Aiming at the industrial scale development of a Scandium (Sc)-selective leaching process of Bauxite Residue (BR), a sufficiently numerous set of process design aspects has been investigated, by appropriate exploitation of available experimental data. The interpretation of experimental data for Sc leaching yield, with sulfuric acid as the leaching solvent, has shown significant impact from acid feed concentration, mixing residence time, liquid to solids ratio, and times of leachate re-usage onto fresh BR. The thin film diffusion model, as the fundamental theory for leaching, either with constant particle size for selective leaching, or with shrinking particle size for less-, or non-, selective leaching, interprets sufficiently well the relevant experimental data. In both cases, a concept for an unyielding core supplements the basic model. Especially for the selective leaching mild conditions, the simplest model version keeps step with the experiments, since both prove 1^st order kinetics, while especially for the extreme conditions including very low solvent excess, it is proposed a combined conversion rate model with diffusion and chemical reaction inside particles. The maximization of Sc recovery per unit of consumed solvent (i.e., specific recovery) emerged as highly critical for the process economics.