Geoscience Reference
In-Depth Information
give a spatial statistical model of reservoir
properties. A good geostatistical model should
give a realistic picture of petrophysical structure
and variability and can be used for flow simula-
tion and for studies to define drilling targets.
However, one realisation is only one possible
outcome, and many realisations normally need
to be simulated to assess variability and proba-
bility of occurrence. To put this in practical
terms, a single realisation might be useful to
define static heterogeneity for a flow simulation
model, but a single realisation would be little
value in planning a new well location. For well
planning or reserves estimation, the average
expectation from many realisations, or a Kriged
model, would be a more statistically stable
Truncated Gaussian Simulation (TGS) is a
simple modification of SGS where a particular
threshold value of the simulated Gaussian ran-
dom field is used to identify a rock element or
petrophysical property group, such as porosity
(Journel and Alabert 1990 ). The indicator trans-
form is defined by:
if z !
i !
if not
where z is the cut-off value for a field of values !
The field ! could be derived from, for exam-
ple, porosity data, the gamma-ray log or seismic
impedance. The important decision is the choice
of the indicator value. Both these methods are
useful for modelling rock elements (Sect. 2.7 ) as
well as for modelling property distributions
within elements.
Figure 3.23 illustrates the different methods of
Gaussian simulation. The methods can be used in
a number of ways, for example to define several
nested groups of facies and the properties within
them. Gaussian simulation is an essential part of
the tool kit for property modelling, and also a key
tool for data integration, especially for combin-
ing well data with seismic inversion data. Doyen
( 2007 ) gives an in-depth account of seismic-
based rock property modelling including a
detailed description of the application of the
SGS and SIS methods to seismic datasets.
X (Fig. 3.23 ). Sequential Indicator Simulation
(SIS) uses a similar approach but treats the
conditioning data and the probability function
as a discrete (binary) variable from the outset
Sequential Gaussian simulation
(SGS) gives a realisation of the
spatial distribution of a correlated
random variable (e.g. porosity).
Truncated Gaussian Simulation
(TGS) applies a threshold value to
a Guassian random field to identify
a facies or rock group (e.g. sand).
Sequential Indicator Simulation
(SIS) treats the data as a discrete
(binary) variable defined by an
indicator (e.g. seismic impedance).
Fig. 3.23 Illustration of the different methods for property modelling using Gaussian simulation
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