At ENEA Brasimone Research Centre, Italy, a new experimental facility named TRIEX-II (Tritium Extraction) was designed and installed. Its aim is to characterize, in the range of operating conditions foreseen for the European Test Blanket System WCLL-TBS, several extraction technologies for hydrogen isotopes (Q2) solubilized in the flowing metallic LiPb alloy (15.7 at. % Li). One of these technologies is the packed column, an example of Gas/Liquid Contactors (GLCs). This paper proposes a multiscale modelling tool, combining different scales through two computational tools. The extraction column mock-up is described by a component-detail level model, developed in COMSOL Multiphysics, and integrated into a system level code of the whole TRIEX-II circuit, developed using MATLAB/Simulink. The integration is carried out by implementing the COMSOL component into an S-function of MATLAB/Simulink, preserving the process flow diagram of the loop. In this way, it was possible to quantify the Q2 concentrations and the permeation fluxes, and to evaluate the theoretical extraction efficiency. The LiPb flow field inside the extractor was also derived. Finally, a comparison with the experimental results was performed. The results suggest that this tool could be adapted for analyses of complex systems, at a multiscale level, in view of design improvements and safety studies for the tritium cycle of ITER.