## 4 Results and Discussion  
Form our previous study, the melting temperatures of T propane/hydrogen-clathrate surfaces were expected to be around 280 K [17]. The evolution in the number of hydrogen uptake into/released from the propane hydrate was judged via the Baez-Clancy criteria, is specified in Figure 3 for both release and uptake at 180, 200, 220, 240, 260 and 273 K. Due to the observed slow kinetics of the uptake simulation, the simulation for hydrogen uptake extended up to 5 \(\upmu\)s while for the case of release study a kind of plateau was observed after 500 ns. The rate constant of the gas uptake/release correlates directly with the simulation temperate as the thermal \"driving forces\" for gas diffusion. The density map of molecules (water, propane and hydrogen) along the X-axis at different time stages can provide a better insight on the hydrate condition, the position of the propane molecules which can also be interpreted as the large-cage occupancy and the cage-filling pattern based on hydrogen diffusion in propane hydrate. Figure 4a illustrates the density map for hydrogen uptake in which hydrogen density in the range of 3.2 to 7.9 along X-axis at the starting time of the simulation (t = 0 ns) is zero while water distribution in this range is well distributed, due to the long-range order of clathrate hydrate. This order also can be observed in the case of propane molecules, those are located in large cages. During the simulation time, the water and propane distributions stay intact while the hydrogen penetrating the hydrate area and filling the first and second column of the small cages in hydrate structure. The existing plateau in Figure 3a after 250 ns for most of the  
Figure 3: Hydrogen uptake (**a**) and release (**b**) in non-equilibrium simulations at various temperature. Figure 2: Schematic of the gas-hydrate rig. The four main sections are gas supplier, distribution terminal, reactor and refrigerator. temperatures can also be noted in the similar density map of hydrogen at 250 and 500 ns. The main reason behind this similarity is attributable to the slow diffusion rate of the hydrogen molecules inside the hydrate structure. Internal hopping of hydrogen inside a hydrogen-hydrate lattice has been previously investigated by [PERSON] and his colleagues [27; 28], but in the case of propane/hydrogen hydrate, since all large cages are already occupied by propane molecules, the only available path for filling the whole hydrate is the small-to-small cage hopping which has to be done by pathing hydrogen molecule through a pentagonal ring. The density map during hydrogen release simulation is illustrated in Figure 4b. Since for release study the hydrate is in contact with vacuum, some propane from the outer layer cages will be released into vacuum part. The presence of propane molecules can be seen in Figure 4b. A hydrogen molecule leaves its small cage, hops into another small cage in its neighbour and finds the way out from the hydrate lattice. The same limitation discussed on the difficulty of small-to-small hopping, the hydrogen exists in the centre of the hydrate lattice may never be able to leave the hydrate lattice. To analyse the diffusion of the hydrogen molecules inside the hydrate structure, 300 sets of hydrogen molecules remaining in the hydrate structure over the whole sampling period (100 ns) were identified using Baez-Clancy method, and the MSD value of each set was calculated. The averaged MSD curve at each temperature for both uptake and release studies is illustrated in Figure 5 and the diffusion coefficient of each is listed in Table 1. It was found that the hydrogen molecules show a higher movement in the case of release studies in which the hydrate is in contact with a vacuum in compare with the uptake study where gas form hydrogen molecules are located on the top of the hydrate structure. This difference is caused following to the presence of some empty large cages due to the migration of propane molecules from the hydrate structure to the vacuum part.