In order to examine the heterogeneous nucleation and growth dynamics of mineral precipitation in reactive transport systems, as well as the evolution of key upscaling parameters, such as porosity and permeability, this study employs a model that integrates pore-scale reactive transport with arbitrary Lagrangian-Eulerian method. This model incorporates a heterogeneous probabilistic nucleation process based on classical nucleation theory, which is used to parametrically simulate the nucleation and growth processes of individual mineral particles within the reactive transport. The findings indicate that fluid velocity, along with nucleation and mineral growth rates, plays critical roles in determining the pattern and spatial distribution of precipitates. Nucleation promotes irregularities in the precipitate pattern and reduces the influence of flow on the spatial distribution of precipitate formation across particle surfaces. Precipitation on the surface of a single mineral particle within a pore channel is more accurately governed by a power law model, which captures the evolutionary relationship between porosity and permeability in porous media with periodic structures.