Page 354 - Petrophysics

322 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

where k is the absolute permeability of the porous medium. Substituting
the capillary pressure equation for the average pore diameter and
rearranging:

or:

(5.19)

Although Equation 5.28 was derived from the physics of fluid equilibria
in a straight vertical tube, it is applied for general analyses of capillary
phenomena in porous media as indicated by applications using the
J-function. Hence, the capillary pressure evaluations of porous media
do not include the effects of tortuosity and alternating constrictions of
the pores.

EXAMPLE

The fluids in a straight tube have an interfacial tension equal to
32 mN/m and exhibit a contact angle of 80' and capillary pressure of
5.5 kPa. What is the radius of the tube?

SOLUTION

-
2
20~0~8 x 32 x x 0.174N/m
r, = -
PC 5.5 x 103N/m2
6
= 2.02 x 10- m = 2.0pm

SEMIPERMEABLE DISK MEASUREMENT
OF
CAPILLARY PRESSURE

The derivation of capillary pressure equations thus far has been based
on a single uniform capillary tube. Porous geologic materials, however,
are composed of interconnected pores of various sizes. In addition, the
wettability of the pore surfaces varies from point to point within the rock
due to the variation in the mixture of minerals in contact with the fluids.
This leads to variation of the capillary pressure as a function of fluid
saturation and an overall mean description of the rock wettability.