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

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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

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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

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

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IntroductionIntroduction

3.. Mathematical shape descriptionA. Form ratio

‐ Pore volume  pore shape

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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)

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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

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 

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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

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

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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

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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