## 3 A Methodology to Differentiate Dissolution from Gas Losses in Gas-Metal Systems
### Simulating a Deuterium Pressure Decrease Curve in the VST Upper Chamber
In contrast, the WALL surface measurement could not be deemed representative of the whole chamber part; instead, the WALL temperature (\(T_{W}\)) was assumed to display a spacial linear profile, analogous to a metal rod connecting two thermal baths, with extremes \(T_{B}\) and \(T_{L}\). This relies on assuming, as a _thermal-system simplification_, homogeneous distributions for the LID and BASE temperatures in comparison to the WALL, which is strongly suggested by the difference in metal volumes: the LID and the BASE have volumes approximately one order of magnitude higher than the WALL (19.0 \(\times\) 10\({}^{5}\) mm\({}^{3}\) and 11.4 \(\times\) 10\({}^{5}\) mm\({}^{3}\), respectively, versus 15.0 \(\times\) 10\({}^{4}\) mm\({}^{3}\)). This approach was supported by the measurements on the single WALL surface sensor (placed approximately 20 mm from the heater). The deviation between the measurements and the theoretical value obtained with the linear temperature profile (temperature gradient of approximately 1 K/mm along the WALL) was considered negligible (\(\approx\)0.06%) for the maximum heater set point of 450 \({}^{\circ}\)C.  
Given the temperature variation on the WALL, computing the average diffusion process through this chamber part (with a single diffusion channel) required determining average values for the diffusivity (\(\overline{D_{\rm D}^{\rm WALL}}\)) and Sieverts' constant (\(\overline{\mathcal{S}_{\rm D_{2}}^{\rm WALL}}\)). Due to their Arrhenius dependency (_vide_ Equations (4) and (5)), and the linear temperature profile of the medium, Equation (8) was used to compute \(\overline{\mathcal{D}_{\rm D}^{\rm WALL}}\) and \(\overline{\mathcal{S}_{\rm D_{2}}^{\rm WALL}}\) (here shown as \(\overline{\rm K}\)). \[\overline{K}=\frac{1}{T_{B}-T_{L}}\int_{T_{L}}^{T_{B}}\kappa_{1}\,e^{-\frac{ \kappa}{K\tau}}\ dT \tag{8}\]In it, \(\kappa_{1}\) is the desired infinite-temperature coefficient (\(D_{\infty}\) or \(S_{\infty}\)) and \(\kappa_{2}\) its respective activation energy (\(E_{d}\) or \(E_{s}\)). Since \(T_{B}\) and \(T_{L}\) can be assumed homogeneous, this procedure is not required for the BASE nor the LID. Given the lack of manufacturer data for the parameters \(\kappa_{1}\) and \(\kappa_{2}\) for the 316L steel used in the UC, planning of the experiments was performed with initial simulations run using literature-averaged dissolution parameters, as indicated in Table 1. While activation energies were arithmetically averaged, infinite-temperature coefficients were geometrically averaged due to their logarithmic scattering. To perform the averages, deuterium diffusivities were extrapolated (using Equation (6)) when data could be found only for other isotopes. Sieverts' constants were assumed to be the same for every isotope (i.e., neglecting zero-point energy differences), as mentioned in literature to be a good approximation for steel [12]. For comparison, the table also shows the literature extremes of the dissolution parameters. Initial simulations were run using a set of temperature measurements obtained during a trial run of the experiment with no gas. Convergence tests were performed both for spacial node and time node counts. Test were done for powers of 10, between \(10^{1}\) and \(10^{5}\). No significant precision is gained by simulating meshes with more than \(10^{3}\) nodes (relative difference between figure of merits of subsequent simulations below 0.05%), so subsequent simulations utilized this mesh resolution. Results of these initial simulations can be seen in Figure 6, which shows the evolution of the atomic concentration of deuterium both in the BASE and the WALL. Notice how the profile in the WALL (Figure 6a) evolves faster than in the BASE (Figure 6b), even though it displays a linear temperature profile with a lower average (\(\approx\)405 \({}^{\circ}\)C). This is attributed to the steeper concentration gradients in the thinner medium, which is the dominating diffusion drive in comparison to the temperature effect on the diffusivity and Sieverts' constant.