Modeling chemical enhanced oil recovery by Alkaline-Surfactant-polymer(ASP)flooding brings in myriads of complicated physics because of complex rheological properties of the complex fluid, complex properties of the porous media and the interaction between them. Accurate Modeling of the fluid flow through such a media by a set of coupled nonlinear partial differential equations raises interesting computational and discretization issues because of the large and multi-scale nature of the problem, in particular in realistic heterogeneous media. In this talk, we will document various physical phenomena, computational methods, and current and past efforts on simplified model problems that shed great insight into the physics that are in play in such complicated process. This work is currently funded by Qatar National Research Fund under This work is made possible by a NPRP grant from the Qatar National Research Fund (a member of The Qatar Foundation).