The injection of low-salinity brines can improve oil recovery in carbonate reservoirs by changing the rock wettability from being more oil-wet to being more water-wet. Existing models use an empirical dependence of wettability based on variables including equivalent salinity and ionic strength. We recently developed a process-based model that mechanistically includes the geochemical interactions between crude oil, brine, and the chalk surface that alter rock wettability. In this research, we extend the previous model by including mineral dissolution reactions, therefore enabling the modeling of low-salinity flooding in chalks and limestone cores with and without anhydrite, which is considered to be a key factor in controlling the extent of improved oil recovery (IOR). We examine the role of mineralogy by including surface complexation, aqueous reactions, and dissolution/precipitation of calcite and anhydrite in the extended model. These reactions, coupled with the equations of multiphase flow and transport, are solved simultaneously using an in-house simulator, PennSim. Relative permeability functions and residual oil saturation during flooding are adjusted dynamically according to the concentration of oil acids attached to the mineral surface. Core flooding experiments from the Stevns Klint (SK) chalk and a Middle Eastern carbonate with a small volume fraction of anhydrite are used to tune the reaction network and predict recovery. Simulation results agree with the observed effluent concentrations of SO42-, Ca2+, and Mg2+ reported from chromatographic wettability tests and the measured recoveries under differing compositions in chalk and limestone cores. For the SK chalk without anhydrite, lower Na+ and Cl- concentrations under constant SO42- conditions leads to IOR by as much as 6% OOIP. Lower salinity alone, however, does not lead to IOR in limestones without anhydrite. Instead, anhydrite dissolution provides a natural source of sulfate and increases oil recovery by 5% when injecting diluted formation water. Simulations of two-dimensional (2D) five-spot patterns using tuned reaction networks demonstrated that IORs from 5% to 20% OOIP can be obtained after two pore volumes are injected. These IORs are greatly dependent on the aqueous chemistry of the injected fluid and sweep. The results highlight the critical importance of understanding the mineralogy and including a mechanistic reaction model in the simulation of low-salinity water floods.