Page 58 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

46 Reservoir Engineering

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These samples included 569 core plugs (from Alaska, California, Louisiana,
Colorado, Trinidad, Australia, and the Middle East) plus 28 samples from
Winsauer et al. [45], 362 samples from Hill and Milburn [49], 788 from Carothers
[52], and 85 samples from other sources [54].
In a recent paper [55], Perez-Rosales presented the following theoretical
expression:

FR = 1 + G(I$-" - 1) (5-59)

and a generalized equation for sandstones:
F, = 1 + 1.03(Q,-'.'~ - 1) (5-60)
Perez-Rosales notes that the previous expressions are fundamentally incorrect
since they do not satisfy the requirement that F, = 1 when Q, = 1. A graphical
comparison of expressions, provided by Perez-Rosales, is shown in Figure 5-32
for Equations 5-48, 5-58, and 5-60. In porosity ranges of practical interest, the
three expressions yield similar results.
Coates and Dumanoir [56] listed values for the cementation exponent of the
Archie equation for 36 different formations in the United States. These data
are presented in the following section under "Resistivity Ratio."
In the absence of laboratory data, different opinions have existed regarding
the appropriate empirical relationship. Some authors [57]' felt that the Archie
equation (Equation 5-46) with m = 2 or the Humble equation (Equation 5-48)
yields results satisfactory for most engineering purposes, but Equation 5-50 may
be more valid (these authors point out that the relationship used should be based
on independent observations of interest). Another opinion was that, while the
Humble relation is satisfactory for sucrosic rocks and the Archie equation with
m = 2 is acceptable for chalky rocks, in the case of compact or oolicastic rocks
the cementation exponent in the Archie equation may vary from 2.2 to 2.5 [58].
Based on the more recent work of Timur et al. [54], it appears that Equation
5-58 may be more appropriate as a general expression for sandstones, if indi-
vidual formation factor-porosity relationships are not available for specific cases.
Water in clay materials or ions in clay materials or shale act as a conductor
of electrical current and are referred to as conductive solids. Results in Figure
5-33 show that clays contribute to rock conductivity if low-conductivity, fresh
or brackish water is present [59,60]. The effect of clay on formation resistivity
depends on the type, amount, and distribution of clay in the reservoir, as well
as the water salinity. Values of m in Equation 5-49 for several clays are given in
Table 5-8 [61].
Other variables that affect resistivity of natural reservoir rocks include
overburden pressure and temperature during measurement. The value of the
cementation exponent, m, is normally higher at overburden conditions [62],
especially if porosity is low or with rocks that are not well-cemented. Thus, F,
increases with increasing pressure. Although the effect of temperature depends
on clay content of the sample, FR tends to increase with increasing temperature,
but the effect is not as great as pressure [63,64]. At a fixed pressure, F, may
go through a minimum and then increase as temperature is increased; the
combined increase of both temperature and pressure will cause an increase in
F, [64]. Factors that affect the exponent, m, and the coefficient, a, in the
modified Archie expression (Equation 5-49) are summarized in Tables 5-9 and
5-10, respectively [65].