Page 318 - Geology and Geochemistry of Oil and Gas

WETTABILITY AND CAPILLARITY 279

Fig. A.5. Rise of water in glass capillary tube (see Binder, 1962; Vennard, 1961). r ¼ R (radius of
curvature).

where g is the specific weight of fluid, d is the diameter of capillary tube, and h is the
height of capillary rise. Thus, Eqs. A.5–A.8 may be combined to yield the following
expression for capillary rise, h:
h ¼ 4s cos y=gd (A.9)
Eq. A.9 can also be derived on considering the equilibrium of vertical forces. The
weight of fluid in the capillary tube, W, which is acting downward, is equal to
2
W ¼ pd hg=4 (A.10)
The vertical component of interfacial tension force acting upward is equal to
F sg ¼ pds cos y (A.11)
Equating these two forces and solving for h gives rise to Eq. A.9.
In reference to Fig. A.6, the interfacial tension can be expressed as
(A.12)
s ws þ s wo cos y ¼ s so
where s ws , s wo , and s so are interfacial tensions at the phase boundaries of
water–solid, water–oil, and solid–oil, respectively, or

cos y ¼ ðs so s ws Þ=s wo (A.13)
As shown in Fig. A.7A, when a solid is completely immersed in water phase,
y ¼ 01, cos y ¼ +1 and, consequently,

s wo ¼ s so s ws (A.14)
When half of the solid is wet by water, and the other half, by oil (Fig. A.7B),