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
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 N_ca < 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.