Page 51 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

Basic Principles, Definitions, and Data 39

where R is the resistivity in ohm-meters, r is the resistance in ohms, A is the
cross-sectional area in m2, and L is the length of the conductor in meters. As
seen in Figure 5-28, resistivity of water varies inversely with salinity and
temperature [41].
During flow through a porous medium, the tortuous flow paths cause the
flowing fluid to travel an effective length, L$ that is longer than the measured
length, L. Some authors have defined this tortuosity, 2, as (LJL) while (LJL)e
has been used by others.
Formation Resistivity Factor
The formation resistivity factor, FR, is the ratio of the resistivity of a porous
medium that is completely saturated with an ionic brine solution divided by the
resistivity of the brine:

(5-45)

where Ro is the resistivity (ability to impede the flow electric current) of a brine-
saturated rock sample in ohm-m, R, is the resistivity of the saturating brine in
ohm-m, and FR is dimensionless. The formation resistivity factor, which is always
greater than one, is a hnction of the porosity of the rock (amount of brine), pore
structure, and pore size distribution. Other variables that affect formation factor
include composition of the rock and confining pressure (overburden).
Archie [42] proposed an empirical fornula that indicated a pa-law dependence
of F, on porosity:
FR = $-" (5-46)
where t$ is porosity and m is a constant (commonly called the cementation factor)
related to the pore geometry. The constant, m, was the slope obtained from a
plot of FR vs. porosity on log-log paper. For consolidated, shale free sandstones,
the value of m ranged from 1.8 to 2. For clean, unconsolidated sands, m was
found to be 1.3, and Archie speculated that m might vary from 1.3 to 2 for
loosely or partly consolidated sands. Fquations 5-45 and 5-46 were also combined
by Archie to give:

so that a reasonable estimate of F, or Ro can be made if the slope, m,
is obtained.
Several other correlations [43-551, mostly empirical, between formation factor
and porosity have been reported in the literature and these are summarized in
Table 5-7.
From an analysis of about 30 sandstone cores from a number of different
reservoirs throughout the United States, Winsauer et al. [45] presented what is
now known as the Humble relation:
F, = 0.62$-*.'5 (5-48)