Page 352 - Petrophysics 2E

320 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

This downward force is opposed by the force due to the capillary
pressure:
20 COS e
Forceup, FZ = (5.13)

Equating the two forces yields Equation 5.14:
20 cos e
Pc = Gpg,h = (5.14)
rC
where Pc is expressed in dyne/cm2 = mN/m2 = Pa( lo-').

CAPILLARY PRESSURE J-FUNCTION

Leverett proposed the J-function of a specific reservoir which
describes the heterogeneous rock characteristics, more adequately by
combining porosity and permeability in a parameter for correlation [2].
The J-function accounts for changes of permeability, porosity, and
wettability of the reservoir as long as the general pore geometry remains
constant. Therefore, different types of rocks exhibit different J-function
correlations. All of the capillary pressure data from a specific formation
usually can be reduced to a single J-function versus the saturation curve.
This is illustrated in Figure 5.6, where Rose and Bruce prepared J-function
correlations for six formations and compared them to data obtained
from an alundum core and Leverett's correlation for an unconsolidated
sand [91.
The J-function can be derived by dimensional analysis or by substitution
of the capillary pressure equation into the Carman-Kozeny equation [ 101.
Permeability has the dimension L2 and porosity is dimensionless;
therefore, (k/+)'j2 may be substituted for the radius in the capillary
pressure equation (Equation 5.1 1) and rearranged as follows:
o COS e
P-
- (k/$)'I2
or

(5.15)

Alternatively, it may be derived from the Carman-Kozeny equation:

(5.16)