A plane axisymmetric (radially converging) flow occurs in case of water extraction from an aquifer through a well. A new physico-mathematical approach is developed for modeling oil pollutant migration near an extraction well in the aquifer. This is done by considering the various dimensionless parameters governing the transport processes and by applying a self-similar scheme. The time-dependent saturation profiles, calculated from several exact analytical solutions, exhibit the effects of various dimensionless parameters related to oil migration, directed to a water extraction well. By using hypothetical saturation data, the model was calibrated and a predication of the temporal oil saturation distribution around the well was calculated.