Page 366 - Petrophysics 2E

334 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

(3
P, = phgc = ph - = 1.1179 x 10-5ApN2hr (5.28)

where P, is expressed in gf/cm2. Equation 5.28 yields the capillary
pressure in gf/cm2 at any height, h, in the core rotating at N revolutions
per minute with a radius of rotation, r. Integrating across the total height
of the core (from the inner radius, r1, of the core to the outer radius, re)
in order to take into account the variation of the centrifugal field within
the core with respect to distance:

(Pc)i = (P& + 1.1179 x 10-5ApN2[(r," - rf)/2] (5.29)

As expressed in Equation 5.29, a capillary pressure gradient exists
within the core; a saturation gradient also exists within the core, and
the only measured quantities are the revolutions per minute, N, and
the average saturation of the core, 3,. Most centrifuge data reported
in the literature adopt the boundary condition, assumed by Hassler and
Brunner, i.e., that the end face of the core remains 100% saturated with
the wetting phase at all centrifugal speeds of the test [ 171. Therefore, the
capillary pressure at the end face, (P,)D, is equal to zero during the entire
range of centrifuge speeds used. As long as there exists a continuous film
on the surface of the rubber pad holding the core at the bottom, which is
the most prevalent assumption, the condition of zero capillary pressure
at the end face is correct.
Equation 5.29 is modified in practice to introduce the core length,
L, because the lengths of cores used in the centrifuge vary slightly. In
addition, the pressure is expressed in kPa rather than grams-force/cm2.
These changes yield the final equation, which is used to obtain the
capillary pressure (in kPa) at the inlet end, ri, of the core:

(Pc)i = (1.096 x 10-')ApN2(r, - L/2)L (5.30)

LIMITING CENTRIFUGE SPEED

Melrose examined the Hassler-Brunner end-face boundary condition
and concluded that the zero capillary pressure assumption is valid for the
maximum centrifuge speeds used in practice [17-191. This conclusion
is reached by considering the mechanism of the wetting phase (water)
displacement by the non-wetting phase (air or oil), commonly referred
to as the drainage capillary pressure.
If the centrifuge speed reaches a sufficiently high value, the non-
wetting phase will finger (or cavitate) through the largest pores to break
through at the end face of the core. The capillary pressure at the end-face