Page 81 - Well Logging and Formation Evaluation

Advanced Log Interpretation Techniques 71

Similar to the Pickett plot made with Archie, the value of the hydro-
carbon saturations is not very sensitive to the value of m*, provided that
a water sand is used to calibrate the value of R w. Note that the value of
R w derived may not correspond to the salinity expected from production
tests. This value also includes the effect of the clay-bound water, which
may be fresher than the free water and will not flow during production.
Hence, it is typically found that R w appears higher than expected.
The effect of using Waxman-Smits will usually be large only for rela-
tively high values of R w. This is because the factor R wBQ v becomes small
compared with unity if R w is small (saline environments). In this situation
the calculated S w will differ only very slightly from that calculated using
Archie’s model.
Note that when the equation is applied, a computational complication
arises from the fact that S w appears on both sides of the equation. This can
be easily overcome as follows. Initially assume that the value of S w in the
right-hand side of equation 5.1.1 is unity. Calculate S w and reinsert the
new value of S w into the right-hand side of the equation. Continue in this
way until the S w on the left-hand side ceases to change beyond 0.001 with
successive iterations. Typically, five or so iterations are sufficient.
Another way to apply Waxman-Smits method is by the so-called nor-
malized Q v method, as proposed by Istvan Juhasz. Readers are recom-
mended to read the relevant paper from the Society of Petrophysicists and
Well Log Analysts that covers this method in detail (see references). A
condensed version will be given here. Juhasz shows that the Waxman-
Smits equation may be rearranged in the form:

S w = ( [ f - m* R t ) ( * S w * R wsh * R w ) ( Q vn * R w + ( S w - Q vn )* R wsh )] 1 n* (5.1.10)

where

Q vn = V sh *ff (5.1.11)
sh
1 R wsh = f - m* R sh (5.1.12)

R sh = resistivity of the shale
f sh = porosity of the shale.

The parameter m* may be determined from plotting log(R t ) vs. log(f)
in water-bearing shaly zones (not clean zones), since the slope of the line
is equivalent to m*. The parameters R wsh and R w may be determined from
plotting C wa vs. Q vn , since the intercept of the points for Q vn = 0 on the