On Barenblatt's model of spontaneous countercurrent imbibition

Dmitry Silin*, Tad Patzek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


Water imbibition is a critical mechanism of secondary oil recovery from fractured reservoirs. Spontaneous imbibition also plays a significant role in storage of liquid waste by controlling the extent of rock invasion. In the present paper, we extend a model of countercurrent imbibition based on Barenblatt's theory of non-equilibrium two-phase flow by allowing the model's relaxation time to be a function of the wetting fluid saturation. We obtain two asymptotic self-similar solutions, valid at early and late times, respectively. At a very early stage, the time scale characterizing the cumulative volume of imbibed (and expelled) fluid is a power function with exponent between 1.5 and 1. At a later stage, the time scaling for this volume approaches asymptotically classical square root of time, whereas the saturation profile asymptotically converges to Ryzhik's self-similar solution. Our conclusions are verified against experiments. By fitting the laboratory data, we estimate the characteristic relaxation times for different pairs of liquids.

Original languageEnglish (US)
Pages (from-to)297-322
Number of pages26
JournalTransport in Porous Media
Issue number3
StatePublished - Mar 2004
Externally publishedYes


  • Asymptotic solution
  • Countercurrent imbibition
  • Non-equilibrium two-phase flow

ASJC Scopus subject areas

  • Catalysis
  • General Chemical Engineering


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