Page 82 - Well Logging and Formation Evaluation

72 Well Logging and Formation Evaluation

C wa axis gives 1/R w, and the intercept for Q vn = 1.0 gives R wsh. Other
equations that are commonly used are:

Dual-water model:

1 R t = S w 2 (F* R w + BQ S F (5.1.13)
)
*
w
v
where
m
-
F = f . (5.1.14)
Simandoux:

n
S w = A R w *f - m * {1 R t - V sh * S R sh } (5.1.15)
*
w
where R sh is the resistivity of the shale.

Indonesia equation:

A R w }
S w = R t - ( 1 n) * { V sh (10 V sh 2 ) R sh + f ( m ) 2 ( * ) - ( 2 n) (5.1.16)
Since Waxman-Smits fulfills all the criteria I require from a shaly sand
equation (i.e., it introduces a clay conductivity element that is related to
the amount of clay as determined by the logs), I have only rarely used
other equations during my career. As stated in Chapter 3, I would always
prefer to derive saturations for STOIIP (stock tank oil initially in place)
and GIIP (gas initially in place) using a saturation/height function cali-
brated against good-quality core measurements.

Exercise 5.1. Shaly Sand Analysis

1. Using data from the water leg in the test1 well, make a relationship of
BQ v to porosity. Also derive R w from the plot.
2. Using the core data in Appendix 2, calculate m* and n*.
3. Calculate saturations using the Waxman-Smits equation and make a
new table of sums and averages.
4. How do the Waxman-Smits saturations compare with those derived
using Archie and those from the core-derived J function?