1. Complex Models from Simple Training Images
– using Auxiliary Variables
Christian Höcker (Baker Hughes | Reservoir Software)
All models and TI’s were generated with JewelSuite
2. • Non-stationarity is omnipresent in geological reality, at all
scales
• In facies modeling it affects
– facies proportions
– facies patterns
• With traditional geostatistic methods, one can honour lateral
variations in facies proportions with various techniques.
– Facies patterns remain unaddressed
– Users tend to over-condition simulations in order to reproduce
patterns they want to see
• The Auxiliary Variables method in the Impala MPS library offers
a more elegant method
Non-Stationarity
3. • Auxiliary Variables introduced by Chugunova et al. 2007
as an alternative mechanism to steer simulations
• Second method developed by Straubhaar et al. 2009;
implemented in Impala MPS
Non-Stationarity Handling with Auxiliary Variables
Training Image Auxiliary of TI Simulation
Auxiliary Variable used
for Simulation
From Chugunova, Hu & Lerat 2007
4. Impala MPS:
Handling Non-stationarity with Auxiliary Variables
Non-stationary training image with
associated aux variable ‘distance to coast’
Training Image
with aux variable
aux variable &
rotation data in
Simulation Model
Simulation
Straubhaar et al. 2009
implemented in Impala MPS library
In JewelSuite, ‘Auxiliary Variables’
are called ‘Trend Properties’
5. Example: channels cutting into carbonate platform
during sea level drop
Trivial Conceptual
2D Training Image
6. Rotation by azimuth
pointing away from
central ‘watershed’
Both Training Image
and Simulation with
overlay of Trend Data
Conditioning of Simulation by Rotation and
Trend Property ‘Facies Belt’
7. Trend Property ‘Depositional Energy’
Example: single conglomeratic turbidite channel
half-sided Training Image:
conglomeratic turbidite with trend
property ‘depositional energy’
Measurement ‘distance to channel axis’ clipped and
scaled to channel width ‘depositional energy’;
azimuth for rotation derived from trend property
8. Trend Property ‘Depositional Energy’
Example: single conglomeratic turbidite channel
half-sided Training Image:
conglomeratic turbidite with trend
property ‘depositional energy’
Measurement ‘distance to channel axis’ clipped and
scaled to channel width ‘depositional energy’;
azimuth for rotation derived from trend property
9. Trend Property ‘Depositional Energy’
Example: bifurcated turbidite channel
half-sided Training Image:
conglomeratic turbidite
with aux variable
‘depositional energy’
Measurement ‘distance to channel axis’ clipped and
scaled to channel width ‘depositional energy’;
azimuth for rotation derived from trend property
10. Trend Property ‘Depositional Energy’
Example: turbidite fan geometry
Depositional Energy in vertical dip & strike sections
11. • Nearly all variations of depositional characteristics can be
captured in an intuitive 3-axis system of geologically
meaningful parameters
Parameterization of Depositional Conditions
• along depositional gradient or
• proximal – distal or
• distance to coast
• along depositional strike or
• depositional energy or
• net-to-gross
• accommodation space or
• subsidence or
• completeness of vertical patterns
12. • Auxiliary Variables in Impala provide easy-to-use means
for Trend Handling in MPS.
With Auxiliary Variables one can …
– … use geologically meaningful parameters as trend
properties, like ‘distance to coast’ and ‘depositional energy’
– … use training images that extend across facies belts, e.g.
fluvio-marine interface, reducing the need for segmentation
– … get good simulation results using simple training images
and small templates as larger-scale context can be
described in the auxiliary variable
– … achieve 3D-consistency in simulation results with 2D
training images
Conclusions Hereto
14. Point Bar Deposits of Meandering Rivers
highly sinuous meandering river
very difficult to model with MPS …
… but this is not what is typically preserved as meandering river deposit
point bar deposit
lateral accretion surfaces
inside point bar units
15. Symmetry / Geometry Opposition
point bar units point in opposite directions
across a +/- central line in the channel belt
‘geometry opposition’
can be modeled if ‘left’ and ‘right’ with
respect to the axis are defined in both
training image and simulation model
a symmetry plane occurs inside point bar units,
w.r.t. the shape of lateral accretion surfaces
and the distribution of lithofacies
can be used modeled symmetry is defined in
both training image and simulation model
16. Simulation result at 2nd level: distribution of point bars in meander belt;
modeled property: direction of point bar
Simulation results at each level are translated into a trend property for the
next deeper level of MPS simulation
Multi-Scale Simulation with Nested MPS
Example: Tidal Drapes in Meander Belt
1st level: meander belt on floodplain (2 belts in this example)
2nd level: point bar lobes in meander belt
3rd level: heterogeneity in point bar (4 facies in lateral accretion geometry)
3rd level - 3D
2nd level - 2D
1st level - 2D
training images
Simulation result at 2nd level: distribution of 4 facies with different flow
properties in point bars within a meander belt
17. Monotonous 3D Training Image representing
heterogeneity inside Point Bar units
JewelSuite contains dedicated methods for creation of 3D Training Images. Paint Tools can be applied in 3D
but also on 2D sections the information of which can be extended to 3D using functions.
The TI above has been generated by drawing the central cross-section (I slice) and extending the pattern to
the complete I range by applying an exponential function.
18. Details of Facies Configurations
in Meander Belt Model
18
Central cross-section with lateral accretion surfaces in point bar deposits;
horizontal slice: facies with overlay of point bar azimuth (lobes)
Detailed shapes in point bar;
only lag facies rendered in 3D
lateral accretion surfaces
size/shape of meander lobes
varies within geological bounds;
each lobe has its own general
accretion direction
20. • Approach is generic and can be applied to all low to high-
sinuosity river deposits and variations in their internal
architecture
• Need only 3-4 training images for patterns of point bar
units inside channel belts and 2-3 images for configuration
of lateral accretion inside point bars
• Symmetry and geometrical opposition can also be found
in many other depositional environments
• But workflow depends on computational methods to
analyze higher level simulations and generate
symmetry/opposition value (patent pending)
Conclusions Meander Belt Trials
21. • For complex multi-scale facies patterns a nested modeling
approach is easier to control and much faster to run than
using a single-pass approach.
– Training Images can be simple
– Higher levels can often be done in 2D
• 2-3 levels can bridge scales between km-scale patterns
and internal heterogeneity of flow parameters relevant for
simulation of fluid flow.
• The ‘Trend Property’ or ‘Auxiliary Variable’ method is an
essential mechanism of communicating results of large-
scale simulations to lower nesting levels.
Monotonous Training Images can create complex
simulation results
Take-Aways from Nested MPS Simulation Trials
