## 3 A Methodology to Differentiate Dissolution from Gas Losses in Gas-Metal Systems
### Simulating a Deuterium Pressure Decrease Curve in the VST Upper Chamber  
Figure 5 shows the length measurements of a setup of interest to be modelled: the Upper Chamber (UC) of the Vacuum Siveve Tray (VST) experiment [8]. As a _geometrical-system simplification_ to apply a numerical model, fittings were neglected and the chamber was considered an assembly of only three parts: the LID, the WALL and the BASE. Both the LID and the BASE can be considered solid cylinders, and the WALL a hollow cylinder, all made of uniform 316L steel, which supports Assumption I [14]. Figure 5: Schematic of the VST Upper Chamber (UC) as modelled using a quasi-2D modelling approach. The dashed line indicates an axis of cylindrical symmetry. On the left, simplified chamber dimensions used in the model (\(D_{L}=305.0\), \(D_{W}=250.0\), \(D_{B}=270.0\), \(H_{L}=26.0\), \(H_{W}=95.0\), \(H_{B}=20.0\), \(W=2.0\); all in mm). On the right, a diagram of the diffusion channels foreseen in the simulation (two cartesian vertical, \(h\) and \(h^{\prime}\), and a cylindrical radial, \(r\)). Boundary conditions are indicated by color: external Fixed BC (in _green_) and internal Coupled BC (in _red_). Experiments of interest with the UC foresaw injecting a fixed amount of deuterium gas (D\({}_{2}\)) inside the chamber and then observing the pressure decrease along time. The technical limitations of the setup forbade an initial pressure in the UC higher than 1.5 bar, so \(\approx\)5 \(\times\)10\({}^{-2}\) mol were chosen as injection amount. This amount ensured initial pressures of \(\approx\)800 mbar in the experiments with the highest foreseen temperatures. This complied with the former requirement and also ensured reliable accuracy for pressure measurements. Notice that this order of magnitude for the deuterium pressure is considerably smaller than its critical pressure (\(\approx\)16 bar) [43], which supports the usage of the ideal gas law and Assumption II. Figure 5 also shows how the model introduced in Section 3 was applied to the UC. Due to the present symmetries, a quasi-2D approach was deemed sufficient: each chamber part was modelled with a single (1D) diffusion channel along a different dimension. The channel lengths (\(H_{L}\), \(H_{B}\) and \(W\)) are considerably smaller than all other measurements, which supports Assumption III [14]. Modelling surfaces exposed to the same finite amount of gas implied that the inner surfaces of the chamber had to be considered coupled (_vide_ Section 3). Thus, all nodes representing the interior of the chamber were modelled as Coupled BC (in _red_, Figure 5). The exterior of the chamber was assumed to be a perfect sink for the diffusion process. Thus, nodes representing the exterior were modelled as Fixed BC (in _green_, Figure 5) with null concentration. Due to their temperature dependency, the diffusivity and Sieverts' constant for deuterium dissolution in 316L steel had to be computed as a function of time for each experimental scenario simulated. For this, additional simulation inputs were planned in the form of the evolution of single surface temperature measurements for each chamber part (LID, WALL and BASE). The UC is fully covered by thermal insulation and the temperature of the chamber parts are determined by a controlled ohmic heater underneath the BASE [8]. Upon choosing a set-point, the gas was planned to be injected only after general thermal steady-state conditions were registered for any chamber part (temperature variations below 1% between subsequent measurements). At each time step of the simulation, the BASE and LID temperatures (\(T_{B}\) and \(T_{L}\), respectively) could be used to compute the diffusivity and Sieverts' constant on those chamber parts, interpolating values in time between measurements when necessary.