10th Asian Regional Conference of IAEG (2015)

Verification of 3 dimensional voids geometry in porous material with μ focus X-Ray CT- example of small glass ball aggregate Manabu TAKAHASHI(1), Haruka MINEMURA(2) and Minoru SATO(2)(1) National Institute of Advanced Industrial Science and Technology, Japan
E-mail:takahashi-gonsuke@aist.go.jp(2) Tsukuba University
Abstract
Three dimensional geometry and connectivity of pore space play a fundamental rolein governing fluid transport properties of ground materials. Small glass ball aggregate wasselected as a standard porous materials representing a ground material. We analyzed three
dimensional geometrical data of small glass ball aggregate obtained by micro focus X-ray
CT. We introduced the three-dimensional medial axis (3DMA) method of Lindquist et al.
(2000) to quantify the flow-relevant geometric properties of the voids structure in small
glass ball aggregate. Using these data, we evaluated the number of total pore, interior pore,throat, coordination number, connecting path between two faces, tortuosity and the shortest
path distribution within an arbitrary region. Various analyzed geometrical information aregood in harmony with theoretical data in geometry of porous media. We also present the
spatial distribution of void space in arbitrary volume set. We can confidently say thatmicrostructural information on geo-materials will greatly advance if micro focus X-ray CT
is used concurrently as a tool of data analysis.
Keywords: voids geometry, µ focus X-Ray CT, 3-Dimensional Medial Axis, small glass ballaggregate
1.

Introduction

dimensional fluid flow distributions during
permeability testing in fault related rocks using a
medical CT. They concluded that fault zone wascharacterized by independent particulate flow as
deformation mechanism act as conduits for fluid flow,whereas cataclastic fault zone act as barriers.
The application of X-ray CT in the
non-destructive testing system of the mechanicalproperties of geomaterials, such as deformation andfailure, is reported by Otani and Obara (2003).
It is well known that X-Ray CT is a goodvisualization tool as non-destructive and non-contact
examination. We have introduced micro focus X-ray
CT with high resolution of 10 micron to visualize andmeasure the voids space in porous media, especiallysedimentary rocks like sandstone. We haveintroduced the three-dimensional medial axis
(3DMA) method to quantify the flow-relevantgeometric properties of the voids structure in porous
media using micro focus X-Ray CT data. The
number of connecting path between two faces,
tortuosity and the shortest path distribution within anarbitrary region of sandstone specimen were analyzed.
Geometrical information on the number of connecting
path in an arbitrary volume CT data shows reasonable
correlation between permeability anisotropy observedby laboratory permeability test and mutually

Physical properties in rock are depending strongly
on existence of voids space in rock. Quantification of
total porosity and pore size distribution in rock can bedone with Mercury Intrusion Porosimetry, butgeometrical and spatial information in voids space are
not obtained. X-ray Computerized Tomography(CT) has become nowadays a common
nondestructive tool in a variety field. Some recent
advances of X-ray CT in rock material fields arereviewed by Vervoort et al. (2003). The following
publications are for example.
1) Determination of open fractures;
Verhelst et al. (1995) observed fracture openings
of natural or induced fractures using a medical CT.
2) Determination of porosity and pore structures;
Coles et al. (2002) used a medical and micro
focus CT and determined porosity and pore size
distribution in sandstone to calculate hydraulicconductivity values. Hidajat et al. (2002) usedmicrofocus CT to develop 3D images of the porosity
in sandstone. Karacan et al. (2003) investigated a
local porosity change of pressurized limestone using
an X-ray transparent triaxial vessel.
3) Determination of fluid flow;
Hirono et al. (2003) measured the three1

10th Asian Regional Conference of IAEG (2015)

Fig.1 Schematic illustration of μ focus X-ray CT imaging system
Table 1 Specification in the TESCO Corporation
HMX225perpendicular directions normal and parallel tobedding planes (Takahashi et al., 2014).
In this paper, we introduce geometricalinformation on voids connectivity, tortuosity
distribution, shortest path distribution, and spatial
distribution on a variety of voids size in aggregate ofsmall glass ball.
2.

CT system for micro focus X-Ray

X-ray

Fig.1 shows the simplified structural layout of
our micro focus X-ray CT apparatus comprising asource, CT imaging system, and CT detector. Theinternal structure of an object is determined according
to the absorption rates of X-rays transmitted to therotating object from many different angles. The
system is able to reconstruct two-dimensional
information of any cross-section, unlike the case for a
fluoroscopic image, which presents information only
for the X-ray projection. Micro focus X-ray CT isdifferent from usual X-ray CT in that electron beams
are narrowed before they reach the X-ray radiation
source. A spatial resolution of 5 μm is attained by thisadditional function. The detector, which is usuallycoated with an image intensifier, acquires data
through a digital camera. X-rays are converted into
photoelectrons and/or visible light by the image
intensifier. The analog signals are digitized by thedigital camera and interpreted as the intensity of thetransmitted X-rays incident to the image
intensifiererns.
In this study, we used an X-ray CT system,
HMX225, assembled by the TESCO Corporation (Fig.
2). The maximum voltage is 225kV, and focal spot
size is 5 micro meter (Table 1). The so-called third
generation CT system, which makes it possible torecord X-ray attenuation at many angles by rotating
an object on a computer-controlled rotation
manipulator stage, is used in this instrument (Fig. 2).

Fig.2 Micro focus X-ray system assembled byTESCO Corporation
Attenuation data is detected by a 12bit CCD camera,
and the recorded attenuation data are analyzed toreconstruct two-dimensionally an internal attenuation
image of an object by means of a numerical techniqueknown as filtered back projection. The resolution of
2D images is 1024 x 1024 pixels in this system. To
obtain a clear boundary image between substances210th Asian Regional Conference of IAEG (2015)

having different attenuation coefficients, X-ray
source must be small enough to minimize scatteringzones on an X-ray detector, image intensifier3.

to a sheet of voxels. The usual conceptual model
divides the void space of a porous medium into nodal
pores connected by pore channels. Nodal pores arelocatedatmultigrainjunctions.
Roughlyequidimensional in geometry, these nodal pores arejoined to one another by pore channels, which include
micro cracks situated along interfaces between two
neighboring grains and tubular pores along
three-grain edges.
Fig. 4 shows the original CT data and an example
of medial axis analysis for the packing of glass beads
with 600 μm diameters. We can visually confirm theaccuracy of the medial axis analysis. The medial axis
is affected by the flow channel, percolating backbone,
and flow path in addition to other factors.

Definition of three dimensional medial axis
analysis and example of glass beads packing

Lindquist and Venkatarangen (1999) developed
the 3DMA computational package as a tool for
analyzing the geometry of the pore and grain phasesin three-dimensional CT data. Using this package, we
can obtain the spatial distributions for pore and throat
sizes, coordination number, tortuosity, and othergeometrical relations between pores and throats.
In general, CT images of porous media aregrayscale images and have a bimodal population, onemode corresponding to the signal from the pore space
and the second to the signal from the grain space. As
we are interested in the pore structure, an appropriate
segmentation procedure is required to quantify thegeometry of the pore space. The most suitable
threshold procedure is selected to match apredetermined bulk density and porosity of theporous medium. In the 3DMA package, thekriging-based algorithm is used to segment the voxel
images. The medial axis for a sphere is a straight line
passing through the center point, and that for acylinder is the axis of rotational symmetry. The
medial axis for any n-dimensional object can befound by an algorithm equivalent to a “burningalgorithm” (see Lindquist et al., 1996). Fig. 3 is a
two-dimensional illustration of medial axis behavior
for two nodal pores. A throat is defined as a local
minimum of the cross sectional area in a channel.
For an object in a spatial continuum, the medial
axis is a network of paths and vertices unless theobject contains embedded cavities, where the medial
axis also contains surface segments. For digitizedobjects, the medial axis consists of digitized paths
corresponding to a connected line of voxels, digitizedvertices corresponding to a cluster of one or more
voxels, and possibly digitized surfaces corresponding

4.

Verification of total porosity in glass ballpacking

In a basis of mechanical behavior in granularmaterial, the geometry of sphere packing is defined
theoretically as Table 2. To confirm applicability of
3DMA method to quartz grain aggregate, we havemeasured pore geometry of small glass ball packing
with various diameters. Fig. 4 shows the original CT
data and an example of medial axis analysis for thepacking of glass ball with 600 μm diameter. In Fig.
4(d), warming color indicates narrow pore space andcooling color shows wide pore space. We canvisually confirm the relation between real magnitudeof void space and medial axis expression
distinguished by different color. Table.3 shows
porosity obtained by image processing technique atvarious glass ball diameter. All of the calculated
porosity ranged from 34% to 38%, and exist in thepacking pattern of tetragonal sphenoidal and cubicaltetrahedral in a realistic packing condition. The
frequency of effective pore and throat radii wereshown in Fig. 5, and its peak value located almost at
70 μm～90 μm in pore radii and 60 μm ~ 70 μm inthroat radii. The maximum pore radii attained to 270
μm correspond to the layer distance of tetragonal
sphenoidal packing pattern. We confirm that 3DMA
method can be applied for geometrical evaluation of
porous media. The medial axis is affected by the flow
channel, percolating backbone, and flow path inaddition to other factors.
Table 2 Each packing system and geometrical
data (refer to Mogami(1969))

Fig. 3 Two Dimensional illustration of Medial
Axis behavior

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10th Asian Regional Conference of IAEG (2015)

Fig. 4 Three Dimensional image of Medial Axis inglass beads with 600 μm diameter. (a) 3
dimensional original CT data. (b) 3 dimensional
pore space image extracted from CT data. (c) grain
distribution (d)3 dimensional medial axis image
calculated from pore network data

Fig. 6 Coordination number frequency of small glassball aggregate

5.

Table 3 Glass ball diameter and porosity obtainedwith μ focus X-ray CT processing

Geometrical and spatial information of small
glass ball aggregate

Fig. 6 shows coordination number distribution.
Coordination number means number of glass ballaround a void space, namely show numerals ofwideness on void space. In this glass ball aggregate
coordination number distribute dominantly at 3 to 4
value. These values indicate almost regular packing
condition and almost same glass ball size. Fig. 7
shows tortuosity distributions for X, Y and Z
direction, respectively. Number of void space andconnecting path at each face on analytical voxel arealso shown for three perpendicular directions.
Tortuosity distribution for three directions are almost
same manner, but number of connecting path fordifferent directions show small different value. Fig. 8
shows the shortest path distribution for three
directions. In composite materials like a sandstone,
the shortest path distributions show little bit different
manner, this anisotropic spatial phenomenon is, ingeneral, considered as main cause of anisotropic fluid
flow of sedimentary rocks. Fig. 9 shows spatial
distribution of each size of void space for different
three perpendicular directions. Large void spacescatter in the voxel, and can’t form a route whichflow a fluid. Network system with connecting void
space are constructing under relatively complicatedaggregate of various size of void space. Fig. 10shows total volume of the shortest path for different
directions. Total volume for all directions are almost
same volume since glass ball has almost same
diameter of 600 μm. We can analyze individual
shortest path volume and summation volume of all
path.

Fig. 5 Analyzed distribution of effective pore radii(a) and effective throat radii (b) for small glass ball4

10th Asian Regional Conference of IAEG (2015)

Fig.7 Tortuosity distribution for three perpendicular
directions, and connecting path and number of void
space information

Fig.8 Whole medial axis distribution and theshortest path distribution for three perpendicular
directions

Fig. 9 Spatial distribution of void space for different category with different void radii

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10th Asian Regional Conference of IAEG (2015)

computed tomography in the geo-sciences,
Geological Society, London, Special publications,
215, pp. 107-115.
Karacan, C. O., Grader, A. S. and Halleck, P. M.
(2003): Evaluation of local porosity changes inlimestone samples under triaxial stress field byusing X-ray computed tomography, In Mees, F.,
Swennen, R., Van Geet, M. and Jacobs, P. (eds),
Applications of X-ray computed tomography in thegeo-sciences, Geological Society, London, Special
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advances of X-ray CT and its applications for rockmaterial, In Otani, J. and Obara, Y. (eds), X-ray
CT for Geomaterials Soils, Concrete, Rocks, pp.
79-91. Lisse : A.A. Balkema Publishers.
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Fig. 10 Total volume distribution of the shortest pathfor different direction

6.

Conclusion

To visualize the microstructure in small glassball aggregate, micro focus X-ray CT system that can
get three dimensional data simultaneously with highresolution of 10 micron is introduced. We analyzed
three dimensional geometrical data of small glass ballaggregate obtained by micro focus X-ray CT. We
introduced the three-dimensional medial axis
(3DMA) method of Lindquist et al. (2000) to
quantify the flow-relevant geometric properties of thevoids structure in small glass ball aggregate. Using
these data, we quantified the number of total pore,interior pore, throat, coordination number, connecting
path between two faces, tortuosity and the shortest
path distribution within an arbitrary region. It was
found that the micro focus X-ray CT provides auseful geometrical and spatial information about
individual particles, voids as a nondestructive
visualizing tool.
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Hidajat, I., Rastogi, A., Singh, M. and Mohanty, K. K.
(2002): Transport properties of porous media
reconstructed from thin-sections, SPE Journal, 7(1),pp. 40-48.
Hirono, T., Takahashi, M. and Nakashima, S. (2003):
Direct imaging of fluid flow in fault-related rocks
by X-ray CT, In Mees, F., Swennen, R., Van Geet,
M. and Jacobs, P. (eds), Applications of X-ray

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