In studies relevant to the contaminant transport in geosphere, the evolution of local physicochemical processes imparts potential challenges in safety and critical assessment issues. The transport of such contaminants in a rock pore structure could occur under the advective or diffusive regime. Such transport over the spatial and temporal scale depends upon the coupling between physical properties of the pore structure (permeability, pore size distribution, porosity) and chemical properties of the dissolved ionic species (pH, ionic strength, and surface interactions). The nature of such interactions leads to the generation of local imbalances in pore solution and thereby enhances the dissolution and precipitation of minerals. To predict the occurrence of such processes over large spatial and temporal scales, it is imperative to demonstrate how these physical and chemical processes interact within the heterogeneous porous media. In this context, numerical simulations were conducted to model the results of experimental dataset investigating barite and gypsum precipitation in chalk. In the experimental approach, the selected two minerals are end-members of the sulfate-alkali family and exhibit large differences in the kinetic rate and solubility, and the reference chalk sample resembles heterogeneity in its pore structure. The numerical simulations revealed that at the 1D scale, it was possible to model the overall experimental observations at the boundary monitoring points such as chemistry evolution in reservoirs, porosity loss during barite and gypsum precipitation, the total amount of barite and gypsum formation in clogging zone and the threshold saturation index to initiate precipitation. However, these simulations could not validate the experimentally observed impact of barite and gypsum clogging on the changes in water tracer transport. The underlying reason for such behavior was the formation of a unique clogging zone due to barite and gypsum precipitation. We showed that the 2D simulations incorporating spatial heterogeneity were able to reproduce the observed precipitation patterns, for both of the barite and gypsum experiments. Through 1D and 2D numerical results, we demonstrate the capability of a reactive transport model to validate the experimentally observed barite and gypsum precipitation behavior in chalk samples. Furthermore, it also highlights the interplays between the physicochemical heterogeneities, mineral reactivity and the transport rates that are responsible for the distinct precipitation pattern of the barite and gypsum in chalk samples, and consequently their impacts on transport properties.