Water injection is used worldwide as an improved oil recovery (IOR) method upstream in the petroleum industry to sweep oil toward production wells or to maintain the appropriate pressure in reservoirs. During the injection of water, differences in the properties of the injection water and the formation water can adversely affect the IOR operations. Such incompatibility leads to supersaturating the water with minerals salts that subsequently precipitate and impair the porous medium. Experiments were performed with three different injection rates to study the effect of the flow rate of the injected brine on damage to the porous medium. In addition, a kinetic mass-transfer model was developed for the transient sweep of the formation water by the injection water within the porous medium. Then, formation damage due to the reduced permeability of the medium was observed and modeled based on the dynamic behavior of scale formation in the cores. The effluent concentrations of magnesium (Mg2+) and calcium (Ca2+) ions were used to obtain the dispersion coefficients and the reaction rate constants for the precipitation of calcium sulfate in the sandstone cores. The formation damage coefficient for each run was calculated by the regression of the experimental and calculated permeability reduction ratios so that the average deviations for this step were less than 3.9%.