Page 81 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

Basic Principles, Definitions, and Data 69

where r, and rn are the principal radii of curvature at the interface. These radii
are not usually measured, and a mean radius of curvature is given by the
capillary pressure and interfacial tension.
For a cylindrical vertical capillary, such as a small tube, the capillary pressure
for a spherical interface is [19]:

2a cos e,
P, = r = gm, - Pe) (5-75)

where r is the radius of the tube, 6, is the contact angle measured through the
more dense phase that exists between the fluid and the wall of the tube, g is
the gravitational constant, p is density, h is column height, and the subscripts
refer to the fluids of interest. For a fluid that wets the wall of a capillary tube,
the attraction between the fluid and the wall causes the fluid to rise in the
tube. The extent of rise in the capillary is proportional to the interfacial tension
between the fluids and the cosine of the contact angle and is inversely pro-
portional to the tube radius.
An analogous situation can occur during two-phase flow in a porous medium.
For example if capillary forces dominate in a water-wet rock, the existing pressure
differential causes flow of the wetting f hid to occur through the smaller
capillaries. However, if viscous forces dominate, flow will occur through the
larger capillaries (from Pouiselle’s law, as a function of the 4th power of the radius).
Figure 5-46 depicts a typical capillary pressure curve for a core sample in
which water is the wetting phase. Variation of capillary pressure is plotted as a
function of water saturation. Initially, the core is saturated with the wetting
phase (water), The nonwetting phase, oil in this case, is used to displace the

SECONDARY DRAINAGE
-.I I PRIMARY DRAIN AGE

rTHRESHOL0 PRESSURE

0 Siw 1- Sor 1.0

WATER SATURATION
Figure 5-46. Example capillary pressure curves.