Page 372 - Petrophysics 2E

340 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

using the hyperbolic expression (Equation 5.44). Refer to Rajan’s paper
for the details of the derivation [22]. The general solution is:

(5.52)

where:

(5.53)

Rajan used an analytic expression to obtain theoretical pseudo-capillary
pressure data that were used to compare the various solutions
(Figure 5.19). Curve 2 describes the Pc vs. S data from the analytic
expression (shown on the illustration). The pXudo-(P,)i vesus Si data
obtained from Equation 5.52 is illustrated by Curve 3, which exactly
matches the pseudo-experimental data from the analytic expression.
Curve 1 shows the results obtained using the Hassler and Brunner
approximation (Equation 5.43), which gives calculated capillary pressure

10-

ip-

d
[r
fi
w
B

5 4-
d
2 S = 0.25 + 1.5/Pc
0 2-

0.
0 0.2 0.4 0.6 0.8
SATURATION (S)

I
--. HASSLER - ANANllc 8 WAN --.-. WMSW
Figure 5.19.Agreement between various methods for calculation of the inlet
saturation versus capillarypressure CS = 1.0 for Pc < 2; S= 0.25 + 1.5/Pc for Pc >2).