The enhancement of oil recovery (EOR) through low-salinity waterflooding (LSWF) and the emerging hybrid with a polymer (LSP) has proven to be effective at microscale investigations and cost-effective with ease of operation at field-scale tests. Their application in carbonate oil reservoirs, which typically occur oil-wet, presents a particularly essential capacity given that over half of the global oil reserves are hosted in carbonate formation. However, modeling the mechanisms involved to predict and evaluate the performance of low salinity-based EOR at a large scale is complex and requires the integration of geochemistry in reservoir simulation to upscale the interfacial interactions of crude oil, brine, and rock observed at the micrometer scale. This study presents an integrated approach that combines MRST's polymer model with PHREEQC geochemical modeling to simulate LSWF at the reservoir scale. Using single-phase and multiphase experimental flooding data for validation, the coupled model was shown to accurately predict effluent ionic and oil recovery profiles. The simulation of LSWF and LSP both exhibited additional tertiary oil recovery, with LSWF and LSP showing 3 and 2%, respectively, which are consistent with previously reported field and core flooding results. Furthermore, the sequential application of formation water (FW), LSWF, and LSP flooding in secondary mode showed a high increase in oil recovery, with oil recovery percentages of 61, 20, and 19%, respectively. However, the FW results were 50% lower compared to regular core flooding due to upscaling limitations. The modeling of vertical and anisotropic permeability heterogeneity effects showed a positive synergy with low-salinity floodings, resulting in a 4% drop and 3 and 1% increase in FW, LSWF, and LSP, respectively. These findings demonstrate the potential of the coupled MRST-PHREEQC model in accurately simulating hydrogeochemical interactions during LSWF/LSP at the reservoir scale, providing valuable insights for the optimization of low salinity-based EOR strategies in carbonate reservoirs.