Fundamentals of Fluid Flow in Porous Media
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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