1. Fast Pattern Simulation Using Multi‐Scale Search
Stanford Center for Reservoir Forecasting
Fast Pattern Simulation Using Multi‐Scale Search
Pejman Tahmasebi and Jef Caers

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

3. CCSIM Algorithm Training Image Simulation Grid
(Tahmasebi et al. 2012, Multiple-point geostatistical modeling based on the cross-correlation functions, Computational Geosciences,16(3), )
Training Image
Simulation Grid
Using raster path for visiting the simulation grid
Using overlap region
Using cross-correlation for similarity calculations

4. Conditional CCSIM Algorithm
Simulation Grid with Hard Data
Using adaptive recursive template splitting

5. Some Results TI
Re. 1
Re. 2
Re. 3

6. Some Results TI HD
Re. TI
One Realization

7. Limitations of CCSIM CPU
Make it does work fast for multi-million cell 3D grids and TIs
Conditioning
Does not take into account of data ahead of the path
Patchiness problem remains
In the case of continuous properties

8. Scale Constructing of training image at different scales y x x
Original TI
The rescaled TI can be obtained by using any interpolation method

9. Start on a grid (G) with the size of MS0
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

10. MS-CCSIM Method for Conditional SimulationB C
Larger simulation grid cell
cell value is assigned the
category with highest frequency

11. Unconditional examples
TI (192x155x30)
890,000 cells
G(192x155x35)
1,000,000 cells
CPU time: 24 (s)

12. CPU time: 7 (s) Fracture Network G (300x300x50) TI (300x300x10)
4,500,000 cells
900,000 cells
CPU time: 7 (s)
(Data from JAPEX)

13. Conditional Simulation examples
1) Two Neighborhood Shale-Sand
HD(1000x1000)
TI (1000x1000)
Rejection Sampling
(zoom in view)
E-type
Conditional Realization (1000x1000)

14. 2) 3D Conditional TI (98x51x79) E-type Map Conditional Realization
well
Shale drape
Conditional Realization
(Data from ExxonMobil)

15. Minimum Error Boundary for removing patchiness
Input Image B1 B2
Neighboring blocks
constrained by overlap B1 B2
Minimal error
boundary cut B1 B2
Random placement
of blocks
Used in CCSIM

16. Minimal Error Boundary (MEB)
Overlapping Blocks
Vertical Boundary _ = 2
Overlap Error
Min. Error Boundary

17. Gaussian Model
Re.#1
Re.#2
Re.#3

18. Tank Data TI CCSIM CCSIM Improved CCSIM Improved CCSIM G (200x100x40)
CPU time: 30 (S)

19. CPU time comparison
3D Simulation
MS-CCSIM

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

21. Essentially, all models are wrong, but some models are useful [George E.P. Box (Professor Emeritus of Statistics at the University of Wisconsin)]