Page 109 - Well Logging and Formation Evaluation

Advanced Log Interpretation Techniques 99

Above each column, it is necessary to derive randomly generated values
for r m , r f , m, n, and R w between allowable ranges.
At this point it should be noted that applying a range to both m and R w
is not really fair if they have been determined through a Pickett plot, since
any error in one will probably be corrected by adjusting the other so that
the points still go through the waterline. Hence I would apply a range to
one of the two parameters only if no water sand had been available for
calibration and R w has been chosen purely from produced water samples
or regional correlation. At the bottom of each column, average the S wpor
and then take the mean of all the runs and the standard deviation as before.
The mean S w is given by (SWPOR)average/(POR)average and the uncer-
tainty in S w is given by the standard deviation of SWPOR divided by
(POR)average.
Finally one should have arrived at mean and standard deviations for
net/gross, porosity, and saturation that fully take into account uncertain-
ties in all the input parameters. If you are using a saturation/height rela-
tionship instead of Archie, the same process can be applied, but choose
allowable ranges for your a and b values instead of m, n, and R w. I do not
believe it is necessary to take into account error in the poroperm rela-
tionships, S wirr , or fluid densities, since these would be compensated for
when making the log(J)-log(S wr ) plot. If, however, the saturation/height
relationship is derived entirely from core, you could consider adding a
term to accommodate the uncertainty in s.cos(q).
The second stage of the process involves looking at the uncertainties in
the mean values of these parameters for individual reservoir units over the
entire field. At this stage it is probably useful to digress a bit and cover
some elements of basic sampling theory. Imagine that one is trying to esti-
mate the mean value of people’s IQ by randomly sampling n people from
a parent population of N individuals. Say the parent population has a mean
IQ of M with a standard deviation of SD. The best way to estimate M is
to take the mean of the IQs measured on the sample of n people, denoted
by M n . Statistical theory states that if the SD of the sample of n people is
–
S n , the SD of the mean of the parent population is S n / ÷n.
If the accuracy of each individual IQ measurement is d, the overall
uncertainty (one standard deviation) in the value of M is given by:

uncertainty in M = ( ( S n ) 2 n + ). (5.8.2)
2
d
Hence, if we are trying to determine mean and uncertainty in the mean
of, say, the porosity in a reservoir unit over the entire field, this may be