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ABSTRACT

Shales exhibit a wide range of textures, compositions, and mechanical properties, which are interlinked by their diagenetic history. During hydraulic fracturing of shales, the matrix is subjected to shear deformation, which may create microfractures and enhance hydrocarbon transport from nanoscale, organic matter (OM)-hosted pores to the larger, induced fracture network. To study the nanoscale response to shear deformation of shale pore systems with different diagenetic histories, we deformed shale samples from a formation in the Northern Rocky Mountains and the Eagle Ford Group in Texas, using confined compressive strength tests. N2 and CO2 adsorption were performed to quantify fracture effects on pore morphology including pore size distribution, porosity, surface area, and surface fractal dimensions. Most samples increased their gas adsorption quantity, pore volume, and surface area after failure. The surface fractal dimensions were less sensitive to shear deformation. Results show that varying nanometer-to-micron-scale fracture patterns are in part caused by contrasting rock fabrics that are preconditioned by their distinctive diagenetic histories. For example, fractures tend to propagate along the OM laminae, whereas others cut across OM grains and access OM pores. Other possible mechanisms for porosity increase include the deformation of relatively uncemented clay aggregates and contrasting amounts of intra-OM pores between samples. Thus, the mechanisms for syn-deformational porosity changes at the micro scale are highly dependent on diagenetic history, particularly the maturation of OM, and the cementation history relative to clay content.

INTRODUCTION

Mudrocks (including shales and mudstones) exhibit a wide range of textures, compositions, and mechanical properties (Loucks et al., 2009, 2012; Eliyahu et al., 2015; Pommer and Milliken, 2015; Emmanuel et al., 2016). Diagenesis controls much of this variation through burial, compaction, cementation, and thermal maturation. As the original porosity in the sediment collapses with burial (e.g., Velde, 1996), some pores can be preserved within both detrital and diagenetically produced or altered grains (e.g., Desbois et al., 2009). Intragranular porosity is particularly important in organic matter (OM) (Loucks et al., 2009, 2012; Pommer and Milliken, 2015), as opposed to intergranular pores between grains in the surrounding matrix of clay, cement, and other materials (e.g., Schneider et al., 2011). These pore systems can be related to one another because the fine pore network and connectivity can be dependent not just on the abundance of OM but also on its distribution (Loucks and Reed, 2014). Here, we explore how deformation that occurs during unconventional production via hydraulic fracturing can have a varying effect on porosity because of these diagenetically produced textural variations.

Diagenetic processes directly affect the properties of shale, in turn impacting production efforts at the field scale. During hydraulic fracturing, a network of highly conductive fractures enhances hydrocarbon transport to the wellbore (Nolte, 2000; Arthur et al., 2009). The fluid injection brings the rock volume to shear failure, causing microseismicity and enhanced permeability (Dusseault, 2011; Maxwell and Cipolla, 2011). Near the wellbore, shear failure is accompanied by opening-mode fractures, but the relative importance of these fractures for permeability enhancement relative to other distributed deformation in the surrounding shale remains uncertain. This uncertainty is due to the different types of porosity and variable mechanical responses that are both texturally and compositionally controlled. Underscoring the importance of this distributed deformation, modeling of field production data suggests that the permeability of the rock lying between the main, induced, meter-spaced fractures is enhanced by a factor of 10–100 (Patzek et al., 2013). It stands to reason that as the main fractures are reactivated, additional damage in the matrix between the fractures could further expand the zone responsible for production, and numerical simulations have indeed shown that the shear deformation may be able to reactivate networks of preexisting fractures and faults (Johri and Zoback, 2013).

Daigle et al. (2017) experimentally demonstrated the importance of opening-mode fractures at the micron-to-nanometer scale by causing fracture propagation into OM pores during experimental shear deformation. In this effort, we expand the analysis of those experiments by focusing on how different materials appear to have different porosity changes with failure, and qualitatively different fracture networks. Gas adsorption (Sing, 1985; Roque-Malherbe, 2007) was used to characterize pore structure at the nanometer (nm) scale. We build on this previous work by presenting a more thorough analysis of multiple aliquots of each sample to reduce bias of results because of sample heterogeneity. Besides N2 adsorption, we used CO2 adsorption data to measure pore sizes below 1 nm, where the pore sizes of some clays are located (Kuila and Prasad, 2013). Furthermore, we expand the adsorption analysis to include Brunauer-Emmett-Teller (BET) surface area, fractal dimension, defined below. When complemented by scanning electron microscope (SEM) imaging, this allows the more comprehensive study of changes associated with pore structure.

Our results allow us to better understand the relative importance of deformation that occurs through microcracking and grain rearrangement throughout the sample(s), here referred to as “shear deformation,” vs. propagation of opening-mode fractures. Alongside an analysis of pore surface and volume information from the gas adsorption measurement, we draw on fractal theory, which provides a measure of the overall microstructure. Through this effort, we address the following questions:

  • How does shear deformation change the nanoscale pores of shale?

  • Do formations with contrasting compositions and diagenetic histories have different pore structure responses to the shear deformation?

  • What is the significance of OM to syn-deformational porosity change?

  • What is the significance of detrital clay and cement to syn-deformational porosity change?

We suggest that the answer to these questions involves how porosity and, by inference, permeability changes during deformation, wherein opening-mode fractures and surrounding shear deformation are sensitive to diagenetic fabrics and rock composition.

BACKGROUND

Diagenetic History

The distinct depositional setting, characteristic grain assemblages, and systematic contrast in OM content of the two shale units that we focus on here impact the evolution of porosity and mechanical rock properties (Milliken, 2014). By contrasting two very different types of shale (see Table 1 for x-ray diffraction [XRD] data), we aim to resolve the role of diagenetic components in the deformation.

Table 1.

Summary of XRD results in weight percent. I/S = mixed-layer illite/smectite. The total clay = illite/mica + illite/smectite. The total cement = calcite*0.5 + quartz*0.85.

SampleIllite/MicaI/SCalciteQuartzTotal clayTotal cement
EF 1_13511862131942
EF 2_50192140134031
EF 2_936770101344
NoRM 3_1419193413836
NoRM 3_4213101552347
NoRM 3_539111542046
NoRM 4_141090631954
NoRM 4_3419130523244
SampleIllite/MicaI/SCalciteQuartzTotal clayTotal cement
EF 1_13511862131942
EF 2_50192140134031
EF 2_936770101344
NoRM 3_1419193413836
NoRM 3_4213101552347
NoRM 3_539111542046
NoRM 4_141090631954
NoRM 4_3419130523244

The Eagle Ford Formation, in southern Texas, is a coccolithic, organic-rich mudrock that contains a mixture of mineral- and OM-hosted pores of both primary and secondary origins (Pommer and Milliken, 2015). Destruction of primary porosity and generation of secondary porosity in high-maturity samples is controlled by the relative physical and chemical stabilities of the grain assemblage and early diagenetic components as they undergo later burial diagenetic processes, including abundant microquartz cement (Milliken et al., 2016). Pommer and Milliken (2015) reported that the maturity of the samples by vitrinite reflectance ranges from low maturity (Ro 0.5%) to high maturity (Ro 1.3%). The total organic carbon (TOC) has a wide range from 1.2 to 13.6 wt. %.

In contrast, the samples from the northern Rocky Mountains are considerably more quartz rich (40–60 wt. %). In general, the quartz in siliceous shale takes several forms: extrabasinal detrital silt (some with an earlier diagenetic history as exemplified by transported pretransport overgrowths), replacement of skeletal debris, minor overgrowths on detrital quartz and replaced radiolaria, pore-filling in the intragranular pores of allochems, and authigenic microquartz that is dispersed through the clay-size matrix (Milliken and Olson, 2017). The overall porosity decline is compaction-dominated, despite the exceptional abundance of cement. Milliken and Olson (2017) proposed that the presence of significant volumes of cement would lead to brittle behavior where cements are most prominently developed. They reported the maturity of shale samples by vitrinite reflectance ranges from 0.72 to 1.1% Ro. The TOC ranges from 1.55 to 3.75 wt. %. We return to this topic of cementation and embrittlement in the discussion section.

Gas Adsorption

In this study, we rely on the relationship between adsorption and porosity to study the microtextures of the two shale units. During the adsorption process, the adsorbate (N2 or CO2) is dosed into the sample in controlled pressure increments. The adsorbate molecules physisorb on the surface of the solid through intermolecular forces. The pressure for each dose and the quantity adsorbed form the adsorption isotherm. As gas pressure increases, the coverage of adsorbed molecules increases to form a monolayer and then multilayers on the solid surface. As the multilayer adsorption proceeds, the adsorbate eventually condenses in the pores through the Kelvin effect, whereby the condensation pressure in a pore with high curvature is depressed relative to condensation in free space. Thus, the condensation of gas occurs first in the smallest pores and proceeds in order of increasing pore size. At the end of adsorption, the sample will be completely covered and all pores will be filled by the adsorbate. After the adsorption process, desorption then proceeds by withdrawal of gas in prescribed pressure increments.

Given the area covered by each adsorbed molecule, the surface area of the solid surface thus can be calculated. The method used to calculate the surface area is called BET method, which incorporates multilayer coverage (Brunauer et al., 1938; Yang et al., 2014). The pore size distribution (PSD) represents the relative abundance of each pore size in the sample. Here, we used density functional theory (DFT), which is based on statistical thermodynamics, to compute the PSD. This approach treats the fluid in the pores as inhomogeneous with a structure in density across the pore because of forces emanating from the solid walls (see Adesida et al., 2011).

Fractal Dimension

Shale is a multiscale heterogeneous material with a complex pore structure. As such, it is difficult to describe the geometry of the solid surface. Fractal theory provides a powerful tool to characterize heterogeneous media such as shale.

To describe the fractal dimension, we first introduce the concept in a simple fashion using an example of a regular 1-D line (Figure 1). The line initially has a unit length. If we magnify the line by a factor of 2 (the magnification factor r), the line becomes two units long. The total number (N) of unit length lines is also 2. The dimension D for a regular l-D line is

 

D=log(N)log(r)=log(2)log(2)=1.
(1)

Using this formula, we can calculate the fractal dimension of a Koch curve in Figure 2. When the line length increases from 1 unit length to 3 unit lengths (r = 3), the total number of unit lines is 4. The fractal dimension D of the line in the middle panel of Figure 2 is

 

D=log(N)log(r)=log(4)log(3)=1.26.
(2)

Figure 1.

Illustration of the underlying principle for the fractal dimension: a line may be broken into N self-similar sublines, each with magnification factor N.

Figure 1.

Illustration of the underlying principle for the fractal dimension: a line may be broken into N self-similar sublines, each with magnification factor N.

Figure 2.

Demonstration of Koch curve fractal.

Figure 2.

Demonstration of Koch curve fractal.

The fractal dimension of the line in the right-hand panel of Figure 2 is also equal to 1.26.

Surface Fractal Dimension

One widely used fractal model is the surface fractal, where surfaces or boundaries separating mass and pore spaces are quantified in terms of their scale independence. Surface fractals are quantified as a surface fractal dimension Ds, which varies from 2 to 3. A value of 2 indicates a smooth surface, whereas 3 indicates an extremely rough surface.

N2 adsorption data can be used to compute the surface fractal dimension. The method is called Frenkel-Halsey-Hill (FHH) method (Frenkel, 1946; Hill, 1946; Halsey, 1948), and it is the most effective and widely used model for evaluating surface fractal dimension from gas adsorption data (e.g., Yang et al., 2014; Liu et al., 2015; Jiang et al., 2016). The surface fractal dimension Ds can be determined as

 

VVm[RT ln(P0/P)]k,
(3)

where V is the volume of adsorbed gas molecules at equilibrium pressure P, Vm is the volume of gas molecules in a monolayer, R is the universal gas constant, T is the absolute temperature when the isotherm was obtained, and P0 is the saturated vapor pressure of nitrogen at T (Sokołowska et al., 2001; Yang et al., 2014). The range of adsorption data for P/P0 > 0.45 was used in the calculation (Yang et al., 2014) as capillary condensation is dominant in this pressure range. As a result, the relationship between Ds and k is expressed as Ds = k + 3 (Jaroniec et al., 1997).

Incorporating this relationship between Ds and k, Equation 3 can be written in log-log form:

 

ln(V)=(Ds3)ln(ln(P0/P))+C,
(4)

where V is the volume of adsorbed N2, Ds is the surface fractal dimension, and C is an additional constant that accounts for the amount of adsorbed volume when the fractal regime is first reached (Jiang et al., 2016). The value of Ds is obtained by applying a linear regression for ln(V) vs. ln(ln(P0/P)).

Furthermore, two different fractal dimension values (D1 and D2) can be computed from N2 adsorption. As previous studies showed that surface fractal dimension calculated from normalized pressure between 0 and 0.45 was different from the value obtained from relative pressure between 0.45 and 1 (Wang et al., 2015; Jiang et al., 2016). D1 is the fractal dimension calculated from relative pressure less than 0.45, and D2 is the dimension from relative pressure greater than 0.45.

METHODS

A total of eight organic-rich shale cores were used in this study, with three samples (EF 1_223, EF 2_50, and EF 2_93) from the Eagle Ford unit (hereinafter referred as calcareous shale) and five samples (NoRM 3_14, NoRM 3_42, NoRM 3_53, NoRM 4_14, and NoRM 4_34) from the northern Rocky Mountains, referred to as siliceous shale because the location of the siliceous shale is withheld by the donor though the samples are similar to those described by Milliken and Olson (2017). All samples were preserved in mineral oil until experimentation. We found no sign of mineral oil imbibing into the samples through nuclear magnetic resonance measurements (Daigle et al., 2017).

The mineralogy of the shale was analyzed using XRD by Weatherford Laboratories in Houston, Texas. The data are listed in Table 1. Following Milliken (2014), we estimate the total clay content and total cement content using the following equations:

 

Total clay=illite/mica+I/S,
(5)

 

Total cement=calcite*0.5+quartz*0.85,
(6)

where I/S is mixed-layer illite/smectite. The assumption that 50% of calcite takes the form of cement is a common assumption in carbonate-rich rocks (Bathurst, 1975) and authigenic quartz has recently been reported to be 85% (or more) of total quartz in both the calcareous and siliceous shale (see Milliken et al., 2016; Milliken and Olson, 2017).

Calcite dominates the calcareous shale samples, whereas quartz dominates the siliceous samples. Clay minerals (illite/smectite and illite/mica) are present in significant amounts in both lithologies, whereas the quartz and calcite contents differ quite dramatically between the two. The bulk mineralogy is generally consistent with that found from previous research of calcareous shale (Pommer and Milliken, 2015) and siliceous shale (Milliken and Olson, 2017).

Sample cores were subsampled using a low-rate coring machine with mineral oil as a lubricating fluid. One core plug was drilled parallel to the bedding planes, and another one was drilled perpendicular to the bedding planes. Each plug was 2.54 cm (1 in.) in diameter and 5–7 cm (2–2.8 in.) in length. They were preserved in the light mineral oil until experimentation.

Shear failure was induced by subjecting the samples to confined compressive strength tests. The core plug was wrapped in a thermo-shrinkable sleeve before being loaded into the testing cell. During the test, the confining stress increased to 10 MPa over the course of 1 min. The axial stress was increased by displacing the axial ram at a rate of 0.01 in. per minute. The test was completed when sample failure occurred. For simplicity, failed samples drilled parallel to bedding are referred as horizontally failed (HFail), whereas failed samples drilled perpendicular to bedding are referred as vertically failed (VFail).

The imaging was performed using a FEI Nova Nano SEM 430 FE-SEM (field-emission scanning electron microscope) at the Bureau of Economic Geology (BEG) at the University of Texas at Austin. Prior to the confined compressive strength tests, about 1 cm (0.4 in.) of material was removed from the bottom of the core plugs for imaging. After the test, a 1 cm (0.4 in.) slice of material was removed from the middle of each core plug for imaging. Subsamples were prepared in-house (at the BEG) via ion milling (Milliken et al., 2013) and Ir coating (4–5 nm in thickness). Both backscattered electron and x-ray elemental maps via EDS (energy-dispersive x-ray spectroscopy) were collected.

Low-pressure N2 and CO2 sorption measurements were conducted using a Micromeritics 3Flex system at the Hildebrand Department of Petroleum and Geosystem Engineering at the University of Texas at Austin. Sample materials were collected from the core plugs before and after (prior and post) the confined compressive strength tests. Samples were oven dried at 110°C (230°F) for 24 hours and hand crushed to less than 40 US mesh (0.42 mm). Approximately 1–1.5 g of crushed sample was used for N2 gas adsorption–desorption at 77 K and CO2 adsorption at 273.15 K.

Based on the adsorption data, the BET surface areas as well as PSDs by nonlocal density functional theory (Roque-Malherbe, 2007; Adesida et al., 2011) with slit-shaped carbon pores (Tarazona, 1985; Tarazona and Vicente, 1985) were obtained. Integrating the N2 and CO2 PSDs, we calculated the meso-/macropore volume (pore diameter≥2 nm) and the micropore volume (pore diameter < 2 nm), according to the classification of International Union of Pure and Applied Chemistry (IUPAC; Sing, 1985). In addition, we calculated the fractal dimensions D1 and D2. We extend the initial reporting by Daigle et al. (2017) by presenting measurements on multiple aliquots of materials of each sample. Using the mean value and standard deviation yields a more rigorous comparison of intact vs. failed porosity and helps reducing bias of results because of sample heterogeneity.

In any laboratory study of fracturing behavior, there is always the question of which fractures are induced experimentally, which are generated during core retrieval and handling, and which are present in situ in the subsurface. Specifically, the hand crushing procedure for the gas sorption measurements may open new fractures. Though we cannot rule out that some of the fractures presented in Daigle et al. (2017) were caused by the sampling process, we note that there were quantifiable differences between pre- and postfailure porosity that was correlated with lithology, and hence diagenetic history. As we applied the same handling procedures for porosity measurements of intact and failed rock, the uncertainty caused by artifacts from that particular measure is assumed to be minimized. We also note that, regardless of orientation of bedding relative to the imposed stress, in SEM images, most of the fractures follow planes of weakness, and OM laminae in particular, as we will show in detail in the results section. In some instances, fractures branch across bedding planes and connect (also likely weak) clay aggregates and OM particles. We acknowledge that such microtextural relations differ from the general sense that fractures cut across bedding planes at the field scale during hydraulic stimulate. We extrapolate on these microtextural relationships in the Discussion in the context of the bulk porosity data. Regardless of the origin of the observed microfractures (experimental or artifact), they both reflect important variations in grain-scale mechanical properties such that the induced fractures are accommodated along natural planes of weakness, which are in part controlled by variations in mineral and organic diagenesis.

RESULTS

Scanning Electron Microscope Images

SEM images provide the in situ documentation of the microfracture and pore system in siliceous vs. calcareous samples, as well as information on the amount of cement and detrital clay minerals, and textural information about porosity distribution (Figures 35). The microstructure of siliceous samples is a mixture of laminated and particulate OM between predominantly quartz grains. On the other hand, the calcareous samples were dominated by coarser calcite grains, and most OM was dispersed throughout the samples.

Figure 3.

SEM images of the intact samples. The darkest regions of the images are mostly organic matter. The brightest regions are pyrite (Py), pores appear black. (A) SEM image of an intact NoRM sample. The brightest regions are pyrite framboids. The OM particulate contains complex pore structure. (B) SEM image of an intact EF sample. Pores (black) occur within organic matter (OM) dispersed within calcareous matrix of predominantly coccolithic fragments (white).

Figure 3.

SEM images of the intact samples. The darkest regions of the images are mostly organic matter. The brightest regions are pyrite (Py), pores appear black. (A) SEM image of an intact NoRM sample. The brightest regions are pyrite framboids. The OM particulate contains complex pore structure. (B) SEM image of an intact EF sample. Pores (black) occur within organic matter (OM) dispersed within calcareous matrix of predominantly coccolithic fragments (white).

Figure 4.

SEM images of horizontally failed samples. Axial stress applied normal to image. (A) The SEM image of a horizontally failed NoRM sample. The fracture intersected pores in OM, but bypassed intergranular pores. (B) The SEM image of a horizontally failed EF sample.

Figure 4.

SEM images of horizontally failed samples. Axial stress applied normal to image. (A) The SEM image of a horizontally failed NoRM sample. The fracture intersected pores in OM, but bypassed intergranular pores. (B) The SEM image of a horizontally failed EF sample.

Figure 5.

(A) SEM image (backscattered with compositional EDS map overlay) of the siliceous shale NoRM 3_14, horizontally failed, illustrating the composition (relatively cement [Si] poor and clay [Al] rich), and cracks both along the central fracture as well as within clay aggregates. (B) SEM image of the siliceous shale NoRM 3_14 OM, vertically failed, with pores next to cracked clay aggregates. (C) SEM image of the siliceous shale NoRM 3_53, vertically failed, with relatively cement (Si) rich and clay (Al) poor. (D) SEM image of the siliceous shale NoRM 4_34, horizontally failed, with relatively nonporous OM.

Figure 5.

(A) SEM image (backscattered with compositional EDS map overlay) of the siliceous shale NoRM 3_14, horizontally failed, illustrating the composition (relatively cement [Si] poor and clay [Al] rich), and cracks both along the central fracture as well as within clay aggregates. (B) SEM image of the siliceous shale NoRM 3_14 OM, vertically failed, with pores next to cracked clay aggregates. (C) SEM image of the siliceous shale NoRM 3_53, vertically failed, with relatively cement (Si) rich and clay (Al) poor. (D) SEM image of the siliceous shale NoRM 4_34, horizontally failed, with relatively nonporous OM.

After failure (Figure 4), fractures with widths ranging from 10–100 nm to 1–2 μm were observed to follow coarser grain boundaries and laminae of OM and matrix materials. In more laminated materials, fracture lengths were up to hundreds of micrometers, which were likely continuous across entire sample volume. Some fractures initiated along grain contacts and primarily propagated through OM.

Though the textural and diagenetic controls on porosity distribution are undoubtedly more complex, our limited observations find that the siliceous samples in particular have instances where the least-cemented sample (e.g., Figure 5A, B) has highly porous OM and enhanced porosity within deformed clay aggregates, whereas more cemented samples (e.g., Figure 5C, D) have less porous OM and less porosity within the cemented matrix.

Gas Adsorption

Eight horizontally failed samples and two vertically failed samples were characterized using N2 and CO2 gas adsorption measurements. BET-specific surface areas, N2 total pore volume, CO2 total pore volume, and two surface fractal dimensions D1 and D2 were calculated. These data are presented in Table 2.

Table 2.

A summary of pore parameter results. HF = horizontally failed samples; VF = vertically failed samples; In = intact samples.

SampleLabelBET Surface Area (m2/g)N2 Pore Volume (cm3/g)CO2 Pore Volume (cm3/g)Fractal Dimension D1Fractal Dimension D2
EF 1_2231_223 HF 14.80290.014180.0001954912.42232.6364
1_223 HF 24.80150.015090.0001946512.41492.616
1_223 VF 15.26670.014880.0002110372.42732.6339
1_223 VF 25.5640.015752.44832.6377
1_223 In 14.31750.012610.0001835092.40412.6292
1_223 In 14.93910.013930.0001964332.41322.6342
EF 2_502_50 HF 16.19120.017780.0001924942.4142.6416
2_50 HF 25.38470.016020.0002228362.39582.6377
2_50 In 16.21810.017960.0002518442.40492.6288
2_50 In 26.28550.017830.000279942.40822.6349
EF 2_932_93 HF 17.34120.020910.0002047862.43112.6488
2_93 HF 27.9770.022010.0002110752.40752.6495
2_93 In 16.89870.019490.0001909092.41872.6416
2_93 In 26.81820.019690.0001514122.41142.6434
NoRM 3_143_14 HF 111.24720.030830.0006175642.51382.6461
3_14 HF 211.76760.032590.0006017482.54222.6385
3_14 In 18.06450.022130.000468692.53392.645
3_14 In 27.70230.02040.000451912.53682.6473
3_14 In 38.01770.020752.54532.6611
3_14 ln 48.44290.021822.52512.6526
NoRM 3_423_42 HF 110.44310.02010.000482022.65252.7128
3_42 HF 28.94750.018580.0004581172.61542.6959
3_42 In 19.7970.023080.0006524692.60632.6702
3_42 In 210.22390.02190.0006052822.62232.6882
3_42 In 39.23010.0202850750.0005710152.62522.6822
3_42 ln 49.01850.019540.0005868272.63822.6829
NoRM 3_533_53 HF 17.36470.020310.0004373162.55172.6402
3_53 HF 27.23930.020262.54632.6296
3_53 VF 17.78580.022120.0004711562.54272.6281
3_53 In 16.77640.018230.0003540042.55872.6424
3_53 In 26.75680.018760.0003886292.56612.6413
3_53 ln 36.68740.018592.55242.6367
NoRM 4_144_14 HF 18.76540.018070.0005415262.64242.6944
4_14 HF 29.39490.018720.0005775012.63172.704
4_14 HF 38.53960.017220.0004286052.6242.7055
4_14 In 16.91290.016520.0003869712.59012.6654
4_14 In 26.84580.016580.0003835562.57882.6695
4_14 ln 36.2910.015662.55882.6746
NoRM 4_344_34 HF 17.13130.016040.0007023112.67972.6513
4_34 HF 26.91140.016990.0007465192.66092.6813
4_34 In 18.6220.018870.000718232.64392.6856
4_34 In 28.17730.018620.0006968052.65122.6771
4_34 ln 37.26020.016540.0007382442.65752.6749
SampleLabelBET Surface Area (m2/g)N2 Pore Volume (cm3/g)CO2 Pore Volume (cm3/g)Fractal Dimension D1Fractal Dimension D2
EF 1_2231_223 HF 14.80290.014180.0001954912.42232.6364
1_223 HF 24.80150.015090.0001946512.41492.616
1_223 VF 15.26670.014880.0002110372.42732.6339
1_223 VF 25.5640.015752.44832.6377
1_223 In 14.31750.012610.0001835092.40412.6292
1_223 In 14.93910.013930.0001964332.41322.6342
EF 2_502_50 HF 16.19120.017780.0001924942.4142.6416
2_50 HF 25.38470.016020.0002228362.39582.6377
2_50 In 16.21810.017960.0002518442.40492.6288
2_50 In 26.28550.017830.000279942.40822.6349
EF 2_932_93 HF 17.34120.020910.0002047862.43112.6488
2_93 HF 27.9770.022010.0002110752.40752.6495
2_93 In 16.89870.019490.0001909092.41872.6416
2_93 In 26.81820.019690.0001514122.41142.6434
NoRM 3_143_14 HF 111.24720.030830.0006175642.51382.6461
3_14 HF 211.76760.032590.0006017482.54222.6385
3_14 In 18.06450.022130.000468692.53392.645
3_14 In 27.70230.02040.000451912.53682.6473
3_14 In 38.01770.020752.54532.6611
3_14 ln 48.44290.021822.52512.6526
NoRM 3_423_42 HF 110.44310.02010.000482022.65252.7128
3_42 HF 28.94750.018580.0004581172.61542.6959
3_42 In 19.7970.023080.0006524692.60632.6702
3_42 In 210.22390.02190.0006052822.62232.6882
3_42 In 39.23010.0202850750.0005710152.62522.6822
3_42 ln 49.01850.019540.0005868272.63822.6829
NoRM 3_533_53 HF 17.36470.020310.0004373162.55172.6402
3_53 HF 27.23930.020262.54632.6296
3_53 VF 17.78580.022120.0004711562.54272.6281
3_53 In 16.77640.018230.0003540042.55872.6424
3_53 In 26.75680.018760.0003886292.56612.6413
3_53 ln 36.68740.018592.55242.6367
NoRM 4_144_14 HF 18.76540.018070.0005415262.64242.6944
4_14 HF 29.39490.018720.0005775012.63172.704
4_14 HF 38.53960.017220.0004286052.6242.7055
4_14 In 16.91290.016520.0003869712.59012.6654
4_14 In 26.84580.016580.0003835562.57882.6695
4_14 ln 36.2910.015662.55882.6746
NoRM 4_344_34 HF 17.13130.016040.0007023112.67972.6513
4_34 HF 26.91140.016990.0007465192.66092.6813
4_34 In 18.6220.018870.000718232.64392.6856
4_34 In 28.17730.018620.0006968052.65122.6771
4_34 ln 37.26020.016540.0007382442.65752.6749

Gas adsorption isotherms are shown in Figures 6, 7 for N2 and CO2, respectively. Failed and intact samples from the same core are plotted in the same subfigure. After shear failure, most samples from the two formations showed an increase in their adsorption quantity for both N2 and CO2. Sample NoRM 3_14 had the largest increase in the adsorption quantity for N2, whereas NoRM 4_14 had the largest increase in the adsorption quantity for CO2. The vertically failed samples, including samples EF 1_223 and NoRM 3_53, exhibited greater adsorption quantities compared with the horizontally failed samples.

Figure 6.

Comparisons of N2 isotherms for failed and intact samples of the calcareous and siliceous shales. Only one measurement from intact and failed sample are plotted in the graph.

Figure 6.

Comparisons of N2 isotherms for failed and intact samples of the calcareous and siliceous shales. Only one measurement from intact and failed sample are plotted in the graph.

Figure 7.

Comparisons of CO2 isotherms for failed and intact samples of the calcareous and siliceous shale. The CO2 adsorption isotherms were Type I, indicating microporous solids. Only one measurement from intact and failed sample are shown in the graph.

Figure 7.

Comparisons of CO2 isotherms for failed and intact samples of the calcareous and siliceous shale. The CO2 adsorption isotherms were Type I, indicating microporous solids. Only one measurement from intact and failed sample are shown in the graph.

PSDs of N2 and CO2 were calculated, and PSDs of N2 are shown in Figure 8. The N2 pore size ranges from 1.8 to 100 nm. After failure, most of the samples displayed an increase in pore volume in both the micro- and meso-/macropore range. Similar to the isotherm and BET surface area, the vertically failed samples EF 1_223 and NoRM 3_53 had larger increases in pore volume compared to the horizontally failed samples.

Figure 8.

N2 pore size distributions of all eight intact and horizontally failed samples.

Figure 8.

N2 pore size distributions of all eight intact and horizontally failed samples.

BET surface area and pore volume are shown in Figure 9. Surface area (Figure 9A) of intact of calcareous samples varies from 4.32 to 6.98 m2/g. The surface areas of the intact siliceous samples had higher values, varying from 6.78 to 12.08 m2/g. After shear failure, most of the failed rocks displayed an increase in surface area, especially for NoRM 3_14 and NoRM 4_14. The vertically failed samples had a larger surface area compared to both horizontally failed and intact samples. N2 and CO2 total pore volume are shown in Figure 9B, C. The intact calcareous shale had a higher N2 pore volume than the intact siliceous samples, with smaller CO2 pore volume. After shear failure, most of the failed rocks showed an increase in both N2 and CO2. Sample 3_14 displayed large increases for both.

Figure 9.

(A) BET-specific surface area of intact and failed samples. (B) N2 pore volume of intact and failed samples. (C) CO2 pore volume of intact and failed samples. (D) The ratio of meso-/macropore (≥2 nm) volume and the ratio of micropore (<2 nm) volume. In (A), (B), and (C), the mean value is used for each sample. In (D), the calcareous samples are marked in blue, and siliceous samples are marked in red. Horizontally failed sample are in circles, and vertical failed sample in triangle shapes.

Figure 9.

(A) BET-specific surface area of intact and failed samples. (B) N2 pore volume of intact and failed samples. (C) CO2 pore volume of intact and failed samples. (D) The ratio of meso-/macropore (≥2 nm) volume and the ratio of micropore (<2 nm) volume. In (A), (B), and (C), the mean value is used for each sample. In (D), the calcareous samples are marked in blue, and siliceous samples are marked in red. Horizontally failed sample are in circles, and vertical failed sample in triangle shapes.

Furthermore, we calculated the ratio of failed samples and intact samples in terms of meso-/macropore (≥2 nm) volume and micropore (<2 nm) volume (Figure 9D). The meso-/macropore is the total N2 pore volume with pore size greater than 2 nm. The micropore volume is the sum of both CO2 pore size and N2 pore volume with pore size less than 2 nm. Most samples from both formations showed an increase in pore volume in both the meso-/macropore and micropore size range after failure, although a few failed samples had a decrease in porosity. Some samples had their pore volume increased by about 1.5-fold. One calcareous sample and two siliceous samples, however, had a roughly 5–10% reduction in pore volume after failure.

The surface fractal dimensions D1 and D2 are shown in Figure 10. All intact EF samples had similar D1 as well as D2, indicating a more consistent rock fabric structure. Compared to BET surface area and pore volume, the surface fractal dimensions were less sensitive to shear failure. However, NoRM 4_14 and NoRM 3_42 increased their fractal dimension to some degree. This might be the sign that the shear failure caused systematic changes in shale nanoscale pore surface, producing more complex surface textures. However, the magnitudes of such changes were likely small, as we explore in the Discussion.

Figure 10.

Plots of (A) fractal dimension D1 and (B) fractal dimension D2 of intact and failed samples. The mean value is used for each sample.

Figure 10.

Plots of (A) fractal dimension D1 and (B) fractal dimension D2 of intact and failed samples. The mean value is used for each sample.

In short, the BET surface area, porosity, PSD, and fractal dimensions indicate the impact of shear deformation on the nanoscale pores. The pore volume ratio data (Figure 9D) shows that the porosity change is greater in the siliceous samples than in the calcareous samples during deformation. Similarly, the fractal surface dimension appears to be more greatly impacted by deformation in the siliceous samples than the calcareous samples.

DISCUSSION

Effect of Bedding

The absolute change in pore volume for any given sample depends primarily on the direction of loading (Figures 810). The vertically failed samples tend to have a larger increase in the total pore volume than the horizontally failed ones. For sample NoRM 3_53, the vertically failed sample had a similar increase in pore volume for meso-/macropore range and micropore range compared to the horizontally failed sample. The vertically failed calcareous sample (EF_1_223), on the other hand, showed a larger micropore volume increase and a smaller meso-/macropore volume increase. In this context, the primary fabric anisotropy (bedding) in combination with variable cementation states may be imparting heterogeneity in mechanical response.

Effects of Total Clay and Cementation

We offer the following hypothesis for a further role for diagenesis in governing the mechanics of pore-volume and surface-area change with deformation. This hypothesis stems from the ratio of surface area and total pore volume (N2 pore volume plus CO2 pore volume) in failed samples relative to intact samples. We plot the surface area ratio and total pore volume ratio with total clay content and total cement content in Figure 11. The plots show that the calcareous and siliceous shales have similar linear tends. However, an outlier (sample NoRM 3_14) has higher BET surface area ratio and total pore volume ratio. Notwithstanding the outlier, the analyses from the two formations have similar trends, indicating the general impact of mineralogy on porosity changes with deformation. Note that the total clay content has a negative impact on surface area ratio and total pore volume ratio. We suggest that this is because, in general, clay-rich samples also have less cement and have pores that are more prone to collapse during the deformation. On the other hand, the total cement content has a positive impact on surface area ratio and total pore volume ratio because cement favors fracturing surface increase.

Figure 11.

(A) The ratio of BET and total clay content. (B) The ratio of BET and total cement content. (C) The ratio of total pore volume and total clay content. (D) The ratio of total pore volume and total cement content. The EF samples are marked in blue, and NoRM samples are marked in red circles. The outlier NoRM 3_14 is marked in red square. Linear equations for two formations are obtained by removing the NoRM 3_14.

Figure 11.

(A) The ratio of BET and total clay content. (B) The ratio of BET and total cement content. (C) The ratio of total pore volume and total clay content. (D) The ratio of total pore volume and total cement content. The EF samples are marked in blue, and NoRM samples are marked in red circles. The outlier NoRM 3_14 is marked in red square. Linear equations for two formations are obtained by removing the NoRM 3_14.

The outlier (NoRM 3_14) potentially highlights two important aspects of our hypothesized relationship between mechanics and diagenetic history. First, this sample is anomalously cement-poor and clay-rich compared with the samples that we investigated, and therefore the opening of pores within deforming clay aggregates is enhanced relative to fracturing (Figure 5A). Second, the OM in this sample appears to be especially particulate and pore-rich (Figure 5B). Thus, there is an intrinsic high porosity at the submicron scale that is not widely observed in the other siliceous samples. Though clearly limited by the few number of samples that we observed, this hypothesis highlights how thermal maturation leading to OM porosity is one control, whereas cementation and the heterogeneous distribution of clay mineral content is another, and the two together can lead to anomalous porosity increases during hydraulic fracturing.

Effect of the Shape of Organic Matter

The SEM images of intact samples (Figure 3) suggest that the siliceous samples had more fine-scale OM laminations than the calcareous samples. The mechanically soft (OM and clay) and stiff minerals (quartz and carbonate) were more discretely partitioned in laminae for siliceous samples. Under shear deformation, fractures propagated into the OM-rich soft zone at the mechanical contrast of the two layers. SEM imagery of failed samples (Figures 4, 5) indicates that the fracture further propagated along the OM boundary and into the OM pores. Previous research has shown that OM, especially kerogen, has a lower modulus than surrounding carbonate and silicate grains (Eliyahu et al., 2015; Emmanuel et al., 2016), and that some kinds of OM can fracture under certain circumstances (Daigle et al., 2017). In contrast, the clay in the shale matrix exhibits ductile (distributed) deformational textures that formed through grain rearrangements and porosity closure during deformation (Dehandschutter et al., 2004; Laurich et al., 2014). We suggest that the laminations of OM may further enhance its brittle nature, allowing the interconnection of the fractures and the OM pores. This is consistent with gas adsorption results in Figures 810, where the siliceous samples systematically displayed stronger pore volume responses after the shear deformation.

Loucks and Reed (2014) used SEM images of organic-rich shales to study the connectivity of OM pores in the laminated OM and dispersed OM. They have concluded that the connectivity decrease in the laminated OM compared with the dispersed OM because of OM isolation. Our study indicates that, in contrast, the laminated OM was more sensitive to the shear deformation. The poorer connectivity of the laminated OM will receive relatively greater improvements with deformation. Through the newly formed pathway, the hydrocarbons are connected with the main flow channels. Compared to the dispersed OM, the shear failure is more effective to capture OM pores, enhancing the production of shale with the laminated OM. In turn, because many of these microstructural and mechanical properties are developed early in the diagenetic history, the pore evolution of the shale over geologic time will also be impacted by this contrast between shear and fracture deformation across contrasting distributions and types of OM and surrounding matrix. Future research should consider the timing and role of cementation in establishing these OM relationships, and also the relative importance of cementation to these “granular” controls on syn-deformational porosity change.

CONCLUSIONS

We evaluated the shear deformation of organic-rich shale at the nanoscale. Most samples exhibited an increase in their adsorption quantity, pore volume, and specific surface area following failure. The fractal dimensions were sensitive to the shear failure. The SEM images and N2 adsorption data show how the diagenetic differences between calcareous and siliceous samples lead to different responses to deformation. The differences in rock fabric created by different diagenetic histories cause different nanoscale fracture patterns, including anomalous porosity increases because of pore distributions within OM, heterogeneous distribution of cement between samples, and enhanced porosity within deformed clay aggregates. Fractures tended to propagate along the OM laminae and get access to the OM pores. The interaction of the OM laminae and the shear fracturing may improve the connectivity of the OM laminae to the adjacent rock matrix and thus enhance the hydrocarbon mobility.

ACKNOWLEDGMENTS

This work was supported by the Research Partnership to Secure Energy for America under subcontract 12122-52. Hayman was partially supported by CFSES, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under award DE-SC0001114. The finalization of this chapter occurred while Hayman was serving at the US National Science Foundation. The authors wish to thank Donnie Brooks and Xavier Janson for providing access to the triaxial testing apparatus and performing tests, Rodney Russell and Mukul Sharma for assistance in subsampling the preserved core, and Patrick Smith for assistance with the SEM, Terri Olson for assistance with sample and data acquisition as well as her scientific input, and Kitty Milliken and Nicola Tisato for extensive discussions. We would like to thank the editor and two reviewers for their comments and suggestions.

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Figures & Tables

Figure 1.

Illustration of the underlying principle for the fractal dimension: a line may be broken into N self-similar sublines, each with magnification factor N.

Figure 1.

Illustration of the underlying principle for the fractal dimension: a line may be broken into N self-similar sublines, each with magnification factor N.

Figure 2.

Demonstration of Koch curve fractal.

Figure 2.

Demonstration of Koch curve fractal.

Figure 3.

SEM images of the intact samples. The darkest regions of the images are mostly organic matter. The brightest regions are pyrite (Py), pores appear black. (A) SEM image of an intact NoRM sample. The brightest regions are pyrite framboids. The OM particulate contains complex pore structure. (B) SEM image of an intact EF sample. Pores (black) occur within organic matter (OM) dispersed within calcareous matrix of predominantly coccolithic fragments (white).

Figure 3.

SEM images of the intact samples. The darkest regions of the images are mostly organic matter. The brightest regions are pyrite (Py), pores appear black. (A) SEM image of an intact NoRM sample. The brightest regions are pyrite framboids. The OM particulate contains complex pore structure. (B) SEM image of an intact EF sample. Pores (black) occur within organic matter (OM) dispersed within calcareous matrix of predominantly coccolithic fragments (white).

Figure 4.

SEM images of horizontally failed samples. Axial stress applied normal to image. (A) The SEM image of a horizontally failed NoRM sample. The fracture intersected pores in OM, but bypassed intergranular pores. (B) The SEM image of a horizontally failed EF sample.

Figure 4.

SEM images of horizontally failed samples. Axial stress applied normal to image. (A) The SEM image of a horizontally failed NoRM sample. The fracture intersected pores in OM, but bypassed intergranular pores. (B) The SEM image of a horizontally failed EF sample.

Figure 5.

(A) SEM image (backscattered with compositional EDS map overlay) of the siliceous shale NoRM 3_14, horizontally failed, illustrating the composition (relatively cement [Si] poor and clay [Al] rich), and cracks both along the central fracture as well as within clay aggregates. (B) SEM image of the siliceous shale NoRM 3_14 OM, vertically failed, with pores next to cracked clay aggregates. (C) SEM image of the siliceous shale NoRM 3_53, vertically failed, with relatively cement (Si) rich and clay (Al) poor. (D) SEM image of the siliceous shale NoRM 4_34, horizontally failed, with relatively nonporous OM.

Figure 5.

(A) SEM image (backscattered with compositional EDS map overlay) of the siliceous shale NoRM 3_14, horizontally failed, illustrating the composition (relatively cement [Si] poor and clay [Al] rich), and cracks both along the central fracture as well as within clay aggregates. (B) SEM image of the siliceous shale NoRM 3_14 OM, vertically failed, with pores next to cracked clay aggregates. (C) SEM image of the siliceous shale NoRM 3_53, vertically failed, with relatively cement (Si) rich and clay (Al) poor. (D) SEM image of the siliceous shale NoRM 4_34, horizontally failed, with relatively nonporous OM.

Figure 6.

Comparisons of N2 isotherms for failed and intact samples of the calcareous and siliceous shales. Only one measurement from intact and failed sample are plotted in the graph.

Figure 6.

Comparisons of N2 isotherms for failed and intact samples of the calcareous and siliceous shales. Only one measurement from intact and failed sample are plotted in the graph.

Figure 7.

Comparisons of CO2 isotherms for failed and intact samples of the calcareous and siliceous shale. The CO2 adsorption isotherms were Type I, indicating microporous solids. Only one measurement from intact and failed sample are shown in the graph.

Figure 7.

Comparisons of CO2 isotherms for failed and intact samples of the calcareous and siliceous shale. The CO2 adsorption isotherms were Type I, indicating microporous solids. Only one measurement from intact and failed sample are shown in the graph.

Figure 8.

N2 pore size distributions of all eight intact and horizontally failed samples.

Figure 8.

N2 pore size distributions of all eight intact and horizontally failed samples.

Figure 9.

(A) BET-specific surface area of intact and failed samples. (B) N2 pore volume of intact and failed samples. (C) CO2 pore volume of intact and failed samples. (D) The ratio of meso-/macropore (≥2 nm) volume and the ratio of micropore (<2 nm) volume. In (A), (B), and (C), the mean value is used for each sample. In (D), the calcareous samples are marked in blue, and siliceous samples are marked in red. Horizontally failed sample are in circles, and vertical failed sample in triangle shapes.

Figure 9.

(A) BET-specific surface area of intact and failed samples. (B) N2 pore volume of intact and failed samples. (C) CO2 pore volume of intact and failed samples. (D) The ratio of meso-/macropore (≥2 nm) volume and the ratio of micropore (<2 nm) volume. In (A), (B), and (C), the mean value is used for each sample. In (D), the calcareous samples are marked in blue, and siliceous samples are marked in red. Horizontally failed sample are in circles, and vertical failed sample in triangle shapes.

Figure 10.

Plots of (A) fractal dimension D1 and (B) fractal dimension D2 of intact and failed samples. The mean value is used for each sample.

Figure 10.

Plots of (A) fractal dimension D1 and (B) fractal dimension D2 of intact and failed samples. The mean value is used for each sample.

Figure 11.

(A) The ratio of BET and total clay content. (B) The ratio of BET and total cement content. (C) The ratio of total pore volume and total clay content. (D) The ratio of total pore volume and total cement content. The EF samples are marked in blue, and NoRM samples are marked in red circles. The outlier NoRM 3_14 is marked in red square. Linear equations for two formations are obtained by removing the NoRM 3_14.

Figure 11.

(A) The ratio of BET and total clay content. (B) The ratio of BET and total cement content. (C) The ratio of total pore volume and total clay content. (D) The ratio of total pore volume and total cement content. The EF samples are marked in blue, and NoRM samples are marked in red circles. The outlier NoRM 3_14 is marked in red square. Linear equations for two formations are obtained by removing the NoRM 3_14.

Table 1.

Summary of XRD results in weight percent. I/S = mixed-layer illite/smectite. The total clay = illite/mica + illite/smectite. The total cement = calcite*0.5 + quartz*0.85.

SampleIllite/MicaI/SCalciteQuartzTotal clayTotal cement
EF 1_13511862131942
EF 2_50192140134031
EF 2_936770101344
NoRM 3_1419193413836
NoRM 3_4213101552347
NoRM 3_539111542046
NoRM 4_141090631954
NoRM 4_3419130523244
SampleIllite/MicaI/SCalciteQuartzTotal clayTotal cement
EF 1_13511862131942
EF 2_50192140134031
EF 2_936770101344
NoRM 3_1419193413836
NoRM 3_4213101552347
NoRM 3_539111542046
NoRM 4_141090631954
NoRM 4_3419130523244
Table 2.

A summary of pore parameter results. HF = horizontally failed samples; VF = vertically failed samples; In = intact samples.

SampleLabelBET Surface Area (m2/g)N2 Pore Volume (cm3/g)CO2 Pore Volume (cm3/g)Fractal Dimension D1Fractal Dimension D2
EF 1_2231_223 HF 14.80290.014180.0001954912.42232.6364
1_223 HF 24.80150.015090.0001946512.41492.616
1_223 VF 15.26670.014880.0002110372.42732.6339
1_223 VF 25.5640.015752.44832.6377
1_223 In 14.31750.012610.0001835092.40412.6292
1_223 In 14.93910.013930.0001964332.41322.6342
EF 2_502_50 HF 16.19120.017780.0001924942.4142.6416
2_50 HF 25.38470.016020.0002228362.39582.6377
2_50 In 16.21810.017960.0002518442.40492.6288
2_50 In 26.28550.017830.000279942.40822.6349
EF 2_932_93 HF 17.34120.020910.0002047862.43112.6488
2_93 HF 27.9770.022010.0002110752.40752.6495
2_93 In 16.89870.019490.0001909092.41872.6416
2_93 In 26.81820.019690.0001514122.41142.6434
NoRM 3_143_14 HF 111.24720.030830.0006175642.51382.6461
3_14 HF 211.76760.032590.0006017482.54222.6385
3_14 In 18.06450.022130.000468692.53392.645
3_14 In 27.70230.02040.000451912.53682.6473
3_14 In 38.01770.020752.54532.6611
3_14 ln 48.44290.021822.52512.6526
NoRM 3_423_42 HF 110.44310.02010.000482022.65252.7128
3_42 HF 28.94750.018580.0004581172.61542.6959
3_42 In 19.7970.023080.0006524692.60632.6702
3_42 In 210.22390.02190.0006052822.62232.6882
3_42 In 39.23010.0202850750.0005710152.62522.6822
3_42 ln 49.01850.019540.0005868272.63822.6829
NoRM 3_533_53 HF 17.36470.020310.0004373162.55172.6402
3_53 HF 27.23930.020262.54632.6296
3_53 VF 17.78580.022120.0004711562.54272.6281
3_53 In 16.77640.018230.0003540042.55872.6424
3_53 In 26.75680.018760.0003886292.56612.6413
3_53 ln 36.68740.018592.55242.6367
NoRM 4_144_14 HF 18.76540.018070.0005415262.64242.6944
4_14 HF 29.39490.018720.0005775012.63172.704
4_14 HF 38.53960.017220.0004286052.6242.7055
4_14 In 16.91290.016520.0003869712.59012.6654
4_14 In 26.84580.016580.0003835562.57882.6695
4_14 ln 36.2910.015662.55882.6746
NoRM 4_344_34 HF 17.13130.016040.0007023112.67972.6513
4_34 HF 26.91140.016990.0007465192.66092.6813
4_34 In 18.6220.018870.000718232.64392.6856
4_34 In 28.17730.018620.0006968052.65122.6771
4_34 ln 37.26020.016540.0007382442.65752.6749
SampleLabelBET Surface Area (m2/g)N2 Pore Volume (cm3/g)CO2 Pore Volume (cm3/g)Fractal Dimension D1Fractal Dimension D2
EF 1_2231_223 HF 14.80290.014180.0001954912.42232.6364
1_223 HF 24.80150.015090.0001946512.41492.616
1_223 VF 15.26670.014880.0002110372.42732.6339
1_223 VF 25.5640.015752.44832.6377
1_223 In 14.31750.012610.0001835092.40412.6292
1_223 In 14.93910.013930.0001964332.41322.6342
EF 2_502_50 HF 16.19120.017780.0001924942.4142.6416
2_50 HF 25.38470.016020.0002228362.39582.6377
2_50 In 16.21810.017960.0002518442.40492.6288
2_50 In 26.28550.017830.000279942.40822.6349
EF 2_932_93 HF 17.34120.020910.0002047862.43112.6488
2_93 HF 27.9770.022010.0002110752.40752.6495
2_93 In 16.89870.019490.0001909092.41872.6416
2_93 In 26.81820.019690.0001514122.41142.6434
NoRM 3_143_14 HF 111.24720.030830.0006175642.51382.6461
3_14 HF 211.76760.032590.0006017482.54222.6385
3_14 In 18.06450.022130.000468692.53392.645
3_14 In 27.70230.02040.000451912.53682.6473
3_14 In 38.01770.020752.54532.6611
3_14 ln 48.44290.021822.52512.6526
NoRM 3_423_42 HF 110.44310.02010.000482022.65252.7128
3_42 HF 28.94750.018580.0004581172.61542.6959
3_42 In 19.7970.023080.0006524692.60632.6702
3_42 In 210.22390.02190.0006052822.62232.6882
3_42 In 39.23010.0202850750.0005710152.62522.6822
3_42 ln 49.01850.019540.0005868272.63822.6829
NoRM 3_533_53 HF 17.36470.020310.0004373162.55172.6402
3_53 HF 27.23930.020262.54632.6296
3_53 VF 17.78580.022120.0004711562.54272.6281
3_53 In 16.77640.018230.0003540042.55872.6424
3_53 In 26.75680.018760.0003886292.56612.6413
3_53 ln 36.68740.018592.55242.6367
NoRM 4_144_14 HF 18.76540.018070.0005415262.64242.6944
4_14 HF 29.39490.018720.0005775012.63172.704
4_14 HF 38.53960.017220.0004286052.6242.7055
4_14 In 16.91290.016520.0003869712.59012.6654
4_14 In 26.84580.016580.0003835562.57882.6695
4_14 ln 36.2910.015662.55882.6746
NoRM 4_344_34 HF 17.13130.016040.0007023112.67972.6513
4_34 HF 26.91140.016990.0007465192.66092.6813
4_34 In 18.6220.018870.000718232.64392.6856
4_34 In 28.17730.018620.0006968052.65122.6771
4_34 ln 37.26020.016540.0007382442.65752.6749

Contents

GeoRef

References

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