## 2 Thermodynamic Design and Optimization
### Discussion on the Proposed LNG Production Process  
As already mentioned in the introduction of this work, the proposed LNG production process has been developed by Authors and presented in previous studies [23; 24; 26] with the main aim to realize a plug & play solution to be placed directly at vehicles and/or ships refueling stations. Indeed, small-scale LNG production facilities are currently rare and mainly realized in order to reduce the workload on gas reservoirs sites [26] or for offshore compact LNG production [27]. In this scenario, the idea of generating LNG directly at filling stations has been developed, in order to give a compact solution and to avoid the economic and environmental costs related to the LNG transportation by ship, contemporarily promoting LNG as fuel in transport sector. In addition, with respect to the processes usually employed in small-scale applications (i.e., N\({}_{2}\) expander cycle and single-mixed refrigerant process), the proposed process is aimed at the realization of simpler--and, as a consequence--less expensive solutions, which can be competitive in the future global energy scenario.  
Figure 4: Optimum thermodynamic cycles in pressure-enthalpy diagram: (**a**) HPN, (**b**) MHPN, (**c**) MLPN, (**d**) LPN.  
The proposed layout is general and can be easily adapted to different requirements in terms of boundary conditions. In particular, the secondary line (see Figure 1) can vary on the basis of the pressures of the natural gas network and of the storage tank, allowing to install the LNG production plant in a very wide range of conditions. In detail, the secondary line may include: (i) a compression train (with one or more compression stages, eventually inter-cooled) when the LNG storage pressure is lower than the NG network pressure, (ii) an isenthalpic valve when the LNG storage pressure is higher than the NG network pressure or (iii) no additional components when the LNG storage pressure and the NG network pressure differ only for the pressure drops through the line.  
As it concerns the maturity level of technology, at present, a prototype of the LNG production process developed by the Authors has been realized and experimentally tested by the Italian Company Graf S.p.a., with the final aim to commercialize the technology [17]. Finally, the layout has been specifically developed for small-scale applications, namely for liquefaction facilities with a production capacity up to 1 MTPA (Mega Tons Per Annum). Below this value of capacity, the process is scalable and the simplicity of the solution can be maintained with economic convenience. On the other hand, for medium/large scale LNG production plants, the proposed process is not yet competitive with the commonly used technologies from an economic viewpoint.  
In the following section, the calculation model, specifically developed for the proposed LNG production process, will be presented. In this respect, starting from this point, the expansion device considered for the continuation of the study is the lamination valve (JT layouts). To the Authors' opinion, indeed, this choice better reflects the current industrial state-of-the-art, since no commercial models of cryogenic expander are spread in the market yet. In more detail, at present, some prototypes of cryogenic expander are under development or at testing phase, as the advantage in saving consumption of replacing the JT valve with a turbine is indisputable. However, in order to give a larger scale applicability of the proposed approach, the developed off-design calculation model refers to JT expansion layouts for LNG production.