Characterization of multi-scale microstructural features in Opalinus Clay

Microporous and Mesoporous Materials 170 (2013) 83–94

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Microporous and Mesoporous Materials journal homepage: www.elsevier.com/locate/micromeso

Characterization of multi-scale microstructural features in Opalinus Clay Lukas M. Keller a,⇑, Philipp Schuetz b, Rolf Erni c, Marta D. Rossell c, Falk Lucas d, Philippe Gasser d, Lorenz Holzer a a

ZHAW, Zurich University of Applied Sciences, Institute of Computational Physics, CH-8400 Winterthur, Switzerland EMPA, Materials Science and Technology, Laboratory for Electronics/Metrology/Reliability, CH-8600 Dübendorf, Switzerland c EMPA, Materials Science and Technology, Electron Microscopy Center EMPA, CH-8600 Dübendorf, Switzerland d ETHZ, Swiss Federal Institute of Technology, EMEZ, Centre for Imaging Science and Technology, 8093 Zürich, Switzerland b

a r t i c l e

i n f o

Article history: Received 26 March 2012 Received in revised form 2 November 2012 Accepted 9 November 2012 Available online 3 December 2012 Keywords: Shales Porosity Microstructure Imaging methods

a b s t r a c t STEM-, FIB- and X-ray tomography were applied to a sample taken from the Opalinus Clay unit. This allowed characterization of the pore structure in the fine-grained clay matrix at different levels of microstructural detail. On the level of detail that can be resolved by FIB-nt, the observed pore space is largely unconnected and the resolved porosity was in the 2–3 Vol.% range. At higher optical magnification but for smaller sample sizes, STEM tomography resolved a porosity of around 13 Vol.%. This suggests that the transition from an unconnected to a connected pore space in the shale sample occurs on the few nanometer scale. Geometric analyses of larger pores as visualized by FIB-nt revealed that dilation induced formation of bridges of only a few hundred nanometers between tips of neighboring pores may lead to a coalescence of larger pores. The resulting large pore network may allow for gas transport in the finegrained clay matrix. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction In the context of the disposal of radioactive waste, the production of shale gas and CO2 sequestration gas transport along the intergranular pore space in clay rock formations is an important issue. The present investigation focused on 3D visualization and characterization of potential gas transport pathways and their connectivity. This information is required for the validation of the isolation potential of a host rock for radioactive waste and also for a better understanding of gas-deliverability of shale gas reservoirs. A microstructural investigation of shales poses challenges because there are microstructural features on a wide range of scales. On the macroscopic scale, the geometry of compositional layering may control transport properties. At the same time, however, the transport properties of different layer materials are controlled by their structures at the microscopic and submicroscopic scale. Here, we focused on the pore structure related to a clay-supported shalemicrostructure consisting of isolated non-clayey mineral grains distributed within a matrix of fine-grained clay minerals. In such case, it is known that the intergranular pore system is dominated by pores with radii on the nanoscale [1–3]. Thereby, it is proposed that gas flow is controlled by the geometry of comparably larger pores (i.e. radii >10 nm) [4]. Besides these larger pores, a major fraction of the pore space is characterized by radii <10 nm [e.g. ⇑ Corresponding author. Tel.: +41 58 934 7778; fax: +41 58 935 7837. E-mail address: [email protected] (L.M. Keller). 1387-1811/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.micromeso.2012.11.029

2]. These few nanometer wide pores likely connect larger pores and may control connectivity of the pore network [e.g. 2]. Hence, the structure of the pore space may be seen as having different levels of geometrical details (i.e. microstructural levels). In the case of shales, the pore size range covers several orders of magnitude and thus, cannot be visualized in 3D by one single tomographic method. Therefore, we applied and tested several tomographic methods, which cover a resolution range from a few nanometers to the millimeter scale. The following tomographic methods provide increasing resolution but decreasing sample size: X-ray tomography (XCT), focused ion beam nanotomography (FIB-nt) [5] and scanning transmission electron microscopy (STEM) tomography. All of these methods were applied to a shale sample from the Opalinus Clay unit. The 3D geometry of nanoporosity in the clay matrix was investigated by FIB-nt and STEM tomography. Unfortunately, the sample size that can be analyzed by these methods is rather small (see below). In the case of an inhomogeneous distribution of nanoporosity, for example because of the presence of non-clayey minerals grains, in the sample it is useful to perform large-scale scanning electron microscopy (SEM) imaging of broad ion beam (BIB) polished surfaces [6] prior to the application of FIB-nt. This allowed a 2D characterization of the microstructure on the mm-scale and the selection of specific sites, which can subsequently be investigated by FIB-nt. For this study two specific target volumes were selected for FIB-nt analysis: (i) a volume that corresponds to a pressure shadow around a larger grain and (ii) a volume that is located at some distance from larger grains.

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Performing more than one FIB-nt realization gave some ideas on spatial porosity fluctuations. In order to resolve more geometrical detail of the pore space than it is possible with FIB-nt, we also prepared TEM foils and small cylinders (i.e. diameter 200–300 nm) which were investigated by TEM imaging and STEM tomography. In addition, we provide a detailed geometric analysis of the shale pore microstructure in order to address the nature of potential gas transport pathways through shales. Commercial analytical tools allow the extraction of some well-known parameters (e.g. porosity, pore surface area etc.) but they lack options for the quantification of important parameters such as pore path length, pore path tortuosity and the spatial distribution of these quantities. Furthermore, gas migration studies suggest that gas percolation may be associated with the formation of a small number of pathways that are induced by pressure dilation [7]. However, the extent of dilation necessary to form a connected network of larger pores is largely unknown. For example, it is possible that dilation occurs predominately between tips of larger isolated pore objects, which would lead to a coalescence of the larger pore objects and to an interconnected pore space. Therefore, the distance between pore tips and the geometry of the interconnected pore network is of major interest. Thus, in addition to the spatial distribution of pore path geometrical properties [2,3], we analyzed the relationship between different distance distributions that correspond to the distances between grain boundaries of neighboring non-clayey grains (i.e. carbonates/quartz), pore lengths and distances between pore tips of neighboring pores. Based on this geometric information, we analyzed the effects of potential pathways dilation and associated coalescence of larger pores. 2. Methodology 2.1. Sample All methods described herein were applied to the same rock sample (i.e. sample BDR1_oc) that was collected from the Opalinus Clay rock unit at the Mont Terri rock laboratory in northwest Switzerland (Canton Jura, Switzerland; [8]). This laboratory is located adjacent to the safety gallery of the Mont Terri motorway tunnel. Sedimentation of Opalinus Clay occurred around 174 my ago in a shallow marine basin. After sedimentation the rock unit underwent two stages of burial with a maximum burial depth of about 1350 m. Folding of the mountain belt occurred between 10.5 and 3 my ago. The Opalinus Clay can be subdivided into three main facies: shaley facies, sandy facies and carbonate rich sandy facies. The sample was taken from the shaley facies about 250 m below the surface. The shaley facies of Opalinus Clay typically contains 66% clay minerals, 13% calcite, 14% quartz, 2% feldspars, pyrite and organic carbon [8]. On the macroscopic scale, the analyzed shale sample contains fine whitish, presumably carbonate-rich layers on the mm-scale and sub mm-scale. On the microscopic scale, the prepared and analyzed samples can be subdivided into a matrix composed of finegrained clay minerals and within this matrix there are numerous isolated non-clayey minerals (Fig. 1). For the analyzed sample, data from nitrogen adsorption analysis are available [2]. BET surface is 20.0 (m2/g) and the calculated porosity is 11.5 Vol.% (see [2] for more discussion). 2.2. Sample preparation Electron microscopy (FIB/SEM/TEM) requires drying of the samples prior to analysis. Conventional drying and/or freeze-drying of moist clay may cause preparation artifacts such as drying shrinkage (conventional drying), ice formation during freeze drying. Spe-

cial methods such as high-pressure freezing and subsequent freeze-drying were used to avoid these artifacts. The sample preparation includes the following steps: Clay slabs with a thickness of 200–300 lm and a diameter of 5–6 mm were cut with the help of a saw with a very fine (thickness of saw blade = 200 lm) diamond blade parallel to the bedding plane. Then, the slabs were frozen under high pressure (2100 bar) and within milliseconds by using the HPM 100 high-pressure freezing system. Freezing at high pressure occurs by the injection of pressurized liquid nitrogen. This treatment prevents the formation of ice-crystals and thus preserves the delicate framework of the pore space. Then, the vitrified water was sublimated under high vacuum using a system for freeze-drying [2,9]. Details of high-pressure freezing techniques and their application for cryofixation are given by [10]. To stabilize the dry clay slabs, they were sandwiched between two 50 lm thick glass discs which were glued together with epoxy. Then, a cross-section was cut with a diamond saw perpendicular to the bedding plane. The surface of this cross-section was polished by using a broad ion beam (BIB) instrument and subsequently investigated by SEM and FIB-nt. SEM imaging of BIB polished clay samples is used for a material characterization on the mm-scale (for comparison: typical sample size of the FIB-nt analyzed volume is a cube of 10– 30 lm edge length). Such extended SEM images are the basis for the localization of distinct pore microstructures, which can subsequently be investigated by FIB-nt. The SEM images were processed as follows: First several SEM images were stitched together which results in a single high-resolution panoramic image. Second, pores were segmented by grey level thresholding from extended SEM images. 2.3. X-ray tomography The clay sample was scanned with a X-ray micro tomography cone beam setup consisting of a lm spot size X-ray tube ‘‘XT9160-TXD’’ from Viscom, a rotation table ‘‘UPR-160F air’’ from Micos and a X-ray flat panel detector ‘‘C7942 CA02’’ from Hamamatsu covered with a 1 mm thick Al plate. A voltage of 40 kV was applied to accelerate the electrons which impacted on a tungsten target with diamond support. The projection images were taken at angles uniformly distributed over 2p, whereby the last projection served to determine the quality of the measurement (the projections at 0 and 2p should be equal). To correct for dark counts and inhomogeneity of the detector a dark and a flat image were acquired with total integration times of 32 and 64 s, respectively. The projection images were corrected for bad pixels, beam hardening and ring artifacts before a standard filtered backprojection algorithm was used for reconstructing the 1120  1120  1184 voxels 3D absorption image. Based on the detector pixel size and the magnification, the resulting voxel edge length of the reconstructed 3D image is 2.56 lm, which was larger than the focal spot size and ensured that the image was not blurred (Table 1). 2.4. Focused ion beam nanotomography FIB-nt is done with dual beam FIB–SEM instruments, in which an ion beam and an electron beam focus intersect at a point on the sample surface. 3D information can be obtained by acquiring a sequence of cross sectional images spaced evenly through a region of a bulk specimen, and reconstructing those two-dimensional images into a three-dimensional representation of the sampled volume. The process begins by the milling of a wedge shaped trench in the sample. One wall of the trench is vertical (i.e. normal to the specimen surface) and becomes the initial cross section imaged by the electron beam [5]. After imaging, the ion beam is used to remove a layer of uniform thickness of material from this wall,

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(a)

(b)

Fig. 1. Large-scale SEM images of shaly facies of Opalinus Clay. (a) BSE image. The bedding is horizontal. (b) Pores (white) which were segmented from the BSE image. (c) The rose diagram shows the orientation distribution of pore paths (from 2D analysis). Note a preferred orientation of pore paths parallel to the bedding.

Table 1 Overview of properties of data sets for different tomographic methods.

Size (lm3) Voxel size (nm)3 Porosity (Vol.%) Resolved pore radii (nm)

FIB 1: ‘‘pressure shadow’’

FIB 2: ‘‘highly compacted’’

STEM

XCT

331.8 103 2.3 P5

303.6 103 2.8 P5

0.1 2.33 13.5 P2

3870 0150 840 25603 0.6 P2000

advancing the cross section a predetermined distance through the sample volume. Another electron image is collected. By repeating this milling/imaging process, the cross section advances through the targeted volume, which results in a stack 2D images. For this study, we used a Zeiss NVision 40 FIB/SEM instrument and important instrument setup parameters are listed below. SE and BSE image stacks were collected simultaneously to facilitate the segmentation process. Image pixel resolution was 1024  768. For SEM imaging we used a low-acceleration voltage of 1.2 kV and an aperture size of 30 lm. Ion gun milling current was 700 pA. Two image stacks at specific localities were collected (see above and Fig. 2, Table 1).

cylinders with diameters between 200 and 300 nm were prepared by the FIB technique. A JEOL single axis tomography holder was used and annular-dark field scanning transmission electron microscopy (ADF-STEM) images were manually recorded at 2° tilt intervals over a range from 78° to 78°. In ADF-STEM, the signal is known to scale approximately with the square of the atomic number Z; thus to good approximation it can be interpreted in terms of thickness and atomic number contrast. Subsequently, the 79 images were aligned using the StackReg plugin for the free image processing software ImageJ. The 3D volume reconstruction was computed using 50 cycles of the simultaneous iterative reconstruction technique (SIRT) implemented in the TomoJ software, which is also an ImageJ plugin.

2.5. Transmission electron microscopy 2.6. Image analysis For TEM imaging electron transparent clay rock specimens were prepared in form of site-specific TEM foils with the dimension of around 10  10  0.1 lm by using the focused ion beam (FIB) technique. TEM investigations were done on a Philips CM30 transmission electron microscope operated at 300 kV. The tomography and the energy-dispersive X-ray (EDX) spectroscopy experiments were performed on a JEOL 2200FS TEM/STEM equipped with a Gatan DigiScan system and operated at 200 kV. For STEM tomography

2.6.1. X-ray tomography The gray-level contrast of the absorption images allowed an accurate segmentation of pores and carbonate minerals. There were problems with the segmentation of quartz due the low intensity contrast between quartz and the surrounding clay minerals. Therefore, the determined content of quartz must be treated by due caution. We used a techniques known as ‘‘statistical region

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(a)

(b)

z

investigated volume “highly compacted”

z

investigated volume “pressure shadow”

non clayey grains orientation of bedding

x

x

Fig. 2. Stages during site specific FIB-nt analysis. (a) BSE image showing the sample surface of Opalinus Clay with the selected ‘‘highly compacted’’ target volume. (b) SE image showing the selected ‘‘pressure shadow’’ target volume. The sketches below the images show the orientation of the bedding plane and the locations of non-clayey grains with respect to the analyzed volumes.

merging’’ to segment the images [11]. This segmentation approach works in 3D and is implemented in the free image processing software Fiji.

2.6.2. FIB-nt The SE images were aligned by using the algorithm implemented in the free image processing software Fiji. BSE images were aligned according to the image coordinates obtained for the corresponding SE image stack. Then, the maximal overlapping area was cropped from the images of the aligned SE and BSE image stacks. Vertical stripes in the images which are artifacts of ion milling (i.e. the so-called waterfall effect) were then eliminated by applying a destriping filter. Then, a 3D background correction was applied in order to reduce systematic large-scale intensity variations which are caused by shadowing effects related to the oblique imaging angle and to the subsidence of the image plane into the milled trench. Noise in the BSE image stack was reduced by applying an edge preserving 3D median filter of the Avizo software. The reconstruction of a 3D microstructure requires a segmentation of the images, i.e. the pores and mineral grains have to be located in the images. The pores were segmented from the SE images which show a higher grey level contrast between pores and surrounding material when compared to the BSE images. Using a multi-level threshold method based on so-called Otsu thresholding [12] segmented the pores from the SE images (see also [2]). Some mineral grains (e.g. calcite) are bright when compared to the surrounding clay matrix and thus they were segmented from the BSE images using grey level thresholding of the Avizo software. Large clay grains which lack sufficient grey level contrast to the surrounding clay matrix, were segmented manually using the tools for manual segmentation provided by the Avizo software. For 3D visualization, we used the Avizo software.

2.6.3. TEM TEM images allow no automated segmentation of the pores. Thus, pores were segmented manually using the tools provided by the Avizo software. 3. Results 3.1. Large-scale SEM imaging A panoramic SEM image shows the microstructure of the analyzed sample on the hundred of microns scale (Fig. 1). It can be seen that non-clayey mineral grains of various size occur as inclusions in fine-grained clay matrix. Furthermore, clay aggregates and clay flakes show a shape-preferred orientation parallel to the bedding plane. The resolved pores space consists of numerous isolated and unconnected pore objects. These pore objects were skeletonized (see below and [2]) and the orientation of pore paths were analyzed according to the approach outlined by [2]. Plotting the pore path orientation distribution revealed a preferred orientation of pore paths parallel to the bedding plane (Fig. 1). This observation confirmed previous evidence, indicating that tortuosity anisotropy in the pore space and pore path orientation in Opalinus Clay are caused, respectively related to preferred orientation of clay platelets or bedding (see [2]). These authors based their interpretation on small-scale FIB-nt investigations. 3.2. X-ray tomography: shaley facies of Opalinus Clay The absorption images reveal that carbonate grains are often fragments of fossils (Fig. 3). The sample contains also a minor amount of pyrite or other heavy minerals which tend to occur within or along fossils (Fig. 3). Modal amounts of major minerals are given in Fig. 3. Due to limits of resolution the smallest pores have radii around 2 lm and the porosity of the resolved pore space was about 0.60 Vol.%. At this level of geometrical detail, the pore

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(a)

Carbonates

Pyrite

Qtz

(b)

Pore

(c) Pores Quartz Pyrites 4% < 1% < 1% Calcite 8%

Clay mineral matrix 88%

1mm

Fig. 3. Visualization of X-ray tomography data of shaly facies of Opalinus Clay. (a) Raw data showing the image contrast between the different constituents. (b) Projection view and the 3D reconstruction of the segmented mineral grains and pores. (c) 3D reconstruction of the segmented pores (red) and heavy minerals (blue). The pie plot shows the amounts of the segemented constituents. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Cumulative sum: Pore fraction [Vol.%]

14 N2 adsorption

12

3

3

STEM-tomo: voxel size 2.3 nm

10

2

2

STEM 2D: pixel size 1.7 nm 2

8

2

STEM 2D: pixel size 4.0 nm 2

2

STEM 2D: pixel size 4.0 nm

6

3

3

FIB-nt 1: voxel size 10 nm 3 3 FIB-nt 2: voxel size 10 nm

4

3

3

Xray-tomo: voxel size 2.6 µm

2

0 0 10

1

10

2

10

3

10

4

10

5

10

Regarding mass transport processes, non-clayey mineral grains may play an important role because of enhanced porosity along their grain boundaries. This enhanced porosity is related to geometric incompatibilities between platy clay grains and the irregular surface of non-clayey grains (Fig. 6). Among others, the influence of such localized enhanced porosity on transport properties may depend on the spatial density of non-clayey grains. As a measure of spatial density we considered the distribution of grain spacing (i.e. the distance from a grain to its closest neighbor) (see also below). Instead of considering distances between centers of non-clayey grains, the shortest distance from one boundary to the boundary of the next neighboring non-clayey grain might be more relevant. To obtain an idea of distances between boundaries of carbonate grains, the mean grain diameter was subtracted from the center-to-center distance of two grains. The resulting distance distribution is displayed in Fig. 5a and it can be seen that the boundary-to-boundary distance of carbonate grains ranges between 2 and 10 lm.

Pore radius [nm] Fig. 4. Compilation of continuous pore size distributions which were determined on the base of different methods (i.e. FIB-nt, STEM-tomography, TEM imaging, X-ray tomography and N2 adsorption analyzes). To compare the methods, they were all applied to the same sample (BDR; shaly facies of Opalinus Clay). FIB-nt can resolve about 20–30% of the total external pore space, which corresponds to pore radii >10 nm. On the base of TEM imaging and STEM tomography, a higher fraction of the pores space can be resolved but the analyzed image window is very small.

space is not connected. The calculated continuous pore size distribution [13] is displayed in Fig. 4 along with pores size distributions that were obtained on the base of other methods. In contrast to the carbonates and the heavy minerals, the quartz content (i.e. 4 Vol.%) appeared unrealistically low, even if we considered that the method cannot resolve the small grain size fraction. For comparison, the shaley facies of Opalinus Clay has a quartz content of at least 10 Vol.% [8]. Since a considerable fraction of quartz was apparently not resolved, only the grain size distribution of carbonates was analyzed further. Fig. 5b displays the grain size distribution of carbonates and it can be seen that the majority of the resolved grains have diameters in the 2–20 lm range.

3.3. Focused ion beam nanotomography (FIB-nt) Two FIB-nt realizations were performed in order to consider spatial variabilities of the 3D-pore structure of clay-rich domains (‘‘clay matrix’’). The sites for tomography were selected on the base of BIB polished surfaces. The chosen sites exhibit particularly high and low degrees of compaction (‘‘highly compacted zones’’ and ‘‘pressure shadows’’, respectively) (Fig. 2). Subsequently, the 3D pore geometry of these zones were investigated by FIB-nt. Finally, samples for TEM imaging and STEM tomography were prepared by FIB/SEM at the same locality which was previously investigated by FIB-nt (i.e. adjacent to the volume that was previously removed during the FIB-nt process). 3D-reconstructions of the FIB-nt target volumes in ‘‘pressure shadows’’ and in ‘‘highly compacted’’ volumes are shown in Fig. 7. The obtained 3D data were used to reconstruct the microstructural components of the test samples. The porosity determined on the base of FIB-nt ranges between 2 and 3 Vol.% which is substantially lower than the expected interparticle porosity of

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(a)

Cumulative sum: Relative frequency

Cumulative sum: Relative frequency

1.4 1

0.8

0.6

0.4

0.2

0 0 10

10

1

10

2

10

3

10

4

10

(b)

1.2 1 0.8 0.6 0.4 0.2 0 1 10

5

10

2

euclidian length path length

3

10

4

10

5

10

6

Grain diameter carbonates [nm]

Distance [nm] Pore length

10

Shortest distance between pore tips

FIB-nt: voxel size 10 nm3 Xray-tomo: voxel size 2.6 μ m3

Distance between grain boundaries FIB-nt: Carbonates

X-ray: Carbonates

Fig. 5. Distance distributions of microstructural features in shales determined for the ‘‘highly compacted’’ volume in Fig. 7. (a) Distribution of pore path length, distances between neighboring pore tips and distances between neighboring grain boundaries. Euclidian distance of a pore path is the length of the direct link between two ends of the pore path. (b) Grain size distribution determined from FIB-nt and X-ray tomography. The difference is related to the resolution range of the respective method.

(a)

(b)

Fig. 6. TEM images documenting enhanced porosity along non-clayey grains (marked by asterisks). (a) At lower magnification, the image shows several sharped edged nonclayey grains. Edgy grains in combination with platy clay aggregates leads to geometrically incompatible boundaries and to the formation of comparable larger pores. (b) At higher magnification, the image shows clay platelets and aggregates around a more granular grain and associated formation of pores.

about 10–13 Vol.% determined by N2 adsorption analysis and STEM tomography (Fig. 4) (see [2]). The calculated continuous pore size distributions [13] corresponding to ‘‘pressure shadow volumes’’ and ‘‘more compacted volumes’’ are similar to each other (Fig. 4). However, it has to be considered that the two volumes contain different fractions of non-porous mineral grains and porous clay matrix (Table 2). If we consider that the pores are mainly found within the finegrained clay matrix and if we relate the pore volume to the volume of the fine-grained matrix, the porosity of the clay matrix in the pressure shadow volume is higher. In addition, the porosity around non-clayey grains is higher in the pressure shadow volume compared to the one of the highly compacted volume (Table 2). Analysis of the 3D pore path orientation distribution and pore geometry based on geometric 3D graphs [2] revealed a slightly higher pore path tortuosity contrast in the ‘‘highly compacted’’ tar-

get volume when compared to ‘‘pressure shadow’’ volume (Fig. 7). Pore path density distribution revealed a preferred orientation of pore paths within the bedding plane for both analyses (Fig. 7). Geometrical tortuosity of pore paths was relatively high in the direction perpendicular to the bedding and low within the bedding plane. The majority of pores have path lengths between 2–8 lm and the spatial distribution of pore lengths showed a tendency towards a higher frequency of longer pores subparallel to the bedding plane (see also [2]). The intensity contrast in the backscatter images was suitable for the segmentation of carbonates, quartz, larger clay mineral grains and organic materials with different compositions when compared to the clay mineral matrix (Fig. 8, Table 2). In general, nanoscale clay particles in the matrix cannot be segmented from FIB-nt images. Mean grain diameter of carbonates ranges between 100 and 200 nm, which is about two orders of magnitude smaller com-

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L.M. Keller et al. / Microporous and Mesoporous Materials 170 (2013) 83–94 Table 2 Amount of pores and minerals in the analyzed volumes. Locality

FIB 1: ‘‘pressure shadow’’

FIB 2: ‘‘highly compacted’’

Porosity (Vol.%) Porosity around non-clayey grains (Vol.%) Carbonates (Vol.%) Large clay grains (Vol.%) Quartz (Vol.%) Clay matrix (Vol.%)

2.3 1.3 2.3 4.3 35.0 58.4

2.8 0.3 18.0 2.4 17.0 62.6

(a)

(b)

z

(c)

Density

Tortuosity

Path length

(%/% area) y

(Mean values)

(Mean values [nm])

Bedding plane

x x 0

BDR

y

pressure shadow

φ=2.3 vol. %

1

2

3

4

2

4

6

8

10

0

2000

4000

6000

8000

10 0

2000

4000

6000

8000

Bedding plane

z x

0

BDR highly compacted

1

2

3

4

2

4

6

8

φ=2.8 vol. %

Fig. 7. The extraction of orientation anisotropies in the pore space based on FIB-nt. (a) Reconstruction of the analyzed volume. The lateral faces of cuboid are BSE images. The orientation of the bedding plane is indicated by the small cube with a red plane. (b) 3D reconstructions after segmentation showing the pore space of the analyzed volume. Note the porosity that is given in the lower left corner. (c) Lower hemisphere equal area stereographic projections showing the spatial distribution of pore path geometrical properties in the analyzed volume. Left: Contoured plots showing the orientation density (=number of orientations in % per 1% area). Middle: Mean path tortuosity distribution. The colors in the plots are related to a specific numeric value of tortuosity, which can be extracted from the color bar. Right: Mean path length distribution. (see text and Keller et al. (2011) for further discussion) (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

(a)

(b)

3 μm

Non clayey grains (38 Vol. %)

Pores in organic material

Organic material (0.1 Vol. %, Porosity 25 Vol. %)

Pores (2.8 Vol. %)

Fig. 8. Visualization of FIB-nt data. (a) Reconstruction of the analyzed volume based on SE images. (b) 3D Reconstruction of pore space and non-clayey materials (e.g. calcite, quartz).

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(a)

(b)

500 nm

Fig. 9. Visualization of STEM tomography data. (a) Raw data showing different cross-section of the analyzed needle. (b) 3D Reconstruction of pore space.

(a)

(b)

(c) O

Mg

K

Ca

Al

Ti

Si

P

Fe

Ga

Fig. 10. Results of a STEM–EDX spectrum image. (a) and (b) ADF-STEM images of the analyzed clay needle. The rectangle marks the analyzed volume. (c) Element distribution maps showing the distribution of selected elements. The needle is contaminated with Ga during FIB sample preparation.

pared to the grain sizes resolved by X-ray tomography (Fig. 5b). The distance from a grain boundary to its closest neighboring grain boundary is also in the range of hundreds of nanometers and thus, two orders of magnitude smaller than the distances determined on the base of X-ray tomography (see above) (Fig. 5a). As outlined above, non-clayey grains are often associated with an enhanced porosity along their boundaries (Fig. 6). Such localized and enhanced porosity may bridge the gaps between uncon-

nected pore objects within the clay matrix and together may form an interconnected network. In order to test this hypothesis, we added the grain boundaries of the segmented grains to the pore space. Grain boundary width was taken as one pixel or 10 nm. Adding the boundaries of larger grains to the pore space results in an interconnected pore space with a long-range connectivity (i.e. percolating network). This result is in line with the fact that the distances between neighboring carbonate grain boundaries is about

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an order of magnitude shorter than the length of the pores (Fig. 5). Thus, a scenario in which gaps between pore tips of larger pores are bridged via grain boundaries of larger and non-clayey grains is plausible. 3.4. Transmission electron microscopy Regarding STEM tomography, Fig. 9 shows differently oriented cross-sections of the analyzed volume and a 3D reconstruction of the pore space. There is a tendency of a preferred orientation of clay aggregates. Furthermore, it can be seen that the geometry of the pore space is controlled by geometric incompatibilities between individual platy clay aggregates and clay flakes. The 3D reconstruction of the pore space suggests poor connectivity perpendicular to the preferred orientation (i.e. bedding) of platy clay aggregates. Again there is an enhanced porosity along the boundary of a small non-clayey, presumably apatite (see below), granular grain. The porosity in the analyzed volume was around 13.5 Vol.% and the resolved pore radii were in the 2–20 nm size range. The pore size distribution curve (Fig. 4) suggests a higher fraction of larger pores when compared to the curves that were calculated on the base of FIB-nt and gas adsorption analysis. The discrepancy may be related to the large differences in the size of the analyzed volumes. This arises the question of the representativeness and accuracy of the methods when applied to shales. An STEM-EDX spectrum image of the 200–300 nm thick clay needle gives ideas of the mineralogical composition of the sample (Fig. 10). The needle consists mainly of clay minerals with various contents of Mg, Fe, Ti and K. A sheet silicate, presumably mica, is rich in K, Mg, Fe, and Ti (bright slap in Fig. 9). The calcium phosphate phase in

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the needle is likely apatite and the tiny Ti rich grains are probably titandioxid. In addition to STEM tomography we performed also TEM imaging on thin foils. Pores were segmented from images with pixel size ranging between 1.7 and 4 nm (Fig. 11). From the segmented images, we calculated the continuous size distributions [13] (Fig. 4). At similar optical magnification, it seems that 3D STEM tomography resolves a larger fraction of porosity when compared to 2D TEM imaging. The images also show a layer spacing of about 1.3 nm within the interlayer regions. 4. Quantitative analysis The quantification of the geometrical properties is based on graph theory (see for example [14] for more information on graph theory). As initial step, the irregular and complex pore volume, which in terms of image analysis consists of voxels, is transformed into a voxel skeleton which is easier to analyze and reduces the amount of data. During skeletonization the pore space is converted to a lower dimensionality. In general, a skeleton consists of voxels which are arranged as a network of paths (1 dimensional curves). These paths consist of nodes (intersection of three or more paths) that are connected by segments. Here, the voxel skeleton has a strict geometrical relationship to the pore surface as it is defined as the medial axis of the pore space. Therefore, the pore radius can be measured at every voxel position. During a next step the voxel skeleton is converted into a graph which basically means that the voxel segments are replaced by straight lines (i.e. arcs) which connect the nodes. Thus, a graph representation of a pore volume is simply a matter of describing the connection between

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Fig. 11. (a),(b),(c) Transmission electron images showing the pore microstructure in shaly facies of Opalinus Clay. (b), (d), (f) Pores, which were segmented from respective images. These images were used to calculate the pore size distributions depicted in Fig. 4.

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Nanoscale dilation and coalescence of larger pores “Larger” pore

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adjacent pore path intersections (i.e. nodes). Because voxel segments are generally longer than the straight arcs the true length of the corresponding segment (i.e. distance between connected pairs of nodes) is assigned to each arc. Other properties such as information on the pore radius or resistivity (if known) can be associated to arcs as well. Because graphs have simple data structures, many questions can be answered efficiently (e.g. transport simulation by using the graph as a resistor network). With regard to coalescence of larger pores due to dilation or fracturing, the shortest distance between neighboring pore tips is of interest (Fig. 12). For this purpose, the degree of dilation required to form such a connected network must be determined. In addition, also the geometry of the resulting network is of major interest, which can be addressed by the topological analysis of the resulting network. Based on the graph representation of the pore space, we calculated for each pore tip the shortest distance to its next neighbor. The resulting distribution is depicted in Fig. 5 and shows that the majority of the bridges between pore tips have lengths between 100 and 300 nm (dotted line in Fig. 5a), which is about one order of magnitude shorter than the pore path lengths (grey and black line in Fig. 5a). Gas migration through initially water saturated clay rocks might be associated with the formation of a small number of path-

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ways [7]. In the case of uniform and isotropic stress field, the dilatant pathways tend to occur parallel to the bedding plane [7]. Based on the 3D data from FIB-nt and associated graphs for the pore structure we have simulated the effect of fracturing that may lead to a connected network. In this simulation, connections between neighboring pore objects are introduced based on geometrical criteria (i.e. distance and orientation). Coalescence of larger pore is expected to propagate in a certain direction (e.g. away from the applied pressure) and the strategy of searching local pore tip connections was applied to pores tips in a strict directional order that corresponds to increasing coordinate values. In order to account for anisotropic dilation/fracturing, the search for the connection from one pore tip to its nearest neighbor was restricted to occur within a flat rectangular prism which extends from a pore tip in direction of the supposed propagation direction of dilation. In order to simulate different scenarios (as discussed below), the orientation of the flat prism was either parallel or perpendicular to the bedding plane. In this way the effects of dilation within – or perpendicular to the bedding plane can be analyzed separately. Here, we assumed that fracturing occurs preferentially along the shortest connection between two neighboring pores which is, however, supported by crack propagation simulations in porous media [15]. Using the above search strategy, we simulated dilation and coalescence of larger pores for two different scenario: (i) parallel and (ii) perpendicular to the bedding plane. The resulting network was then analyzed by computing the shortest path network that corresponds to the two different dilation scenarios. The shortest path network corresponds to all possible combinations of shortest paths that connect pairs of source and sink nodes within opposite boundary faces of the analyzed volume. The shortest path problem involves the finding of the smallest path length from a source node to a sink node and was found by running Dijkstra’s algorithm (e.g. [16]). For each path, we also calculated the geometrical tortuosity defined as s = L/D, where L is the effective length of the path and D is the length of the connection between its end points. The shortest path network of the two considered dilation scenario are depicted in Fig. 13. The geometry of the evolving connected pore network depends on the direction of dilation. Dilation parallel to the bedding results in a network with comparably low geometric

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Fig. 13. Effects of dilation or fracturing induced pore coalescence. (a) Graph representation of the pore network corresponding to the ‘‘highly compacted’’ volume in Fig. 7. Note: the network is not connected. The small surface below Fig. 13a indicates the orientation of the bedding plane. (b) The resulting connected network for parallel bedding dilation and coalescence of larger pores. (c) The same as (b) but for dilation perpendicular to the bedding plane.

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Fig. 14. Effects of dilation or fracturing induced pore coalescence. (a) y-z view showing a graph representation of the pore network corresponding to the ‘‘highly compacted’’ volume from FIB-nt in Fig. 7. Note: the network is not connected and there is no pore path, which links the two z-planes. (b) and (c) Bridges between pore tips are added to the previously unconnected pore network from (a). The bridges are added for all gaps between pore tips which are shorter than 200 and 300 nm. The resulting pore network is shown in (d) and (e). (d) If pore coalescence occurs between neighboring pores, which are no more than 200 nm apart, only a few transmitting paths evolve and flow is suggested to be largely localized. (e) If coalescence occurs between more and more distant pores, more and more transmitting pathes evolve and flow is expected to by more evenly distributed.

tortuosity when compared to dilation perpendicular to bedding. This agrees well with the results that were obtained on the base of the stereographic projection method (for disconnected pore paths) (see Fig. 7). To study the effects of progressive increase of nanoscale dilation and pore coalescence, we successively added longer and longer connections between pore tips. The calculations were done for dilation parallel to the bedding. If fracturing is restricted to bridge length <200 nm, the resulting network has only a few transmittant paths. If fracturing occurs between more and more distant pores, the density of transmittant paths increases (Fig. 14).

5. Discussion Gas transport in clay rocks is controlled by morphological features of the pore structure at different length scales. Nanopores between the clay-flakes constitute a large fraction of the total porosity. Good agreement between porosities derived from densities (i.e. dry bulk densities and grain densities) and from water content [8] indicates that a major part of the pore space in Opalinus Clay is water-saturated. Therefore, the nanopores may not represent the main transport pathways for gas. In the fine-grained matrix a pore fraction is observed with FIB-nt which is coarser than 10 nm. These pore are potentially the ones which are hosting the

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gas. However, these coarser pores do not form a connected network. Enhanced porosity is observed at the interface between clay matrix and embedded mineral grains (Fig. 6). The non-connected pores in the clay matrix can either be bridged via the boundaries of non-clayey mineral grains and associated enhanced porosity or by dilation/fracturing of the nanopores. X-ray tomography reveals numerous micronscale carbonate and quartz grains. These grains are isolated and are far apart from each other. Based on quantitative analyses, we show that the distance between these grains is larger than the pore path length of larger pores (i.e. radii >10 nm) and bridging of larger pores via these grains is therefore considered as an unlikely scenario. However, there are numerous non-clayey mineral grains (i.e. carbonates and quartz) with grains sizes <1 lm, which can only be resolved by FIB-nt. The shortest distance between neighboring grains is much smaller than the pore length, which makes bridging of larger pores via the grain boundary of these small grains a likely scenario. Adding the grain boundary of these smaller grains to the pore space (i.e. the carbonate/clay interface) results in a connected network. The significance of such a pore/grain boundary network depends largely on the nature of the interface between carbonates/quartz and the fine-grained clay matrix. Due to surface roughness and geometric incompatibilities between granular carbonate/ quartz grains and platy clay grains there is an increased porosity along this interface which supports the significance of the above network. For the quantitative geometric analyses of the reconstructed pore space we used an approach that is based on graph theory and documented and quantified an anisotropy in the pores space of clay-rich shales (see also [2]). Recently, an anisotropic pores space structure in shales was also proposed by other authors [17], but based on indirect measurements (i.e. ultrasonic velocity measurements). FIB-nt can only resolve comparatively large pores (i.e. radii >10 nm), which correspond to about 20–30% of the total pore space. These larger pores are relevant for gas flow processes since gas flow in small pores is likely hampered due to capillary forces. Apparently, larger pores are isolated objects, which are separated from each other by distances of several hundreds of nanometers. The distance between neighboring larger pores is, however, much smaller (i.e. a magnitude of order) than the length of the pores and is in the range of distances between nanoscale non-clayey grains. In the context of gas transport in shales, the propagation of dilatant pathway and associated coalescence of larger pores as well as the resulting pore network connectivity is of interest. Here, we show that a hypothetical dilation process that bridges nanogaps with a few hundred nanometers separation between neighboring larger pores leads to a percolating pore network. 6. Conclusions Tomographic methods with different resolution limitations and methods for the geometric analysis of 3D pore reconstructions were used to characterize a clay-supported shale microstructure at different levels of geometric detail. Each of the used methods has its own limitations in the size of the sample that one is able to analyze. Unfortunately an increase in optical magnification is associated with a decrease of sample size and it is thus, mandatory to ask if the captured geometric content in the analyzed volume is

sufficient to be a good approximation of the investigated structure. This question is discussed in a forthcoming study. Geometric analyses of 3D pore space reconstructions based on FIB-nt presented herein suggest a geometric anisotropy in the pore space with a higher pore path density, lower geometric pore path tortuosity and longer pore paths within the bedding plane. All these indicates to a connectivity anisotropy with a higher connectivity within the bedding plane when compare to the direction perpendicular to the bedding. On the microstructural level that can be resolved by FIBnt, however, the pore space is poorly connected. At a higher optical magnification but for the same pore size range, STEM tomography suggests higher porosity when compared to FIB-nt. In combination, all these suggest that the transition from unconnected to a connected pore space occurs at a level of geometrical detail that can only be visualized by STEM tomography. Hence, the pore space of the analyzed shale with porosities in the 10–15 Vol.% range is considered as connected at the few nanometer scale. For such a pore structure gas transport may occur via the above discussed nano-scale dilation process and/or along a network that combines porosity and the boundary region of non-clayey grains. Finally, we would like to mention that the porosity and connectivity of comparable larger pores related to grain-supported shale microstructures in layers with low clay contents is still an open question which must be addressed to understand transport on a larger scale. Acknowledgments This work was funded by the Swiss National Cooperative for the Disposal of Radioactive Waste (NAGRA) as part of the SHARC consortium, a research collaboration between the Commonwealth Scientific and Industrial Research Organization (CSIRO), Curtin University of Technology and NAGRA. A constructive review by M. Mazurek and an unknown reviewer helped to improve the manuscript substantially. Miriam Lucas is thanked for helping with sample preparation. References [1] P. Marschall, S. Horseman, T. Gimmi, Oil Gas Sci. Technol. 60 (2005) 121–139. [2] L.M. Keller, L. Holzer, R. Wepf, P. Gasser, Appl. Clay Sci. 52 (2011) 85–95. [3] L.M. Keller, L. Holzer, R. Wepf, P. Gasser, B. Münch, P. Marschall, Phys. Chem. Earth 36 (2011) 1539–1544. [4] C.J. Clayton, S.J. Hay, Bull. Geol. Soc. Den. 41 (1994) 12–23. [5] L. Holzer, F. Indutnyi, Ph. Gasser, B. Münch, M. Wegmann, J. Microsc. 216 (2004) 84–95. [6] G. Desbois, J.L. Urai, P.A. Kukla, J. Konstanty, C. Baerle, J. Pet. Sci. Eng. 78 (2011) 243–257. [7] J.F. Harrington, S.T. Horseman, in: A.C. Aplin, A.J. Fleet, J.H. Macquaker (Eds.), Muds and Mudstones: Physical and Fluid Properties, vol. 158, Special Publications, Geological Society, London, 1999, pp. 107–124. [8] P. Bossart, M. Thury, Mont Terri Rock Laboratory: Project, Programme 1996– 2007 and Results, Reports of the Swiss Geological Survey, No. 3, 2008. [9] L. Holzer, B. Münch, M. Rizzi, R. Wepf, P. Marschall, T. Graule, Appl. Clay Sci. 47 (2010) 330–342. [10] L. Bachmann, E. Mayer, in: R.A. Steinbrecht, K. Zierold (Eds.), Cryotechniques in Biological Electron Microscopy, Springer, Berlin, 1987, pp. 3–31. [11] R. Nock, F. Nielson, IEEE Trans. Pattern Anal. Mach. Intell. 26 (2004) 1452– 1458. [12] N. Otsu, IEEE Trans. Syst. Man Cybern. 9 (1979) 62–66. [13] B. Münch, L. Holzer, J. Am. Ceram. Soc. 91 (2008) 4059–4067. [14] D. Jungnickel, Graphs, Network and Algorithms, Springer, Berlin, 1999. [15] T. Nakamura, Z. Wang, J. Appl. Mech. 68 (2001) 242–251. [16] T.H. Cormen, C. Stein, C.E. Leiserson, R.L. Rivest, Introduction to Algorithms, MIT Press, Cambridge, Massachusetts, 2009. [17] W. Kanitpanyachareon, H.-R. Wenk, F. Kets, C. Lehr, R. Wirth, Geophys. Prospect. 59 (2011) 536–556.