The objective of this paper is to model low-salinity waterflooding by honoring physico-chemical complexity, namely, the effects of reaction kinetics and dispersion. Recent literature provides evidence for the potential of low-salinity water injection to improve oil recovery through wettability alteration through a complex network of reactions. However, there is lack of consensus with respect to the exact chemical species that are responsible for the alteration process. Therefore, in this study, we develop a a simplified binary multiphase reactive transport model that honors the general surface reaction for wettability alteration, but at the same time includes effects of reaction kinetics and dispersion in the governing equations. We lump the reactants, such as sodium, calcium, and petroleum acids, into two characteristic components based on their contribution to oil or water wetness. The wettability alteration process is modelled as a competition between these primary characteristic components to occupy the rock surface as described by reaction kinetics. The simulation results show a significant impact of reaction kinetics on the rate of wettability alteration compared to assuming instantaneous equilibrium. In the limiting case of a very slow reaction rate (Da ~ 0), low-salinity injection does not alter the wettability. Particularly, no effect on ultimate oil recovery is observed, regardless of the injected salinity level. For the case of an instantaneous reaction the ultimate oil recovery is sensitive to the injected fluid salinity. Moreover, during fast reactions (Da ~ 10-4), the wettability alteration front moves slower than the injected fluid front caused by excess salt in the solution that desorbs from the rock surface. The delay in wettability alteration is crucial to consider for an appropriate slug size design of low-salinity injection. Lastly, we observe that dispersion does not affect the ultimate oil recovery during wettability alteration as compared to reaction kinetics.