This document describes building a pore network model from 3D images of a pore space to precisely predict permeability. Key steps include: 1) Skeletonizing the 3D image to extract the pore network topology. 2) Partitioning the pore space to identify individual pores and throats. 3) Constructing the pore network model (PNM) graph from the skeleton and partitioning. 4) Computing local resistances within the PNM to predict permeability and comparing with direct numerical modeling.

1. Building a
Pore Network Model from a
Pore Space 3D Image to
Precisely Predict
Permeability
D. BERNARD, N. COMBARET, E. PLOUGONVEN,
J. LESSEUR
Institut de Chimie de la Matière Condensée de Bordeaux,
ICMCB-CNRS, Univ. Bordeaux, PESSAC

2. Availability of large high-resolution 3D images

3. Direct computation of the permeability
At the local scale


Ae
From STOKES to DARCY Closure problem

4. Direct computation of the permeability
Numerical code
Pressure Vx Vy Vz

5. Pores network model

6. Pores network model

7. Pores network model
Represent
TOPOLOGY Skeleton Noise effects
GEOMETRY Local resistance

8. Skeletonisation
Pore space partitioning
PNM construction
Example
Local resistances computation
Example
Conclusions

9. Skeletonisation
Binary image
Homotopic thining

10. Skeletonisation
Skeletonization

11. Skeletonisation
Skeletonization

12. Skeletonisation
Filtering : morphological closing, majority filter, median filter, …
Problems:
 Modifies too many irrelevant pixels
 Does not remove all artefacts
New solution: directly identify
pixels causing artefacts in the
skeleton
0D, 1D, 2D
EP & DB, AWR, 34 (2011) 731–736

13. Skeletonisation
Pore space partitioning

14. Pore space partitioning
Pores identification

15. Pore space partitioning
Pores construction

16. Skeletonisation
Pore space partitioning
PNM construction

17. PNM construction

18. PNM construction

19. PNM construction

20. Skeletonisation
Pore space partitioning
PNM construction
Example

21. Example

22. Example

23. Example

24. Example

25. Example

26. Example

27. Skeletonisation
Pore space partitioning
PNM construction
Example
Local resistances computation

28. Local resistances computation
j
 .v  0


 p   2 v  0

B.C. : v  0 on A fs
M
Q
j 1
ij 0
Cij 

 p.c dC    2 v.c dC  0
Cij
p H j   pH i   ij .Qij  0
1 2 

29. Local resistances computation

30. Local resistances computation
0,636
0,722

31. Skeletonisation
Pore space partitioning
PNM construction
Example
Local resistances computation
Example

32. Example
500 x 500 x 500
voxels of 5m

33. Example
PNM construction

34. Example
PNM construction

35. Example
PNM construction

36. Example
Local resistances computation

38. Example
DNM: 92.62 m2
PNM: 88.26 m2
500 x 500 x 500
voxels of 5m

39. Skeletonisation
Pore space partitioning
PNM construction
Example
Local resistances computation
Example
Conclusions

40. Conclusions
PNM based only on 3D geometry
Good comparison with DNM
Different examples are presently treated
Comparison with experimental data
Local resistances computation to be simplified
Full permeability tensor is considered