Page 351 - Petrophysics 2E

CAPILLARY PRESSURE 319

The shape and height of the meniscus depends on the relative
magnitudes of the molecular cohesive forces and the molecular adhesive
forces between the liquids and the walls of the capillary. The more dense
liquid wets the solid preferentially when the contact angle is less than
90" (Figure 5.5a). When the contact angle is O", the molecular forces
are balanced and the two fluids wet the walls equally pigure 5.5b).
When the contact angle is greater than 90", the denser fluid wets
the walls of the capillary to a lesser extent than does the fighter fluid
(Figure 5.5~).
The denser fluid will rise in the capillary until the weight of the column
of fluid balances the pressure difference across the meniscus. Consider
the surface of the meniscus in a circular tube of radius r, as a segment of
a sphere with radius r,, Figure 5.3. Then cos 9 = rc/rs, and substitution
into Equation 5.9 yields Equation 5.1 1.
The downward force 0, expressed in dynes (one dyne is 1.01 97 16 x
10-3g x cm/s2) due to gravity, exerted by the cylindrical column
(Figure 5.5a) is:

2
Force down (W - B) = (pw - po)gchnr, (5.12)

where: pw = density of water in g/cm3,
po = density of oil in g/cm3, and
g, = gravitational acceleration = 981 cm/s2.