Analytical solutions for spontaneous imbibition: Fractional-flow theory and experimental analysis

K. S. Schmid, N. Alyafei, S. Geiger, M. J. Blunt

Research output: Contribution to journalReview articleScientificpeer-review

57 Citations (Scopus)


We present analytical solutions for capillary-controlled displacement in one dimension by use of fractional-flow theory. We show how to construct solutions with a spreadsheet that can be used for the analysis of experiments as well as matrix-block-scale recovery in field settings. The solutions can be understood as the capillary analog to the classical Buckley-Leverett solution (Buckley and Leverett 1942) for viscous-dominated flow, and are valid for cocurrent and countercurrent spontaneous imbibition (SI), as well as for arbitrary capillary pressure and relative permeability curves. They can be used to study the influence of wettability, predicting saturation profiles and production rates characteristic for water-wet and mixed-wet conditions. We compare our results with in-situ measurements of saturation profiles for SI in a waterwet medium. We show that the characteristic shape of the saturation profile is consistent with the expected form of the relative permeabilities. We discuss how measurements of imbibition profiles, in combination with other measurements, could be used to determine relative permeability and capillary pressure.

Original languageEnglish
Pages (from-to)2308-2316
Number of pages9
JournalSPE Journal
Issue number6
Publication statusPublished - Dec 2016
Externally publishedYes


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