Page 245 - Petrophysics 2E

2 18 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

Figure 4.8. Ideal porous material of n straight cylindrical capillaries.

would be transmitted if the entire bulk volume conducted to the same
degree as the water [6].
Assuming the saturated porous rock sample in Figure 4.2 can be
represented by an equivalent system of n straight capillary tubes as in
Figure 4.8, the relationship between A, the total cross-sectional area of
the block sample of length L, and An (= nnr:), cross-sectional area of
n capillary tubes of length L, is:

An = $A (4.26)

where $ is the fractional porosity of the rock sample. The resistivity of
saline solution in the capillaries is:

Dividing Equation 4.3 by Equation 4.27 gives FR or:

Ro
A Iwc
FR = - -- (4.28)
=
Rwc An Io
Assuming I,, = Io, because the system of n capillaries is supposed to be
equivalent to the porous rock sample, and substituting for An (Equation
4.26) in Equation 4.28, one obtains:

1
Fn=5 (4.29)

This is the simplest relationship between the formation resistivity
factor, FR and porosity. Oil-bearing rock, however, is much more
analogous to a container filled with sand than it is to parallel capillaries
embedded in a rock matrix. Consequently, the actual formation
resistivity factor value is considerably greater than that obtained using
Equation 4.29.