Page 169 - Petrophysics
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142 PETROPHYSICS: RESERVOIR ROCK PROPERTIES
(2) the cross-sectional area of each tube, Aa, is constant; and
(3) the fluid path and the electric current path are same and the
true conductivity, i.e., the reciprocal of resistivity, of the bundle
of tubes is:
where C, is the water conductivity and m is the cementation factor.
Because the apparent conductivity Ca of a block having a cross-sectional
area A and length L is related to the true conductivity C& by the following
expression:
(3.71)
where A is the cross-sectional area of all tubes, then
(3.72)
assuming that the bundle-of-tubes model contains n tubes, the
conductivity of the ith tube (Ci) can be defined as:
(3.73)
where is the length of the ith tube.
The porosity of the tube is unity. The apparent conductivity of the
block is the sum of the individual conductivities of all the tubes. Thus:
(3.74)
From the assumption that A2 is constant:
(3.75)
By definition:
(3.76)