The Mathematical Model of Non-Equilibrium Effects in Water-Oil Displacement

G. I. Barenblatt*, Tadeusz Patzek, D. B. Silin

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

26 Scopus citations


Forced oil-water displacement and spontaneous countercurrent imbibition are crucial mechanisms of secondary oil recovery. The classical mathematical models of these phenomena are based on the fundamental assumption that in both these unsteady flows a local phase equilibrium is reached in the vicinity of every point. Thus, the water and oil flows are locally redistributed over their flow paths similarly to steady flows. This assumption allowed the investigators to further assume that the relative phase permeabilities and the capillary pressure are universal functions of the local water saturation, which can be obtained from steady-state flow experiments. The last assumption leads to a mathematical model consisting of a closed system of equations for fluid flow properties (velocity, pressure) and water saturation. This model is currently used as a basis for predictions of water-oil displacement with numerical simulations. However, at the water front in the water-oil displacement, as well as in capillary imbibition, the characteristic times of both processes are comparable with the times of redistribution of flow paths between oil and water. Therefore, the non-equilibrium effects should be taken into account. We present here a refined and extended mathematical model for the non-equilibrium two-phase (e.g., water-oil) flows. The basic problem formulation as well as the more specific equations are given, and the results of comparison with experiments are presented and discussed.

Original languageEnglish (US)
Number of pages10
StatePublished - Dec 1 2002
EventSPE/DOE Thirteenth Symposium on Improved Oil Recovery - Tulsa, OK, United States
Duration: Apr 13 2002Apr 17 2002


OtherSPE/DOE Thirteenth Symposium on Improved Oil Recovery
Country/TerritoryUnited States
CityTulsa, OK

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Geotechnical Engineering and Engineering Geology


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