Page 265 - Petrophysics 2E

238 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

Assuming the Humble equation is applicable, i.e.

0.81
F=-
+2
the porosity of the core sample is:

(b) The log-log plot of the resistivity index versus water saturation
normally yields a straight line in a homogeneous core. The saturation
exponent n is equal to the slope of this straight line, as indicated by
Equation 4.55.
The true resistivity of the rock sample when S, = 90% is:

A 2.835 x lo-*
& = r,- = 678 = 6.007 Q-m
L 0.032

The resistivity index IR for S, = 100% is unity. For Sw = 90% the
resistivity index is:

Rt 6.007
IR=-- - 1.301
k-m-

Table 4.7 shows the values of IR for other values of &.
Figure 4.25 is a plot of water saturation vs. the resistivity index.
The slope of the log-log straight line is -2.4 (found by regression).
Thus: n = 2.4.

TABLE 4.7
EXAMPLE RESULTS

S, (fraction) ro (a)
1 .ooo 52 1 4.616 1 .Ooo
0.900 678 6.007 1.301
0.800 913 8.089 1.752
0.730 1,151 10.197 2.209
0.640 1,510 13.378 2.898
0.560 2,255 19.978 4.328
0.480 3,135 27.774 6.017
0.375 5,270 46.689 10.115
0.350 6,820 60.421 13.090
0.300 10,400 92.138 19.962