Page 394 - Petrophysics 2E

362 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

interface and the walls of the container, the molecules attract each other
in all directions. At the surface between two immiscible fluids, there
are no similar molecules beyond the interface and, therefore, there is an
inward-directed force that attempts to minimize the surface by pulling it
into the shape of a sphere. This surface activity creates a film-like layer
of molecules that are in tension, which is a function of the specific free
energy of the interface. The interfacial tension has the dimensions of
force per unit length (newtons/meter) which is the modern standard
expression of the units. In the earlier literature, however, it is
expressed as dynes/cm, which is numerically equal to millinewtons/m
[(N x 10A3)/m or mN/ml.

CONTACT ANGLE

When the interface is in intimate contact with the walls of a container,
for example a capillary tube, the interface intersects the solid surface at an
angle, 8, which is a function of the relative adhesive tension of the liquids
to the solid. This angle is described by Young’s equation below [ 113. The
relationships are illustrated in Figure 6.1 where two liquids, water (w)
and oil (o), are associated with a solid surface (s). The contact angle
(measured through the denser phase) is:

where: oso = interfacial tension between the solid and oil.
osw = interfacial tension between the solid and water.
owo = interfacial tension between water and oil.

Direct measurement of the solid-fluid surface tensions is not possible;
however, by considering a three-phase system one can eliminate the
solid-fluid surface tensions to obtain a measurable relationship between

-- - ----
c---------
Oil- - -

as0 =sw
Figure 6.1. Relationships between the contact angle and interfacial tension expressed
by the Young equation where os, = solid-oil, ossw = solid-water, and ow0 = water-oil
interfacial tensions.