Geology Reference
In-Depth Information
transforming the stochastic impedance realisations
with various statistical approaches such as linear
regression functions, collocated cokriging (Doyen
et al.,
1996
) and Bayesian classification (e.g. Coulon
et al.,
2006
). However, a relatively early development
was the co-simulation of lithofacies with impedance
(e.g. Torres-Verdin et al.,
1999
; Sams et al.,
1999
)).
The logic of using the seismic directly to condition
reservoir properties in the 3D model via the facies
concept is compelling (e.g. Saussus and Sams,
2012
).
For example, ensuring that elastic properties are
consistent say with a saturation height function is
difficult unless saturation is part of the inversion
model (Sams et al.,
2011
). Notionally, applying all
constraints simultaneously will lead to tighter integra-
tion and a more robust and consistent reservoir
model.
Since the work of Buland and Omre (
2003
) and
Buland et al. (
2008
), Bayesian inference has increas-
ingly been used to frame the model space from which
stochastic realisations are drawn (e.g. Eidsvick et al.,
2004
; Moyen and Doyen,
2009
; Escobar et al.,
2006
;
Merletti and Torres-Verdin,
2010
). In Bayesian
reasoning, the model space (or posterior distribution)
is the product of the prior information (i.e. the
distributions and spatial characteristics of elastic
parameters from well data, plus other constraining
geological information) and the likelihood of the prior
given the seismic observation (i.e. as determined by
the synthetic match to seismic). Added levels of
sophistication have been incorporated into the prior
model by some authors, for example with the use of
Markov random fields or Bayesian networks to define
dependencies and spatial couplings (e.g. Eidsvick
et al.,
2004
; Rimstad and Omre,
2010
).
Figure 9.34
shows a workflow based on the work of Saussus and
Sams (
2012
) and Sams et al. (
2011
), and
Fig. 9.35
illustrates typical outputs.
Given the level of data conditioning required and
the use of sophisticated algorithms, stochastic inver-
sion is usually performed by specialists on fields in the
appraisal or development stages. Although Bayesian
inversion software code has been made publicly avail-
able (e.g. Gunning and Glinsky,
2003
) there are as yet
a)
Figure 9.35
Volumes output from a
single geostatistical inversion realization
include facies, petrophysical parameters
(i.e porosity, volume of shale and
hydrocarbon saturation). The realistic
detail, heterogeneity and geological
plausibility arise from the inversion being
conditioned to geological as well as
elastic parameters (after Saussus and
Sams,
2012
).
b)
220
