Page 335 - Petrophysics 2E

304 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

Calculate Sw, using the following three methods: (a) Archie,
(b) Simandoux, and (c) approximate shale relationship. Compare
results. Assume the saturation exponent n is equal to 2.
9. (a) Show that the Waxman and Smits relationship for calculating
S, sands with dispersed clays may be written as [ 281 :

The following parameters correspond to a shaly (clayey) sand
interval

Qv = 0.40 meq/ml Rt = 22 ohm-m

$ = 0.25 R, = 6.1 ohm-m
m* = 1.65 n* = 2.0

(b) Estimate the water saturation in this interval.
(c) Calculate the resistivity index and the formation factor.
(d) What is the value of h?

10. The total shale model, i.e., the Simandoux equation, may be
rewritten as:

Rt
-- - aRw
Gsh Oms$

(a) Derive the equation of the total shale group Gsh and prove
mathematically that, for intervals with constant aRw and &,,
a log-log plot of Rt/G,h vs. $ should result in a straight line with
a slope of -m.
(b) Develop a trial-and-error method for calculating a, m, and Rw .
(c) Table 4C shows data obtained from a well in a shaly (clayey)
formation. Intervals 4 and 5 are known to be 100% water satu-
rated. Analyses of rock samples indicate the existence of both

TABLE 4C
Zone Rt Porosity (“A) Vsh (“h)

1 12.0 26.5 0.12
2 11.0 24.2 0.17
3 12.0 25.9 0.15
4 2.6 27.6 0.00
5 2.5 31.0 0.00