Contamination pattern in groundwater resulting from an underground source

Arieh Pistiner*, Michael Shapiro

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Pages (from-to)15-30
Number of pages16
JournalJournal of Engineering Mathematics
Issue number1
StatePublished - 1998
Externally publishedYes


  • Aquifer
  • Groundwater
  • Oil saturation
  • Pollution
  • Self-similar solution


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