Sequential Simulation with Complex Training Images using Search Tree Partitioning

Alexandre BoucherDept. of Environmental Earth System Science

Stanford University

SCRF 21st ANNUAL MEETINGMay 8, 2008

Two SNESIM Drawbacks

Size of the search tree• Function of TI, template size and # of categories

• Controls the simulation speed

Unrealistic training image• Requirements of training image do not conform to analogs

• Uses a single complex training image

• Affects pattern reproduction in an unknown manner

• Difficult to know if probability fields are consistent with TI

Current Practice : Probability Field

Encourages some classes at certain locations by providing pre-defined high local probability of occurrence

Current Practice : Regions Simulation

• Awkward from modeler perspective

• Possible incompatibility between training images

• Does not refer to a unique geological concept

Divide simulation grid into regions and simulate each region with a different training image

Search Tree PartitioningPartitioning TI into partition classes such that their associated patterns are

• homogenous

• can be efficiently stored in a search tree

Building imbricated search tree

1. Process the TI with spatial filters that respond to critical patterns

2. Transform these filter scores into partition classes

– Dual training image : Categories and the partition classes

3. Generate a vector of imbricated search trees

Simulation

1. Simulate the partition classes

2. Simulate the categories

– The partition classes act as a look-up table to retrieve the search tree.

– Adequate imbrication of the search trees ensure patterns reproduction

FracturesFractures with varying orientation

Simulation with a global search tree

Two options : 1 – Deconvolution of the patterns into regions2 – Generate partition classes that reflect the patterns

The trends are not reproduced

Generation of Partition ClassesSobel filters to detect the lineation direction

East-West gradient North-South gradient Average angle

Average angles clustered into5 partition classes

A search tree is build for each partition class

Patterns Recorded by the Paritition Classes

Build one search tree per partition : 5 small imbricated trees

Partition #1 Partition #2 Partition #5

Unconditional simulation associated with each search tree:

#1 #2 #3 #4 #5

Simulation with Search Tree Partitioning

1. Simulation of the angles using direct sequential simulation with a trend

2. Clustering the simulated angles into partition classes

3. Simulation of the fractures

Multiple-Facies Simulation

7 facies simulation

Three geologically meaningful partition classes

TI courtesy of Chevron

Grid upscaled: block size 5x5x5

Simulating the Partition Classes

1. Thickness for each layer is simulated using a 1-D direct sequential simulation

2. Simulation

Conditioning with Search Tree Partitioning

Building imbricated search tree1. Forward transform TI into ancillary data

2. Cluster simulated ancillary data into partition classes

– Dual training image : Categories and partition classes

3. Generate vector of imbricated search trees; one tree per partition class

Simulation1. Partition the actual ancillary data into partition classes

2. Simulate the categories

– Partition classes act as a look-up table to retrieve the search tree

– Adequate imbrication of search trees on the grid ensure patterns reproduction

Partition classes derived from ancillary data and used for

constraining/soft conditioning

Reference facies Layer 7 Reference facies Layer 8

ShaleConglomerateWater SandGas Sand

Constraining to Seismic Attributes

L. Stright

P-Im

peda

nce

S-Im

peda

nce

Vp/

Vs

Coarse Scale Seismic AttributesReference Layer 7 Test Case Layer 8

k-means

Classification from vector quantization

L. Stright

Reference facies Layer 8

ShaleConglomerateWater SandGas Sand

Partition Class Layer 8

Realization #2Realization #1

Simulations with search tree partitioning

Coarse Data Constrained Simulations

L. Stright

Downscaling Directional Continuity

No connection

E-W connection only

N-S connection only

N-S and E-W connection only

Extract directional connectivity in block of size 10x10

Upscaled connectivity index

E-W ConnectivityN-S Connectivity

Existence of a continuous path across the coarse pixel

Accuracy Assessment

Constraining directional connectivity index

Simulation #1 Simulation #2

0.340.610.570.770.62STP

0.230.210.150.680.39Tau-model

0.080.220.200.480.29No constraint

Global No EW NS EW and NSAccuracy assesment:

Accuracy of connection:

0.70.590.53

STPTau-modelNo constrain

Lessons Learnt

Defining partition classes• number of partition classes matters• must relate to the patterns (smart clustering)• can be simulated

Simulating partition classes• clustered from continuous simulation• simulated directly• choose the most suitable simulation algorithm

Advantages

Adds local information without distorting TI-derived ccdf

Improves on region approach by

- requiring only one training image

- implicitly modeling transitions between regions

Facilitates hierarchical framework

Provides soft conditioning to coarse scale measurements

Dichotomy : simulation - modeling

Modelers

• Focus at finding an analog

• Fewer compromises for algorithmic requirements

Geostatisticians

• Access to a larger set of training images

• Better visualization of the sought-after patterns

Efficient use of their respective strengths

Thank You

Questions?

Regions Approach

The transitions betweens regions are never modeled

A N-S fractures training images is rotated to the mean fractures angles for eacg partition classes