efficient topological and morphological...
TRANSCRIPT
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EFFICIENT TOPOLOGICAL AND MORPHOLOGICAL
CHARACTERIZATION OF POROUS MICROSTRUCTURES
Mascot-Num 2019
Johan Chaniot*, Maxime Moreaud*†, Thierry Fournel’, Jean Marie Becker’, Loïc Sorbier* *IFP Energies nouvelles, Rond-point de l'échangeur de Solaize, BP 3, 69360 Solaize, France ‘Université de Lyon, Université Jean Monnet de Saint Etienne, CNRS UMR 5516, Laboratoire Hubert Curien, 42000 Saint Etienne, France † MINES ParisTech, PSL-Research University, CMM, 35 rue Saint Honoré, 77305 Fontainebleau, France
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POROUS NETWORK CHARACTERIZATION
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3D POROUS MEDIA CHARACTERIZATION ( ALUMINA SUPPORT )
Standard geometrical descriptors: Porous volume fraction
Specific surface area
Granulometry
Average curvature
Maximal included ball
Not sufficient*
New descriptors are needed Quantifying topology and accessibility
A single scalar value
Electron tomography reconstructions, size ≈ 500 nm
* G. Edder, CO2 Adsoprtion from Synthesis Gas Mixtures: Understanding selectivity and capacity of new adsorbents, Ph.D Thesis Univ. Lyon, 2012.
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GEOMETRICAL TORTUOSITY*
Which answer can we give to this question:
Is it easy to go through a given porous media ?
Purely geometric calculation, notion of flux, no consideration of chemical / surface interaction
Accessibility: easy or not
Diffusion: at a given constant speed, time to go from one location to another
Difference between:
Vs.
* C. Lantuejoul, S. Beucher, On the use of the geodesic metric in image analysis, J Microsc 121(1):39–49, 1981
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GEOMETRICAL TORTUOSITY
Definition: need two points, ratio of two distances
Vs.
Difference between:
) p ,p D(
X ;p ,p D=τ
mn
mng
mn,
pn
pm
pm
pn
X
1=τ mn,1τ mn,
X
X
pm
+
+ +
+
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TORTUOSITY FOR A “CUBIC SAMPLE”
A and B being fixed parallel planes, computation of
3D tortuosity mapa,b
Distribution considering all pathsc
Average or minimal pathd
a. L. Decker, D. Jeulin, I. Tovena, 3D morphological analysis of the connectivity of a porous medium, Acta Stereol 17(1):107–12, 1998 b. M. Moreaud et al., Analysis of the accessibility of macroporous alumino-silicate using 3D-TEM images, Material Science and Technology 2008 conference, Pittsburgh USA. c. C. Peyrega, D. Jeulin, Estimation of Tortuosity and Reconstruction of Geodesic Paths in 3D, Image Analysis & Stereology 32(1):27-43, 2013 d. C.J. Gommes, et al. Practical methods for measuring the tortuosity of porous materials from binary or gray‐tone tomographic reconstructions. AIChE Journal 55(8):2000-2012, 2009
c
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HOW TO TAKE INTO ACCOUNT COMPLEX MICROSTRUCTURES ?
How to define two planes or points ?
How to be representative ?
Electron tomography reconstruction, size ≈ 500 nm
?
?
?
?
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M-TORTUOSITYa,b,c
a. J. Chaniot et al., Tortuosimetric operator for Complex Porous Media Characterization, Stereology, Spatial Statistics and Stochastic Geometry , Prague, Czech Republic, June 25th, 2018 b. J. Chaniot et al., From Tortuosity to Narrowness: Straightforward Porous Media Characterization, Workshop in Honor of Dominique Jeulin "Physics and mechanics of random structures: from morphology to material properties" , Oléron, June 18th – 22th, 2018 c. J. Chaniot et al., Tortuosimetric operator for complex porous media characterization, Image Analysis and Stereology, accepted, 2019.
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STOCHASTIC TORTUOSITY
Random sampling of two points, and calculation of tortuosity
Not representative…
Several points are needed, but how to combine them ?
Representativity?
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M-TORTUOSITY
Random sampling of points
For each point:
Tortuosity calculated for each pair
Weighted average by respective geodesic distances*:
Gives less importance to nearby points, where the tortuosity is often equal to 1
Combination of all points:
Weighted average with respect to center of mass: Gives more importance to points nearby outer border
* C.G. Berrocal et al., Characterisation of bending cracks in R/FRC using image analysis, Cement and Concrete Research 90:104-116, 2016.
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TORTUOSITY
Proper random sampling is important!
Uniform distribution introduces a bias: dense porous areas are given
more weight
Volumic distribution: same importance for all areas
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M-TORTUOSITY*: FORMULATION
mn
mnGmn,
p ,p D
X ;p ,p D=τ
∑
∑
≠
≠
1 - N
n m 0, = mmnG
1 - N
n m 0, = mm n,mnG
n
X ;p ,p D
τX ;p ,p D
=C
∑
∑1 - N
0 = nn
nn
1 - N
0 = nM
c ,p D1
C c ,p D1
=τ
Center of mass
* J. Chaniot et al., Tortuosimetric operator for complex porous media characterization, Image Analysis and Stereology, accepted, 2019
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MULTIPLE COMPONENTS CASE
mn
mnGmn,
p ,p D
X ;p ,p D=τ
∑
∑
1 - N
n ≠m 0, = mmnG
1 - N
n ≠m 0, = mm n,mnG
n
X ;p ,p D
1
τX ;p ,p D
1
=C
∑
∑1 - N
0 = nn
n
n
1 - N
0 = n
M
c ,p D1
C
c ,p D1
1
τ
* J. Chaniot et al., Tortuosimetric operator for complex porous media characterization, Image Analysis and Stereology, accepted, 2019
How to deal with disconnected components ?
Undefined standard combination for infinite tortuosities
Our solution: consider inverse geometric tortuosity*
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M-TORTUOSITY, ILLUSTRATION
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ILLUSTRATION ON MOFS CHARACTERIZATION*
Complementary to the classical descriptors
*C. Nieto-Draghi et al., New descriptors to characterize porous materials, 11th International Symposium on the Characterization of Porous Solids (COPS-XI). 2017
M-tortuosity discriminates distinct topologies, unlike usual descriptors
ZIF-68
ZIF-CN ZIF-68 ZIF-CN
As 2 523 248 2 535 168
Vv 0.51 0.51
rmax 15 15
τM 1.30 1.20
Cumulated granulometric curve
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ILLUSTRATION ON MOFS CHARACTERIZATION*
Fills a large gap in the classical descriptors
*C. Nieto-Draghi et al., New descriptors to characterize porous materials, 11th International Symposium on the Characterization of Porous Solids (COPS-XI). 2017
M-tortuosity is the only descriptor that singles out the topological similarity
ZIF-68
ZIF-71 ZIF-68 ZIF-71
As 2 523 248 2 640 580
Vv 0.51 0.57
rmax 15 43
τM 1.30 1.30
Cumulated granulometric curve
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CONCLUSION AND PERSPECTIVES
M-tortuosity new descriptor Mixture of geometrical tortuosity and narrowness Applicability to complex microstructures and disconnected components Scalar value containing topological information
M-Tortuosity gives a thorought characterization of alumina supports and zeolites Work in progress: extension to gray-level microstructures
No segmentation needed
One more thing…
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* S. Drouyer et al., Sparse Stereo Disparity Map Densification using Hierarchical Image Segmentation. 13th International Symposium, ISMM 2017, pp.172-184,
Mathematical Morphology and Its Applications to Signal and Image Processing
*
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Efficient Topological and Morphological Porous Microstructures Characterization
Johan Chaniot, Maxime Moreaud ( [email protected] ), Thierry Fournel, Jean Marie Becker, Loïc Sorbier
M-Tortuosity available soon under plug im!