Page 110 - Well Logging and Formation Evaluation

100 Well Logging and Formation Evaluation

estimated as follows. Take the mean and standard deviation of the various
average porosities as measured in all the wells. Say these are denoted by
(POR) and (POR) SD . From the Monte Carlo analyses, one has denoted an
uncertainty in the individual zonal average porosities of d. The best esti-
mate of the average porosity over the entire field is POR and the uncer-
tainty in POR is given by:

+ )
2
uncertainty in POR = ( ( ( POR) ) n d . (5.8.3)
2
SD
where n is the number of wells.
For determination of STOIIP, many parameters, including net/gross,
porosity, and S w may be input as distributions to a further statistical
package that will use Monte Carlo analysis to come up with a global
probability function for the STOIIP (or GIIP).
Most programs either require only a minimum and a maximum value
for the parameters or require a mean, standard deviation, min, and max.
In the former situation, it is recommended to take ± twice the uncertainty
as calculated above as the min/max. All values within this range are
treated as being equally likely. If a min, max, and SD are required, it is
recommended to use the uncertainty calculated above as the SD and to
take three SDs on either side of M as min/max, usually referring to
absolute minima/maxima (zero probability of values lying outside) with
something like a normal distribution about the mean. These are not the
same min/max as referred to in a boxcar distribution, in which they are
just ranges outside of which the values are unlikely to fall within a
confidence of about 70%.
A few concluding remarks about error analysis. With regard to the
Monte Carlo analyses, it is always necessary to use good judgment when
considering whether the uncertainties resulting are to be considered rea-
sonable. An experienced petrophysicist should already have a good feel
for the uncertainties in the average zonal parameters he is presenting,
which should roughly agree with those derived from the spreadsheets.
The sampling theory presented above assumed that n, the number of
samples, is large. If this is not the case (e.g., a structure penetrated by two
wells), then the results need to be treated with caution. Care should also
be taken in the event that all the wells are crowded in one part of the field
and there are large areas unpenetrated. This effectively means that the
sampling is not random. Of course, wells are never drilled “randomly” on
purpose, although looking at the actual locations of wells drilled in mature
fields, they may approximate randomness rather well!