Page 263 - Petrophysics

236 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

Manipulating Equations 4.40, 4.54, and 4.55 yields a general relation-
ship, which can be used to estimate the cementation factor m and
Humble constant a:

1
log @ = - - [log Rt - log (aR,) - log IR] (4.58)
m

Thus, a plot of Cp vs. Rt on a log-log graph s,,ould yield a straight line
with a slope (- l/m) for 100% water-saturated zones, having constant
resistivity index, IR and aR,. Figure 4.24 shows such a plot for the case
of a homogeneous sandstone oil reservoir.
The water zones, where IR = 1, form a straight line with a slope
approximately equal to 2. When Cp = 100% and IR = 1, Equation 4.58
reduces to log Rt = log(aR,). Therefore, the product aR, can be deter-
mined directly from Figure 4.24 by simply extrapolating the straight line
to Cp = 100% and reading the corresponding value of aR, on the Rt
axis. Knowing the water resistivity R,, from Figure 4.24 for instance,
one can calculate a. The log-log plot of Cp vs. Rt also can be used to
estimate the water saturation of the reservoir from Equation 4.55, i.e.,
S, = by assuming the cementation factor m and the saturation
exponent n are equal. The limitation of this equation is that a significant
number of water-bearing zones of constant a, m, and R, must be
available [ 181.

100

I

0.1 1 10 100
Total Resistivity, ohm-m

Figure 4.24. Porosity us. total resistivity for S, = 100%.