Page 153 - Well Logging and Formation Evaluation

Production Geology Issues 143

=
Ÿ
(
gamma h) = (12* N h))* Â iN h ( ) ( V xi yi - V xi yi) 2 (10.1.3)
(
,
¢
¢,
i=1
where V xi¢,yi¢ = (known) value of the parameter at point xi¢, yi¢
V xi,yi = (known) value of the parameter at point xi, yi
h = distance from xi, yi to xi¢, yi¢
N(h) = the number of pairs that are a distance h apart.
A plot of gamma(h) vs. h constitutes the semivariogram. The semivar-
iogram captures the contribution to the total uncertainty when using a data
point that is a certain distance away from the point at which the estima-
tion is being made. Kriging involves finding a set of weighting factors
(done automatically within a computer) that minimizes the total uncer-
tainty in the estimate made at the intermediate point. Moreover, kriging
also provides the variance of the estimation error from which an error map
can be drawn.

10.1.4 Quantitative Analysis from Maps

While maps are invaluable in helping the petrophysicist and geologist
understand the areal variation of properties, they may also be used for
quantitative analyses. In most petroleum engineering departments, quan-
titative work is always done on the computer these days. However, it is
always recommended to make a reality check using more basic tech-
niques, since lack of full understanding of how software works, or bugs
in the program, can lead to erroneous results.
Initially we will show how GBV may be determined from maps, then
extend the concept to show how HIIP can also be determined. Consider
an oil reservoir where both the top and base of the structure have been
mapped, and the oil/water contact (OWC) is known. The first step is to
make an area-depth map for the top of the structure. This is done by mea-
suring the area contained within each contour, starting at the shallowest
and working gradually deeper, until one is at the first contour that falls
below the OWC.
The area contained within this contour, since it is an irregular shape, is
most often measured using a device called a planimeter, which (once
the area has been completely traced) will determine the area contained
therein. Obviously, since the planimeter measures only the area on the
paper, a conversion has to be made using the map scale. Hence, for
example, if the map is 1:25,000, a traced area of X square centimeters