Steady distribution of oil pollutant within an aquifer, discharging from an underground source, is modeled by a two-dimensional nonlinear diffusion-convection equation. This equation describes oil transport in the immiscible zone, containing large oil blobs. This zone serves as a secondary source of contaminant in the dispersed zone, containing freely flowing oil drops. A self-similar solution is obtained for the steady saturation distribution in the immiscible zone, which is valid at distances greatly exceeding the source size across the water-flow direction. The distribution of oil saturation within the aquifer is investigated numerically and analytically as a function of the water-flow rate, pore sizes and the leakage rate of the oil-pollution source. This rate is characterized by a dimensionless parameter, dependent on the oil viscosity, aquifer permeability and the water-flow rate in the aquifer. Various flow regimes are described which yield plum-like contamination patterns. The location of the boundary between the immiscible and dispersed oil zones is calculated in terms of the source-strength parameter, water and oil properties and porous-medium structure. A closed form analytical solution is obtained in a particular case where a linear relationship exists between parameters governing advection and dispersion oil-transport rates.
- Oil saturation
- Self-similar solution