1. Pejman Tahmasebi and Jef Caers
Stanford Center for Reservoir Forecasting
MS‐CCSIM: accelerating pattern‐based geostatistical simulation categorical variables using a multi‐scale search in Fourier space
Pejman Tahmasebi and Jef Caers

2. Pattern based multiple point geostatistics
Advantages
Disadvantages
Fast
Better Pattern reproduction
Conditioning
Less variability
Pattern patchiness
CPU time

3. Using adaptive recursive template splitting
Conditional CCSIM
Multiple-point geostatistical modeling based on the cross-correlation functions, Computational Geosciences, 2012
MS‐CCSIM: accelerating pattern‐based geostatistical simulation categorical variables using a multi‐scale search in Fourier space, Computers & Geosciences, 2014 TI
Simulation Grid with Hard Data
Using adaptive recursive template splitting

4. TI TI Realization HD Realization 1 Realization 2
(WCA dataset from Chevron) TI
Realization

5. Limitations of CCSIM CPU
Make it does not work fast for multi-million cell 3D grids and TIs
Conditioning
Does not take into account of data ahead of the path
point data

6. i) Fourier Acceleration
CPU time
CCSIM uses a cross-correlation function as a measure for doing the pattern matching
Cross-correlation acts as a convolution
Computation time can be reduced by transferring the data to the Fourier space by using the convolution theorem
Transferring the TI and the
Overlap areas to the Fourier space
Calculating the cross-correlation
Inverse Fourier transforming the result to the
Spatial domain

7. ii) Constructing of training image at different scales
CPU time
ii) Constructing of training image at different scales
Scale x y x
Original TI
The rescaled TI can be obtained by using an interpolation method

8. Start on a grid (G) with the size of MS0
CPU time
MS-CCSIM Algorithm
MS 2
MS 1
MS 0
Start on a grid (G) with the size of MS0
search boundary
final search boundary
Find the pattern location
Find the pattern location
Project the location
Move to finest scale
Select the similar pattern and insert in G
END

9. Unconditional Simulation
Realization 1
Realization 2
Realization 3
4.8(s)
1000x1000
Unconditional Simulation
4.8(s)
1000x1000
50(s)
180x140x30
450 (s)
200x200x50

10. CPU time comparison
3D Simulation

11. MS-CCSIM Method for Conditional Simulation
Conditioning A B C
Larger simulation grid cell
cell value is assigned the
category with highest frequency

12. Accounting for the data ahead of the raster path
Conditioning
primary pattern
co-pattern
point data
co-template
primary template
Simulation Grid TI
another solution: Using Kriging as an auxiliary variable

13. Using multiple raster path
Hard Data
Conditioning
Using multiple raster path
Reproducing better long-range channels
using co-template
and multiple-path
using single path
using multiple-path

14. Conditional Simulation examples
Local ANODI
Global ANODI
ccsim
ms-ccsim
Rejection sampling
Two Neighborhood Shale-Sand HD TI
Rejection Sampling
ensemble average
ms-ccsim
ensemble average
Conditional Realization

15. Sensitivity Analysis (Tank Dataset)
Number of Candidates
Candidate:
Categorical: 3-10
Continuous: 3-30
CPU time
Quality
Variability
TI (200x500)
Candidate = 4
Candidate = 40
Candidate = 400

16. Sensitivity Analysis Template Size CPU time Quality Variability
Realizations
T = 10
T = 20
T = 50
Ensemble Average

17. Sensitivity Analysis CPU time Quality Overlap Size
OL: (1/4 – 1/5)*Template size
Variability
OL = 3
OL = 8
OL = 15

18. Conclusion
MS-CCSIM can give a tremendous acceleration to geostatistical simulation
Proposed data relocation and Co-template can be used for any hard data distribution
Hereafter, using very rich, large and complex process based training image will be possible!

19. The code are available online !