## 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 it can be seen in Figure 8, the net effect is an underestimated initial pressure used as input for the simulations (\(p_{\text{init}}\)), which would lead to simulated pressure decrease curves lower than experimental ones. However, as the curve-match procedure aims at determining the set of dissolution parameters that minimizes the overall least-squares deviation between experimental and simulated curves, it tends to raise the simulated pressure curve by decreasing \(D_{\infty}\) and \(S_{\infty}\), and increasing \(E_{d}\) and \(E_{s}\), to compensate. This effect was taken into account and mitigated by performing longer experiments, to reduce the overall weight of the first phase of the pressure decrease curves in the deviation calculation, and thus on the dissolution parameters estimates. In other words, this discrepancy did not meaningfully affect the results. Figure 7: Cont. Figure 8: Visualization of the difference between first pressure points in simulated curve (\(p_{\text{init}}\)) and experimental curve (\(p_{0}\)), and the resulting effect that simulated pressure decrease curves are necessarily lower than experimental ones. The value \(p_{0}\) is equivalent to the pressure associated with all the gas injected in the UC if no dissolution happened, and cannot be directly measured. The value \(p_{\text{init}}\) is chosen as the first pressure measurement after injection, that does not coincide with \(p_{0}\) due to the finite injection rate. An infinite injection rate would lead to \(\Delta t_{\text{inject}}=0\) and allow one to measure \(p_{0}\). Table 2 displays the estimated parameters and Figure 9 shows the diffusivities and Sieverts constants calculated with them in function of temperature. The figure also displays curves derived from literature, in a similar fashion as the ones presented for Pb-Li (_vide_ Section 2). As it can be seen, the results of this work are in good agreement with literature, which shows that the methodology developed here is considered suitable for the  
Figure 7: Comparison between the experimental and simulated curves for the pressure decrease in the VST UC during the deuterium experiments, for three different temperatures. Propagated uncertainty for experimental data is displayed with two extra curves (in _gray_) to increase visibility. Simulated curves use dissolution parameters determined by the curve-matching strategy (_vide_ Table 2). Increased data fluctuation seen in (**a**) results from: the graph scale (due to a smaller total pressure variation during the experiment), and a larger set of collected experimental points. (**a**) Experiment and simulation for heater set at 100 \({}^{\circ}\)C. (**b**) Experiment and simulation for heater set at 350 \({}^{\circ}\)C. (**c**) Experiment and simulation for heater set at 400 \({}^{\circ}\)C.  
determination of dissolution parameters (and thus, diffusivity and Sieverts constant) of deuterium dissolution in 316L steel. As seen in Figure 9a, the diffusivity obtained in this work is somewhat higher in comparison to other values reported in literature. This was attributed to an ultimate underestimation by the simulation of the total gas loss experienced by the metal chamber; and a subsequent attempt of the curve-match procedure to adjust for that by assuming a larger diffusivity for deuterium in steel. A study was performed to assess whether the geometric simplification of the UC was responsible. Assuming that the steel thickness of the fittings are the same as the chamber parts to which they are attached, the total inner surface of each part and the total inner volume of the chamber were altered to include the dimensions of the fittings in the simulations. However, the net effect of this adjustment was a change in the total pressure loss of only \(\approx\)0.5%, which corresponds to \(\approx\)0.03% in terms of absolute pressure variation.