The Rock Model - Reservoir Model Design - page 38

The shape of the semivariogram model can
be derived from any data set, but the dataset is
only a sample, and most likely an imperfect
one. For many datasets, the variogram is diffi-
cult to estimate, and the modeller is therefore
often required to choose a variogram model
'believed' to be representative of the system
being modelled.

vertical variogram

g

horizontal variogram

anisotropy

2.6.1.4 Variograms and Anisotropy
A final feature of variograms is that they can vary
with direction. The spatial variation represented
by the variogram model can be orientated on any
geographic axis, N-S, E-W, etc. This has an
important application to property modelling in
sedimentary rocks, where a trend can be
estimated based on the depositional environment.
For example, reservoir properties may be more
strongly correlated along a channel direction, or
along the strike of a shoreface. This directional
control on spatial correlation leads to anisotropic
variograms. Anisotropy is imposed on the
reservoir model by indicating the direction of
preferred continuity and the strength of the con-
trast between the maximum and minimum
continuity directions, usually represented as
an oriented ellipse.
Anisotropic correlation can occur in the hori-
zontal plane (e.g. controlled by channel orienta-
tion) or in the vertical plane (e.g. controlled by
sedimentary bedding). In most reservoir systems,
vertical plane anisotropy is stronger than hori-
zontal plane anisotropy, because sedimentary
systems tend to be strongly layered.
It is generally much easier to calculate vertical
variograms directly from subsurface data,
because the most continuous data come from
sub-vertical wells. Vertical changes in rock
properties are therefore more rapid, and vertical
variograms tend to have short ranges, often less
than that set by default in software packages.
Horizontal variograms are likely to have much
longer ranges, and may not reach the sill at the
scale of the reservoir model. This is illustrated
conceptually in Fig. 2.25 , based on work by
Deutsch ( 2002 ). The manner in which
horizontal-vertical anisotropy is displayed (or
calculated) depends very much on how the well
data is split zonally. If different stratigraphic

distance (lag)

Fig. 2.25 Horizontal-vertical anisotropy ratio in
semivariograms (Redrawn from Deutsch 2002 , # Oxford
University Press, by permission of Oxford University
Press, USA ( www.oup.com ))

Table 2.1 Typical ranges in variogram anisotropy ratios
Element

Anisotropy ratio

Point bars 10:1-20:1

Braided fluvial 20:1-100:1

Aeolian 30:1-120:1

Estuarine 50:1-150:1

Deepwater 80:1-200:1

Deltaic 100:1-200:1

Platform carbonates 200:1-1000:1

From Deutsch ( 2002 )

zones are mixed within the same dataset, this
can lead to false impressions of anisotropy. If
the zones are carefully separated, a truer impres-
sion of vertical and horizontal semivariograms
(per zone) can be calculated.
At the reservoir scale, vertical semivariograms
can be easier to estimate. One approach for
geostatistical analysis which can be taken is there-
fore to measure the vertical correlation (from well
data) and then estimate the likely horizontal
semivariogram using a vertical/horizontal anisot-
ropy ratio based on a general knowledge of sedi-
mentary systems. Considerable care should be
taken if this is attempted, particularly to ensure
that the vertical semivariograms are sampled
within distinct (deterministic) zones. Deutsch has
estimated ranges of typical anisotropy ratios by
sedimentary environment (Table 2.1 )andthese
offer a general guideline.