The FIB-SEM analyses were performed on a Zeiss Auriga with EDX and FE-Cathode. The tilt-corrected BSE and SE images were collected with a current of 1.5 kV to reduce charging and improve resolution. For slicing 500 pA has been used, resulting in 25 nm-thick slices. Voxel size is dependent on the slice thicknesses as well as magnification. The resulting voxel size was 40×40×25 nm for HAD and 56×56×25 nm for WIC. In the following, x- and y directions are referred to as the horizontal and vertical image directions. Z is equal to the direction of the slicing. Before the slice and view, we sputtered the sample with Pd to minimize charging and improve the imaging of the slices. The result of the slice and view were 400 SE and BSE images for each sample. After the image collection the image stacks were aligned and filtered. Porespace and organic matter were binarized and qualitatively and quantitatively analyzed, for which the Avizo-Fire 9.0 and GeoDict software was used. Images were filtered in Avizo by applying a shading correction filter, a FFT filter to remove vertical stripes and a Non-Local Means filter in 2-D mode to remove noise. 2-D was chosen over 3-D because the generated FIB volume is a stack of 2-D images rather than real 3-D data. The Non-Local Means was preferred because it removes noise without blurring the contrasts between the organic matter and pore space and without decreasing the resolution of the pores and the organics. Therefore it is possible to clearly distinguish between these phases and the matrix (Fig. 1). At times it is difficult to differentiate between pore and organic based on grey scale values especially for small objects within the mineral matrix as can be seen in Fig. 1. Effects of these difficulties in distinguishing between these two phases are being discussed later.

After the binarization we resampled the pore space creating cubic voxels (25 nm), essential when determining orientations of the pores. The resulting volume was slightly cropped to meet GeoDict modelling requirements. The pore space was separated into individual pore clusters with quite extensive pore networks of up to 6 µm in length (Figs. 2 and 3). For this study we considered a cluster if the labeled object is connected by voxels which share a face, edge or vertex. Vertex connection was allowed since GeoDict can model transport along these links. The separated objects were tested for axis connectivity, a test that shows if clusters exist that connect the faces of the investigated volume for every spatial direction. The porosity is described by its individual volume, open and closed porosity (Table 2), continuous pore size distribution (Fig. 5) and pore path orientation (Fig. 7). Open porosity describes the fraction of the total porosity that has a connection to the borders of the volume. Pore clusters that are not in contact with the borders belong the closed porosity. High values of closed porosities reflect a poorly connected pore space. If the open porosity is similar to the total porosity, then the connectivity of pores is high.

A detailed description of the geometrical concept of the continuous pore size distribution is given in Münch and Holzer (2008).

After processing, the pore space was visually analyzed. In Fig. 2 the 10 largest pore clusters of the two samples reveal strong similarities. In both samples the pore clusters run mainly through the mineral matrix but are in places in contact with the smaller organic matter particles. All of these clusters are made up of a complex pore network as shown in Fig. 3 with flow being the fastest in the pore necks. Only one of the pore clusters shows signs of orientation which could be attributed to drying, all the other pore clusters show no signs of being drying cracks.

The porosity obtained from FIB-SEM is very low compared to the total porosity as shown in Table 1. For sample WIC we found a FIB-SEM porosity of 1.5 % and for HAD of 2.4 % similar to the SEM analyses by Klaver et al. (2012, 2016) and Mathia et al. (2016). If we compare these values to the total porosity determined by Kaufhold et al. (2016) who worked on exactly the same samples we find that only 10 % for WIC (or 24 % for HAD respectively) of the total porosity can be resolved using FIB-SEM. These differences are also similar to the results of Klaver et al. (2012, 2016) and Mathia et al. (2016). However, no trends towards higher porosities in one or the other sample were observed, likely due to spatial inhomogeneity. Similar results were reported by Keller et al. (2011) for Opalinus clay who obtained a FIB-SEM porosity of 1–2 % compared to a total porosity of 10–12 %.

The test for axis connectivity showed that no connection of pores exists between the different axes. Open and closed porosity analysis (Table 1) revealed that for HAD only 1/3 of the total pore space has a connection to the borders of the volume (1/6 for WIC). This shows that most of the pore clusters, even the largest ones, lie isolated within the matrix or the organics.

Münch and Holzer (2008) showed that the continuous pore size distribution determined from FIB-SEM can be compared with other analytical methods quantifying the pore size distribution (MIP, N2, CO2). However, the absolute porosity cannot be determined by FIB-SEM due to the limitations of resolution and investigated volume. Nonetheless, results show good agreement of FIB-SEM continuous pore size distributions of this study and MIP performed on the same samples by Kaufhold et al. (2016) when only the range of the overlapping pore radii of both methods is compared (Fig. 5). Comparing MIP data with the FIB-SEM results shows that the FIB-SEM of the WIC sample under estimates pore radii larger than 150 nm by about 0.2 % total porosity compared to MIP. Sample HAD on the other hand over estimates the pore radii smaller than 150 nm compared to MIP measurements. As shown in Fig. 1 the 0.9 % more porosity of sample HAD is mainly composed of pore throat radii smaller than 100 nm, indicating an increase in small pore throat sizes with higher thermal maturity. Visually these < 100 nm pores can be seen in Fig. 1 within the organic matter.

It is not always easy to distinguish in SEM images the organics from the pore space. We used the SE images to separate the two based on the gray scale. Figure 1 shows that the gray values of organic matter and pore space are close to each other, but can be separated by thresholding. The histogram in Fig. 1 points out that two distinct peaks exist after filtering that can be assigned to the pore space and to organic matter including small and thin pores. The organic matter for both samples show connectivity between the different axes. The total volume of the organic matter in the WIC sample is 21.8 vol % and in the HAD sample is 12.3 vol %. Using a density of 1.25 g cm-3 the TOC in wt % was calculated. This resulted in 11.8 wt % TOC in WIC and 6.1 % in HAD. This compares fairly well with the TOC results from Kaufhold et al. (2016) (WIC 8.5 wt % TOC and HAD 5.2 wt %). The decrease in TOC is also confirmed by Gasparik et al. (2014), Ghanizadeh et al. (2014), Mohnhoff et al. (2015) and Mathia et al. (2016).

Visually it can be seen that with increasing maturity the pores (< 100 nm) in the organic matter increase (Fig. 6). The OM in WIC has very few pores, while the HAD kerogens are filled with pores. We binarized the largest organic particles together with its pore space in HAD (Fig. 4). The results were that the organic particle contained an internal pore space of 5.5 %. The binarized pores contain only a small pore networks and are not interconnected with the surrounding mineral matrix.

The pores for both samples do not show any connectivity (permeability = 0) between the different sides. The next assumption we made was that, the organics had an extremely low permeability of 1×10-21 m2 itself (similar to Monteiro et al., 2012) and corresponding to a diameter of 3.2 nm after cubic law flow (Taylor et al., 1999). We assigned this number to the organic phase in the binarized domain to apply a coupled free air and porous media flow. Doing this, a connected porous media was built up and the organics with the small pores below the FIB detection resolution limit contributed to the pressure drop and flux. This allowed us to perform permeability calculations using GeoDict. The permeability tensors for both pores and organics were calculated from binarized images (resolution 25 nm per voxel, dimension of computational domain is 768×768×384 respectively 768×512×384 voxels) with as special Navier–Stokes–Brinkman–LIR solver for coupled free and porous media flow and implemented in the GeoDict software (Iliev and Laptev, 2004; Wiegmann, 2007). To determine a tensor of permeability, it is necessary to apply each side of the domain in x, y, z direction with an pressure gradient separately and simulate the flux through the sample. As permeating medium we use air with a temperature of 293.15 K, a density of 1.204 kg m-3 and a dynamic viscosity of 1.834×10-5 kg m-1 s-1. The boundary conditions were a constant pressure gradient in flow directions and all domain sides were defined as symmetric (mirrored over sides) with periodic boundaries which means that inflow and outflow boundaries see the same structure (Khan et al., 2012). These setups give numerically stable and accurate flow simulations in low and heterogeneous porous media. Simulations will stop if the system reaches steady state and the flux will become constant over time meaning that a numerical accuracy of 1×10-4 residual change of permeability is reached. An alternative setup would have been to assign flat inflow and outflow planes as boundary conditions, which have a lot of numerical problems in numerical convergence of the system. Therefore, it was not utilized.

Figure 6b shows the resulting pressure field for one side case after numerical convergence. The resulting pressure and velocity fields are shown in Figs. 3 and 6. If we assume this organic permeability, the total permeability increases by a factor of up to 12 in sample WIC and decreases by up to 0.3×10-21 m2 for HAD if compared to the permeability of organic matter (Table 1).

These calculated values are in a range of experimental determined permeabilities for Posidonia shale samples (Ghanizadeh et al., 2014 and Mohnhoff et al., 2015) that were measured perpendicular to the bedding. Both studies have shown a decrease in permeability with increasing maturity (for comparison see Table 2). However, Ghanizadeh et al. (2014) determined that the permeability measured parallel to the bedding is up to 3 orders of magnitude higher. This indicates that the main transport along this plane may not occur within a clay lamina but rather elsewhere, probably along cracks or naturally occurring weak spots, e.g., between clay laminae. Therefore, our calculations may only consider intra-laminae transport.

Nonetheless, spatial anisotropy was observed even for intra-laminae calculated permeabilities. For the HAD sample, the lowest permeability was observed in the y direction (0.7×10-21 m2 vs. 0.99×10-21 m2 in x and 1.8×10-21 m2 in z), which is the direction running perpendicular to the bedding. WIC showed lowest permeability in y (1.2×10-21 m2) and z (1.4×10-21 m2). For WIC the highest permeability was observed in x direction (11.9×10-21 m2). Since the bedding, as discussed in Sect. 2.5, is not parallel to the b x–z plane, no connection between anisotropic permeability coefficients and bedding can be drawn.

The resulting average velocities for air flow at 100 000 Pa show the same anisotropy. Lowest velocities are observed in x and y for HAD (2.8×10-7 and 2.9×10-7 m s-1) and in y for WIC (3.3×10-7 m s-1). Velocities for the water flow are 2 orders of magnitude lower than for air simulations.

The spatial distribution of the pore paths was evaluated by analyzing stereographic projections. A skeleton of the binarized pore space was generated by using the Centerline Tree module of Avizo 9.0 (Tube parameter: slope = 3:5; zeroV al = 4). It is based on the TEASAR algorithm (Sato et al., 2000) which generates tree-like vector-based skeletons that do not allow circles. Dip and plunge of each vector were plotted using Stereonet software of Cardozo and Allmendinger (2013). Orientation of a vector represents the orientation of the pore path. It does not take into account how long or skewed the path itself is. Only pores larger than 200 voxels were analyzed in order to obtain reliable orientations. Equal area projections in combination with 1 % net area contouring (interval: 1 %) were used for a better visualization.

Results are shown in Fig. 7. It becomes apparent that pore paths in sample HAD are oriented homogenously along the bedding plane which is equal to the x–z plane. In contrast sample WIC shows a strong preferred orientation that differs from the x–z plane, which indicates that the slicing with the FIB was not performed perpendicular to the bedding plane

Porosity using FIB-SEM can be described either as pore clusters or through continuous pore size distribution (PSD). PSD describes best the pore geometry and therefore hydrodynamic properties in shales. The thin throats within the pore clusters are what control its hydrodynamic properties (Fig. 3). The typical range of pore radii detectable in our study are between 25 and 300 nm. Even though investigated volumes are small and rather not representative the PSD trends of HAD and WIC are almost identical between 300 and 100 nm, while for the mature sample HAD pores with radii < 100 nm increase by 0.9 % compared to WIC. This supports the argument that small pores formed during maturation. What complicates this issue is that most pores are not detectable at the given resolution. As reported by others, summarized in Table 1, the majority of pores in the Posidonia shale are within the micro- and smaller mesopore range.

A fraction of small pores within the mineral matrix is misinterpreted as organic matter (Fig. 1). Therefore, the increase in volume generated by radii < 100 nm in the PSD should be bigger. This would result in higher total porosity values as well. As shown in Fig. 5 pores with radii < 100 nm contribute to the 0.9 % higher porosity of HAD. This is because small pores within organic matter are easier to identify as pores than those within mineral matrix. Figure 1 shows that HAD contains small pores within OM at the resolution used, which is not the case for WIC. Therefore, at the used scale the increase in thermal maturity only leads to an increase in porosity but not in connectivity, because the new formed pores seem to be isolated, closed pores within the organic matter. This would correspond well to the determined MIP values of Kaufhold et al. (2016) which decreased with increasing maturity (WIC: 11.9 %, HAD: 8.0 %). Therefore, FIB-SEM porosity increases while MIP decreases. However, SEM images of Mathia et al. (2016) have shown the diverse nature of organic matter-hosted porosity at the nanometer scale. For HAD they observed spherical organic matter pores which did not show connectivity as well as sponge-like pore systems which clearly exhibit potential pathways. Because of this the contradictory trends of FIB-SEM and MIP porosities cannot be related to isolated pores alone.

Although we were able to show that the pores align along the bedding plane, no connectivity between the axes was observed in both samples. Similar results have been reported by Keller et al. (2013) who found that the connectivity of shales is highest along the bedding plane and decreases with increasing sample length. Further they conclude that the connectivity depends on the porosity of the investigated volume and that a local porosity between at least 6 and 10 % is needed to realize percolation paths along the bedding plane. These findings are supported by Hemes et al. (2015) who found that at a total porosity of about 18 % almost 87 % the pore space contribute to the axis connectivity. In our work we observed that at porosities of about 2 % connected pore clusters only exist at the scale of a few µm.

When considering the misinterpretation of pores as organics we can assume that the real connectivity of pores is higher. Improvements in image resolution could offer valuable clues to solve this problem. However, Kuila et al. (2014) state that in organic-rich shales 10–70 % of the total porosity might not even be detectable with methods like field emission scanning electron microscopy, due to overly small pore sizes (< 5 nm) within organic matter and clays. Additionally, the type of organic matter controls its porosity with increasing maturity (e.g., Klaver et al., 2016). Although we did not classify the type of organic matter it is very likely that the observed matrix-filling OM in both samples is solid bitumen which becomes mesoporous by gasification processes at gas-window maturities (Mathia et al., 2016).

As shown in Fig. 6 the pressure field develops continuously when the size of pores and organic matter is rather large. Jumps appear when the connectivity is limited by thin throats or is not given at all (Fig. 5b, WIC bottom right). After analyzing the pressure field for all directions it becomes obvious that the pathways through the material are restricted by those throats throughout the material. The velocity fields illustrate this as well. Flow of air and water only appears within parts of the pore. Figure 3 shows a close-up of the skeleton of single pore cluster in combination with the velocity field. By comparing both we found that the highest velocities are reached within throats between areas where the pore is rather wide and where velocities are comparatively low. Dead ends depend on the direction of pressure and on the chaining to the organic matter system.

Calculated permeability coefficients depend strongly on the assumed permeability of the organic matter (1×10-21 m2). Calculated values scatter around it since the segmented solid bitumen is clearly the main permeable medium. It was shown that permeability for WIC decreases relative to the OM permeability by 1 order of magnitude. For HAD calculated values along the bedding were close to the assumed OM permeability. Perpendicular to bedding the permeability decreased relative to the OM.

Anisotropy of permeability and average velocity calculations for HAD correspond well to the analysis of the pore path orientation which showed horizontal bedding parallel to the x–z plane (Fig. 7). Permeability is highest along the bedding which is in good agreement with the results of Ghanizadeh et al. (2014) and others (see Table 1) although they demonstrated that the parallel permeability is 3 orders of magnitude higher. Bhandari et al. (2015) on the other hand find only 1 order of magnitude difference. Their observations on the Barnett Shale – a shale similar to the mineralogical composition and TOC content of the Posidonia shale – indicate directional differences of only 1 order of magnitude (⊥ 2.3×10-21 m2, ∥ 9.5×10-20 m2). This is in the range of our calculated anisotropy.

Permeability coefficients of WIC are up to 17 times higher than those calculated for HAD. This is likely caused by the higher OM and lower clay mineral content in the early mature sample (WIC 21.9 % OM & 21 % clay minerals vs. HAD 14.7 % OM & 35 % clay minerals). The decrease in OM leads to a less homogenous distribution of permeable media in sample HAD. This is shown in Fig. 6a and b. While the porosity distribution is more homogenous in sample HAD (almost no larger regions with no pores), the pressure field exhibits several voids (upper left, lower left and right). These regions are clearly porous but not connected due to the lack of OM. This indicates that decreasing OM contents lead to more tortuous and less abundant pathways. Although higher porosities should enhance flow properties the opposite is the case since the increase in porosity (+0.9 %) cannot compensate for the decrease in OM content (-7.2 %). As a result the permeability decreases with increasing maturity. The same trends were observed by Ghanizadeh et al. (2014) and Mohnhoff et al. (2015).

The approach to include the OM into the simulations with a permeability of 1×10-21 m2 resulted in permeability values that show good agreement with experimental data of other researchers (see Table 1). A series of permeability measurements on 152 samples of 9 potential shale gas formations performed by Javadpour et al. (2007) resulted in an average permeability of 5.3×10-20 m2. However, it is very likely that the assumed OM permeability changes with increasing maturity. OM in the gas window is likely to be more permeable than OM in lower mature shales. In order to be able to relate changes in the calculated permeability values to changes in porosity and organic matter content, we used a static OM permeability. A next step is to perform ultra-high resolution FIB-SEM analyses on selected solid bitumen particles in order to model permeability of OM for specific maturities. Therefore, calculated permeability coefficients represent the current state of research and shall not be taken as true material properties.