The penetration of a fuel pollutant from an external source into the groundwater is studied theoretically. The fuel migration in the aquifer is affected by viscous, capillary and gravitational forces. The contaminant is usually introduced into the main body of the aquifer due to seasonal oscillations of the groundwater level. Some portions of the fuel are trapped in the interstices of the porous medium. Other fuel portions are subjected to the flow as a continuous or a discontinuous phase. In this paper a one-dimensional model is developed describing the transport and accumulation of fuel in these two phases. By using power- law dependences of transport and kinetic properties of the fuel upon its saturation in the porous medium, several similarity solutions are obtained. The effect of fuel rupture and coalescence upon the migration of the bulk volume of the fuel spill is studied by employing a perturbation technique. As a result, the details of mass transfer between the continuous and the discontinuous fuel phases are provided.