Analytical Solutions for Spontaneous Imbibition: Fractional-Flow Theory and Experimental Analysis
- Karen S. Schmid (The Boston Consulting Group) | Nayef Alyafei (Texas A&M University at Qatar) | Sebastian Geiger (Heriot-Watt University) | Martin J. Blunt (Imperial College London)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2016
- Document Type
- Journal Paper
- 2,308 - 2,316
- 2016.Society of Petroleum Engineers
- Fractured Reservoirs, Analytical solution, Spontaneous Imbibition, Capillary flow, Reservoir Engineering
- 5 in the last 30 days
- 707 since 2007
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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 water-wet 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.
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