Page 256 - Petrophysics 2E

FORMATION RESISTIVITY FAaOR 229

If this Berea Sandstone core has a length L = 6 in., the actual mean
length of the flow path of an electric current La can be estimated
from the definition of tortuosity @quation 3.20):

For viscous fluid flow through this Berea Sandstone core, the value
of La will be slightly closer to the value of L because the stagnant
porosity will be lower than 0.143 and the flowing porosity will be
higher than 0.073. In any case, the large value of z indicates that the
internal geometry of porous systems is extremely complex, which is
in accordance with microscopic observations indicating that regions
of stagnation or traps should be the rule rather than the exception,
especially from the standpoint of the flow of electric current.

CORRELATION BETWEEN FR AND WATER SATURATION

In a formation containing oil and/or gas, both of which are
nonconductors of electricity, with a certain amount of water, the
resistivity is a function of water saturation S,. For the same porosity,
the true resistivity, Rt, of this formation is larger than & (the resistivity
of a formation 100% saturated with brine), because there is less
available volume for the flow of electric current. Archie determined
experimentally that the resistivity factor FR of a formation partially
saturated with brine can be expressed by the following relation [2] :

(4.53)

Substituting for FR from Equation 4.40 into Equation 4.53 gives:

(4.54)

where: Rt = true resistivity of formation containing hydrocarbons and
formation water.
R, = resistivity of formation when 100% saturated with water.
n = saturation exponent.

The ratio R&, is commonly referred to as the resistivity index IR.
If the formation is totally saturated with brine, i.e., R, = Rt, the resistivity
index is equal to one. IR is greater than one when hydrocarbons are
present in the formation. The resistivity index is then a function of the