Reactions caused by the diffusion of reactants from different sources can alter rock diffusivity and are therefore the critical mechanisms for evaluating short and long-term behavior of low-permeability rocks used as confinement layers for underground storage, for instance. This paper presents and discusses a set of two diffusion-driven reaction experiments focusing on precipitation of two end-member types of sulfate minerals (gypsum: CaSO4.2H2O and barite: BaSO4) in low-permeability chalk. The time-resolved changes in porosity and effective diffusion coefficient (De) were evaluated along the duration of the experiments (~140 days), by analyzing the behavior of passive tracers and evaluating the amount of precipitated gypsum or barite from measuring the reactant concentration evolution in the reservoirs at both ends of the sample. Then SEM-EDS and X-ray microtomography (μCT) imaging were used to characterize the initial rock structure and the precipitated materials.Results showed that the change in porosity (from 45% to about 43%) corresponding to the volume of sulfate precipitated, are similar for gypsum and barite. Conversely, the precipitation impact on diffusion properties of the water tracers that were injected 70 days after the beginning of the precipitation step is distinctly different for the each of the studied sulfate mineral. The precipitation of barite generated a more significant impact than gypsum: Deintact = 4.15 × 10−10 m2·s−1 vs. Debarite = 1.1 × 10−10 m2·s−1 and Degypsum = 2.5 × 10−10 m2·s−1. Post-mortem imaging revealed a thin precipitated zone (~250 μm) in the center of the sample for the barite precipitation experiment, whereas isolated quasi-spherical clusters resulted from the gypsum precipitation. The μCT images at higher resolution showed that the precipitation of barite is heterogeneous at small scale, which explains the HTO diffusion curve. For gypsum, the post mortem imaging around the quasi-spherical clusters showed a significant presence of initial macropores of the connected porosity that were still unfilled. These intact chalk zones allowed HDO to diffuse through the precipitated zone lowering the impact on water tracer diffusivity. These experimental results indicate that the morphology and the distribution of barite precipitates is mainly controlled by homogeneous and heterogeneous nucleation phenomena, whereas gypsum precipitation is mainly controlled by the spatial variability of the initial porous system properties (reactive surface area, tortuosity, pore network structure).