International Journal of Coal Geology 146 (2015) 42–54

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The representative sample size in shale oil rocks and nano-scale characterization of transport properties Soheil Saraji, Mohammad Piri Department of Chemical and Petroleum Engineering, University of Wyoming, 1000 E. University Ave., Laramie, WY 82071, USA

a r t i c l e

i n f o

Article history: Received 23 December 2014 Received in revised form 12 April 2015 Accepted 13 April 2015 Available online 23 April 2015 Keywords: Shale oil Representative sample size Transport properties Pores size distribution Pore types

a b s t r a c t The experimental determination of petrophysical properties for shale rocks is dependent on measurement techniques and often produces inconsistent results. Alternatively, high-resolution three-dimensional imaging techniques coupled with image analysis and direct numerical simulations have been employed to estimate these parameters in shale samples. Nevertheless, the application of these results at the core and reservoir scales are uncertain due to the limited size of imaged samples. Here, Focused Ion Beam milling and Scanning Electron Microscope tomography is employed to study transport properties for the three upper layers of the Bakken formation. The representative size of each shale sample is characterized. Pore types, their connectivities, and pore size distributions are studied using high-resolution micrographs and their implications to mass transport at the macro scale are discussed. Porosity and permeability of the samples are also calculated from threedimensional images, and the results are compared to experimentally-measured values at the core scale. It is shown that the representative size of shale samples is dependent on the scale of analysis and could range from tens to hundreds of microns. We found that the upper Bakken layer is rich in clay and organic materials, the dominant pore type is pores associated with organic matter, and no connected porosity was observed in the preserved core samples. In contrast, the middle Bakken layers (upper and lower layers) have about 1% connected porosity mainly as intraplatelet pores within clay aggregates and interparticle pores, resulting in permeabilities between 4 and 30 μ D. Moreover, comparison of pore types and modeled flow pathways suggests the presence of water-wet connected pores in the middle Bakken rocks, whereas mainly oil-wet pores are present in the upper Bakken shale. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The ever-growing demand for energy, relatively high price of hydrocarbons, and recent advances in production technologies have brought tight hydrocarbon-bearing shale formations into attention as a vast source of energy. Shale rocks are defined as laminated fine-grained (≤62.5 μm) argillaceous sedimentary rocks with varying compositions [Potter et al. (2005)]. Pores within these rocks are orders of magnitude smaller (nanometer scale) than those in conventional carbonate and sandstone samples (micrometer scale)[Nelson (2009); Bertoncello et al. (2013)]. Therefore, compared to conventional rocks, shales typically have low porosities (5–10%) and permeabilities (10 nano-Darcy to 10 micro-Darcy) [Bertoncello et al. (2013)]. The experimental measurements of petrophysical parameters in shale rocks using conventional techniques have reported inconsistent results [Bertoncello et al. (2013); (Sinha et al., 2013), (Lasswell, 2013)]. It was shown that the results are sensitive to the measurement techniques and experimental conditions. Alternatively, high-resolution three-dimensional images of rocks coupled with image analysis and direct numerical modeling of single- or twophase flow has been used to characterize the shale rocks [Keller et al. (2013); (Gelb et al., 2011), (Al-Raoush and Papadopoulos, 2010), (Chen 0166-5162/© 2015 Elsevier B.V. All rights reserved.

et al., 2013), (Suhrer et al., 2013)]. The currently available imaging tools for three-dimensional analysis of rock samples include non-destructive instruments, such as traditional medical X-ray computed tomography (CT) and modern higher resolution X-ray computed micro- and nanotomography, and destructive instruments such as dual beam Focused Ion Beam and Scanning Electron Microscope (FIB-SEM) tomography. X-ray based CT technique uses computer-processed X-ray intensities from various realizations, allowing the reconstruction of threedimensional images of intact objects. In FIB-SEM tomography, a sequence of two-dimensional cross-sectional images, spaced evenly through a region of bulk specimen, is acquired by physical sectioning of an object (using FIB). This stack of two-dimensional images is then re-constructed into a three-dimensional digital gray-scale representation of the sample volume. Since the latter technique directly obtains an electron micrograph of the rock surface, less imaging artifacts are produced and smaller features can be resolved at higher resolutions (e.g., ~1 nm). However, higher resolutions provided by advanced imaging techniques such as FIB-SEM tomography and computed nanotomography inevitably limit the field of view under study. Meanwhile, the instruments with larger field of view such as conventional (medical) CT and micro-CT have much lower resolutions (e.g., ~250 μm and ~1 μm, respectively) and

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(a) B2

(b) B3

(c) B4

Fig. 1. 3D macro images of the preserved core samples (pixel resolutions of 235 μm in X–Y and 1 mm in the Z direction).

thus cannot resolve the majority of pores in shale rocks. Therefore, it is critical to determine the optimal sample size and resolution for obtaining flow properties in shale samples. In order for quantitative analysis of porous rocks at nano or micro scales to be relevant at the macro scale, selection of a representative averaging volume is required. The concept of representative elementary volume (REV) for porous rocks was first introduced by (Bear, 1972). REV is defined as a minimum averaging volume over which the macroscopic measurable characteristics of a porous medium remain constant.


Usually, porosity is used as the desired macroscopic parameter in this type of analysis, but other parameters such as specific surface area and permeability have also been used for this purpose [Zhang et al. (2000); (Hendrick et al., 2012), (Nordahl and Ringrose, 2008)]. (Zhang et al., 2000) proposed the use of statistical REV (sREV) for heterogeneous rocks, which is less restrictive compared to the deterministic REV. Later, this concept was used by other researchers to find sREV in FIB-SEM images of rocks such as chalk [Yoon and Dewers (2013)] and shale samples [Chen et al. (2013); (Gelb et al., 2011)]. Yoon and Dewers (2013) analyzed a ~123 μm3 FIB-SEM image with a resolution of about 15 nm and found the sREV of their chalk sample to be between 5–10 μ m (1D). In another study, (Chen et al., 2013) investigated intrakerogen pores by FIB-SEM imaging on a shale sample (3.4 × 1.4 × 1.2 μm3) with the resolution of 12 nm. They proposed that sREV for their sample is less than 1 μm (1D). X-ray nanotomography was used by (Gelb et al., 2011) to image a shale rock sample (~ 653 μm3) at 50 nm resolution. The main image was divided into smaller cubes and the porosity of each cube was compared to that of the original sample for the standard deviation. Based on the standard deviation of each cube set, they established a ~30 μm REV for the sample (1-D). Unlike all the previous studies, (Keller et al., 2013) used a geostatistical analysis on multiple FIB-SEM images of Opalinus clay 63 –163 μm3 in size at 2–20 nm resolutions. They proposed an REV of a few hundred microns for their clay samples by extrapolating their analysis beyond the actual size of the images. As mentioned earlier, high-resolution imaging tools suffer from a limited field of view. Thus, in all of the studies mentioned above, it is unknown whether the size of the original sample was sufficient for REV analysis. It is, therefore, likely that REV or sREV proposed by these studies is an underestimation of the true REV of their samples. Consequently, the pertinence of the mass transport simulation results typically performed on small three-dimensional images (b1003 μm3) to fluid transport at the reservoir scale is uncertain. One way to estimate the representative

(a) B1

(b) B2

(c) B3

(d) B4

Fig. 2. Elemental maps of rock samples from EDS analysis [10 kV, 3200 nA, and 150 nm image resolution] (Q:Quartz, Ca: Calcite, P: Pyrite, D: Dolomite, I/S: Illite/Smectite, F: Feldspar, Ap: Apatite, Z: Zercon, I: Illite, Ch: Chlorite).


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size of the shale rocks while avoiding size limitations associated with three-dimensional imaging instruments is to use large high-resolution two-dimensional images of shale samples. (Bear and Bachmat, 1990) defined, in analogy to REV, representative elementary area (REA) for a porous medium as a minimum averaging area over which the macroscopic characteristics of the porous media remain constant. The REA concept has been applied to study spatial heterogeneity and scale-related problems in two-dimensional thin sections of soils [Vandenbygaart and Protz (1999)]. Here, we applied both REV and REA analysis on reservoir shale samples to estimate their representative size at two different scales. A key aspect in the assessment of productivity in shale reservoirs is the nature and topology of their pore systems. Although an induced hydraulic fracture network is commonly created to enhance permeability of shale formations, flow of hydrocarbons to this network occurs through the intrinsic matrix porosity [Josh et al. (2012)]. Furthermore, the ability of reservoir rocks to store hydrocarbons is also dependent on their pore structure. Pores in shale rocks are believed to have formed during either depositional or diagenetic processes and their formation is a function of original matrix mineralogy, fabric (arrangement of grains), texture (size and sorting of grains), and composition and thermal maturity of organic matter[Loucks et al. (2012)]. (Loucks et al., 2012) categorized pore types in shale rocks as: (a) pores associated with organic matter (OM), (b) pores between grains and crystals (interparticle),

and (c) pores within grains, crystals, and clay aggregates (intraparticle). This classification allows a better understanding of the possible fluid distribution and flow pathways in shale rocks [Passey et al. (2010); Fishman et al. (2012), (Bohacs et al., 2013)]. Interparticle and intraparticle pores are believed to be originally water-wet and expected to remain mostly water-wet even after hydrocarbon generation by organic matter in the oil and gas window [Bohacs et al. (2013)]. In contrast, pores within OM are likely to be hydrocarbon-wet due to the hydrophobic nature of the organic walls [Passey et al. (2010)]. The origin of porosity in the organic material is hypothesized to be due to a volume change during and after hydrocarbon generation [Jarvie et al. (2007)]. However, it is suggested by Fishman et al. (2012) that nanopores may already be present in organic matter at the time of deposition. Regardless of their origin, OM pores are mostly sponge-like with circular cross-sections in the gas window, while crack-like OM pores are observed in the oil window [Curtis et al. (2013)]. In the current study, four reservoir rock samples across layers of Bakken formation (upper, upper middle, and lower middle) were selected and imaged using a dual beam FIB-SEM instrument. First, pore types in each sample were characterized using multiple twodimensional SEM micrographs and Scanning Transmission Electron Microscopy (STEM) images at ultra-high resolutions (~ 1 nm). Next, several three-dimensional images at high resolutions were obtained

Fig. 3. Various steps in image segmentation and analysis on Image B1-4 (pixel resolution = 2.5 nm): (a) filtered, aligned, and corrected gray-scale 3D image, (b) segmented 3D image including various phases, (c) segmented pores from the image, (d) extracted pore network using skeletonization algorithm.

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Fig. 4. Back-scattered SEM micrographs from uncoated shale samples using TLD lens [Beam energy, Beam current, Pixel resolution]. (Pore types in each image is highlighted with red boxes.)


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Fig. 4 (continued).

and analyzed to study the following characteristics of the rock samples: pore morphology, pore size distribution, pore aspect ratios, specific surface area, spatial distribution of porosity, total organic content, and absolute permeability. These results enabled us to identify the main flow paths and associate pore types in each sample. The REV of the samples were also characterized using porosity and permeability as the target parameters. Furthermore, large two-dimensional SEM maps (N1 mm2) were acquired from polished rock surfaces and REA analysis was performed to estimate representative sample sizes at a larger scale.

2. Materials and methods 2.1. Rock samples Four rock samples from the Bakken formation were used in this study: B1 (upper Bakken, unpreserved), B2 (upper Bakken, preserved), B3 (upper middle Bakken, preserved), and B4 (lower middle Bakken, preserved). The three preserved reservoir cores (i.e., B2, B3, and B4) were first imaged at the macro scale using a medical X-ray CT scanner

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(Figs. 1a–c, pixel resolution of 235 μm in X and Y, and 1 mm in the Z directions). The bedding orientation in these cores is perpendicular to the Z axis. Therefore, the X-Z and Y-Z planes are perpendicular to the horizontal flow paths while the X-Y plane is perpendicular to the vertical flow. The elemental composition and mineralogy of the rock samples were characterized using X-ray diffraction (XRD) and energy dispersive X-ray Spectroscopy (EDS) analysis and are shown in Figs. 2a–d. Different types of minerals are highlighted and color-coded in these figures. It was found that B1 and B2 samples were clay-rich shales mainly composed of illite/smectite, dolomite and quartz grains, scattered pyrite framboids, and scarcely distributed apatite and zircon minerals. In contrast, B3 and B4 samples were siltstones with quartz, dolomite, calcite, and illite as the most abundant minerals. It is known that rocks with high quartz and carbonate contents (N 50%) and low clay contents are often more brittle and hence respond better to well stimulation practices [Passey et al. (2010) (Glorioso and Rattia, 2012)]. Therefore, we argue that the fracturing operation can be more successful in the upper and lower middle Bakken layers with higher contents of quartz and calcite compared to the upper Bakken with more clay minerals. The macro-CT images, interestingly, reveal fractures in B3 and B4 core samples parallel to the bedding planes (Figs. 1b and c) that we believe caused by the exerted stress or stress relief during the coring operation. Further geomechanical studies on these rocks will be necessary for the characterization of elastic modulus, planes of weakness, and brittleness index in order to develop a well stimulation strategy [Glorioso and Rattia (2012)]. 2.2. Sample preparation and imaging Small rectangular rock samples (1–2 cm in length and width and 1–2 mm in thickness), parallel or perpendicular to the bedding, were slowly dry-cut from areas of interest by a diamond saw. In order to avoid introducing artifacts on rock surfaces by mechanical polishing [Loucks et al. (2012)], the samples were polished by an Argon ion mill with two ion sources (Model 1060, Fischione Instruments). Each sample was polished in 6 sessions of 30 minutes using a beam energy of 5 kV, beam angle of 5 deg, and 45% focus with a continuous stage rotation. The polished samples were mounted on either a flat or a pre-tilted (45 deg) aluminum specimen Mount using a conductive carbon tape and then lightly carbon-coated with a carbon sputter coater (EMS150R ES, Quorum Technologies Ltd.). A dual-beam Helios 650 Nanolab FIB-SEM instrument was employed to image the rock samples. The samples on pre-tilted Mounts were used to generate the highest resolution three-dimensional images

Fig. 5. A ternary diagram showing pore types for different rock samples from Bakken shale formation.


(2–10 nm pixel resolutions), while the other samples were used to obtain both large two-dimensional maps and lower resolution three-dimensional images (10–40 nm pixel resolutions). Prior to three-dimensional imaging, a layer of platinum was deposited on the ion-milled surface at a desired spot to protect the surface from long exposure to ion beam and also to prevent vertical striations or curtaining effect. Serial sectioning was then performed using 30 kV Gallium ion beam with beam currents between 790 and 2500 pA. A Through Lens Detector (TLD) in electron backscattered mode typically at 1–2 kV beam energies, 100–400 pA beam currents, and 10–30 μs dwell times were utilized for SEM imaging. Moreover, multiple side-by-side SEM images from polished rock samples were obtained by a Central Backscattered (CBS) detector at 100–150 μm horizontal field of views, 30– 45 nm pixel resolutions, and a 4% areal overlap. The overlapping area between these individual images was later used for image alignments. Then, a set of aligned images was stitched together to build a large two-dimensional areal micrograph typically larger than 1 mm2. These large two-dimensional micrographs, hereinafter referred to as SEM maps, are the largest (and highest resolution) images that could be analyzed using the computational power used in this study (see the next section). 2.3. Image visualization and processing AvizoFire 8.0 software installed on a computer with two Intel® Xeon® processors (8 core, 3.10 GHz), 256 GB memory and GeForce® GTX TITAN GPU (6 GB integrated memory) was used for image visualization and analysis. FIB-SEM data were processed as follows. Firstly, image filtration (usually non-local means routine) was performed for noise cancellation and shear correction, if applicable. Then, the stack of images was aligned using the least squares method to correct for

Fig. 6. Dark field STEM micrograph from B2 rock sample: (a) a lamella with 10 × 10 × 0.1 μm 3 dimensions, (b) and (c) zoom in locations showing nano scale organic matter pores [Beam energy, Beam current, Pixel resolution].


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slight lateral shifts. We employed a shading correction algorithm to eliminate background-shading artifacts. Finally, the resulting image stack was trimmed and segmented to different phases based on the gray-scale contrast. There were several distinct phases in SEM/FIB-SEM images of shale samples: dark spots (pores), organic matter, clay sheets, siliceous minerals, calcareous minerals, and pyrite (Fig. 3a). Each of these phases was first segmented using a gray-scale thresholding technique, then used as input seeds in a watershed algorithm to automatically identify boundaries between them. The resulting segmented twodimensional or three-dimensional images of the rock samples (Fig. 3b) were used for further analysis. In order to characterize pore topology, segmented three-dimensional images were converted into binary images containing solely pore information (Fig. 3c). A skeletonization algorithm was implemented on these binary images to extract models for three-dimensional pore networks by preserving the major characteristics of the pore geometry (Fig. 3d). Consisting connecting branches (throats) and nodes (pores); the resulting pore network offers a representation of the complex pore space topology and connectivity with information relevant to the mass transport in shale rocks. 3. Results and discussion 3.1. Pore types SEM micrographs in back-scattered mode (BSE) were acquired from ion-polished non-coated rock surfaces, both parallel and perpendicular to the bedding planes (Figs. 4a-j). These images were visually examined and different pore types were identified (highlighted with red boxes in Figs. 4a-j). The area fraction occupied by each pore type was then quantified using pixel counting and averaged for each rock sample. The results are illustrated in Fig. 5 as a ternary diagram showing fractions of different pore types in each sample. We found that the majority of porosity in B1 sample is constituted by crack-like OM pores (Fig. 4a and b). However, the majority of pores in B2 are interparticle pores in strain shadows surrounding large grains (Fig. 4c). Sponge-like OM nanopores are also visible in B2 (Fig. 4d). Fishman et al. (2012) argued that interparticle pores between grains and organic matter in shale rocks could be artificially induced. These features are possibly a result of shrinkage due to desiccation after the cores were brought to the surface and allowed to dry. A main indication of these induced features is their sharp edges that typically mirror each other [Fishman et al. (2012)]. Therefore, we treated these pores with caution in the analysis of B2 sample. The OM nanopores in B2 rock are the smallest features found in this study and the resolution of SEM micrographs might not have been enough to fully reveal the characteristics and connectivity of these pores. Thus, a thin lamella (b 100 nm in thickness) from B2 rock containing organic matter was prepared by FIB (Fig. 6a) and imaged with Scanning Transmission Electron Microscopy (STEM) detector at the highest possible resolution (i.e., ~1 nm). Fig. 6b and c show dark field STEM micrographs of the thin organic material. Although the sponge-like nanopores in OM (black spots in Fig. 6b and c) form a well-connected network, their role in mass transport is likely to be limited due to their small sizes (b 10 nm). Pore structures in B3 and B4 samples are very similar and are mainly comprised of intraparticle slit-like pores between clay aggregates (Fig. 4g, h, and i) and interparticle pores between grains/crystals (Figs. 4f and j). There are also some scattered intracrystalline pores in dolomite crystals and OM pores in the scarcely distributed organic material in these samples. The connectivity of different type of pores and their importance to mass transport is discussed later in this manuscript. 3.2. Pore network Petrophysical parameters that can be computed from high-resolution three-dimensional SEM micrographs include: porosity, permeability,

pore connectivity, pore size distribution, specific surface area, mean pore aspect ratio, and total organic content (TOC). In this study, eight three-dimensional images, (6–30) 3 μm3, were obtained from the four rock samples at 2.5–16 nm resolutions (Fig. 7). Total organic content, specific surface area, and mean pore aspect ratio for all threedimensional images were calculated through image analysis and are listed in Table 1. The upper shale layer in the Bakken formation is considered as a source rock, while the middle layers store producible oil and are regarded as reservoir rocks [Nojabaei et al. (2013); (Egenhoff and Fishman, 2013)]. This is consistent with high total organic content found in B1-1 to 4 and B2-1 to B2-2 images as well as low TOC in B3-1 and B4-1. The measured total organic contents for the upper Bakken images were 8–20 vol.% (compare to 3–10 wt.% reported by (Egenhoff and Fishman, 2013)) while it was less than 2 vol.% for the middle Bakken samples. The specific surface area (As) was determined by generating three-dimensional pore surfaces using modified marching cube algorithm [Hege et al. (1997)] and then dividing the total pore surface area by the total pore volume (Table 1). Furthermore, Feret diameter analysis was performed on each individual pore to find the three-dimensional maximum (length) and minimum (width) pore diameters. We then calculated and averaged width-to-length ratios to find the mean pore aspect ratio (α in Table 1). We observed that the last two parameters were very sensitive to the size and resolution of three-dimensional images. For instance, the location of the first four images in Table 1 were selected randomly on B1 rock sample, and they vary in size and resolution. As for these images varies between 28 and 81 (μm−1) and α ranges from 0.45 to 0.59. 3.2.1. Pore size distribution Pore size distributions (PSD) of the three-dimensional rock images were calculated by image analysis using two methods: discrete and continuous as described previously [Münch and Holzer (2008)]. In the discrete method, a single pore is defined as a void volume including all connected sub-regions. This method involves counting detached pore objects directly from three-dimensional images. In contrast to the discrete method, pore structure in the continuous PSD is regarded as one single continuum, independent of possible connectivities. Therefore, each single pore object is decomposed into a continuous size spectrum. In order to find discrete PSD for rock samples under study, the radius of an equivalent sphere for each pore was calculated and plotted in a histogram. In continuous PSD, a three-dimensional distance map function was first computed from each FIB-SEM image. A distance map holds the closest distance to the boundaries separating pore and matter for each point inside the pore volume. Then, using this map and a distance-ordered thinning algorithm proposed by (Pudney, 1998), a skeleton (a medial surface or branch and node network) was extracted from the segmented pore phase (see Fig. 3d). A skeleton of a pore space may be generally defined as the locus of centers of all maximal inscribed spheres in pore phase [Liang et al. (2000)] or as the set of points (voxels) equidistant from at least two points on the solid wall [Adler (1992)]. At this stage, radii histogram of the inscribed sphere was plotted. The average pore sizes obtained from these methods are listed in Table 1. As shown in this table, assessments based on discrete PSD results in much higher pore radii compared to continuous PSD. (Münch and Holzer, 2008) argued that the continuous PSD is more relevant to mass transport studies in porous media and the results are comparable to the experimentally measured PSD by mercury injection capillary pressure (MICP) method. We, therefore, used continues PSDs obtained from the three-dimensional images for further analysis. The continuous PSDs calculated here are plotted in Fig. 8. Fig. 8a compares pore size distributions from four images acquired from random locations in B1 rock sample. The images with higher resolutions can resolve smaller pores and hence shift the PSD towards the left of the graph (i.e., smaller pore sizes). PSDs for all the shale samples from images of comparable size and resolution (i.e., B1-2, B2-2, B3-1, and B4-1) are plotted in Fig. 8b. The majority of pores in these samples are

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between 10-100 nm. Finally, the PSDs for total visible pores and connected pores were compared for Image B3-1 in Fig. 8c. The connected pores are the ones that are connected across the image and thus contribute to mass transport. Both curves have similar shapes and start at the same pore size on the right side of the figure, but the difference between the two curves are more pronounced at the smaller pore radii. This indicates higher contribution of larger pores to the connected porosity in this rock sample. 3.2.2. Porosity and permeability The three-dimensional FIB-SEM images of rocks from the Bakken formation were further analyzed for porosity, pore connectivity, and permeability. All the images show very low total visible porosity, less than 2%, which is expected from shales and siltstones. Additionally, due to anisotropy in the shale samples, higher pore connectivity was observed parallel to the bedding plane (X-Y plane in Fig. 1). The connected porosity for these images were calculated in this direction and are listed in Table 1. The permeability of the rock samples were also calculated parallel to the bedding plane using Avizo XLab Hydro package. This module calculates permeability by numerically solving the Stokes equation for single-phase flow in pore space using a finite volume method with no-slip boundary conditions. The resulting permeabilities are reported in Table 1 and the velocity fields for Images B1-3 and B4-1 are shown in Figs. 9a and b, respectively. The connected porosities for B11 to 4 images are between 0.2-0.7 % resulting in permeabilities between 1-6 μ D. The major flow pathways in B1 rock are through crack-like OM


pores, tens of nanometers in size (Fig. 9a). On the other hand, the spherical/elliptical OM pores (typically smaller than 10 nm in size) and interparticle pores (possibly artificially induced as argued earlier) are not connected across B2-1 and B2-2 images and therefore their permeabilities are zero. Although both B1 and B2 rocks are from the same formation, the major difference between the nature of their OM pores suggests different level of thermal maturity in the organic matter in these samples. A geological formation can be in different depths at various locations and thus experience different pressure and temperature history. Although, there is no available data on the depth of the sampling for B1 core, we believe different thermal maturity is the reason for different permeabilities obtained from the upper Bakken shale samples. Furthermore, as suggested by Fig. 9b, the dominant flow pathways for B4 rock (and also B3) are through both the pores between particles and in the phyllosilicate clay platelets. The connected porosities in these samples are more than 50% of the total porosity and hence much higher pearmeabilities ranging from 4 to 30 μ D were calculated for these rocks. According to discussions on wettability of different pore types in shale samples [Passey et al. (2010); (Bohacs et al., 2013)], we suspect the relevant pores to flow in the upper Bakken samples are mainly oil-wet, while dominant flow pathways in the middle Bakken layer are waterwet. Further studies on these rocks, for example by nondestructive imaging methods in the presence of fluids, are required to characterize local pore wettabilities. In order to make a comparison between the results obtained from image analysis (at micro-scale) and experimental measurements (at

Fig. 7. Visualization of 3D images acquired from the rock samples [height×width× depth, pixel resolution].


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Fig. 7 (continued).

macro-scale), porosity and gas permeability for core plugs from B3 (3 cores) and B4 (1 core) were experimentally determined using Nitrogen expansion porosimetry and transient permeability measurements with 500 psig overburden pressure. The plugs were, first, dry-cut from the preserved cores parallel to the bedding plane and then dried in an oven at 105°C for 24 hours before measurements. Air was used as the cooling agent for cutting the cores to avoid possible contamination and pore structure alteration by water-based and oil-based coolants. Since gas expansion porosimetry measurement is based on percolation

of Nitrogen inside porous rock sample, the measured porosity value is the connected porosity of the rock. Comparison between connected porosities and permeabilities calculated from the image analysis (Table 1) and experimental measurements (shown in Table 2) reveals an inconsistency between these two measurements. The small size of threedimensional images (b303 μm3) compared to core plugs is most probably the main reason for this inconsistency (please refer to the next section). There are other reasons proposed in the literature for this behavior. For instance, microfracture networks inside the rock samples

Table 1 Specification of 3D images and results from image analysis for the shale samples. [Φtotal: total observable porosity, Φeffec: connected porosity, AS: specific surface area, α: mean pore aspect ratio, k: permeability, r dis: : average pore radius from discrete PSD, r cnt: : average pore radius from continuous PSD]. Sample

B1-1 B1-2 B1-3 B1-4 B2-1 B2-2 B3-1 B4-1

Sample size








(vol. %)




30 × 23 × 2.2 17 × 13 × 1.5 14 × 12 × 1.4 10 × 10 × 3.91 17 × 18 × 3.1 39 × 37 × 13.1 37 × 38 × 8.5 39 × 38 × 15

16 8 5 2.5 4.4 10 10 10

13.7 8.4 8.3 8.3 19.7 12.7 0 1.53

2.04 1.30 1.42 1.23 0.32 1.24 1.50 1.75

0.45 0.68 0.59 0.18 0 0 0.83 0.94

28.1 41.7 67.0 80.8 80.5 65.1 59.4 66.6


0.46 0.45 0.36 0.59 0.62 0.46 0.44 0.46


r dis:



r cnt: (nm)

5.82 1.49 1.30 5.25 0 0 3.81 30.2

101.2 25.6 13.4 10.0 17.1 21.1 50.4 21.3

18.0 13.9 10.3 7.3 5.1 11.9 18.0 19.6

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Fig. 9. Simulated flow pathways in 3D images.

are usually ignored during high-resolution imaging, while they play an important role at the core scale [Bertoncello et al. (2013)]. Also, uncertainties associated with laboratory measurement techniques, such as transient permeability measurements compared to steady-state measurements for tight cores, may result in variations in experimental values [Lasswell (2013)]. 3.3. Representative sample size As mentioned earlier, knowing the representative sample size is essential for up-scaling the image analysis results to higher scales. We performed analysis at two different scales to investigate this for the shale samples in this study. First, REV analysis was performed on selected three-dimensional images (53–303 μm3) using porosity as well as permeability as the parameters of interest due to their implications for mass storage and transport. Next, we extended this investigation to a much larger scale by employing large two-dimensional SEM

Table 2 Experimentally measured porosity and permeability.

Fig. 8. Comparison of continuous pore size distributions between 3D images.










B3-C1 B3-C2 B3-C3 B4-C1

2.54 2.53 2.54 3.79

3.39 5.47 7.07 6.66

4.3 2.7 4.0 6.5

14 1 2 1


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Fig. 10. Large 2D high-resolution SEM maps from the shale samples using CBS detector [beam energy, beam current, pixel resolution].

Fig. 11. Characteristic sample size analysis.

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maps (N1 mm2) (Figs. 10a–d) and conducting REA analysis. The results are presented in the following subsections. 3.3.1. Representative elementary volume We selected a FIB-SEM image from each sample (images B1-2, B2-2, B3-1, and B4-1) to perform REV analysis based on the method proposed by (Bear, 1972). The sampling volume on the segmented threedimensional image (hereby referred to as box for simplicity) starts from the entire image and then gradually decreases in all dimensions (Fig. 11a). The volume fraction of pores (i.e., porosity) and permeability are then computed at each step. The results are plotted against the size of the box (i.e., characteristic size) in Fig. 12a and b. The values of REV for porosity are less than 10 μm in 1D. These results are comparable with the previously reported values by (Gelb et al., 2011), (Chen et al., 2013), (Suhrer et al., 2013), and Yoon and Dewers (2013). However, it is important to note that we could not identify REV values for permeability. This may stem from the fact that the size of three-dimensional images are too small for this analysis. 3.3.2. Representative elementary area The SEM maps were acquired from polished rock surfaces perpendicular to the bedding planes, which are expected to be more heterogeneous compared to the parallel plane. The size of these two-dimensional images are an order of magnitude larger than three-dimensional images that could be obtained using FIB-SEM tomography. A deterministic approach proposed by (Bear and Bachmat, 1990) was employed. Similar to REV analysis, the sampling area on the segmented two-dimensional map starts from the entire map and then gradually decreases in size to about 100 μm2 in the center of the map (shown as rectangles in Fig. 11b). The area fraction of the pores inside the box is quantified and compared to the original value. The results are plotted in Fig. 12c. The REA values are found to be a few hundred μm in 1D, which is an order of magnitude larger than the values from previous section. However, they are comparable to the results from geostatistical analysis performed by (Keller et al., 2013). 4. Conclusions

Fig. 12. Representative sample size analysis.

The current recovery assessments predict that less than 10% of the estimated oil reserves can be recovered from the Bakken formation. Improving the oil recovery from this formation requires better understanding of the pore space topology and connectivity. FIB-SEM tomography was utilized here to characterize pore networks in the three upper layers of the Bakken formation. These layers are considered as the major contributors to the hydrocarbon production from this reservoir [Nojabaei et al. (2013); (Egenhoff and Fishman, 2013)]. We found that the upper Bakken layer is rich in clay and organic materials, the dominant pore types are pores associated with organic matter, and there is no connected porosity in the preserved core samples analyzed from this layer. In contrast, the middle Bakken layers (upper and lower layers) have about 1% connected porosity mainly as intraplatelet pores within clay aggregates and interparticle pores. The presence of well-connected pores, for the sample analyzed here, resulted in permeabilities ranging from 4 to 30 μD. Moreover, comparison of pore types and modeled flow pathways suggests the presence of water-wet connected pores in the middle Bakken layer, whereas mainly oil-wet pores are present in the upper Bakken shale. We showed that the representative size of shale samples was dependent on the scale of analysis (from 10s to 100s of micrometer). In addition, there was a discrepancy between measured parameters from core samples and estimated values from image analysis. Therefore, we argue that multiple random threedimensional images are required from each sample in order to perform a statistically representative analysis for these rocks. One way to reduce the number of required images is targeting specific parts of the samples with known structures. This requires a priori knowledge of the sample inter-structure that can be, for instance, resolved by nondestructive X-


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[American Academy of Neurology, Washington, 18-25 April 2015].

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