Alkali-surfactant-polymer (ASP) floods can recover significant amounts of remaining oil after a water flood. Currently, commercial and academic chemical flooding simulators use Hand's model and linear interpolation rules based on a salinity scan to model micro-emulsion phase behavior. Those simple models have significant limitations when the reservoir conditions are different than experimental conditions. Recently an equation-of-state (EoS) based on HLD-NAC was developed that gives improved phase behavior predictions away from the tuned experimental data. The new EoS for SP modeling was incorporated into our in-house compositional simulator, PennSim. In this research, we expand PennSim with an updated flash calculation module that includes alkali and geochemistry. The new simulator can more accurately model ASP flooding since phase behavior changes consistently with aqueous chemistry, oil saturation, alkali concentration, salinity, pressure, and other key variables. ASP phase behavior depends on many factors including pressure, temperature, oil EACN, and geochemistry. PennSim solves the mass conservation equations of oil acidic components, water, and aqueous solute along with phase equilibrium relations and chemical reactions using an IMPEC approach. The reactions between oleic acids, aqueous and solid species, surfactant adsorption and mineral dissolution reactions are considered. A scalable capillary desaturation curve (CDC) with permeability and porosity is used for heterogeneous field cases. An algebraic multigrid linear solver is used to speed up simulation. The functionalities of the developed code are demonstrated with multiple injection scenarios, such as the combination of an alkali and polymer slug with and without added synthetic surfactant. Simulations are made to model 1D core floods and 2D heterogeneous reservoirs with multiple wells. The simulation results show that the main difference between the new CDC and traditional CDC curve is the size of the developed oil bank, where the traditional CDC predicts a larger oil bank in the high permeability channel.