## 1 Introduction  
It is well known that in decades to come, natural gas (NG) is expected to cover an increasing portion of the supply demand in all the energy fields. Among all fossil fuels, it is the one with the best combination of natural reserves and acceptable emissions levels [1]. Focusing on the transport sector, at present, the fossil fuels utilization is responsible of about 26% of the total greenhouse gases emissions in the European Union, with the largest impact determined by road transport (72.9%), followed by aviation (13.3%) and the naval sector (12.8%) [2]. The naval industry is also responsible for local air pollution, since it causes consistent concentration of NO\({}_{\rm x}\), SO\({}_{2}\) and PM in port areas [3]. These emissions have risen substantially since the 1970s with the growth of international trade [4]. Ships' propulsion systems are currently based on internal combustion engines fueled with diesel fuel or MDO (Marine Diesel Oil), the latter being often adopted due to its lower price compared to more refined fuels, despite the consistent content of sulfur [5]. The EU recently set stringent limitations on fuels for ships: starting from 2020, in the naval sector, the current fuels must be replaced with products with a maximum concentration of sulfur equal to 0.5% (at present it is equal to 3.5%) [6]. In this context, the conversion of oil engines for working with liquefied natural gas (LNG) can become a convenient solution, as it has been assessed in several studies [7, 8], observing a substantial benefit in terms of fuel cost and quantity of produced emissions. Compared to diesel, the adoption of LNG leads to an emission reduction of nearly 99% of particle and sulfur dioxide, around 80% of nitrogen oxides and close to 20% of carbon dioxide [7, 8]. In [9], the authors investigated the possible solutions for the replacement of oil-based fuel within 2050 in naval sector, finding that the conversion to LNG fuel may be already cost effective, while other technologies like fuel cells and bioenergy could be convenient after 2040 and only if the NG supply becomes limited. [PERSON] et al. [10] performed a comparison of internal combustion engines as a propulsion system in a ferry or Ro-Ro ship, considering a dual fuel engine (LNG + diesel) versus a conventional diesel engine, including waste heat recovery systems for covering the electricity demand of the ship. They observed a reduction in annual costs due to the higher overall efficiency and to the lower price of LNG compared to diesel, in addition to a substantial reduction of emissions. Currently, the production of LNG is realized almost exclusively in large scale plants (i.e., with capacity greater than 5 mega tons per annum-MTPA), via three main technologies: cascade process [11, 12], mixed refrigerant process [13, 14] and expansion process [15, 16]. The latter is seldom implemented with an expander instead of the Joule-Thomson valve for recovering useful power to reduce the process energy demand [17] involving a set of operations including transportation, storage and distribution, whose cost has a significant impact on the entire cost of the LNG value chain [18]. Relating to the small-scale LNG production plants, the most used configurations consist in single mixed refrigerant liquefaction process and nitrogen expansion liquefaction process, which are considered a good solution, being compact in size, efficient and flexible to different feed gas compositions [19]. A comparison and an optimization analysis of these two processes has been carried out in [20], where a model based on genetic algorithms has been proposed. The single mixed refrigerant process efficiency strongly depends on the optimization of mixed refrigerant composition and on the ambient conditions [21] and the power consumption of this process is usually lower than the N\({}_{2}\) expander cycle one. On the other hand, the efficiency of the latter is almost independent of feed gas condition. Moreover, nitrogen is a nonreactive refrigerant, then the safety is greater [22].