Page 66 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

54 Reservoir Engineering

where R, is the resistivity of the rock at some condition of partial water
saturation, S, and R, is the resistivity of the rock when completely saturated
with water or brine.
Citing the work of Martin et al. [74], Jakosky and Hopper [75], Wyckoff and
Botset [%I, and Leverett [77], in which the variation in resistivity with water
saturation was studied, Archie [42] plotted the resistivity ratio versus Sw on log-
log paper (see Figure 536). For water saturations down to about 0.15 or 0.20,
the following approximate equation appeared to hold, regardless of whether oil
or gas was the nonconducting fluid
S” = (%) (5-68)
I/n

where n has been commonly referred to as the saturation exponent. For clean
sands and for consolidated sandstones, the value of n was close to 2.0, so the
approximate relation was given by Archie as:

By substituting the equation for Ro (refer to Equation 5-47), Archie presented
the relationship between water saturation, formation resistivity factor, brine
resistivity, and the resistivity of the rock at the given Sw:

I IO IO0
RESISTIVITY INDEX . I

Figure 5-36. Variation of resistivity index with water saturation [42].