Injection of low salinity brines can improve oil recovery (IOR) in carbonate reservoirs by changing the rock wettability from oil-wet to more water-wet. Existing numerical simulation models for low salinity flooding use empirical relationships that do not properly capture important processes for wettability alteration, such as aqueous species concentrations, oil acidity, and rock mineralogy. In our previous research on modeling spontaneous imbibition with tuned water (SPE170966), we developed a processbased and predictive model that explicitly includes the chemical interactions between crude oil, brine, and the carbonate surface. In this research, we extend the previous model for low salinity water flooding to both chalk and limestone cores. We examine the role of mineralogy in low salinity waterflooding by developing a mechanistic model for wettability that includes surface complexation, aqueous reactions, and dissolution/precipitation of calcite and anhydrite. The reactions coupled with the equations of multiphase flow and transport are solved simultaneously using an IMPEC 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 (Fathi et al. 2010), a limestone with small amount of anhydrite (Austad et al. 2012), and a Middle Eastern carbonate with 6% volume fraction anhydrite (Yousef et al. 2011) are used to tune the reaction network and make recovery predictions. Simulation results give remarkable agreement with the effluent concentrations of SO42, Ca2+ and Mg2+ reported from chromatographic wettability tests and the recoveries for injection of various brines into chalk and limestone cores of differing compositions. For SK chalk without anhydrite, reducing the Na+ and Cl concentration of seawater, while keeping SO42 (sulfate) leads to improved oil recovery (IOR) by as much as 6% OOIP. The presence of anhydrite, which provides a natural source of sulfate, also significantly increased oil recovery for injection of diluted formation water and seawater. Simulations of 2D five-spot patterns using tuned reaction networks demonstrated that IORs from 5% to 20% OOIP can be obtained at reasonable values of pore volumes injected (2.0 PVI). These IORs depend greatly 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.