Alkaline−surfactant−polymer (ASP) flooding is potentially the most efficient chemical EOR method. It yields extremely high incremental recovery factors in excess of 95% of the residual oil for water flooding on the laboratory scale. However, current opinion is that such extremely high recoveries can be achieved under optimum salinity conditions, i.e., for the Winsor Type III microemulsion phase characterized by ultralow interfacial tension (IFT). This represents a serious limitation since several factors, including alkali-rock interaction, the initial state of the reservoir water, and the salinity of injected water, may shift the ASP flooding design to either sub-optimum or over-optimum conditions. A recent experimental study of ASP floods, based on a single internal olefin sulfonate (IOS) in natural sandstone cores with varying salinity from sub-optimum to optimum conditions, indicated that high recovery factors can also be obtained under sub-optimum salinity conditions. In this paper, a mechanistic model was developed to explore the causes behind the observed phenomena. The numerical simulations were carried out using the UTCHEM research simulator (at The University of Texas at Austin), together with the geochemical module EQBATCH. UTCHEM combines multiphase multicomponent simulation with robust phase behavior modeling. An excellent match of the numerical simulations with the experiments was obtained for oil cut, cumulative oil recovery, pH profile, surfactant, and carbonate concentration in the effluents. The simulations gave additional insight into the propagation of alkali consumption, salinity, surfactant profiles within the core. The study showed that the initial condition of the core is important in designing an ASP flooding. Because of uncertainties in the various chemical reactions taking place in the formation, an accurate geochemical model is essential for operating an ASP flooding in a particular salinity region. The simulation results demonstrate also that, for crude oil with a very low total acid number (TAN), the ultralow IFT and low surfactant adsorption can be achieved over a wide range of salinities that are less than optimal. The results provide a basis to perform better modeling of the suboptimum salinity series of experiments and optimizing the design of ASP flooding methods for the field scale with morecomplicated geochemical conditions.