A new 3D pore shape classification using Avizo Fire
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Transcript of A new 3D pore shape classification using Avizo Fire
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
Overview
1. Introduction
2. CT: Petrography in 3D
3. Mathematical shape description
4. Conclusion
IntroductionIntroductionIntroduction CT Mathematical shape description Conclusion
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
IntroductionIntroduction
1.. IntroductionB. Different scales
‐ Different types of porosity working on different scales
Rahman, et al 2011
Introduction CT Mathematical shape description Conclusion
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
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
IntroductionIntroduction
2.. CT: Petrography in 3DB. Principle:
Introduction CT Mathematical shape description Conclusion
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
IntroductionIntroduction
2.. CT: Petrography in 3DC. Example:
Late Calcite vein
Dolomite fragment (Fe rich)Dolomite cement
Introduction CT Mathematical shape description Conclusion
IntroductionIntroduction
3.. Mathematical shape descriptionA. Form ratio
‐ Pore volume pore shape
Introduction CT Mathematical shape description Conclusion
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
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
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
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
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
IntroductionIntroduction
3.. Mathematical shape descriptionC. Goodness of fit?
‐ Complex pores:‐ Define different pore bodies:
‐ Watershed algorithm
Introduction CT Mathematical shape description Conclusion
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
IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes
‐ Based on L, I and S:
Introduction CT Mathematical shape description Conclusion
IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes
‐ Based on L, I and S:
Introduction CT Mathematical shape description Conclusion
IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes
‐ Rod like shape:
Introduction CT Mathematical shape description Conclusion
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
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
IntroductionIntroduction
3.. Mathematical shape descriptionD. Defining pore shapes: Compactness
‐ Compactness:
Introduction CT Mathematical shape description Conclusion
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
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
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