multi-scale characterization of porosity in boom clay (hades-level

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Microporous and Mesoporous Materials 208 (2015) 1e20

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Microporous and Mesoporous Materials

journal homepage: www.elsevier .com/locate/micromeso

Multi-scale characterization of porosity in Boom Clay (HADES-level,Mol, Belgium) using a combination of X-ray m-CT, 2D BIB-SEM andFIB-SEM tomography

Susanne Hemes a, *, Guillaume Desbois a, Janos L. Urai a, Birgit Schr€oppel b,Jens-Oliver Schwarz c

a Structural Geology, Tectonics and Geomechanics, Energy and Mineral Resources Group, RWTH Aachen University, Lochnerstrasse 4-20, 52062 Aachen,Germanyb Natural and Medical Sciences Institute (NMI) at the University of Tübingen, Markwiesenstrasse 55, 72770 Reutlingen, Germanyc Institute of Geosciences, Johannes Gutenberg University Mainz, J.-J.-Becher-Weg 21, D-55128 Mainz, Germany

a r t i c l e i n f o

Article history:Received 30 September 2014Received in revised form7 January 2015Accepted 15 January 2015Available online 29 January 2015

Keywords:Radioactive waste disposalBoom ClayPore space connectivityFIB-SEM tomographyPore network modeling

* Corresponding author. Tel.: þ49 241 80 98446.E-mail addresses: [email protected]

ged.rwth-aachen.de (G. Desbois), [email protected]@nmi.de (B. Schr€oppel), schwarj@uni-main

http://dx.doi.org/10.1016/j.micromeso.2015.01.0221387-1811/© 2015 Elsevier Inc. All rights reserved.

a b s t r a c t

The Oligocene age Boom Clay is a potential host material for radioactive waste disposal in Belgium. Tobetter understand the physical basis of transport mechanisms of radionuclides, we aim to characterizethe pore space and its connectivity at nm-scale in 3D. In the present study, X-ray m-CT and FIB-SEM(focused ion beam scanning electron microscopy) tomography were combined, to investigate the 3Dpore space of a Boom Clay sample from the Mol-1 borehole (depth corresponding to the level of theHADES-URF e ‘high activity disposal experimental site underground research facility’) at the MoleDesselresearch site for radioactive waste disposal (Belgium). BIB-SEM (broad ion beam scanning electron mi-croscopy) was used to bridge the gap in resolutions between X-ray m-CT and FIB-SEM and to optimize theselection of a relevant spot for FIB-SEM. Pore network extraction (PNE) modeling (Dong and Blunt, 2009[1]) was used to simplify the results into a set of pore bodies and pore throats, which are suitable for astatistical description. Resulting pore-size distributions are interpreted to be power-law distributed over~6 orders of magnitude, showing the scale-invariance of the pore space. We present a conceptual modelof the 3D pore network in Boom Clay. The extracted 3D pore network model can be used to estimatetransport properties e in digital rock models.

© 2015 Elsevier Inc. All rights reserved.

1. Introduction

There is a rapidly growing interest in the analysis of porosity infine grained geomaterials using high resolution BIB-SEM, FIB-SEMand X-ray m-CT data. Numerical modeling of effective bulk samplephysical properties such as permeability, electrical resistivity anddiffusivity, as well as of processes like single and multi-phase fluidflow, or radionuclide transport in porous media by diffusion andmigration, needs these data as input [2,3]. The understanding ofthese processes is relevant for the oil and gas industry, for the safelong term disposal of radioactive waste and carbon dioxide (CO2)sequestration. BIB-SEM, FIB-SEM and X-ray m-CT are moreover

en.de (S. Hemes), [email protected] (J.L. Urai), Birgit.z.de (J.-O. Schwarz).

relevant for studying forms of porous coal or biochar, which is usedfor example for carbon dioxide (CO2) storage [4]. Recent advancesin porous materials characterization, down to the nm-scale in 2Dand in 3D e e.g. by using multiplex coherent anti-Stokes Ramanscattering (CARS) microscopy [5e9], optical coherence tomography(OCT) with suitable digital post-processing [10], proton NMRrelaxation (NMRR) and NMR cryo-porometry [4], or aberrationcorrected transmission electron microscopy (TEM) under liquidnitrogen conditions [11], have led to an increasing understandingand improvement of porous materials synthesis, characterizationand catalysis [9]. Campello et al. [10] imaged microstructures inporous media and established pore-size distributions in 2D and in3D using optical coherence tomography (OCT) on oil source rocksamples and showed that “OCT images in combination with digitalpost processing are suitable to measure pore-size distributions innatural and artificial materials, with the advantage of being non-invasive, faster and less expensive than other available methods”

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S. Hemes et al. / Microporous and Mesoporous Materials 208 (2015) 1e202

[10]. Webber et al. [4] applied proton NMR relaxation to charac-terize the quantity and mobility of hydrocarbon material in driedshale and carbonate rocks, as well as in biochar pores. Moreover,they used NMR cryo-porometry tomeasure the structure (pore-sizedistribution and pore volumes) of the shale and carbonate rocks, aswell as of the stable carbon skeleton. They found that, combininghydrocarbon mobility information from NMRR with structural datafrom NMRC allows for evaluating the mobility of hydrocarbons inshale or carbonate rocks, calculating the lifetime of labile compo-nents in biochar and estimating the lifetime of the stable biocharcarbon skeleton” [4]. Wiktor et al. [11] used aberration correctedtransmission electron microscopy (TEM) under liquid nitrogenconditions, to image and study intact metal-organic framework(MOF) pores in MOF-5 nanocrystals, allowing “detailed analyses ofMOF interfaces, MOF-nanoparticle interaction and MOF thin films”[11].

In the present study, X-ray m-CT, BIB-SEM and FIB-SEM tomog-raphy image analyses are combined with pore network extractionmodeling (PNE; [1]), to investigate the 3D pore space and micro-structure of a well characterized Boom Clay sample from the Mol-1borehole (Mol-Dessel research site, Belgium), from the level ofdepth of the HADES underground research facility (URF).

The Boom Clay (Rupelian, Lower Oligocene) is, besides theYpresian clays, one of the potential host rocks for the deepgeological disposal of high- and medium-level, long-lived radio-active waste in Belgium and the Netherlands [12,13]. For this pur-pose, chemical and mechanical properties of the low permeable,fine-grained, elasto-plastic Boom Clay [14e16] are investigated insitu, at the HADES-URF, located at about 223m below the surface inMol (Belgium) [17]. The clay host rock has to delay and attenuatethe radionuclides and other contaminants from being released tothe biosphere after failure of the engineered barrier system [18].Since the transport of radionuclides in Boom Clay is mainlycontrolled by diffusion through the accessible pore space [19,20], adetailed characterization of the pore space down to nm-scale isrequired for a full microphysical understanding of the material'stransport properties. Moreover, the pore space morphology and itsconnectivity in 3D are of major interest to gain a better under-standing of the geo-mechanically anisotropic behavior of the BoomClay.

Standard bulk porosity measurements, using Mercury injectionPorosimetry (MIP), on dried Boom Clay samples give inter-connected porosity between 23 and 40 Vol.-%, accessible throughpore throat diameter above 3.6 nm [21e26].

Other indirect methods, including radionuclide (HTO) diffu-sion experiments, gas generation and migration experiments, gasbreakthrough experiments and water content porosity mea-surements are performed on water-saturated samples and resultin total porosities between 35 and 49 Vol.-% from HTO (iodide)diffusion experiments [19,27e34], ~35 Vol.-% from gas (hydrogenand methane) generation and migration experiments [20,35],and between 36 and 39 Vol.-% from water content porositymeasurements [22,24e26,36]. A total porosity of ~38 Vol.-% wasreported in FUNMIG [37] based on density difference calcula-tions. Hildenbrand et al. [25,26] measured significantly lowereffective transport porosities between 1E-05 and 1E-02% fromgas breakthrough experiments and derived pore-size distribu-tions mostly between 8 and 60 nm (pore radii), suggesting thatonly a very small fraction of the total porosity in Boom Clay isavailable for gas flow [26].

All of the above methods allow characterizing bulk transportproperties of the Boom Clay; however, they yield only indirect in-formation on the connectivity and the morphology of the porespace. For direct observations of pore space in fine-grained, clayeymaterials X-ray m-CT (micro-computed tomography) and SEM

(scanning electron microscopy) provides an alternative. X-ray to-mography currently provides a maximum resolution of ~0.027 mm3

voxel-size [38]. For example, Van Geet et al. [39] used X-ray m-CT tovisualize the fracture self-sealing behavior in Boom Clay at a res-olution of 100 mm. First 2D nm-scale direct observations on BoomClay microstructures were made by Baeyens et al. (1985) [40] andAlMukhtar et al. (1996) [21], using SEM on broken surfaces of BoomClay samples, but these studies suffered from the low quality of theresulting SEM-images, due to the rough sample surfaces. Recentprogress in broad- and focused-ion-beam (BIB and FIB) milling[41e49] overcomes this problem, by providing atomically smoothcross-sections for SEM at high resolutions. BIB milling producescross-sections of a few mm2 to cm2 [50], enabling to analyzerepresentative elementary areas (REAs) [24,51e55]. Desbois et al.[50] conducted first experiments using serial BIB cross-sectioninginside a SEM, in order to gain information on microstructures in3D, but slice thickness was insufficient to provide 3D resolution forpore space connectivity analyses. In contrast, Gaþ-FIB-SEM to-mography is a powerful tool to investigate the pore space ofargillaceous materials in 3D, down to a few nanometers in reso-lution [46,56e60]. However, FIB also suffers from limitations, e.g.regarding the size of the sample volumes available for 3D porespace analysis, of maximal several hundred mm3. Representativevolume element (RVE) calculations on clayey materials [61] haveshown that typical FIB-SEM tomography volumes are smaller thanthe sizes of representative volume elements and characteristiclength scales of spatial homogeneity, regarding the porosity dis-tribution in clayey materials. Thus, either larger, or more sampleshave to be investigated [61,62]. Without additional information onlarger scale microstructure, Gaþ-FIB-SEM analyses are blind inchoosing representative locations.

As proposed by Desbois et al. [50], due to their complementaryand overlapping resolution ranges, X-ray m-CT, BIB-SEM and FIB-SEM tomography are combined to gain information on the distri-bution of different mineral phases in a sample, the relation be-tween porosity and the different mineral phases, as well as theporosity distribution at very high resolution.

Keller et al. [58,63] and Houben et al. [57] used Gaþ-FIB-SEMtomography to characterize the pore space in Opalinus Clay (MontTerri, Switzerland), with a resolution of 10e20 nm and showed thatpore throats in Opalinus Clay are mostly below 10 nm in diameterand thus not resolvable by Gaþ-FIB-SEM. Recent studies of Boomclay [24] suggest that pore throats in this material are large enoughto be resolved by Gaþ-FIB-SEM and larger pores can be resolved byX-ray m-CT.

The 3D pore space in fine grained geomaterials is too complex tobe described by simple stereological concepts [64] alone. In thepresent study, we therefore used a pore network extraction (PNE)modeling approach after Dong and Blunt [1], to simplify andanalyze the pore space connectivity, the pore body and pore throatsize distributions, as well as the orientation of the pore throats.Pore network modeling has so far been applied to X-ray m-CT dataof coarse-grained porous materials, like sandstones [1,65e69] and/or carbonate rocks [65,67,69,70], but until now, never to high res-olution (nm-scale) porosity data of fine-grained, argillaceousmaterials.

This contribution builds on 2D BIB-SEM results by Hemes et al.[24] to select relevant spots for high-resolution 3D FIB-SEM to-mography and to bridge the gap in resolutions between 3DX-ray m-CT and Gaþ-FIB-SEM tomography. Thus, this approach enablesanalyzing the 3D pore space at two different scales of resolution:(1) X-ray m-CT, for pore-sizes in the range between 100 and 7 mm (inequivalent pore diameter), and (2) FIB-SEM, for pore-sizes between5 mm and 40 nm (equivalent pore diameter). The resulting 3Dporosity volumes are modeled in 3D pore networks using PNE; and

Fig. 1. Results by Hemes et al. [24], relevant for the present study. a) BIB-SEM area analyzed, location and orientation of FIB-SEM tomography (present study) and orientation of thesample bedding. b) Typical 2D pore morphologies within the fine-grained clay matrix of sample ON-Mol-1-196, HADES-level Boom Clay. c) and d) results of representativeelementary area (REA) calculations using ‘box counting method’ [93] on mineralogical composition (c) and on segmented porosity data (d).

S. Hemes et al. / Microporous and Mesoporous Materials 208 (2015) 1e20 3

results are compared to bulk sampleMercury injection Porosimetry(MIP) data on the same reference sample [24].

2. Samples and methodology

2.1. Sample characteristics and sub-sample preparation

We studied the same Boom Clay sample ON-Mol-1-196 asanalyzed by Hemes et al. [24]. The sample originates from a depthof �196 m (TAW1) from the Mol-1 borehole, corresponding to thelevel of depth of the HADES-URF at the Mol-Dessel research site(Belgium), where most of the methodological studies on Boom Clayare being carried out [12]. The sample is a very fine-grainedexample of Boom Clay, with a peak in grain-size distributionbelow 1 mm (grain diameter) and a median grain-size of ~1.4 mm[24]. XRD and bulk rock analysis [73] give a mineralogical compo-sition of ~52 dry wt.-% clay, consisting of about 40 dry wt.-% Illite

1 TAW: ‘Tweede algemeene waterpassing’ or S.G.L. (‘second general leveling’) is theaverage horizontal water level of low tide at Oostende. In Belgium, as reference forcomparing heights, the second general leveling of 1948 [71] is used, which is about2.33 m lower than the reference Geoid [72].

and Smectite, ~9 dry wt.-% Kaolinite and ~3 dry wt.-% Chlorite; the~48% non-clay minerals are composed of ~32 dry wt.-% Quartz, 7dry wt.-% Feldspars, 4 dry wt.-% Calcite, 2 dry wt.-% Plagioclase, 2dry wt.-% Pyrite and ~1 dry wt.-% organic matter.

Prior to sample drying, which is required for BIB-SEM, FIB-SEMand X-ray m-CT analyses, the wet-preserved sample core of 10 cmdiameter and ~30 cm length, was sub-sampled using a rotary dia-mond saw at low speed. Samples suitable for FIB-SEM/BIB-SEM andX-ray m-CT are 0.5 � 0.5 � 1 cm; these were cut off the sub-sampleusing a razorblade. To minimize the evolution of drying artifacts,sample pieces were afterward slowly dried in an oven, increasingthe temperature gradually in 5e10 �C steps from ambient tem-perature (~23 �C), up to 100 �C, over a period of time of 10 days [24].Cylindrical samples for X-ray m-CT (~2 mm in diameter and ~0.5 cmin sample height) were prepared after drying, using carbidegrinding papers (grit sizes P500-2400, ISO/FEPA Grit), by manualpolishing. For FIB-SEM tomography and BIB-SEM, the surface of thedried, cuboidal-shaped sample piece (~0.5 � 0.5 � 1 cm) was pre-polished by the same method; afterward the sample was gluedonto a sample holder for BIB- and FIB-SEM analyses.

BIB cross-sectioning was performed using a JEOL SM-09001cross-section polisher at 6 kV for 7.75 h, with the broad ion beamhitting the shielded sample surface perpendicular to the sample

Fig. 2. Image pre-processing steps for FIB-SEM and X-ray m-CT porosity analyses.


bedding, in such a way that the resulting polished cross-section of~1 mm2 is also oriented perpendicular to the sample bedding(Fig. 1a). A detailed description of the BIB-SEM method is given inHemes et al. [24]. The FIB-SEM experiment was carried out on thesame sample piece, with the FIB slicing in the z-direction e parallelto the sample bedding and parallel to the BIB cross-section surface.The resulting FIB-SEM slices are thus oriented perpendicular to thesample bedding, which is parallel to the yz-plane, and perpendic-ular to the BIB-SEM cross-section surface, oriented parallel to xz(Fig. 1a). Based on the results by Hemes et al. [24], an area withinthe clay-matrix of the sample was chosen for FIB-SEM tomography(Fig. 1a, b).

2.2. X-ray m-CT

X-ray computed micro-tomography [74,75] was performed atthe University of Mainz (Institute of Geosciences), using a custom-built m-CT scanner (ProCon CT Alpha, Germany). The m-CT isequipped with a microfocus X-ray tube (Feinfocus, Germany),featuring a diamond-coated anode target, with a focal spot size of afew mm, and a flat panel CCD detector (Hamamatsu, Japan), with asize of 105 mm � 105 mm and a maximum resolution of2048 � 2048 pixels. The sample was scanned with X-rays set to55 kV source voltage and a current of 0.2 mA at the target. X-raysare filtered by a 0.65 mm thick aluminum plate, in order to reduce


beam hardening artifacts [74,75]. The detector resolutionwas set to1024 � 1024 pixels and 800 projections were acquired during arotation of 360�, corresponding to a rotation step-size of 0.45�. Foreach rotation step, 10 projections were captured and averaged fornoise reduction; the total acquisition time per step was 10 s. Slice-images were recorded with a resolution of 1023�1023 pixels and a

Fig. 3. Semi-automatic porosity segmentation, carried out in Fiji/ImageJ [77] and Avizo [83and manual cleaning of the automatic segmentation results; the latter two steps were only

pixel-size of 2.5 � 2.5 mm; the inter-slice spacing was also 2.5 mm,resulting later on in a voxel-size of 15.625 mm3. The “loss” of onepixel from detector to slice resolution is due to a hardware-basedring artifact reduction, which repeatedly moves the detector backand forth by one pixel, during the measurement. In total, 938 slice-images were stacked to generate a 3D dataset.

], using automatic thresholding (‘Huang threshold’ [84]), watershed segmentation [85]applied to the FIB-SEM data.

Fig. 4. Illustration of the most important output parameters from pore networkextraction (PNE) modeling (modified after Dong and Blunt [1]). Ri and rj are the porebody radii, rt is the radius of the connecting pore throat and lij is the total pore throatlength, measured from the center of pore i to the center of pore j.


2.3. FIB-SEM tomography

FIB-SEM tomography was performed at the Natural and MedicalSciences Institute (NMI) at the University of Tübingen (Reutlingen,Germany), using a Zeiss AURIGA FIB-SEM and following a proce-dure described in Holzer et al. [43] and Schroeppel et al. [76]. Im-ages were recorded using a secondary electron (SE2) detector, withthe following settings applied during the FIB-SEM slice and viewprocedure; FIB-milling was performed at a current of 500 pA andwith an electron voltage of 30 keV. Single FIB slices were cut at adistance of 15 nm between each successive slice and SE2-imageswere taken at an electron voltage of 2 keV, with a probe currentbetween 600 and 800 nA. The working distance was 5 mm and amagnification of 20,000-times, resulting in a pixel-size of14.84 � 14.84 nm. The cycle-time during image acquisition was33.4 s, the sample tilt angle 36� and the tilt axis 90�. In total, about300 FIB slices were cut and SEM images taken.

2.4. Pre-processing of the FIB-SEM and X-ray m-CT data

All 2D image-processing steps, prior to volume rendering and3D visualization, are illustrated in Fig. 2. Single FIB-SEM and m-CTimages were re-aligned using the Fiji/ImageJ [77] plugins ‘StackReg’or ‘TurboReg’ [78]; volumes of interest were also cropped in Fiji/ImageJ, using the plugin ‘VolumeJ’ [79]. A destriping filter (‘xStri-pes.jar’) by Münch et al. [80] was applied on the FIB-SEM image-stack, to eliminate vertical curtaining irregularities, which formduring ion-beam milling of heterogeneous materials. Imageenhancement filters, including background equalization (‘Gra-dientXTerminator’ [81]), noise reduction (median filter) andsharpening of pore edges, were applied in Adobe Photoshop [82], toimprove the quality of the subsequent semi-automatic porositysegmentation (Fig. 3). Reconstruction of the FIB-SEM and m-CTvolumes and analysis of the segmented pore space (see Section 2.7),was carried out using the 3D visualization software Avizo [83].

2.5. Porosity segmentation

The process of semi-automatic porosity segmentation, illus-trated in Fig. 3, was carried out on 2D FIB-SEM and X-ray m-CT (pre-processed) image-stacks, using Fiji/ImageJ [77] and Avizo [83] in-tegrated functions. Afterward, the 2D segmented porosities werereconstructed into 3D volumes in Avizo [83] (Fig. 2). Automaticporosity segmentation, especially on very high-resolution data, isnon-trivial, due to the complexity of the pore morphologies, noisein gray-scale SE2-images and the high focus-depth of SEM-imaging.In addition, imaging of larger pores can produce gray-scale gradi-ents inside the pores and at the pore boundaries [24,52,53]. Toobtain realistic porosity segmentations, in the present study, acombination of thresholding (‘Huang threshold’ [84]) in Fiji/ImageJ[77] and watershed segmentation (‘watershed transform of theEuclidean distance map’ [85]) in Avizo [83], was applied to the FIB-SEM data, whereas for the X-ray m-CT data, thresholding alonealready delivered satisfying segmentation results. Finally, for theFIB-SEM data, a manual cleaning of the results was applied in Avizo[83] (Fig. 3).

2.6. Evaluation of representative volumes

In the present study, a method based on the principles of localporosity theory e after Biswal et al. [86], Hilfer [87], Hilfer andHelmig [88] and Hu and Stroeven [89] e was applied, usingcovariance analysis, to check for the spatial homogeneity of a

certain property at the scale of observation [61], and to calculate therelative error of the property estimation, based on the size of theanalyzed volume element and the number of realizations of thatvolume [61,62]; definitions used in the present study are fromKanitet al. [62] and Keller et al. [61]:

After Kanit et al. [62], the covariogram K(X, h) is defined as “themeasure of the intersection of the set (X) (surface in 2D and volumein 3D) and the translated version of the set (X), by the distance h(X�h)”, applied to the measurement of porosity (F), this gives:

KðX;hÞ ¼ FðX∩X�hÞ ¼Z

kðxÞkðxþ hÞdx; (1)

where k(x) is defined as:

kðxÞ ¼ 1; if x2ðXÞ and kðxÞ ¼ 0; else: (2)

The covariance function C(X, h) was also defined after Kanit et al.[62], as “the probabilistic version of the covariogram for a sta-tionary set (X)” and describes the probability (P) of two points (x)and (x þ h), to be in the set of (X), with

CðX; hÞ ¼ Pfx2X; xþ h2Xg: (3)

The covariance typically tends to an asymptotic theoreticalvalue. If this value is reached before h /∞, for example for a valueh¼ A, “the points of the structure with a distance larger than A are notcorrelated” [62,90e92]; and after Kanit et al. [62] “this distance (A) isthe range of the covariance”. The covariance range was interpretedas the length scale at which the pore space reaches a certain level ofspatial homogeneity at the scale of observation, i.e. the resolution[61] (Fig. 6). This approach can be applied to all directions in spaceewith respect to the direction of translation of he andwill providedifferent values of A, as a measure of the degree of microstructuralanisotropy.

Relative errors (Ɛr) of porosity estimations were calculated afterKeller et al. [61] and Kanit et al. [62], based on the size of theanalyzed sample volume (V) and the number of realizations (N) ofthat volume element, using [61]:

Fig. 5. Orientation data analysis. a) Orientations of the sample bedding, parallel to yz, and the BIB-SEM cross-section area analyzed by Hemes et al. [24], parallel to xz; the directionof FIB-SEM slicing was in the z-direction. b) Conversion of Cartesian (x, y, z) coordinates to spherical (4, q) coordinates, used for pore throat orientation analysis (Section 2.7.2).


εr ¼ 2DFðVÞ.�

FmeanN1=2�; (4)

withDF(V), the standard deviation of porosity, measuredwithin thevolume V; i.e. the square root of the variance of porosity [61], whichis given by [61,62]:

D2FðVÞ ¼ Fmeanð1� FmeanÞA3

.Va; (5)

A3 is the integral range and “gives information on the domainsize of the pore structure for which the measured porosity withinthe volume V has a good statistical representativity” [61,62], and ais the coefficient, which controls the slope of the fit to the varianceof porosity, plotted against L, (the length of themeasuring cell), on adouble logarithmic scale. For approximation of the integral range(A3), the variance DF

2(V) is computed for porosities measuredwithinthe respective cells of size V; afterward, the integral range (A3) canbe obtained by fitting Equation (5) to the data. Note that the meanvalue of porosity in each case depends on the resolution. In thepresent study, covariance analysis was used to determine therelative errors of porosity estimations within the analyzed X-ray m-CT and FIB-SEM sample volumes in 3D, as well as within the BIB-SEM cross-section area analyzed by Hemes et al. [24] in 2D.Moreover, the results should substantiate REA calculations using‘box-counting method’ after Kameda et al. [93], presented inFig. 1ced [24].

Covariance functions were used to estimate the length scales atwhich a certain degree of spatial homogeneity of porosity can beexpected at the respective scales of observation, i.e. the resolutionsof X-ray m-CT, BIB-SEM and FIB-SEM.

2.7. Pore space analysis

2.7.1. Volume rendering and connected component analysisTo visualize the 3D geometry of the pore space and for quali-

tative inspection of the data, volume rendering of 2D segmentedporosities was done in Avizo [83] (Fig. 2). To quantify the porosity,an Avizo built-in function (‘connected component analysis’; [83])was used, which automatically detects connected porosity vol-umes, down to a minimum threshold size (set to 10 voxels),resulting in smallest connected porosity volumes of ~3.3Eþ04 nm3

for the FIB-SEM data and ~156 mm3 for the X-ray m-CT data. Porosityvolumes are interpreted to be connected in 3D, if they share at leastone common voxel-face. Output data from connected component

analysis are the connected porosity volumes and their center po-sitions in x-, y- and z-coordinates.

2.7.2. Pore network extraction (PNE) modelingInput data for pore network extraction (PNE) modeling are the

2D segmented porosity image-stacks from FIB-SEM and X-ray m-CT,saved as 3D binary tiff-files. The pore network extraction (PNE)code used in the present study is the latest version of a networkextraction code by Dong and Blunt [1], by courtesy of the group ofMartin Blunt at Imperial College London (UK, Department of EarthScience and Engineering). The process is based on the so called‘maximum ball approach’, after Silin and Patzek [94,95], wheremaximum spheres are fitted to and centered on each voxel of thepore space. Afterward, the spheres are classified into pore bodiesand pore throats by a successive ranking and clustering process, asdescribed in Dong and Blunt [1]. The largest spheres are defined as‘masters’ and form the pore bodies, whereas the chains of succes-sively smaller spheres connecting them are called ‘slaves’ andrepresent the pore throats. At a local minimum sphere betweentwo pore bodies (maxima or ‘master spheres’), the interconnectingpore throat diameter (dt ¼ 2 * rt; Fig. 4) is measured [1]. For a moredetailed description of the method, see Silin and Patzek [94,95], Al-Kharusi and Blunt [65], as well as Dong and Blunt [1]; and for an upto date review of pore-scale imaging and pore network extractionmodeling, we refer to Blunt et al. [2]. For further analysis, measuredpore body and pore throat volumes, as well as the interconnectingpore throat diameters (dt) were used. The pore body volumesdescribe the pore space, whereas the pore throat volumes compriseall the spheres along a connecting pore throat chain [1]. Here it isimportant to note, that sphere equivalent pore body and porethroat diameters, calculated from the pore body and throat vol-umes, are significantly larger than the diameters (di/j and dt),measured from the radii of the largest and smallest spheres (ri/j andrt; Fig. 4), respectively. Further important output parameters are thecoordination numbers of the pore bodies (CN ¼ number of con-nected pore bodies) and the pore throat total lengths (lij), which arethe distances from the center of one pore body (i) to the center ofthe connected pore body (j) (Fig. 4). Moreover, dimensionless shapefactors (G ¼ volume * length/surface area2; [96]) are extracted forthe pore bodies and the pore throats, describing the pore surfacemorphologies (i.e. the larger the shape factor (G), the more regularor smooth is the pore surface). The positions of the centers of allpore bodies (in x-, y- and z-coordinates) were used to perform anearest neighbor analysis, giving the distance of a pore body to its(potentially connected) nearest neighbor, which was thencompared to the respective connecting pore throat's total length.

Fig. 6. Results of variance and covariance analyses after Kanit et al. [62] and Keller et al. [61], on segmented porosity data from X-ray m-CT (a) and FIB-SEM (c) in 3D, as well as on 2D BIB-SEM porosity data (b) [24]. Relative errors ofporosity estimations are shown in dependence of the size of the analyzed volume/area and for a given number of realizations (N ¼ 1, 10, 100). Moreover, the range of the covariance (mm) is indicated, suggesting the characteristic lengthscale at which a certain degree of spatial homogeneity can be expected for the analyzed property of porosity at the respective resolution.

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8


Moreover, after conversion of the pore throat locations from Car-tesian (x, y, z) to spherical (4, q) coordinates (Fig. 5b), a pore throatorientation analysis was performed, resulting in a density distri-bution of the angles phi (4) and theta (q), indicating the preferredpore throat orientations, with respect to the orientation of the x-, y-and z-axes.

2.7.3. Analysis of pore-size distributions from FIB-SEM and X-ray m-CT, in 2D and in 3D and comparison to 2D BIB-SEM pore-areadistributions [24]

Following the findings of Klaver et al. [54], Houben et al.[52,53] and Hemes et al. [24], 2D pore-area distributions in clayeymaterials can be described using power-laws. To link the obser-vations made at different levels of resolution and to bridge the gapin representative pore detection ranges (PPRs) between X-ray m-CTand FIB-SEM, pore-area distributions obtained from the analysis of2D X-ray m-CT and FIB-SEM image-stacks were compared to porearea data from 2D BIB-SEM investigations by Hemes et al. [24],carried out on the same reference sample (ON-Mol-1-196) andwithin a representative elementary area (REA; Fig. 1a) of about

Fig. 7. Results of X-ray m-CT porosity analysis. a) Total analyzed, reconstructed sample volumvolume rendered pore space, consisting of 15,322 connected components down to a minivolume (a). c) Five largest detected connected components at the scale of observation ocontribution distributions of connected porosity volumes from X-ray m-CT.

2.4Eþ04 mm2. Since the BIB-SEM cross-section surface was ori-ented perpendicular to the sample bedding (Fig. 1a; Section 2.1)and parallel to the xz-plane, 2D pore areas from FIB-SEM and X-ray m-CT image-stacks should be measured within the sameorientation of the image-stacks. Therefore, FIB-SEM and X-ray m-CT image-stacks were re-sliced in Avizo [83] and orientationscorresponding to the orientation of the BIB-SEM cross-sectionsurface, i.e. parallel to the xz-plane (Fig. 1a), were used for porearea analysis. To compare the 3D pore body and pore throat vol-ume distributions from PNE (Section 2.7.2) to 2D pore area data,the 3D volumes were converted into corresponding cross-sectional areas, assuming spherical pores. A non-linear binningof always doubling the subsequent bin-size and starting with abin-size of one, was used for the pore area distribution analyses[24,52e54]. To check for a hypothesized power-law behavior ofpore-size distributions, pore-size frequencies (Ni) per bin werenormalized by the bin-sizes (bi) and the size of the area analyzed(Sarea), and plotted against the centers of the respective bins (Si) ona double logarithmic scale. Power-law exponents (D) can bederived from the slopes of the linear fits to the logelog pore-area

e (~4.78 mm3). b) Results of connected component analysis in Avizo [83], showing themum size of 10 voxels (¼156 mm3) and covering ~0.85% of the total analyzed samplef X-ray m-CT (voxel-size ¼ 15.6 mm3). d) Number fraction and total porosity volume

Fig. 8. Visualization of the results of connected component analysis [83] on X-ray m-CT data. a) All resolved connected components are shown in different colors per at the scale ofobservation of X-ray m-CT connected porosity volume. b) Zoom into the connected porosity volumes, displaying roundish and smooth pore morphologies, with relatively low surfacearea to volume ratios and sizes between 156 and 7.4Eþ05 mm3; the distances between isolated porosity volumes are ~30 mm (geometric mean). (For interpretation of the referencesto color in this figure legend, the reader is referred to the web version of this article.)


distributions, using the following equation (Equation (6))[24,52e54]:

logðNi=ðbiSareaÞÞ ¼ �DlogðSiÞ þ logðCÞ; (6)

C is a constant of proportionality.

2.8. Mercury injection porosimetry (MIP)

Mercury injection Porosimetry (MIP) data from Hemes et al.[24], on the same reference sample (ON-Mol-1-196), werecompared to results of PNE modeling on FIB-SEM and X-ray m-CTdata; the number fraction distribution of pore bodies and porethroats from PNE was plotted together with the porosity volumeintrusion distribution from MIP, against the pore diameters, usingthe binning of the MIP data [24] (Fig. 15). The comparison is rele-vant, since the major porosity volume intrusion regimes from MIPshould correspond to the peaks in the pore body and pore throatfrequency distribution. Moreover, the comparison should help toevaluate the representativeness of our investigations, since Mer-cury injection Porosimetry is carried out on bulk sample volumes.Washburn's equation [97] was used to relate porosity volumesintruded per pressure step (Pi) to the access pore throat diameter(d), via [97]:

Pi ¼ �4gcosw=di; (7)

Pi are the Mercury injection pressures, between 58.6 kPa and413.3 MPa [24], g is the surface tension of the Mercury (~0.484 N/mat 25 �C, after Kemball [98] and Nicholas et al. [99]); wis the contactangle between the Mercury and the pore walls (~139� for Bentoniteand Montmorillonite clays and ~147� for Illite and Kaolinite clay;after Diamond [100]) and di are the resulting pore throat entrydiameters, between 25.3 mm, down to 3.6 nm [24].

MIP is able to access only interconnected porosity volumes, andmoreover, analysis of the data assumes cylindrical pores.

Table 1 summarizes all definitions of pore space, connectedporosity volumes, pore networks, pore bodies/throats, as well aspore throat diameters, used in the present contribution.

3. Results

3.1. 2D BIB-SEM and mercury injection porosimetry (MIP) resultsfrom Hemes et al. [24], relevant for the present study

Hemes et al. [24] investigated the 2D porosities in four repre-sentative samples of the Boom Clay Formation from the Mol-1borehole (Zeelmaekers [73] sample series), at the nm-scale reso-lution and within representative elementary areas (REAs) of BIBcross-sections, using scanning electron microscopy (SEM) (Fig. 1a).The most important outcomes of the study are that the majority ofthe nano-porosity in typical fine-grained, clay-rich (�50 dry wt.-%clay) Boom Clay resides within the clay-matrix. Characteristic poremorphologies and total porosities were identified in differentmineral phases (Fig. 1b) and BIB-SEM, as well as MIP results suggestmost of the pore space connectivity in fine-grained Boom Clay to becontrolled by small pores within the clay-matrix of the samples. Forthe sample investigated in the present study (ON-Mol-1-196;HADES-level), representative elementary area (REA) calculationsusing the so called ‘box counting method’ (after Kameda et al. [93]and Houben et al. [52]), resulted in REAs of about 5.6Eþ03 mm2,based on the mineralogical composition segmented within a BSE-image mosaic (Fig. 1c) and ~7.1Eþ03 mm2, using the box countingmethod on automatically segmented porosities (Fig. 1d), within theSE2-image mosaic shown in Fig. 1a. The total BIB-SEM resolvedporosity in sample ON-Mol-1-196, down to a practical poredetection resolution (PPR) ~960 nm2 (¼10 pixels), was 12% of therepresentative area analyzed (2.4Eþ04 mm2; Fig. 1a). The total MIPconnected porosity volume, within a pore throat diameter rangebetween 25.3 mmdown to 3.6 nm (see Section 2.8), was 26.5 Vol.-%,andmajorMercury intrusion peaks were identified between 60 and74 nm pore throat diameter, as well as at 2 mm [24] (Fig. 15). Thetotal water content, measured by Hemes et al. [24] from the weightloss of the sample during oven drying, was 18% of the wet sampleweight, resulting in a total water content calculated porosity of36 Vol.-%, using an average grain density of 2.6 g/cm3 and a densityof the pore water of 1.02 g/cm3 [101]. The differences between thetotal water content calculated porosity and the MIP measuredinterconnected porosity volume (1), as well as the total BIB-SEM

Fig. 9. Results of pore network extraction (PNE) modeling [1] on X-ray m-CT data. a) Extracted pore network model, displaying 13,111 pore bodies and 4746 pore throats. b) Numberfractions and total porosity volume contributions of pore bodies and pore throats. c) Frequency and total porosity volume contribution distributions of pore body coordinationnumbers. d) Distributions of average pore shape factors (G) and pore body coordination numbers (CN) vs. pore body volumes. e) Distance to nearest neighbor pore body and porethroat total length distributions. f) Density distribution of pore throat orientations (4 vs. q; Fig. 5b; Section 2.7.2).


observed porosity (2), were interpreted to be (1) either due toisolated pores, or porosity volumes connected via pore throatssmaller than 3.6 nm in diameter, and (2) resulting from larger poresand/or drying artifacts, existing within the bulk sample volumeanalyzed during MIP. The comparison of Mercury intrusion vs.extrusion curves allows estimating pore body to pore throat sizeratios, giving values between 1.3 and 47 for the sample investigatedin the present study, which hints towards an ‘ink-bottle-like’ shapeof the pores [24,102e105].

3.2. Estimation of the analyzed samples' representativeness, usingcovariance analysis

Variance and covariance analyses on segmented porosities fromX-ray m-CT and FIB-SEM tomography, within analyzed sample vol-umes of ~4.78 mm3 (X-ray m-CT) and ~377.24 mm3 (FIB-SEM),respectively, give relative errors of ~26% (N ¼ 1), 8.5% (N ¼ 10) and~3% (N ¼ 100) for the X-ray m-CT data (Fig. 6a); and ~40% (N ¼ 1),12% (N ¼ 10) and ~3.5% (N ¼ 100), for the FIB-SEM data (Fig. 6c).

Fig. 10. Results of 3D FIB-SEM porosity analysis. a) Analyzed 3D reconstructed sample volume of ~377.24 mm3. b) Volume rendered porosity from connected component analysis inAvizo [83] on 2D segmented porosities (Sections 2.5 and 2.7.1), displaying 6629 connected porosity volumes, down to ~3.3Eþ04 nm3 volume (¼10 voxels), which are covering18.39% of the analyzed sample volume. c) Largest connected porosity volume at the resolution of FIB-SEM (~3.3Eþ03 nm3 voxel-size), accounting for 87% of the total resolved porespace. d) Second and third largest connected components, with sizes of 0.41 and 0.5 mm3, accounting for 0.59 and 0.73% of the total resolved pore space, respectively. e) and f)number fractions and total porosity volume contributions of connected components; f) after removal of the largest connected porosity volume, shown in c).


Using a 2D version of the approach on BIB-SEM porosities,segmented within the SE2-image mosaic of ~2.4Eþ04 mm2, shownin Fig. 1a [24], results in a relative error of the porosity estimation(for N ¼ 1) ~5% (Fig. 6b).

Characteristic length scales of spatial homogeneity of theobserved porosities at the respective levels of resolution are ~40 mmfor the X-ray m-CT data (Fig. 6a), ~10 mm based on 2D BIB-SEMporosity analysis (Fig. 6b) and in the range between 1 and 2 mm

for covariance analysis on segmented porosities from FIB-SEM to-mography (Fig. 6c).

3.3. Pore space characteristics from X-ray m-CT

Automatic porosity segmentation, as described in Section 2.5and illustrated in Fig. 3, on X-ray m-CT data of sample ON-Mol-1-196 (Fig. 7a), reveals a total porosity of ~0.85 Vol.-% by connected

Fig. 11. Visualization of results of connected component analysis [83] on FIB-SEM data. a) Largest connected porosity volume (~60.35 mm3), covering 87% of the total resolved porespace. b) Remaining, “isolated” porosity volumes with sizes between 3.3Eþ04 (¼10 voxels) to 5Eþ08 nm3. c) Zoom into the largest connected porosity volume, showing pore throatsdown to ~100 nm in diameter, as well as ‘dead-end pores’ of about the same size. d) Zoom into the, at the scale of observation of FIB-SEM, isolated porosity volumes, displayingmuch more complex pore morphologies, with higher surface area to volume ratios compared to X-ray m-CT data (Fig. 8). Distances between “isolated” porosity volumes are ~180 nm(geometric mean).


component analysis in Avizo [83] (Fig. 7b), down to smallest con-nected porosity volumes of ~156 mm3 (¼10 voxels). In total, 15,322connected components were detected (Figs. 7b and 8a). The fivelargest connected porosity volumes are between 3.7Eþ05 and7.4Eþ05 mm3 and account for between 0.91 and 1.82% of the totalresolved porosity (Fig. 7c). The porosity volume frequency distri-bution shows a peak ~400 mm3, whereas porosity volumes between9.1Eþ03 and 7.3Eþ04 mm3 contribute to the major fraction of thetotal resolved pore space (Fig. 7d). Fig. 8a visualizes the results ofconnected component analysis on X-ray m-CT data, showing everyinternally connected porosity volume in a different color. In Fig. 8b,a zoom into the porosity volumes is depicted, showing a ratherhomogeneous spatial distribution of the different porosity vol-umes, with roundish, smooth pore morphologies, low surface areato volume ratios and ink-bottle shaped pores. Isolated porosityvolumes are between 156 and 7.4Eþ05 mm3 in size and at distances~30 mm (geometric mean) to each other.

Quantitative pore space connectivity analysis using porenetwork extraction (PNE) modeling (Section 2.7.2) on X-ray m-CTdata confirms the results of connected component analysis, byshowing a total number of 13,111 extracted pore bodies, but only4746 pore throats (Fig. 9a). Pore body and pore throat size distri-butions from PNE (Fig. 9b) are similar to the porosity volume dis-tribution of connected components (Fig. 7d). However, showing ashift of the number fraction distribution of pore throats towardssmaller pore-sizes, resulting in a peak ~400 mm3, but with smaller

pore-sizes, down to ~17 mm3 existing; and a shift of the numberfraction distribution of pore bodies towards larger pore-sizes, witha peak ~1.1Eþ03 mm3 pore body volume. The total porosity volumecontributions of pore bodies and pore throats are shifted towardssmaller pore-sizes, showing peaks between 1.1Eþ03 and3.2Eþ03 mm3 for the pore throats and ~9.1Eþ03 mm3 for the porebodies (Fig. 9b). These observations can be simply explained by thedifferentiation between pore bodies and pore throats during PNE,whereas during connected component analysis, pore throats areincorporated in and measured as part of the connected porosityvolumes. Further connectivity analysis substantiates the lowinterconnectivity of the pore space at the resolution of X-ray m-CT,with pore body coordination numbers mostly below five and clearpeaks in the frequency, as well as total porosity volume contribu-tion distributions of pore body coordination numbers at zero,indicating isolated pore bodies (Fig. 9c). Pore shape factor analysisshows only a low dependency of the pore shape on the size (vol-ume) of the pores, however, a slight increase in the average porebody coordination number with increasing pore body volumes canbe observed (Fig. 9d). Distance to nearest neighbor pore body andpore throat total length distributions from PNE on X-ray m-CT dataare very similar, with peaks ~25 mm in both distributions (Fig. 9e).This is in good agreement with the observations made duringconnected component analysis (Fig. 8b). Moreover, these resultsindicate a connectivity of the pore space, resolved by X-ray m-CT,mostly to nearby pore bodies.

Fig. 12. Results of pore network extraction (PNE) modeling ([1], Section 2.7.2) on FIB-SEM data. a) Extracted pore network, showing 15,201 pore bodies and 14,823 pore throats, aswell as high coordination numbers of the pore bodies. b) Number fractions and total porosity volume contributions of pore body and pore throat sizes. c) Number fraction and totalporosity volume contribution distributions of pore body coordination numbers. d) Distribution of average pore shape factors (G) and average coordination numbers (CN) vs. porevolumes. e) Comparison of pore throat total length and distance to nearest neighbor pore body distributions. f) Density distribution of pore throat orientation angles phi (4) andtheta (q), suggesting a preferred orientation of the pore throats parallel to the sample bedding (Fig. 5).

Fig. 13. Results of power-law analyses on pore-area distributions from porosity seg-mentations on 2D FIB-SEM and X-ray m-CT image-stacks, as well as on 2D BIB-SEMporosity data [24], suggesting power-law distributions of pore-sizes over ~6 ordersof magnitude, i.e. within the practical pore detection resolution ranges of FIB-SEM/BIB-SEM and X-ray m-CT, and with a power-law exponent (D2D) ~2.2.


The density distribution of pore throat orientations from PNE onX-ray m-CT data clearly shows two maxima (Fig. 9f): (1) centered atphi (4) ~0� and theta (q) ~�40� and (2) with phi (4) alsocentered ~0� and theta (q) ~þ140�, which suggests only onepreferred orientation of the pore throats, since cases (1) and (2) areequivalent. This preferred pore throat orientation was interpretedto correspond to the orientation of the bedding in the X-ray m-CTsample volume.

3.4. Pore space characteristics from FIB-SEM tomography

Within the analyzed FIB-SEM sample volume of 377.24 mm3 andwith dimensions of 13.1 � 7 � 4.1 mm (Fig. 10a), a total porosity of

Fig. 14. Results of power-law analyses on pore-area distributions, obtained from theprojection of 3D pore body and pore throat volumes from PNE [1] on FIB-SEM and X-ray m-CT porosity data, onto sphere equivalent 2D cross-sectional areas, suggestingpower-law distributions of pore-body and pore-throat sizes over ~6 orders of magni-tude, within the practical pore detection resolution ranges, and with power-law ex-ponents (D3D) ~2.34 for the pore bodies and ~2.38 for the pore throats.

18.39 Vol.-% was detected by connected component analysis inAvizo [83], down to smallest porosity volumes of 10 voxels, corre-sponding to ~3.3Eþ04 nm3 (Fig. 10b). A total number of 6629connected components was detected, but with the largest con-nected porosity volume covering 87% of the total pore space,resolved by FIB-SEM tomography (Figs. 10c and 11a, c). The secondand third largest connected components account for ~0.73 and0.59% of the resolved pore space respectively, with sizes between0.41 and 0.5 mm3 (Fig. 10d). Porosity volume distribution analysisshows a peak ~7.3Eþ04 nm3 pore volume, with regard to pore-sizefrequencies. However, the contribution of porosity volumes to thetotal resolved pore space is severely biased by the largest detectedconnected component (Fig. 10c). Therefore, this porosity volumewas removed from the analysis, resulting in a peak of connectedporosity volume contributions between 4.7Eþ06 and 3Eþ08 nm3

(Fig. 10f).For further, semi-quantitative analysis of pore space morphol-

ogies, the largest connected porosity volume (Fig. 10c) and theremaining porosity volumes, were plotted separately (Fig. 11a, b),and by zooming into the pore space (Fig. 11c, d). Thus, pore throatconnections down to ~100 nm in diameter (estimated), as well asdead-end pores of about the same size, could be visualized(Fig. 11c). The remaining, unconnected porosity volumes showcomplex pore morphologies, with high surface area to volume ra-tios, sizes below 5Eþ08 nm3 and distances ~180 nm (geometricmean) to each other (Fig. 11d).

Quantitative pore space connectivity analysis using porenetwork (PNE)modeling on FIB-SEM data shows a total 15,201 porebodies and 14,823 pore throats, as well as a high connectivity of thepore space, indicated by high pore body coordination numbers(Fig. 12a). Pore body and pore throat size distributions are similar toporosity volume distributions obtained by connected componentanalysis, after removal of the largest connected component(Fig.10f). However, a shift of pore throat frequencies, as well as totalporosity volume contributions towards smaller pore-sizes can beobserved, resulting in a peak ~7.3Eþ04 nm3 for the frequency dis-tribution, but with smaller pore-sizes down to ~3.3Eþ03 nm3

existing; and ~4.7Eþ06 nm3 for the total porosity volume contri-bution distribution. The frequency distribution of pore bodies is

Fig. 15. Comparison of Mercury injection Porosimetry (MIP) intrusion data [24] to porebody and pore throat frequency distribution from PNE [1] on FIB-SEM and X-ray m-CTdata, suggesting two major porosity intrusion, as well as pore space connectivity re-gimes, corresponding to (1) pores below 100 nm in pore throat diameter, resolved byFIB-SEM and (2) pores with pore throat diameters between 1 and 7 mm, resolved by X-ray m-CT.

Table 1Terms and definitions used in the present contribution, to describe the pore space in 3D.

Term used Definition Abbreviation orsymbol used

Porosity Void space in a sample (unconnected or connected), relative to the sample volume F

Pore space Equivalent to porosityConnected porosity

volumes/componentsAt the scale of observation connected porosity volumes (minimum size ¼ 10 voxels) from connected componentanalysis in Avizo [83]

CC

Pore network Connected pore space from pore network extraction (PNE, [1]), down to 1 voxel in connecting pore throat PNPore body Pore space filled by maximum spheres from PNE [1] PBPore throat Chain of successively smaller spheres, connecting two pore bodies from PNE [1] PTPore throat diameter Either the diameter of the locally smallest sphere, connecting two pore bodies (Fig. 4; dt ¼ 2 * rt); or the porosity

intrusion diameter from Mercury injection Porosimetry (MIP), calculated using Washburn's equation [97] (Equation(7); d)

dt/d


shifted towards larger pore-sizes, compared to the results of con-nected component analysis (Fig. 10f), showing a peak between2.1Eþ05 to 5.8Eþ05 nm3 pore body volume; whereas pore bodycontributions to the total porosity from PNE (Fig. 12b) and porosityvolume contributions from connected component analysis, afterremoval of the largest connected porosity volume (Fig. 10f), arenearly identical. They show peaks between 3.7Eþ07 to1.1Eþ08 nm3 for the pore bodies' porosity contributions from PNE(Fig.12b) and between 4.7Eþ06 to 3Eþ08 nm3 for the contributionsof connected porosity volumes (Fig. 10f).

Detailed analysis of the pore space connectivity from PNE sub-stantiates the interpretation of a highly connected pore spaceresolved by FIB-SEM. The pore bodycoordination number frequencydistribution shows a peak at CN¼ 1,whereas pore bodieswithmuchhigher coordination numbers, between 10 and 20 and up to 47contribute to significant fractions of the total porosity (Fig. 12c).

Pore shape analysis shows a much higher dependence of thepore shape on the size (volume) of the pores, compared to X-ray m-CT data, with clearly decreasing average pore shape factors (G) withincreasing pore volumes, indicating a higher complexity of poremorphologies for larger pores (Fig. 12d). Larger pores moreovershow significantly higher average coordination numbers thansmaller pores (Fig. 12d).

Comparison of pore throat total length and distance to nearestneighbor pore body distributions shows a difference in the peakpositions, as well as the shape of the distributions (Fig. 12e).Whereas the distribution of distances of pore bodies to theirnearest neighbor is Gaussian shaped, with a peak ~150 nm and ageometric mean of 151 nm, the distribution of pore throat totallengths is skewed towards longer pore throats, showing a peak~210 nm, but a geometric mean of 289 nm (Fig. 12e). The maximumdistance of a pore body to its nearest neighbor is 502 nm, whereasthe longest pore throat is with ~2.6 mm significantly longer.Moreover, the direct comparison of pore body connections tonearest neighbors shows that only ~10% of the pore bodies areconnected to their nearest neighbor, whereas the remaining 90%are connected to more distant pore bodies.

The density distribution of pore throat orientations suggeststwo rather broad maxima, which are both centered at phi (4) ~0�,but with theta (q) (1) ~�75� and (2) ~þ100� (Fig. 12f). This suggestsagain only one preferred pore throat orientation, with phi (4) ~0�

and thus within the yz-plane (Fig. 5b); and theta (q) with an angleof more or less±90� from the xz-plane towards yz-. Pore throats arethus preferably oriented parallel to the bedding in the FIB-SEMsample, which is parallel to the yz-plane (Figs. 1a, 5a and 12g;Section 2.1).

3.5. Power-law analysis of pore size distributions

Double logarithmic plots of bin-size and area analyzednormalized frequencies of pore areas measured from 2D BIB-SEM,

as well as within X-ray m-CT and FIB-SEM image-stacks (Section2.7.3), show a continuous power-law distribution of pore-sizes over~6 orders of magnitude e from ~3.1Eþ03 nm2, interpreted as thepractical pore detection resolution (PPR) of BIB-SEM and FIB-SEMin 2D, up to ~3.2Eþ09 nm2, corresponding to the largest poreareas measured by X-ray m-CT porosity analysis in statisticallyrepresentative amounts (Fig. 13). Fitting a power-law to thecontinuous distribution gives a power-law exponent (D2D) ~2.2.There exists only a small gape indicated as (2) in Fig. 13 e betweenthe largest pore-sizes measured by 2D BIB-SEM in representativeamounts (~6.3Eþ06 nm2) and the practical pore detection resolu-tion of 2DX-ray m-CT porosity analysis (~1Eþ08 nm2); we thereforeassume pore-sizes within this range (2) to follow the same power-law distributions as larger pore-sizes resolved by X-ray m-CT as wellas smaller pores resolved by 2D BIB-SEM and FIB-SEM. Resultsmoreover show a very good agreement between the 2D BIB-SEMpore-area distribution measured by Hemes et al. [24] and 2Dpore areas measured in the present study within single FIB-SEMslices.

In 3D, very similar results were obtained by analyzing thenormalized frequencies of pore bodies and pore throats from PNE,after conversion of their volumes into sphere equivalent cross-sectional areas (Section 2.7.3; Fig. 14). Pore body and pore throatsize distributions were analyzed separately, but give very similarresults (Fig.14). Least square linear regression analyses on the pore-size distributions results in power-law exponents D3D

pore bodies~2.34 and D3D

pore throats ~2.38, over ~6 orders of magnitude, be-tween ~3.1Eþ03 nm2 and ~6.4Eþ09 nm2 (Fig. 14). The slightlyhigher power-law exponent obtained for the pore throat size dis-tribution is due to the relatively higher amount of smaller porethroats, compared to relatively more, larger pore bodies. As a resultof the lack of 3D data within the pore-size range resolved by 2DBIB-SEM (Fig. 13), the gap in representative pore detection resolu-tion ranges between FIB-SEM (<1.6Eþ06 nm2) and X-ray m-CT(>1Eþ08 nm2), denoted by (2) in Fig. 14, is slightly larger; however,we still assume pore-sizes within this range to follow the samepower-law distributions as pore-sizes above and below.

4. Discussion

4.1. Representativeness of the analysis

Using high-resolution image-analysis for porosity investigationswithin limited volumes or areas of investigation, the questions ofcontinuity of the scales of observation, as well as representative-ness of the analyzed areas or volumes, remain crucial. Basic localporosity theory and covariance analysis [61,62,86e92] were used inthe present contribution to determine the characteristic lengthscales at which a certain degree of spatial homogeneity of theinvestigated bulk sample property of porosity can be expected atthe respective microstructural level of observation; and to calculate

Fig. 16. Conceptual model of the pore space connectivity in fine-grained HADES-level Boom Clay; a) results of preferred pore throat orientation analysis after PNE [1] on FIB-SEMdata (Fig. 12f, g), showing preferred pore throat orientations parallel to the sample bedding. b) Conceptual model of the 3D pore network in Boom Clay (within the bedding plane),showing large, at the scale of observation of X-ray m-CT isolated porosity volumes, with distances (d1) ~30 mm to each other; distances between nearest neighbor pore bodies, as wellas pore throat total lengths from PNE [1] on X-ray m-CT data (d2) are ~27e29 mm (geometric means). The pore space resolved by FIB-SEM tomography is highly interconnected,showing distances between nearest neighbor pore bodies (d3) and pore throat total lengths (d4) from PNE [1] on FIB-SEM data ~151 nm and ~289 nm (geometric means),respectively. Note that the size differences between pore structures resolved by X-ray m-CT and FIB-SEM are not to scale!


and evaluate the relative errors of porosity estimations carried outwithin the limited areas or volumes of investigation (Fig. 6). Resultsshowcharacteristic length scales of about 40 mmat the resolution ofX-ray m-CT (Fig. 6a), ~10 mm for the 2D BIB-SEM porosity in-vestigations by Hemes et al. [24] (Fig. 6b), and between 1 and 2 mmfor FIB-SEM tomography based porosity analyses (Fig. 6c). Consid-ering the sizes of the areas and volumes analyzed in the presentstudy, as well as by Hemes et al. [24], shows that our methodo-logical approach of successively increasing the resolution andsimultaneously decreasing the size of the volume or area analyzed,by stepping from 3D X-ray m-CT (resolution ~15.6 mm3, volume ofseveral mm3), to 2D BIB-SEM (resolution ~96 nm2, area analyzed~155 � 155 mm2; Fig. 1a, [24]), to 3D FIB-SEM(resolution ~3.3Eþ03 nm3, volume ~13.1 � 7 � 4.1 mm3), allows ateach step to cover the characteristic length scale of spatial homo-geneity of porosity, calculated at the previous level of resolution(Fig. 6). This indicates both, the conservation of representativenessof our investigations, as well as the continuity of the scales ofobservation of the analyses. Although 2D BIB-SEM does not givemuch information on the pore space connectivity and pore throatsizes, this contribution demonstrates that it is essential to bridgethe gap in observational scales between 3DX-ray m-CT and FIB-SEMtomography, since sample volumes analyzed by FIB-SEM are by fartoo small to cover the characteristic length scale of spatial homo-geneity of porosity, calculated based on X-ray m-CT (~40 mm in thepresent study; Fig. 6a). FIB-SEM is not able to cover microstructuralheterogeneities, existing on a larger scale, but BIB-SEM provides theopportunity to prepare and analyze large, representative 2D cross-

sectional areas, covering the characteristic length scale calculatedfrom X-ray m-CT, but at the scale of observation of FIB-SEM. Basedon BIB-SEM porosity analysis, relevant spots for high resolution 3DFIB-SEM tomography can be chosen [50] (Fig. 1a).

Results of characteristic length scale calculations using covari-ance analysis moreover do not suggest any significant anisotropy,regarding the observed porosities in the directions parallel orperpendicular to the sample bedding (Fig. 6). However, 3D porethroat orientation analyses on PNE data from X-ray m-CT (Fig. 9f)and FIB-SEM (Fig. 12f, g) show preferred pore throat orientationsparallel to the sample bedding and suggest an existing anisotropyof the pore space connectivity in Boom Clay, with the major porespace connectivity oriented parallel to the bedding and thus locatedwithin the bedding planes (Fig. 16).

Following the discussion of Keller et al. [61] and Kanit et al. [62]:“from a statistical point of view, an error free estimation of porosityand other bulk sample properties, can never be obtained from a finitevolume of investigation”. Therefore, covariance analysis was used tocalculate the relative errors of porosity estimations within thelimited area and volumes analyzed in the present study. Resultsfrom FIB-SEM tomography porosity analysis are in a similar rangeto results obtained by Keller et al. [61], using FIB-SEM tomographyon sandy and shaley facies Opalinus Clay samples from the MontTerri rock laboratory (Switzerland). The relative error of ~5%(N ¼ 1), calculated for the 2D BIB-SEM porosity analysis by Hemeset al. [24] (Fig. 6b), however, is significantly lower, indicating that,to obtain an as accurate estimation of porosity in 3D, either a muchlarger sample volume or a much higher number of samples would


have to be investigated, which in practice is not easy to achieve, dueto time and costs.

With regard to the overall representativeness of our in-vestigations, one has to take into account that very small samplevolumes were analyzed, compared to the extent of the Boom ClayFormation and considering the heterogeneity of the formation,regarding mineralogical composition and grain-size distribution(i.e. clay vs. silt content). We therefore can only assume theinvestigated samples to be representative of the respective layer(Putte Member at a depth of ~�196 m TAW), which is defined as ahomogeneous clayey unit, representative of fine-grained, clay-richend member samples of the Boom Clay.

4.2. Pore-size distribution analyses

Analyses of pore-size distributions obtained from 2D segmentedpore areas (Fig. 13), as well as from calculated (sphere equivalent)cross-sectional areas of 3D pore bodies and pore throats after PNE(Fig. 14), indicate power-law distributions of pore-sizes over ~6orders of magnitude, which were interpreted to reflect the scale-invariance of pore space microstructures in fine-grained (HADES-level) Boom Clay. Moreover, comparable power-law exponentsobtained in 2D (D2D ~2.2; Fig. 13) and in 3D (D3D

pore bodies ~2.34 andD3D

pore throats ~2.38; Fig. 14) suggest that 2D pore areas measuredwithin the representative BIB-SEM cross-section area analyzed byHemes et al. [24] (Fig. 1a), as well as within the 2D image-stacks ofFIB-SEM and X-ray m-CT, represent to some extent the complex 3Dpore morphologies, modeled by pore network extraction (PNE) onX-ray m-CT and FIB-SEM data. Hemes et al. [24] moreover calculatedthe power-law exponent of the pore-throat size distributionderived from Mercury injection Porosimetry (MIP) (DHg) to ~2.1,which is again in a similar range to results obtained in the presentcontribution, indicating representativeness of the present results,since MIP is carried out on bulk sample volumes. The slightly lowerpower-law exponent obtained from MIP porosity analysis could beattributed to larger pores and/or drying artifacts, possibly existingwithin the analyzed MIP sample volume, but were not measured orat least not in representative amounts by BIB-SEM and X-ray m-CTporosity analyses in the present contribution.

Power-law distributions of pore-sizes have also been found forother fine-grained, clay-rich geomaterials, like Opalinus Clay[52,53], gas shales [54], or coal [106].

The actual pore body and pore throat diameter (di/j and dt) fre-quency distribution was moreover compared to the MIP porosityvolume intrusion distribution of the same reference sample (ON-Mol-1-196, [24]), showing a very good agreement of the results(Fig. 15). Both distributions show major peaks located below100 nm pore throat diameter and secondary peaks between 1 and7 mm (Fig. 15). The slight shift of the Mercury intrusion distributiontowards smaller pore-sizes was attributed to the ‘ink-bottle-effect’[24,102e105,107] (see also Section 3.1).

4.3. Pore network model in Boom Clay

At the scale of observation of X-ray m-CT (~15.6 mm3 voxel-size),a large number of mostly isolated porosity volumes and pore bodieswas detected by connected component analysis [83] and from PNEmodeling [1] (Figs. 7e9), with only very limited connectivity be-tween the pore bodies (Fig. 9). This shows that X-ray m-CT isinsufficient to resolve the relevant pore space connectivity in fine-grained Boom Clay, since permeability measurements give a low,but existing permeability in the order of about 10�18 m2, in typicalfine-grained Boom Clay [108]. In contrast, FIB-SEM tomographyresolves a highly connected pore space, down to equivalent porethroat diameters ~20 nm and mostly within the clay-matrix of the

sample, with one large connected porosity volume covering ~87% ofthe total resolved pore space (Figs. 10 and 11). Pore networksextracted from FIB-SEM tomography show high coordinationnumbers of pore bodies up to 47, with connections existing not onlyto the nearest neighbor pore body, but also to much more distantpore bodies (Fig. 12; Section 3.4). Pore throat orientation analyseson pore networks extracted from X-ray m-CT (Fig. 9f) and FIB-SEM(Fig. 12f, g) show a strong anisotropy of the pore space connectiv-ity, with preferred pore throat orientations parallel to the samplebedding, suggesting a higher permeability in this direction, i.e.within the bedding planes (Fig. 16). Anisotropy of the permeabilityin Boom Clay has been measured both from laboratory [25,26], aswell as from in-situ experiments [109]; always resulting in a higherpermeability in the horizontal, bedding parallel than in the vertical,bedding perpendicular direction.

A conceptual model of the 3D pore network in Boom Clay(HADES-level) is presented in Fig. 16: Large, mostly isolatedporosity volumes, identified by connected component analysis onX-ray m-CT data may correspond to large inter-aggregate pores,previously detected by BIB-SEM porosity analysis [24]. Distances(d1) between “isolated” porosity volumes are ~30 mm (geometricmean) (Section 3.3; Figs. 8b and 16b). Moreover, these porosityvolumes are supposed to correspond to the connectivity regimeidentified by both PNE on X-ray m-CT data, as well as by MIP, withpore throat diameters mostly between 1 and 7 mm (Fig. 15). Dis-tances between single pore bodies (d2) and pore throat total lengthsfrom PNE on X-ray m-CT data show geometric means between 27and 29 mm (Figs. 9e and 16b). The highly connected pore space,resolved by FIB-SEM tomography (Figs. 10e12) is proposed tocorrespond mostly to intra-clay-matrix porosity, with major porethroat connections below 100 nm in diameter (Fig. 15) and dis-tances between nearest neighbor pore bodies (d3) ~151 nm (geo-metric mean; Figs. 12e and 16b). Pore throat total lengths from PNEon FIB-SEM data (d4) show a geometric mean ~289 nm (Figs. 12eand 16b).

Due to the gap in practical pore detection resolutions (PPRs)between X-ray m-CT and FIB-SEM (Figs. 14 and 15; Section 3.5),combining the results of pore network extraction (PNE) modelingon X-ray m-CT and FIB-SEM data, does not help in concludingwhether the pore space is connected at the scale of observation inbetween X-ray m-CT and FIB-SEM. However, MIP indicates anexisting, but lower connectivity of the pore space in fine-grainedBoom Clay within this range, with pore throat diameters between~200 and 800 nm (Fig. 15). MIP moreover gives evidence that porespace connectivity in Boom Clay exists even below the resolution ofFIB-SEM.

The present contribution demonstrates that a combination ofFIB-SEM tomography, X-ray m-CT and pore network extraction(PNE) modeling [1] provides a realistic direct description and rep-resentation of the major pore space connectivity regimes in fine-grained HADES-level Boom Clay (Fig. 15).

Comparing the results of the present study to previous porespace connectivity analyses on Opalinus Clay from the Mont Terrirock laboratory (Switzerland), e.g. by Keller et al. [58,61,63] orHouben et al. [57], it appears that for both e the Opalinus Clay andthe Boom Clay, pore networks within the clay matrix control themajor diffusivity of the material. However, the pore space in BoomClay shows a much higher interconnectivity at the scale of obser-vation of FIB-SEM, with a significant fraction (~87%) of the totalresolved porosity being connected to one large porosity volume(Figs. 10 and 11). Also, at the scale of observation of X-ray m-CT,limited pore space connectivity can be observed in Boom Clay,showing pore space connections up to ~12 mm in diameter (Figs. 9,15). In Opalinus Clay, on the contrary, most of the pore spaceconnectivity is assumed to be even below the resolution of FIB-SEM


[52,57,58,61,63]. This difference could relate to the difference inmeasured intrinsic permeabilities between the Opalinus Clay(~10�20 to 10�21; [110]) and the Boom Clay (~10�18; [108]), of about2 orders of magnitude.

Drying performed during sample preparation for subsequent X-ray m-CT, BIB-SEM and FIB-SEM investigations may damage thesample microstructure and result in a change of pore space mor-phologies and total porosity, due to the shrinkage of the clayminerals [111e113]. However, the pore space morphologies detec-ted by X-ray m-CT in the present contribution show mostlyroundish, very smooth pore shapes and no laminar structures withapertures above a few micrometers, which are typically associatedwith microfractures and desiccation cracks [57,114]. Thus, theanalyzed sample volume does not seem to have undergone criticaldamage of its microstructure, due to sample drying; at least notindicated by X-ray m-CT observations in the present contribution.

5. Conclusions

In the present study, X-ray m-CT and FIB-SEM tomography wereapplied to investigate the 3D pore space of a Boom Clay samplefrom the HADES level (URF) at Mol (Belgium). Pore networkextraction (PNE) modeling [1] allows simplifying the complexity ofthe 3D pore space for quantitative pore space connectivity analyses,by discriminating between pore bodies and pore throats. Thecombination of these methods allows providing a realistic directdescription of the pore space and its connectivity in 3D, resulting ina conceptual model of the 3D pore network in fine-grained BoomClay (Fig. 16). Moreover, the power-law distributions of pore-sizesover several (~6) orders of magnitude in 2D and in 3D (Figs. 13and 14) suggest scale-invariance and self-similarity of the porespace characteristics, hinting towards the possibility of up-scalingof our nm-to mm-scale observations to larger scale characteristicsof the Boom Clay Formation. Furthermore, it has been shown thatBIB-SEM is essential to bridge 3D observations at the resolutions ofX-ray m-CT and FIB-SEM, as well as to optimize the selection ofrelevant spots for FIB-SEM tomography.

The extracted 3D pore networks and pore throat size distribu-tions should be used in the future as input for modeling of singleand multi-phase fluid flow and of radionuclide transport in porousmedia by diffusion and migration [2,3]. Moreover, they should beused to estimate fluid flow properties, such as permeability, of fine-grained argillaceous materials.

The presented methodological approach delivers advances inporosity characterization techniques at different levels of micro-structural detail, relevant for material characterization in the oiland gas industries, for carbon dioxide (CO2) storage, as well as forradioactive waste disposal.

Acknowledgments

The authors would like to thank ONDRAF/NIRAS for financialsupport and the group of Martin Blunt (Imperial College London;Faculty of Engineering, Department of Earth Science& Engineering)for support during the application of pore network extraction (PNE)codes on segmented high resolution 3D FIB-SEM and X-ray m-CTporosity data.

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multi-scale characterization of porosity in boom clay (hades-level

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