## 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
This is explained by the competing effects that inner surfaces and chamber volume have on the model:  
* a larger volume decreases the pressure calculated at each time step, which reduces the Coupled BCs experienced by the inner surfaces, thus reducing the surface density of escaping molecular flows; but,
* larger inner surfaces increase the total escaping molecular flows. This implies a limited impact of neglecting the fittings in the UC model: the additional pressure loss can be singly attributed to the fact that fittings have thinner steel thicknesses than the chamber parts, which leads to steeper concentration gradients and increased diffusion flows (_vide_ Figure 6). That is to say, the dissolution parameters estimated by the curve-match procedure could moderately gain accuracy by adding (a) diffusion channel(s) to the UC model that represent(s) the fittings. As also seen in Figure 9a, the estimated dissolution parameters for the diffusivity (\(D_{\infty}\) and \(E_{d}\)) lead to a consistent behavior across the temperature range of all experiments (100-400 \({}^{\circ}\)C). In Figure 9b, however, the estimated dissolution parameters for the Sieverts' constant (\(S_{\infty}\) and \(E_{s}\)) in the experiment performed at 100 \({}^{\circ}\)C present a slight disagreement with the ones performed at 350 \({}^{\circ}\)C and 400 \({}^{\circ}\)C. This can be explained by the smaller pressure decrease induced by lower temperatures: \(\approx\)3 mbar loss over 70 h of experiment at 100 \({}^{\circ}\)C, as opposed to \(\approx\)30 mbar loss in the experiment of similar duration at 350 \({}^{\circ}\)C. This limited pressure loss affects the accuracy of measurements, which impacts the precision of the curve-match procedure, as multiple sets of dissolution parameters can retrieve curves inside the uncertainty range. This implies a higher fidelity in the dissolution parameters for the Sieverts' constant (particularly \(S_{\infty}\)) estimated from experiments at 350 \({}^{\circ}\)C and 400 \({}^{\circ}\)C.  
Taking the comparison between experiments and simulations into account, it was concluded that the model is able to reproduce the dissolution of deuterium in steel during both curve phases, when using the dissolution parameters estimated by the curve-match procedure. Given the comparison of the diffusivity and Sieverts' constant obtained with these parameters to literature results, the methodology was considered _validated_. \begin{table}
\begin{tabular}{c c c c c} \hline
**316L** & \(D_{\infty}\) & \(E_{d}\) & \(S_{\infty}\) & \(E_{s}\) \\ **(\(D_{2}\))** & **(m\({}^{2}\)/s)** & **(M/k\(\cdot\)mol)** & **(mol/m\({}^{3}\cdot\)1/\(\sqrt{\text{Fa}}\))** & **(k/k\(\cdot\)mol)** \\ \hline
100 \({}^{\circ}\)C & \(7.17\times 10^{-7}\) & 42.50 & \(1.50\times 10^{0}\) & 12.87 \\
350 \({}^{\circ}\)C & \(8.18\times 10^{-7}\) & 42.50 & \(5.50\times 10^{-1}\) & 17.50 \\
400 \({}^{\circ}\)C & \(5.14\times 10^{-7}\) & 42.50 & \(4.20\times 10^{-1}\) & 15.95 \\ \hline \end{tabular}
\end{table} 
Table 2: Dissolution parameter estimates from applying the curve-matching procedure to the experiments presented in this work.