Page 368 - Petrophysics 2E

336 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

substituting Equation 5.34 into Equation 5.35 and rearranging:

Then, substituting Equation 5.36 into Equation 5.33 yields the critical
capillary pressure for breakthrough in terms that can be evaluated:

(5.37)

Melrose used estimates of the terms in Equation 5.37 to examine
the range of critical capillary pressure with respect to the permeability
of the rock. Using J = 0.22, H = 5.55, o = 25, and $ = 0.25, he used
Equation 5.37 to compute the values of (Pc)i-crit as a function of k as
shown in Figure 5.18. For a 100 mD sample, the critical pressure exceeds
the limitations of capillary pressure attainable with the Beckman core
analysis centrifuge. Even at 1,000 mD, the critical pressure is 552 kPa
(80 psi), which is still higher than capillary pressures expected for all but
the most unusual reservoirs. Except for very unusual cases, therefore,
the Hassler-Brunner boundary condition of zero capillary pressure at the
outflow face of the core will be sustained.

APPROXIMATE CALCULATION OF THE INLET SATURATION

The capillary pressure calculated using Equation 5.30 is the capillary
pressure at the inlet end of the core; however, the saturation, measured
from the amount of fluid displaced, is equal to the average saturation. In
order to use the centrifugederived capillary pressure, it must be related
to the saturation at the inlet.
The length of the core can be considered negligible with respect to the
radius of rotation of the centrifuge; in other words, the distance to the
top of the core is equal to the distance to the bottom of the core (q = re).
Using this approximation, a method for calculating the inlet saturation
can be derived directly from the mathematical definition of the average
saturation, 3. Hassler and Brunner stated that if the ratio ri/re is greater
than 0.7, the error introduced by this assumption is negligible [17]. This
ratio is 0.88 for the Beckman L5-50P Rock Core Ultracentrifuge and is
even greater for the modified International centrifuge used by Donaldson
et al. [16].
By definition, the average saturation in the core, 3, is:

3 = 1 / S x dl (5.38)
L