The use of standard Enhanced Oil Recovery (EOR) techniques allows improving the recovery factors after traditional waterflooding processes. Chemical EOR methods comprise alkalis, surfactant or polymers, which modify different properties of fluids and/or rock in order to mobilize the remaining oil. A series of combined chemical flooding techniques has been developed in order to maximize the performance by using the combined properties of the chemical slugs. In the present research, a new model is developed to study a surfactant-polymer flooding. A novel compositional simulator is presented based on a two-phase, five-component system (aqueous and organic phases with water, petroleum, polymer, surfactant and salt) for a 2D reservoir model. Polymer and surfactant together affect each other interfacial and rheological properties as well as the adsorption rates. This is a phenomenon known as Surfactant-Polymer Interaction (SPI). New numerical models of these interactions show their effect on the recovery processes. The analysis of the chemical injection strategy was also included in the scope of this research. The latter plays a major role in the efficiency of the recovery process, including both the order and the time gap between the injection of each chemical slug. When the latter is increased, the combined flooding tends to behave as two separate chemical EOR processes. Best results were found when both slugs are injected overlapped, with the polymer in first place which improves the sweeping efficiency of the viscous oil. This also hinders the surfactant adsorption rates. This is because the latter is more sensitive to this phenomenon than the polymer. This novel simulator can be then used to study different chemical combinations and their injection procedure in 2D fields to optimize the EOR process.