## 5 Simulation of Future VST Experiments with Pb-Li Using Literature-Averaged Dissolution Parameters
### Sensitivity Analysis with Diffusivities and Sieverts' Constants for Pb-Li Taken from Literature  
The model of the UC with Pb-Li was then used to perform a sensitivity analysis. This aimed at evaluating the impact of the diffusivity and Sieverts' constant of deuterium in Pb-Li on:  
* the time required by the system to reach dissolution equilibrium; and
* the minimum amount of gas to be absorbed by the liquid metal. For that, dissolution parameters associated with the literature's minimum and maximum \(\mathcal{D}_{\mathrm{D}}^{\mathrm{Pb-Li}}\) and \(\mathcal{S}_{\mathrm{D}_{2}}^{\mathrm{Pb-Li}}\) values (at the simulated BASE temperature) were compared to those computed using literature-averaged parameters (minimum and maximum diffusivities and Sieverts' constants were not computed directly using combinations of the extreme values displayed in Table 3 because they result in coefficients that are not representative of the ranges seen in Figure 2). Using the same geometry from before (_vide_ Figure 10), and for a simulation of the BASE temperature set at 450 \({}^{\circ}\)C and an initial pressure of 780 mbar, the analysis was done with dissolution parameters derived from:  
* Edao-2011 [20] for highest and Shibuya-1987 [10] for lowest diffusivities;
* Aiello-2006 [29] for highest and Feuerstein-1991 [11] for lowest Sieverts' constants. It should be noted that the diffusivity from the reference Legarda-2010 [18] was neglected due to its large disparity with other curves (_vide_ Figure 2a). Figure 14 displays the evolution of deuterium dissolved in Pb-Li for different scenarios. As expected, the final amount of deuterium dissolved increases significantly with \(\mathcal{S}_{\mathrm{D}}^{\mathrm{Pb-Li}}\) and the speed of profile evolution is impacted by \(\mathcal{D}_{\mathrm{D}}^{\mathrm{Pb-Li}}\). However, due to the application of the chemical potential continuity principle, the Co-Dependent BC in the Pb-Li side of the interface depends on both the diffusivity and the Sieverts' constant. Thus, scenarios simulated with Edao-2011 and Shibuya-1987 diffusivities do not tend to the same equilibrium conditions. Figure 14: Impact of \(\mathcal{D}_{\mathrm{D}}^{\mathrm{Pb-Li}}\) and \(\mathcal{S}_{\mathrm{D}}^{\mathrm{Pb-Li}}\) on the amount of deuterium dissolved in Pb-Li. As before, initial gas pressure set to 780 mbar and BASE temperature set to 450 \({}^{\circ}\)C. Averages diffusivity and Sieverts’ constant obtained using dissolution parameters introduced in Table 3; so curve in _black_ is the same as the one presented in Figure 12a. Others are calculated applying dissolution parameters derived from literature [10; 11; 20; 29]. Curves and respective legends displayed in the same descending order; line colors in agreement with Figure 2.  
While coupled and Fixed BCs only explicitly depend on the Sieverts' constant (as seen in Figure 4), Equation (7) ensures that Co-Dependent BC will also be dependent on the diffusivities. This implies that, for the computed pressure curves:  
* time-related properties do not depend exclusively on the diffusivities; and,
* the relative difference between initial and final pressures does not depend exclusively on the Sieverts' constants. That is, each curve characteristic is governed by more than one dissolution parameter, in an effective parameter space, and different sets of parameters may lead to indistinguishable characteristics (such as the final pressure). This, and the fact that the typical operation of the UC foresees a finite amount of injected gas, entail that some traditional strategies, such as the time-lag method [14], cannot be used to directly measure dissolution parameters. However, pressure curves simulated with the model bring new insight to VST experiments and, with the strategy presented in Section 4, enable the setup to also measure dissolution parameters, which was not initially planned with this facility.