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 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.
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<< DOMINANCE OF CAPILLARY FORCES OVER VISCOUS FORCES
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BOND NUMBER >>
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References
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