Page 367 - Petrophysics 2E

CENTRIFUGE MEASUREMENT OF CAPILLARY PRESSURE 335

boundary will no longer be equal to zero if the non-wetting fluid breaks
through. The non-wetting fluid will reach the end face when the capillary
pressure at this point exceeds the displacement pressure required by the
largest pore channel. This condition can be expressed in terms of the
basic capillary pressure equations.
On considering a distance, r = re - R,, where R, is the radius of the
largest grain determining the sizes of pore openings at the end face of
the core, the capillary pressure in the core at this point must be equal
to the displacement pressure, (Pc)~, of the wetting fluid; thus from
Equation 5.29:

(P,)D = CApN2[r: - (re - Rg)2] (5.31)

at the top face of the core:

(P& = CApN2(r2 - r;) (5.32)

dividing Equation 5.32 by 5.31 and neglecting the small term q:

(5.33)

breakthrough of the non-wetting phase will occur when (Pc)i > (Pc)~
which establishes the critical breakthrough capillary pressure: (PC)iy-t.
In order to evaluate Equation 5.33 quantitatively, R, and (Pc)~ must be
expressed in terms that can be measured or estimated. (Pc)~ can be
expressed in terms of the capillary pressure equation (Equation 5.1 1)
replacing cos 8 with Equation 5.10, where H = re/ri, and introducing
the grain radius, Rg, in place of the mean pore radius:

(5.34)

Melrose estimated that H assumes values between 4 and 6, which
can occur when the fluid-fluid interface is entering the constriction of a
cone-shaped capillary between two grains of equal size [ 181.
The Leverett J-function can be expressed as follows [2]:

(5.35)