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

estimate.

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
!

z

1,

z

i
!

¼

ð

3

:

26

Þ

;

0,

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

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).

Variable

Truncated Gaussian Simulation

(TGS) applies a threshold value to

a Guassian random field to identify

a facies or rock group (e.g. sand).

Threshold

Variable

Sequential Indicator Simulation

(SIS) treats the data as a discrete

(binary) variable defined by an

indicator (e.g. seismic impedance).

p<z

p>z

Variable

Fig. 3.23
Illustration of the different methods for property modelling using Gaussian simulation