Turbine disc Ni-based superalloys form a surface oxide layer when exposed to high-temperatures and corrosive reagents. Growth of the oxide layer results in a $\gamma$´ precipitate depleted region at the oxide-matrix interface due to preferential transport of oxide-forming elements to the growing surface oxide. As these superalloys are strengthened by the dispersion of these coherent $\gamma$´ precipitates, their depletion results in a deterioration of mechanical properties. A mean-field model has been developed to predict the $\gamma$´ precipitate depletion zone in RR1000, a commonly used Ni-based turbine-disc superalloy. Initial particle size distributions (PSDs) are divided into a series of discrete size classes, corresponding to the equilibrium phase fraction of $\gamma$´. A multicomponent diffusion driven growth-rate law is formulated to determine the dissolution rate of each discrete particle size class. This is based on CALPHAD obtained energy and mobility expressions of the solutes contained within the oxide. The model is first validated against existing precipitate depletion zone kinetics for RR1000. The effect of temperature on the PSD, specifically as the $\gamma$’ solvus temperature (~1100$^{\circ}$C) is approached, is then investigated, and the effect of oxygen partial pressure (ppO₂) on the PSD, where a larger ppO₂ leads to an increased oxide growth rate, hence a higher $\gamma$´ dissolution rate. Finally, the effect of altering alloy composition on the PSD is studied. Further work would involve coupling this model to a crystal plasticity model for deformation, to predict the competition between stress build-up due to oxide wedge protrusion and relaxation due to crack tip blunting as a result of the precipitate dissolution.