Page 232 - Petrophysics 2E

FORMATION RESISTIVITY FACTOR 205

rt-------rl

Figure 4.1. Resistivity measurement of salty water (11.
, ” +;r- ,

E

+L----C(
Figure 4.2. Resistivi@ measurement of aporous rock sample [l].

Dividing Equation 4.3 by Equation 4.2 and canceling similar terms gives

Archie defined this ratio as the “formation resistivity factor FR” or [2]:

Ro
FR - (4.5)
RW
For a given value of E, Iw will be greater than Io. Hence & will be greater
than Rw and FR will always be greater than unity. Figure 4.3 shows the
qualitative effect of brine resistivity (assuming all other factors, such
as porosity, cementation, and amount of shale remain constant) on FR
for limestone and clean sand, and shaly (“dirty”) sand. The formation
factor is essentially constant for clean sand and limestone. For dirty or
shaly sand, FR decreases as brine resistivity, Rw , increases; and although
& increases, it does not increase proportionately because the clay in
the water acts as a conductor. This effect is dependent upon the type,
amount, and manner of distribution of the clay in the rock. Equation 4.5