Page 369 - Petrophysics 2E

CENTRIFUGE MEASUREMENT OF CAPILLARY PRESSURE 337

30
PERMEABILITY (MICRO-METER)Y x lO"3

- ONE-INCH PLUG ------- TWO-INCH PLUG

Figure 5.18. Estimated relationship between the critical breakthrough capillav
pressure and permeability for the Beckman PIR-20 and RIR-I 65 rotors for an air-oil
system with 25% porosity.

- 1
S = - 1 S x d(pgL) (5.39)
PgL
The total pressure across the core is:

pc = PgcL (5.40)
Using the assumption that ri = re, Equation 5.39 becomes synonymous
to the inlet pressure of the core, where (Pc)i = p&L; therefore:

(5.41)

differentiating and rearranging,

d[S x (P,)i] = S x d(P,) (5.42)
dS
Si = d[d(P,) x S x (P,)i] = S x (Pc)i x - (5.43)
Wc)i

To calculate the inlet saturation as a function of the inlet capillary
pressure, the derivative of the average saturation with respect to