold the main difference with the previous case in the absence of the inter-cooler in the secondary compressor line. This is due to the lower difference between the storage pressure (p\({}_{10}\)) and the supply pressure (p\({}_{1}\)), that requires a lower compression work. The compressor C2 is now modelled with one unit refrigerated by an after-cooler. The optimized layout of the medium-low supply pressure case (MLPN) provides for no compressor for the recirculation of NG vapor. Nevertheless, in Figure 2c the compression line C2 is still represented, since in the parametric analysis it was still necessary for storage pressures below 15 bar. Thus, the compressor C2 can be removed from the plant layout, determining a drop of power consumption and resulting the optimum configuration within the MLPN scenario. In addition, the costs of purchase and installation of the compression line are avoided, reducing the total investment for the liquefaction plant. On the other hand, clearly increasing the complexity and costs for the high-pressure storage facilities must be considered too. In a low supply pressure case (LPN, Figure 2d), the secondary compression line C2 results unnecessarily within the whole parametric analysis because the pressure in the flash tank is always higher than the supply pressure. Rather, a lamination valve (V2) could be necessary to reduce the pressure in case of high storage pressure. The resulting layout is the simplest among the analyzed scenarios and this results in less complexity and number of components to be installed, less maintenance and lower investment cost. The thermodynamic results of the sensitivity analysis are described by Figure 3a-d, that report the performance indicator \(e\) and the quality of the fluid at the flash tank (\(x_{\text{ft}}\)) as function of the maximum pressure (p\({}_{6}\)) and of the storage pressure (p\({}_{10}\)), for the four supply pressure scenarios. In the 3D plots, the JT valve and the turbo-expander cases are represented, respectively, by the upper surface and by the lower one. In Table 2 the specific values of the parameters that allow the lowest consumption for the liquefaction process are collected, i.e., the values representing the minimum points of each surface in Figure 3a-d. Finally, in Figure 4a-d, the thermodynamic cycles related to each process are traced in pressure-enthalpy diagram. The following comments can be considered valid for all the four scenarios. Figure 2: Optimum layouts for the considered supply pressure scenarios: (**a**) high pressure supply network (HPN), (**b**) medium-high pressure supply network (MHPN), (**c**) medium-low pressure supply network (MLPN), (**d**) low pressure supply network (LPN).