## 3 A Methodology to Differentiate Dissolution from Gas Losses in Gas-Metal Systems
### Applying Curve-Match to Obtain Dissolution Coefficients for the VST's 316L Steel  
As introduced in Section 3, the dissolution parameters \(D_{\infty}\), \(S_{\infty}\), \(E_{d}\) and \(E_{s}\) for a gas-metal pair can be determined using the curve-matching strategy proposed. For that, each parameter was varied between the literature extremes (_vide_ Table 1), subdividing these ranges in 10 steps per parameter (for a total of \(10^{4}\) pressure decrease simulations per experiment). Figure 7 shows the measured pressure decrease curves for the experiments and their respective simulated curves for simulations run with the dissolution parameters determined through curve-matching. All curves display two phases:  
* the first one shows a faster pressure decrease and lasts for only a fraction of the total experiment time (roughly: 15 h for the experiment at 100 \({}^{\circ}\)C, and less than 1 h for the others);
* the second one shows an apparent linear (and slower) pressure decrease (after the first phase ends). The correlation between experimental temperatures and time for the transition between first and second phases is explained by the increase of diffusivity with temperature. The first phase corresponds to larger fluxes of deuterium gas diffusing through the metal parts, caused by steeper concentration gradients (as exemplified by the _light blue_ lines on Figure 6), which lead to a sharp pressure decrease in the beginning. The second phase corresponds to smaller fluxes, because the system is close to pseudo-steady-state conditions (_dark blue_ lines tending to _dashed black_ lines on Figure 6). These phases could be considered similar to the diffusive and permeative stages of the theoretical dissolution process, as defined in Section 2. However, it should be noted that these stages are not technically equivalent to the first and second curve phases, respectively, because this type of experiment is not expected to ever reach true steady-state conditions (i.e., permeative stage). Since the amount of gas in the chamber is finite, the metal experiences a pressure decreasing in time, and thus, BCs that change in time. This is successfully taken into account by the model presented in this work with the implemented Coupled BCs on the inner side of the chamber, that are recalculated at every time step. In fact, it should be noted that [PERSON]'s Permeation Law, often applied in literature to compute passage of gases through metals [12; 14], is not capable of computing the first phase of the curves presented, since it would assume pseudo-steady-state conditions from the start of the experiment. Since the pressure decrease in the first phase amounts to a significant portion of the total pressure decrease (especially for experiments made at lower temperatures and for shorter periods of time, e.g., Figure 7a), such approach should not be used in static absorption/desorption experiments. Contrary to that, the model presented in this work is able to properly simulate the pressure decrease in a metallic chamber both _before and after_ pseudo-steady-state conditions have been reached. Experimental and simulated pressure decrease curves present the same qualitative behavior in Figure 7a-c. In particular, good agreement can be seen in Figure 7a, where pressure fluctuations attributed to temperature variation in the laboratory environment during the period of a day were also reproduced by the model. The only modest discrepancy, visible in Figure 7c, is the sharper pressure decrease in the first phase of the simulated curve, in comparison to the experimental one. This is explained by the injection process in the experiments (not shown in Figure 7 due to scale), which is considered instantaneous in the simulations. Due to the real finite injection rate, the process lasts for a non-null period of time (\(\Delta f_{\text{inject}}\
eq 0\)). During this time, the quantity of gas in the chamber increases due to the injection, but also decreases due to diffusion already taking place through the metallic walls.