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78
JPT • NOVEMBER 2006
Abstract
Some engineers are skeptical of statistical, let alone geosta
tistical, methods. Geostatistical analysis in reservoir charac
terization necessitates an understanding of a new and often
unintuitive vocabulary. Statistical approaches for measuring
uncertainty in reservoirs is indeed a rapidly growing part of
the bestpractice set of methodologies for many companies.
For those already familiar with the basic concepts of geosta
tistics, it is hoped that this overview will be a useful refresher
and perhaps clarify some concepts. For others, this overview
is intended to provide a basic understanding and a new level
of comfort with a technology that may be useful to them in
the very near future.
Introduction
Geoscientists and geological engineers have been making
maps of the subsurface since the late 18th century. The evo
lution of our ability to predict structure beneath the surface
of the Earth has been a complex interaction between quanti
tative analysis and qualitative judgment. Geostatistics com
bines the empirical conceptual ideas that are implicitly sub
ject to degrees of uncertainty with the rigor of mathematics
and formal statistical analysis. It has found its way into the
field of reservoir characterization and dynamic flow simula
tion for a variety of reasons including its ability to success
fully analyze and integrate different types of data, provide
meaningful results for model building, and quantitatively
assess uncertainty for risk management. Additionally, from a
management point of view, its methodologies are applicable
for both geoscientists and engineers, thereby lending itself to
a shared Earth model and a multidisciplinary workforce.
Why Geostatistics?
Fig. 1
depicts two images of hypothetical 2D distribution
patterns of porosity. Fig. 1a shows a random distribution of
porosity values, while Fig. 1b is highly organized, showing a
preferred northwest/southeast direction of continuity. While
this difference is obvious to the eye, the classical descriptive
summary statistics suggest that the two images are the same.
That is, the number of red, green, yellow, and blue pixels
in each image is the same, as are the univariate statistical
summaries such as the mean, median, mode, variance, and
standard deviation (Fig. 1c). Intuitively, as scientists and
engineers dealing with Earth properties, we know that the
geological features of reservoirs are not randomly distrib
uted in a spatial context. The reservoirs are heterogeneous
and have directions of continuity in both 2D and 3D space
and are products of specific depositional, structural, and
diagenetic histories. Strangely, that these two images would
appear identical in a classical statistical analysis is the basis of
a fundamental problem inherent in all sciences dealing with
spatially organized data. Classical statistical analysis inad
equately describes phenomena that are both spatially con
tinuous and heterogeneous. Thus, use of classical statistical
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 Spring '10
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