statistical analysis of pore space geometry stefano favretto supervisor : prof. martin blunt...
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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 distribution- throats 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
Imperial College London, January 5th 2005
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 ?
Imperial College London, January 5th 2005
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...)
Imperial College London, January 5th 2005
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).
Imperial College London, January 5th 2005
Example : Medial Axis calculation on artificial pore systemExample : Medial Axis calculation on artificial pore system
2D slice 3D Rendering
Throats visualization3D Medial Axis
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Pore throatsPore throats Pore bodiesPore bodies
Pore bodies and pore throatsPore bodies and pore throats
Imperial College London, January 5th 2005
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)
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Throats calculation on Sample 1Throats calculation on Sample 1
Medial AxisMedial Axis
Medial Axis & Throats barriersMedial Axis & Throats barriers
Imperial College London, January 5th 2005
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
Imperial College London, January 5th 2005
Statistical resultsStatistical results
• 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
Imperial College London, January 5th 2005
equivalent throats radius
occ
urr
en
ces
Statistical resultsStatistical results
• 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
Imperial College London, January 5th 2005
CL
PL
Statistical resultsStatistical results
• 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
Imperial College London, January 5th 2005
Statistical resultsStatistical results
1
23 Nc = 3
• Coordination number Coordination number
distributiondistribution
Imperial College London, January 5th 2005
Statistical resultsStatistical results
• 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
Imperial College London, January 5th 2005
Statistical resultsStatistical results
• Pore diameters in three Pore diameters in three orthogonal directions ( X ; Y ; Z )orthogonal directions ( X ; Y ; Z )
z
x
y
Imperial College London, January 5th 2005