## 1 Introduction
Later, new technologies emerged such as the Volume Optimized TRANsport and Storage (VORANS) [2; 3] of EnerSea Transport, the Pressurized Natural Gas (PNG) [2] of Knutsen OAS, the Gas Transportation Module (GTM) [2; 3] of TransCanada, the Composite Reinforced Pressure Vessel (CRPV) [2] of Trans Ocean Gas (TOG), and the Compressed Energy Technology (CETech) [3]. Tables 1a and 1b, adapted from [3], with the only addition in the last column of Table 1b of the GAVESSEL project [4], shows a summary of the various technologies. As far as the ratio between the gas transported and the weight of the containers is concerned, only the weight of the tanks without valves, pipes, and flanges is considered. The first and only CNG ship currently in service, the \"Jayanti Baruna\", was launched in January 2016 in Indonesia and has a capacity of 0.67 M\(\mathrm{N}\mathrm{m}^{3}\) @250 bar of gas, allowing linking East Java with the island of Lombok. The gas is stored in an 832 vertical cylinder (height 12 m, diameter 615 mm, thickness 19 mm), and the ratio container/cargo weight is 0.15 [4]. Therefore, the currently too low ratio between the mass of transported gas and the vessels-cargo weight can be considered one of the reasons why CNG technology currently has such a limited diffusion. However, the problems relating to loading and unloading processes must also be considered. These processes affect both the overall time required for transport and the quantity of transported gas and, therefore, they have an impact on the economic feasibility of the whole project. Based on these considerations, in this paper, it is first shortly described the GASVESSEL project, which focuses on the development of innovative lightweight composite pressure cylinders with a diameter of more than 3 m: loaded on a ship, they could allow transporting quantities of CNG as big as 10,000 tons [4]. Then, a newly developed process simulation model is presented and realized in the Matlab(r) environment, which allows assessing the duration of the loading and unloading processes, the mass of transported CNG, and the amount of power and energy required by the process. The model is useful to support the design of the system considering different plant components and operating strategies. Almost all the calculation models of the filling and emptying processes of CNG tanks found in the literature refer to the use of CNG to power road vehicles with spark ignition engines, replacing petrol. In fact, today, this is the most widespread use of CNG (the share is about 1.6% in total vehicle feet worldwide [5]), while the use as a supplying system of NG on ships is currently under development. The gas is taken from the low-pressure distribution network, and then, it is compressed in the storage tanks of the filling station. Then, the vehicle's cylinder is filled by the pressure difference. These models are based on the first law of thermodynamics, appropriate assumptions about components efficiency, and on the choice of a suitable Equation of State (EOS) for the calculation of the thermodynamic properties of NG, which are treated as a real gas. The main problems are related to the so-called Fast Filling Process (FFP). They concern the reduction of the filling time without an excessive reduction of the fill efficiency. The fill efficiency is the ratio of the actual filled mass to the capacity at the rated pressure and ambient temperature. The underfilling is due to the heat generated by the re-compression of CNG in the cylinder. Another problem is the required compressor input work,