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

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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

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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

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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

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2.. CT: Petrography in 3DB. Principle:

Introduction CT Mathematical shape description Conclusion

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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

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2.. CT: Petrography in 3DC. Example:

Late Calcite vein

Dolomite fragment (Fe rich)Dolomite cement

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3.. Mathematical shape descriptionA. Form ratio

‐ Pore volume  pore shape

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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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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

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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 )

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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

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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

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3.. Mathematical shape descriptionC. Goodness of fit?

‐ Complex pores:‐ Define different pore bodies:

‐ Watershed algorithm 

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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

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3.. Mathematical shape descriptionD. Defining pore shapes

‐ Based on L, I and S:

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3.. Mathematical shape descriptionD. Defining pore shapes

‐ Based on L, I and S:

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3.. Mathematical shape descriptionD. Defining pore shapes

‐ Rod like shape:

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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

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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

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3.. Mathematical shape descriptionD. Defining pore shapes: Compactness

‐ Compactness: 

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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

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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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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

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