This study analyses the hydrogen permeation flux model with (1) modifications in the defect concentration calculations where the concentration of substitutional cation on cerium site is utilised as the independent variable for the calculation, instead of the previous step-wise calculation with the concentration of oxygen vacancy as the independent variable and (2) the additional terms to include the oxygen partial pressure gradients for calculation of hydrogen permeation flux. The modification in the defect concentration method allows a short model simulation run time, which consequently allows incorporation of the concentration constraints in the parametric sensitivity analysis, but still produces the same set of defect concentrations as calculated in the previous methods. It is also found in this study that the discrepancy between the model and experimental results (in terms of the effect of changes in hydrogen partial pressure gradients on the hydrogen permeation flux) is not due to the influence of oxygen partial pressure gradients. Parametric sensitivity analysis shows that there is no significant difference in the sensitivity of the model by comparing Case A and B. The result of parameter tuning to predict the hydrogen permeation flux for 5% thulium doped strontium cerate in Case B shows a similar trend to the previous study (Case A). These results suggest negligible oxygen ion conductivities in these types of membrane, as reported in the literature.