The erosion of refractory is a major limitation to the campaign life of a blast furnace hearth. Titanium from titania addition in the burden or tuyere injection can react with carbon and nitrogen to form titanium carbonitride, giving the so-called titanium rich scaffold on the hearth surface, to protect the hearth from further erosion. In the current paper, a mathematical model based on computational fluid dynamics and multi-phase flow method is proposed to simulate the formation of solid particles. The model considers the fluid flow through a packed bed, conjugated heat transfer, species transport and thermodynamic of chemical reactions. A region of high solid concentration is predicted on the hearth bottom surface. Regions of solid formation and dissolution can be identified which depend on the local temperature and chemical equilibrium. Several operation parameters are analyzed, including the hearth erosion profile, inlet titanium concentration, effect of nitrogen. The model provides an insight into the fundamental mechanism of scaffold formation in the blast furnace.