Page 294 - Petrophysics 2E

LABDERIVED EVAL.UATION OF SHALY 265

where: Ct = specific conductance of a partially water-saturated sand.
f T; = geometric factor.
S, = water saturation.

The factor fT; is a function of porosity, water saturation and pore
geometry, but independent of clay content. f$ tends to increase with
increasing oil saturation. For clean sands F* and f T; become, respectively,
FR = Cw/Co = Rt/Rw and fc = Cw/Ct = Rt/Rw, and the resistivity index
is equal to:

By analogy, for shaly sands one can obtain:
E (4.135)
-_ - s-n*
F*
where n* is the saturation exponent for shaly sand. Combining Equations
4.127, 4.133, 4.134, and 4.135 and solving for the resistivity index, one
obtains:

(4.136)

or, in terms of water resistivity:

(4.137)

where Rw and CeqQv are expressed in ohm-m and (ohm-m)-’,
respectively. If Qv is expressed in equil/L, Ceq can be correlated by:

Ce, = 4.6 (1 - 0.6e0,”’Rw) (4.1 38)

Figures 4.37 and 4.38 show logarithmic plots of the resistivity index
as a function of water saturation for different values of R, and Qv,
respectively. Waxman and Smits observed that even small amounts of
clay have a considerable effect on the resistivity index and that Equation
4.137 predicts higher oil saturation estimates than are obtained from
conventional clean sand equations.
A laboratory study by Waxman and Thomas involving a large number
of shaly rock samples from seven different fields demonstrated excellent
agreement between experimental oil saturations and those calculated