Building a Pore Network Model from a

Pore Space 3D Image to Precisely Predict

Permeability

D. BERNARD, N. COMBARET, E. PLOUGONVEN, J. LESSEURInstitut de Chimie de la Matière Condensée de Bordeaux,

ICMCB-CNRS, Univ. Bordeaux, PESSAC

Availability of large high-resolution 3D images

Direct computation of the permeability

At the local scale

From STOKES to DARCY Closure problem

Ae

Numerical code

Pressure Vx Vy Vz

Direct computation of the permeability

Pores network model

Pores network model

Pores network model

Represent

TOPOLOGY Skeleton Noise effects

GEOMETRY Local resistance

Skeletonisation

Pore space partitioning

PNM construction

Example

Local resistances computation

Example

Conclusions

Skeletonisation

Binary image

Homotopic thining

Skeletonization

Skeletonisation

Skeletonization

Skeletonisation

Filtering : morphological closing, majority filter, median filter, …Problems:

New solution: directly identify pixels causing artefacts in the skeleton

Modifies too many irrelevant pixels Does not remove all artefacts

0D, 1D, 2D

Skeletonisation

EP & DB, AWR, 34 (2011) 731–736

Skeletonisation

Pore space partitioning

Pore space partitioning

Pores identification

Pores construction

Pore space partitioning

Skeletonisation

Pore space partitioning

PNM construction

PNM construction

PNM construction

PNM construction

Skeletonisation

Pore space partitioning

PNM construction

Example

Example

Example

Example

Example

Example

Example

Skeletonisation

Pore space partitioning

PNM construction

Example

Local resistances computation

fsAonvCBvp

v

0:..0

0.2

01

M

jijQ

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2

2

1

ijij CC

dCcvdCcp 0. ijijij QHpHp

Local resistances computation

j

Local resistances computation

Local resistances computation

0,636

0,722

Skeletonisation

Pore space partitioning

PNM construction

Example

Local resistances computation

Example

500 x 500 x 500voxels of 5m

Example

PNM construction

Example

PNM construction

Example

PNM construction

Example

Local resistances computation

Example

500 x 500 x 500voxels of 5m

Example

DNM: 92.62 m2

PNM: 88.26 m2

Skeletonisation

Pore space partitioning

PNM construction

Example

Local resistances computation

Example

Conclusions

Conclusions

PNM based only on 3D geometryPNM based only on 3D geometry

Good comparison with DNM

PNM based only on 3D geometry

Good comparison with DNM

Different examples are presently treated

PNM based only on 3D geometry

Good comparison with DNM

Different examples are presently treated

Comparison with experimental data

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