Page 246 - Petrophysics

FORMATION RESISTMTY FACTOR 219

CORRELATIONS BETWEEN FR AND TORTUOSITY

The departure of the porous system from being equivalent to a system
made up of straight capillary tubes is measured by the tortuosity factor,
7, which is defined by Equation 3.20, i.e., T = where L is the
length of the rock sample, and La is the actual length of the flow path as
shown in Figure 4.9. Using Equation 4.27, the resistivity of the brine in
the capillaries of length La is:

Dividing Equation 4.3 by Equation 4.26 gives (for Iwc = Io):
1La fi
Fp, = -- - (4.31)
9L 9

Cornell and Katz derived a slightly different expression. Their deriva-
tion was based on the inclined capillary tube model of porous media
shown in Figure 4.10 [7]. For an inclined capillary tube, Equation 3.13
becomes:

(4.32)

or

(4.33)

Substituting for An in Equation 4.27, one obtains:

E 9A(L/Ia)
Rwc = - (4.34)
Iwc L
Dividing Equation 4.3 by Equation 4.34 (assuming Iwc = Io) gives:

(4.35)

Equation 4.35 gives the right order of magnitude for the formation
resistivity factor in naturally fractured reservoirs. For the theoretical case
of a horizontally fractured formation, the tortuosity factor z is equal to 1,
and consequently:

1
F=- (4.36)
9