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Capillary Number 2016-10-25T11:54:43+00:00

Fundamentals of Fluid Flow in Porous Media

 

Chapter 2

Multi-phase Saturated Rock Properties:

Dominance of Capillary Forces over Viscous Forces: Capillary Number

The capillary number is a dimensionless number that describes the relative importance of viscous forces to capillary forces during the course of an immiscible displacement. Table 4 offers a fairly comprehensive list of the various forms of the capillary number as used by different authors.  The most common versions of the capillary number are number 6, 10.

Table 4: Capillary Number or “Displacement Ratio” Correlating Groups

No. Author(s) Year Porous Media Correlating Group
1 Fairbrother and Stubbs 1935 Capillary Fairbrother and Stubbs Capillary (1935)
2 Leverett 1939 Sandstone ( LPc ) / ( DΔP )
3 Brownell and Katz 1947 Sandstone ( KΔP ) / (g cos(θ) Lσ)
4 Ojeda, Preston and Calhoun 1953 Sandstone σ / ΔP
5 Moore and Slobod 1956 Sandstone ( vμ ) / ( σ cos θ )
6 Saffman and Taylor 1958 Hell-Shaw Cell ( vμ ) / σ
7 Taber 1969 (Berea) Sandstone ΔP / ( Lσ )
8 Foster 1973 (Berea) Sandstone ( vμ ) / ( σφ )
9 Lefebvre duPrey 1973 Teflon, Steel, and Aluminum σ / ( vμ )
10 Melrose and Brandner 1974 Unconsolidated Glass Beads ( vμ ) / ( σφ )
11 Ehrlich, Hasiba and Raimondi 1974 Sandstone ( KΔP ) / ( σφL )
12 Abrams 1975 Sandstone, Limestone ( vμ1.4w ) / ( σμ0.4o )
13 Reed and Healy 1977 Various ( KΔP ) / ( σLcosθ )

 

According to the work of Chatzis and Morrow (1984) the range of capillary numbers over which capillary displacement is predominant is Nca < 10-5 to 10-4. When the capillary number exceeds a value of 10-4 then the residual oil is mobilized through a stripping process.

References

[1]

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