Statistical analysis of pore space geometry Stefano Favretto Supervisor : Prof. Martin Blunt Petroleum Engineering and Rock Mechanics Research Group Department

Statistical analysis of pore space geometryStatistical analysis of pore space geometry

Stefano FavrettoStefano Favretto

Supervisor : Prof. Martin BluntSupervisor : Prof. Martin Blunt

Petroleum Engineering and Rock Mechanics Research GroupDepartment of Earth Science and Engineering

Imperial College London

Imperial College London, January 5th 2005

• Segmentation and images cleaningSegmentation and images cleaning

• Medial Axis constructionMedial Axis construction

• Pore space analysis: pore bodies and pore throatsPore space analysis: pore bodies and pore throats

• Geometrical statistical parameters: Geometrical statistical parameters: - pore volume distribution- pore volume distribution

- throats area distributionthroats area distribution

- channel length- channel length

- coordination number- coordination number

- pore and channel - pore and channel diameters and shapediameters and shape

IntroductionIntroduction

In order to construct a realistic model for flow and transport simulations, it is fundamental to analyze in details the geometrical structure of the pore space.

Here we verify the use of a software, called 3DMA_Rock, to extract (on the basis of a statistical analysis) some geometrical parameters, later used as input data to network generating code for flow simulations.

The 3DMA_Rock code was designed to take as input 3-dimensional digital grey-scale images, as those from –computed tomography.

The main steps of the analysis are:The main steps of the analysis are:

pore space

medial axis (MA)

throats calculation

...throats area distribution...pore volume distribution

pores identification

3DMA_Rock analysis approach3DMA_Rock analysis approach


Image segmentationImage segmentation

- CT data: SAMPLE1, 256x256x256 cube (resolution is - CT data: SAMPLE1, 256x256x256 cube (resolution is 8,683 8,683 mm))

originaloriginal

segmentedsegmented

intensities

occ

urr

en

ces

• Simple threshold or other more advanced

techniques (i.e. Indicator Kriging)

which threshold ?


Cleaning images after segmentationCleaning images after segmentation

1) Remove isolated pore from the grains1) Remove isolated pore from the grains

2) Remove unphysical grains from the pore void space2) Remove unphysical grains from the pore void space

segmentedsegmented cleanedcleanedoriginaloriginal

A - generally, isolated pore in the grains are very small...so we A - generally, isolated pore in the grains are very small...so we remove them by size criterionremove them by size criterion

B – we are looking at effective porosity...so we B – we are looking at effective porosity...so we preserve a pore only if connected to the borderpreserve a pore only if connected to the border

Working on the complementary images, we remove all isolated grains (size criterion, local erosions...)Working on the complementary images, we remove all isolated grains (size criterion, local erosions...)


Medial Axis constructionMedial Axis construction

3DMA_Rock thinning algorithm (Lee et. al., 1994)3DMA_Rock thinning algorithm (Lee et. al., 1994)

• Each voxel is labeled with a “burn number”, depending on its distance from Each voxel is labeled with a “burn number”, depending on its distance from grains surface - LKC [Lee, Kashyap, Chu; 1994] algorithm.grains surface - LKC [Lee, Kashyap, Chu; 1994] algorithm.

• Medial Axis are produced by a thinning algorithm based on Simple Points Medial Axis are produced by a thinning algorithm based on Simple Points (this guarantees topology preservation).(this guarantees topology preservation).


Example : Medial Axis calculation on artificial pore systemExample : Medial Axis calculation on artificial pore system

2D slice 3D Rendering

Throats visualization3D Medial Axis


Pore throatsPore throats Pore bodiesPore bodies

Pore bodies and pore throatsPore bodies and pore throats


Medial Axis calculation on Sample 1Medial Axis calculation on Sample 1

3D visualization of a 128x128x128 cube3D visualization of a 128x128x128 cube

Original with MAOriginal with MA

cluster C

cluster B

cluster A

path I(leaf-leaf)

path II(branch-leaf)

path III(branch-branch)


Throats calculation on Sample 1Throats calculation on Sample 1

Medial AxisMedial Axis

Medial Axis & Throats barriersMedial Axis & Throats barriers


Statistical resultsStatistical results

Unit = 1 voxelUnit = 1 voxel

L = 8.683 L = 8.683 mmLL

Equivalent pore radius:Equivalent pore radius:

R =R =3 V

4

1/3

• Pore radius Pore radius

distributiondistribution

equivalent pore radius

occu

rren

ces



• Throats radius distributionThroats radius distribution

Unit = 1 voxelUnit = 1 voxel

L = 8.683 L = 8.683 mmLL

Equivalent throat radius:Equivalent throat radius:

R =R =A

1/2


equivalent throats radius

occ

urr

en

ces


• Path length & channel lengthPath length & channel length

Channel length [voxels]

3DMA assumes the channel length 3DMA assumes the channel length CCLL as the distance between two pore center (path length Pas the distance between two pore center (path length PLL))

We could calculate channel length as:We could calculate channel length as: CL = n PL with 0<n<1


CL

PL


• Throat radius vs pore radiusThroat radius vs pore radius

throats equivalent radius

po

re e

qu

iva

len

t ra

diu

s

throats / pore radius

occ

urr

en

ces



1

23 Nc = 3

• Coordination number Coordination number

distributiondistribution



• Throats shape factor Throats shape factor

distribution distribution

G = A

p2

G = 1/4 = 0.0796G = 1/16 = 0.0625G = √3 / 36 = 0.0481

...we can distinguish between different cross section shape

G

occ

urr

en

ces



• Pore diameters in three Pore diameters in three orthogonal directions ( X ; Y ; Z )orthogonal directions ( X ; Y ; Z )

z

x

y


Documents

Statistical analysis of pore space geometry Stefano Favretto Supervisor : Prof. Martin Blunt Petroleum Engineering and Rock Mechanics Research Group Department