A new 3D pore shape classification using Avizo Fire
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A new 3D pore shape classification using Avizo Fire
FACULTY OF SCIENCEDepartment : Earth and Environmental SciencesGeology
Ir. Steven ClaesDr. A. FoubertProf. Dr. M. OzkülProf. Dr. R. Swennen
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Overview
1. Introduction
2. CT: Petrography in 3D
3. Mathematical shape description
4. Conclusion
IntroductionIntroductionIntroduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
1.. Introduction
Choquette and Prey,1970
AAPG, 77
Introduction CT Mathematical shape description Conclusion
A. Heterogeneity
‐ Carbonate reservoirs typically have a complex texture and are very heterogeneous concerning porosityy measurements
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IntroductionIntroduction
1.. IntroductionB. Different scales
‐ Different types of porosity working on different scales
Rahman, et al 2011
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
1.. IntroductionB. Different scales
‐ Working on different scales
10 cm
15 cm2 cm
4 cm
1.5 cm
0.4 cm
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
2.. CT: Petrography in 3DA. Workflow
‐ 3D information:‐ Filtering
‐ Pre reconstruction‐ Post reconstruction
‐ Segmentation‐ Dual thresholding
‐ Visualization‐ Avizo‐ CT‐an / CT‐vox
‐ Calculations‐ Matlab‐ Avizo
Data acquisition Reconstruction 3D information
1979, Houndsfield
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
2.. CT: Petrography in 3DB. Principle:
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
2.. CT: Petrography in 3DB. Principle:
‐ Advantages:‐ Non‐destructive‐ Full 3D information of internal structure‐ Little sample preparation‐ Qualitative and quantitative interpretation
‐ Disadvantages:‐ Limited object size‐ Relative high recording time‐ Relative high calculation time
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
2.. CT: Petrography in 3DC. Example:
Late Calcite vein
Dolomite fragment (Fe rich)Dolomite cement
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionA. Form ratio
‐ Pore volume pore shape
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionA. Form ratio
‐ Several parameters are defined in the last century:‐ E.g. :
‐ Most are calculated using L (longest dimension in a shape), I (longest dimension perpendicular to L) and S (dimension perpendicular to both L and I) (Krumbein, 1941)
‐ Above definition of L, I and S does not always provide the most information about a shape e.g. cube
L I2S (Wenthworth, 1922)
(Blott and Pye 2008)
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionB. Calculation L, I and S
‐ Individual pores are considered as solid objects‐ Calculate the mechanical moments of the pore:
‐ Using the spectral theorem for real, symmetric matrices:
‐ I1, I2 and I3 are the principal moments of inertia solving an eigenvalue problem
I xx I xy I xz
I yx I yy I yz
I zx I zy I zz
I1 0 00 I 2 00 0 I 3
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionB. Calculation L, I and S
‐ I1, I2 and I3 can be used to calculate L, I and S as the dimensions of the principal axis of the approximated ellips:
‐ Is the fit of an approximating ellipsoid correct?
I1 15
m(I 2 S2 )
I 2 15
m(L2 S2 )
I 3 15
m(L2 I 2 )
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionC. Goodness of fit?
‐ Can be evaluated using the Vs or Es parameter:
‐ en: the surface area of the approximating ellipsoid‐ S: the surface area of the pore
‐ vn: the volumeof the approximating ellipsoid‐ V: the volume area of the pore
‐ Es also proofs to be an adequate parameter in order to describe the sphericity of a pore
Es en
S
VvV n
s
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionC. Goodness of fit?
‐ Histogram of Vs:
‐ Mean: 1.38‐ Median: 1.08
Good fit for most pores but some exceptions
Complex pores
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionC. Goodness of fit?
‐ Complex pores:‐ Define different pore bodies:
‐ Watershed algorithm
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes: based on shapes
‐ Based on L, I and S:‐ Ratio’s: I/L and S/I‐ 5 shape classes are defined Equant shape
Cuboid shape
Rod like shape
Blade like shape
Plate like shape
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes
‐ Based on L, I and S:
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes
‐ Based on L, I and S:
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes
‐ Rod like shape:
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes
‐ Working with an approximating ellipsoid allows to assess the orientation of the pores
Tot vol = 58578 mm3 Tot vol = 26061 mm3
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes
‐ Allows to differentiate between facies types:
rod blade plate cube cuboid0,22 0,17 0,35 0,07 0,18
rod blade plate cube cuboid0,14 0,27 0,13 0,15 0,31
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes: Compactness
‐ Compactness:
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes: clustering
‐ Objective way of defining clusters:
‐ Model based clustering:‐ Based on Probability methods‐ Clusters are ellipsoidal
‐ Centered around the mean value‐ Covariances determine the geometrics
‐ Number of clusters are statistically optimized
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes: clustering
‐ Based on L, I and S:‐ Ratio’s: I/L and S/I‐ Compactness
Introduction CT Mathematical shape description Conclusion
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IntroductionIntroduction
4.. Conclusion
A. Computer tomography
‐ Visualizes porosity networks in 3D‐ Allows Petrography in 3D
B. Mathematical shape description
‐ Establishes a new 3D classification for pores in travertine rocks‐ Classification is confirmed to be statistically relevant‐ Allows to define facies types
Introduction CT Mathematical shape description Conclusion