Polymer flooding is one of the most used chemical enhanced oil recovery (CEOR) technologies worldwide. Because of its commercial success at the field scale, there has been an increasing interest to expand its applicability to more unfavorable mobility ratio conditions, such as more viscous oil. Therefore, an important requirement of success is to find a set of design parameters that balance material requirements and petroleum recovery benefits in a cost-effective manner. Then, prediction of oil recovery turns out to handle more detailed information and time-consuming field reservoir simulation. Thus, for an effective enhanced oil recovery project management, a quick and feasible tool is needed to identify projects for polymer flooding applications, without giving up key physical and chemical phenomena related to the recovery process and avoiding activities or projects that have no hope of achieving adequate profitability. A detailed one-dimensional mathematical model for multiphase compositional polymer flooding is presented. The mathematical formulation is based on fractional flow theory, and as a function of fluid saturation and chemical compositions, it considers phenomena such as rheology behavior (shear thinning and shear thickening), salinity variations, permeability reduction, and polymer adsorption. Moreover, by setting proper boundary and initial conditions, the formulation can model different polymer injection strategies such as slug or continuous injection. A numerical model based on finite-difference formulation with a fully implicit scheme was derived to solve the system of nonlinear equations. The validation of the numerical algorithm is verified through analytical solutions, coreflood laboratory experiments, and a CMG-STARS numerical model for waterflooding and polymer flooding. In this work, key aspects to be considered for optimum strategies that would help increase polymer flooding effectiveness are also investigated. For that purpose, the simulation tool developed is used to analyze the effects of polymer and salinity concentrations, the dependence of apparent aqueous viscosity on the shear rate, permeability reduction, reversible–irreversible polymer adsorption, polymer injection strategies on petroleum recovery, and the flow dynamics along porous media. The practical tool and analysis help connect math with physics, facilitating the upscaling from laboratory observations to field application with a better-fitted numerical simulation model, that contributes to determine favorable scenarios, and thus, it could assist engineers to understand how key parameters affect oil recovery without performing time-consuming CEOR simulations.