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Methods of shale pore space characterization
The precise characterization of the pore network of shales from macroscopic to nanoscopic scale requires a combination of several laboratory methods. The methods, which imply the penetration of fluids within the pore network, may be classified as indirect techniques, since they require the application of various models to describe the pore network organization. To convert the directly observed result to the pore size distribution (PSD), different assumptions should be considered.
From these methods, beyond the PSD description, the information about sample density may be obtained, to calculate the total porosity. While He-pycnometry is widely applied technique for grain density measurements with high precision (Thommes et al., 2015), different methods may be used to determine the bulk volume and corresponding density of the sample. The calculation of total porosity is based on the bulk and grain densities (Equation 2), where is the total porosity, Vp – volume of pores [m3], Vs – volume of the solid phases [m3], Vt – total volume of the sample [m3], – bulk density [kg/m3] of the dried sample and – grain density [kg/m3].
Sample preparation
Sample preparation is one of the most crucial step, which controls the reliability of the bulk measurements results. First, the selected drying method may directly impact the pore volume available for the measurements. Secondly, crushing the samples, which is a common preparation technique used for bulk measurements, may impact the microstructure organization. All the literature data, discussed in the present bibliographic section, have been achieved on crushed samples down to powder or broken into pieces (results obtained on well-preserved blocks were not found in the available publications). The application of outgassing, as well as time of outgassing, may lead to the split of the sample, the pore closure, some microstructural elements disruption, among many other artifacts.
Houben et al. (2016a) have reported gas adsorption measurements on small pieces of samples ( 200 mg), which were either used as a “whole sample” or crushed into a coarse powder. The authors have not indicated in their paper if the displayed curves of adsorption and MIP were obtained from the coarse powder or from their “whole samples”.
According to the API core analysis practice (PR40-1, 1998) drying temperature should vary from 60°C for the shale samples up to 116°C for sandstones. In some case, this temperature range is applied to the shale samples (Chalmers et al., 2012b; Clarkson and Bustin, 1999b; Houben et al., 2016a, among many others). In some publications, the drying temperature is varying according to the method of analysis, like in the work of Kaufhold et al. (2016), for which outgassing at 150°C is proposed for CO2 adsorption measurements (probing microporosity, Figure 1), while other methods are applied on samples dried at 105°C.
Mercury intrusion porosimetry
Mercury intrusion porosimetry (MIP) is widely accepted as a standard measurement of total pore volume and pore size distribution in the macro- and mesopores ranges (Thommes et al., 2015). This method is routinely applied and most of the researchers are using it to obtain the references values of total porosity. Most of the time, no details and supplementary data are given, including the shape of intrusion and extrusion curves or the apparent dry density.
Similarly, capillary pressure curves are a standard way to classify the porosity of reservoir rocks, that correlates to their capacity to produce hydrocarbons. For standard reservoir rocks, assuming comparable porosity, the higher the pressure, at which mercury intrusion occurs, the lower the permeability (Sigal, 2013).
Theoretically MIP relies on Washburn’s equation (as well as other non-wetting intrusion techniques) (Equation 3), which indicates the minimum pressure, required for the fluid to penetrate the pore with given size (Washburn, 1921). The diameter of the intruded idealized cylindrical pore (dp, [m]) is determined through surface tension of mercury-air interface (γ, [Pa•m]), which is temperature dependent, and contact angle between mercury and pore wall (θ), which is temperature and material type dependent, at each point of applied pressure (Pi, [Pa]).
The kinetic diameter of Hg atom is around 0.3 nm, and the modern techniques allow applying high pressure up to 60’000 psi (or 4.14•108 Pa), which corresponds to the pore throat diameter of ~3 nm. This allows to apply the mercury intrusion for probing the pores in the range ~100000 – 3 nm.
While the surface tension of mercury is only temperature depended, solid/liquid contact angle varies as a function of the pores surface material (Figure 9). In the literature various values of θ are applied for the PSD calculation in the diapason of 130-140°.
Meanwhile, this range provides only a slight shift along dp axe. For example, at maximum pressure of 60’000 psi, with θ =130° and (mercury-air) = 485.5 mN•m-1 (at 25°C), dp is equal to 3.017 nm, while with θ =140°, dp is 3.596 nm.
Figure 9. A) Interfacial contact angle of mercury, measured on various substrates; B) interfacial contact angle of various substrates on the surface of quartz (Ethington, 1990; information for pyrite is from Bagdigian and Myersont, 1986).
The main limitation, which is provided by Equation 3, is the geometry of pores. Equation 3 is often associated with cylindrical pores, for which the throat and the body are equal, considering porous materials, which contain the bundles of capillaries with different sizes (Lowell et al., 2004). In case of more complex pore network organization, like in shale samples, where throats are expected to be much smaller than the bodies (see section 1.1), this technique would provide information only about pores’ throats. In addition, the equilibrium at each pressure step should be ensured, to allow the mercury to fill all the voids. Monitoring the amount of mercury intruded into pores as a function of increasing applied pressure, therefore, leads to pore throats sizes distribution. Meanwhile, often in the literature, the distribution, obtained by MIP is referred as pore body sizes.
Although, the mercury extrusion curves are not always provided for the shale samples (mostly only intrusion ones), they may give some useful information about the pore network of probed material. In most of the cases, a hysteresis appears between the intrusion and extrusion curves (Figure 10). Currently, three explanations of hysteresis loop, can be found in the literature: (i) the ink-bottle pore assumption (intrusion describes only the pore throats distribution, but not the pores body sizes); (ii) network effects (an extension of the ink-bottle concept which is supported by complex computer simulations); and (iii) a pore potential theory (whereby mercury is not subjected to pore wall interactions during its initial intrusion but is partly held in pores upon extrusion as a function of wall interactions) (Leon y Leon, 1998).
For the total porosity calculation ( , Equation 2), the bulk density can be estimated, when the sample is immersed in mercury, before the first pressure step ( , [kg/m3]). The grain density may be measured with the last pressure step, assuming that mercury fills all the available pores, and no closed porosity is expected in the sample ( , [kg/m3]) (Micromeritics, 2012).
The disadvantage of the intrusion techniques is the destruction of the sample, excluding the opportunity to repeat the test on the same sample. This way of operating requires careful localization of studied rock volumes to be able to perform the intercomparison and correlation of the results, which have never been described in the available literature data sets. The dimensions of the sample, which can be probed by MIP, varies a lot and is limited only by available penetrometers (millimetric – centimetric sample), but always in the size range of observed laminae (Figure 3).
The raw intrusion curves may contain at least two experimental artifacts. The first one is associated with the compressibility of the mercury, the compressibility of some parts of the capillary set and that of the sample itself under high pressure (due to the existence of substantial amounts of ductile components, such as organic matter). This compressibility/compression effect, occurring in the region of maximum pressure, results in extra mercury injection into the system. This extra injected mercury volume is not part of the actual pore volume and must be corrected (Peng et al., 2017). To eliminate this effect, “blank” measurements are usually performed (measurement of mercury intrusion into the empty capillary, as these components contribute the most to the estimation error, while the compressibility of the sample is very difficult to account for, and often is assumed as negligible). Results of “blank” measurements are subtracted from the curves measured on samples.
The second source of error occurs at the low-pressure region. In the Micromeritics’ manual book (Figure 10) the example of such an artifact is presented. At the low-pressure step, the high intrusion volume of mercury, which contributes up to 20% of the total intruded volume, was correlated with interparticle filling by mercury, so-called “confirmation error”. Indeed, in MIP analysis, before mercury enters the pores of the sample, it first fills the voids between grains and irregularities on the crushed sample surfaces. The voids become smaller under increasing pressure; therefore, higher pressure is needed to fill all the voids before mercury intrusion to the actual pore system. This extra volume of injected mercury, that fills the grain voids and irregularities of the sample surface, is not part of the pore volume in the sample and has to be corrected as well (Peng et al., 2017).
Figure 10. Uncorrected data from analysis of a glass sample with controlled porosity created of a mixture of three pore sizes. The apparent intrusion at size above 10 µm is explained to be due to interparticle filling (Micromeritics, 2012).
Considering unconventional hydrocarbons reservoirs, Sigal (2013) published an extensive set of mercury capillary pressure measurements from 92 plugs, taken from two Barnett-shale gas wells. The author has described several types of intrusion curves, which can be divided in four types: (i) Type 1 incremental intrusion curve with archived maximum; (ii) Type 2, incremental intrusion curve, which is « flat » at 60,000 psi; (iii) Type 3, curve with no apparent maximum; and (iv) Type 4, with no mercury intrusion. The incremental curves were normalized to the pore volume calculated from the He-porosimetry (Figure 11). Sigal (2009) reported a study, dedicated to the blank correction methodology on the samples, such as tight gas sands, in order to improve the post treatment and the interpretation of MIP intrusion/extrusion curves. Clarkson et al. (2013) published mercury intrusion curves for different shale deposits (Figure 12). Most of the estimated pore-throats have a diameter in the order of 30-100 Å, even if the authors erroneously assume to probe pore size distribution. Therefore pore sizes inferred from MIP are very often reported to be underestimated due to the ink-bottle effect (Münch and Holzer, 2008). Pores’ “bottle” – shape is common for plate shaped clay particles and describes the pores with the throat radius smaller than the body radius.
Figure 11. Capillary pressure curve for Barnet shale sample: A) normalized cumulative intrusion/extrusion curves; B) normalized incremental intrsuion curve (Sigal, 2013).
Figure 12. Incremental pore throats sizes distributions obtained for various shales (Clarkson et al., 2013).
In addition, most of the reported results obtained on shale samples show that the MIP measurements results often take place at the detection limits of the method, due to very small pore throats of the samples. This is, for example, illustrated in Figure 11, which demonstrates non-equilibrated (with continuous increase up to the maximum pressure, without any plateau) intrusion curve at the end of the test (“type 3” curve following the classification, proposed by Sigal (2013)). This indicates, that the method chosen in that case does not allow to reach the smallest pores within the sample, leading to an underestimation of grain density and total porosity.
Gas adsorption methods
Gas adsorption methods are extensively used for investigating porous materials. Since the first study of adsorption of nitrogen were performed by J. Dewar in 1904 (reviewed by Sing, 2001), these methods were developed for all kind of porous materials, and experiments were performed with different gases in a wide range of temperatures and pressures. For shale samples, these methods are often used to determine reference values for the pore size distribution and surface area calculations, when several methods are applied.
Low-pressure adsorption measurements are more convenient for pores system characterization (pore volume, pore size distribution, surface area, pores morphology and connectivity) than high-pressure methods, since the application of high pressure may lead to the pores collapse. The temperature, under which the isotherms are obtained, also depends on the gas applied for the measurements. Normally, it corresponds to the optimal physical state and kinetic diameter of the adsorptive (adsorbate, if liquid). Some of the gases, which have found an application for adsorption/desorption experiments on shales are presented in the Table 2.
Two gases are mostly used for the characterization of porous materials: nitrogen (N2) and carbon dioxide (CO2). As for other penetration techniques, resolution of gas adsorption result is limited by the data treatment approach selected by the operator. The shape of adsorption/desorption isotherms can provide the information about adsorption energy, monolayer capacity, specific surface area and assessment of microporosity/mesoporosity of the sample. There are several methods, which can be used to analyze the adsorption/desorption data to extract the pore size distribution of the sample. The method of Brunauer, Emmet, and Teller (BET) is employed to determine surface area based on a model of adsorption, which incorporates multilayer coverage. The BET–method is the mathematical transformation, applied for calculating the monolayer capacity and energy constant (C), which depends on the adsorption energy of the first layer of gas molecules (Lowell et al., 2004).
Classically, the PSD for mesopores and macropores is achieved by N2 adsorption/desorption experiments. The method of Barrett, Joyner, and Halenda (BJH) is a procedure for calculating pore size distributions from experimental isotherms using the Kelvin model of pore filling. This formalism integrates the pore diameter on the adsorption isotherm for each relative pressure. Application of the BJH treatment, which uses the Kelvin equation (Barrett et al., 1951), allows to distinguish both pores bodies and throats sizes, assuming cylindrical pores (Equation 4). This equation implies several assumptions on the pore network: (i) pores are perfect cylinders, open at both ends; (ii) gas perfectly wets the pores’ walls (cos θ = 1); (iii) nitrogen is considered to be in a liquid state.
where rk – Kelvin radius [m], γ – liquid nitrogen surface tension [Pa•m], θ – liquid nitrogen/sample contact angle, VN – molar volume of adsorbed nitrogen [m3/mol], f – form factor, Rgas – the gas constant (8.3144598(48) kg•m2•s−2•K−1•mol−1), T – absolute temperature [K], P/P0 – relative adsorption/desorption pressure. The form factor f = 1 should be selected for cylindrical meniscus, expected for adsorption (Figure 13), and f = 2 – for the hemispherical meniscus, when applied for desorption. The term rk indicates the radius, into which condensation occurs at the required relative pressure. The increasing thickness of the multilayer adsorbed on solid surface when the relative pressure increases is added to obtain the true pore radius rp, [m] (Equation 5; Figure 13).
Carbon dioxide, due to smaller kinetic diameter (Table 2), is widely used for the micropores characterization. For CO2 isotherms, Dubinin and Radushkevich (DR) approach is often applied (Clarkson et al., 2013; Chalmers et al., 2012a), among many other models developed for the gas adsorption within micropores (Lowell et al., 2004). The basis of the DR theory puts forward an equation based on Polanyi’s potential theory, which allows the micropore volume to be calculated from the adsorption isotherm (Equation 7).
Further extension of this theory on microporosity estimation from adsorption isotherms performed on coals can be found in the work of Marsh (1987). Indeed, historically, at the dawn of unconventional hydrocarbons development, shales were very often compared with coals. Due to the similarity in pore size range, the methods developed for coals characterization, are often directly applied on shale samples. Coals are also heterogeneous material composed of both organic and inorganic substances. The organic contents, called “coal macerals”, are the useful portion of the coal (up to 100%). The inorganic contents, called mineral matter, are pollution components that dilute coals and are undesirable. Meanwhile, porosity measurements on coals often show, that most of the pores are less than 10 nm in diameter (Gan et al., 1972), exhibiting mono- or bimodal distribution, which corresponds to the pore size expected in shale samples (Figure 14 and Figure 8). The N2 adsorption/desorption isotherms obtained on coal also present an irreversible hysteresis indicating some trapping of N2. The PSD provided on Figure 14.B was achieved using the BJH method (transformations of desorption curve, which corresponds to the pore throat size distribution). In that case the intense peak at ~4 nm on Figure 14.B is an artifact, induced by the cavitation occurring at P/P0 ~0.45 on the desorption isotherm. The pores of coals, filled by gas are, however, located mainly within OM, with a relatively homogeneous spatial distribution, whereas the pores spatial distribution of shales is more complex.
Figure 14. A) Nitrogen adsorption and desorption isotherms for coal sample: B) pore size distribution by BJH transformations on desorption curves (Clarkson and Bustin, 1999a).
To evaluate a wide range of pores sizes adsorption measurements using different gases are often combined. For example, Clarkson et al. (2013) and Chalmers et al. (2012a) used a combination of N2 (at -196°C) and CO2 adsorption (at 0°C) techniques for shale samples. Due to smaller kinetic diameter of CO2 (0.33 nm, compared with 0.37 nm for N2 (Table 2)), this combination allowed investigation of pores sizes in the range of 7-1000 Å, which includes some part of microporosity (Figure 15). The reliability of such a combination is questionable, since different mathematical calculations are applied for different measurements, the assumptions and limitations of each model should be correlated, i.e. consistent in between each other. The same way of combining nitrogen and carbon dioxide adsorption measurements can be found in Kaufhold et al. (2016) or Mastalerz et al. (2013).
Figure 15. Nitrogen (A) and carbon dioxide (B) isotherms collected for the shale samples (Clarkson et al., 2013).
The pore size distributions achieved by BJH and DP approaches are presented in Figure 16, where most of the pores correspond to micropores smaller than 2 nm.
Figure 16. Pore size distribution curves for shale samples, defined by differential pore volume using low-pressure gas (N2 and CO2) adsorption analysis (Chalmers et al., 2012a).
From the reviewed list of publications, most of adsorption/desorption isotherms (when they were shown) do not present the desorption curves. Meanwhile, the hysteresis loop provides important information about the geometry of the pores, which can be defined through its shape (Lowell et al., 2004). Figure 17 illustrates the isotherms for powdered shale samples, exhibiting a very small hysteresis loop. Such a close shape of adsorption and desorption isotherms indicates the homogenized pore network of the powdered sample (throats size distribution is expected to be close to pore bodies’ sizes distribution). This feature does not reflect the real microstructure organization of the rock. Meanwhile, the measurements by gas adsorption on centimetric blocks were not found in the literature.
Figure 17. Nitrogen gas adsorption and desorption isotherms for the samples from lower Silurian black shales (Tian et al., 2013).
Moreover, with gas adsorption experiments it is possible to quantify the relative pore volume content hosted in organic matter. For example, Kuila et al. (2014) performed gas adsorption before and after solid organic matter removal for Baltic shale samples (Figure 18).
Figure 18. Representative isotherms (A) on natural (in blue) and NaOCl treated (in red) samples and (B) corresponding pore size distribution curves (I+S = illite + smectite clay group in mass%; TOC = Total Organic Carbon in mass%; Eff. = OM removal efficiency in %; HI = Hydrogen Index in mg HC/g TOC) (Kuila et al., 2014).
These data have shown that the distribution of OM, with respect to the clay microstructure, is heterogeneous (Figure 18, Table 3). Solid OM exists as separate particles or laminations, where clay porosity may be open to adsorption, or OM can partially or completely fill the space between clay aggregates within dimensions <5 nm. Removal of OM from thermally mature organic rich shales resulted in a significant reduction of the pore volume network below a diameter of 5 nm. This reduction of pore volume is interpreted as an indication of pores, hosted within organic matter (which would account for 24–77% of the total pore volume within the < 5 nm pore-size interval) (Table 3; Kuila et al., 2014).
Besides the porosity characterization, gas adsorption experiments can be done to understand natural gas adsorption selectivity. Such experiments were performed by Gasparik et al. (2014) (where the high-pressure adsorption of separated components of natural gas was carrying out) and by Cheng and Huang (2004) who used the hydrocarbon gas mixture as adsorbate, controlling the changes in gas composition after desorption.
For shale samples investigations, the most suitable fluids will be those with the smallest kinetic diameter (Table 2). However, due to complex organization of the shales and presence of kerogen, the reactivity of the pore space is likely heterogeneous even within a single sample and the characterization of this heterogeneity at the sample scale remains a challenging area of research.
Some important parameters, which may influence the adsorption isotherms are temperature, moisture, total organic carbon content and mineral composition, which affect the characteristics of isotherms. Hartman et al. (2008) indicated, that changing the relative humidity within the apparatus could alter the shape of the shale gas adsorption isotherm (methane was used here), due to large surface area exposed by dehydrated clays (Figure 19). Meanwhile, temperature plays much smaller role than moisture content if clays are only considered. The reliability of the data depends on equilibrium occurring at every pressure step in the adsorption isotherm experiments (in gas shale due to low diffusion rate, the penetration of gas to the system could take a long time) (Hartman et al., 2008). The high-pressure adsorption measurement can be used to determine the adsorbed gas capacity at simulated reservoir pressure and temperature conditions (Ross and Marc Bustin, 2009). Such a kind of experiments is needed to study the rock behavior in modelled “in-situ” environments.
Figure 19. Methane adsorption isotherms on powder shale samples of various maturity under different temperature and humidity conditions (Hartman et al., 2008).
Nuclear magnetic resonance spectroscopy
Nuclear magnetic resonance (NMR) spectroscopy is a useful tool for conventional reservoirs investigations. Based on hydrogen contents measurements, NMR spectroscopy can be applied during boreholes evaluation to obtain information about the matrix porosity, fluids content and lithology of the well. A lot of modelling methods for interpretation of NMR measurements were investigated (Schlumberger, 1991a). NMR methodology is based on the existence of a strong magnetic moment of the proton in the hydrogen nucleus. At thermal equilibrium in a static magnetic field, the volume of interstitial fluids (hydrocarbons/water) in a shale sample exhibits a small net magnetic moment that results from the sum of all the magnetic moment associated with each of the protons in the volume.
As a matter of fact, in a classical NMR relaxometry experiment, the moments of protons, initially at thermal equilibrium, are perturbed by an energizing pulse tuned to the Larmor frequency, which is an intrinsic physical property of a given nucleus. If this pulse is applied and then removed, these moments process from their thermal equilibrium and then relax back to this same thermal equilibrium. As these moments relax, they emit a measurable magnetic signal which allows the calculation of two parameters: relaxation times T1 and T2, which are associated with relaxation longitudinal and transversal to the static field, respectively. Considering transverse relaxation, which is most commonly used to estimate pore size distribution, parameter T2 is usually described by two relaxation processes occurring in parallel (Equation 10).
Table of contents :
Chapter 1. Bibilographical review
1.1. General characteristics of shales
1.2. Methods of shale pore space characterization
1.2.1. Sample preparation
1.2.2. Mercury intrusion porosimetry
1.2.3. Gas adsorption methods
1.2.4. Nuclear magnetic resonance spectroscopy
1.2.5. Small angle scattering techniques (SANS/USANS)
1.2.6. Thermal analysis
1.3. Imaging techniques
1.3.1. Representativity
1.3.2. Sample preparation
1.3.3. Autoradiography
1.3.4. X-Ray tomography
1.3.5. Scanning electron microscopy
1.3.6. Transmission electron microscopy/scanning transmission electron microscopy (TEM/STEM)
1.3.7. Imaging acquisition and data treatment
1.4. Combination of methods for pore space characterization – role of the organic matter maturity
Chapter 2. Materials and methods
2.1. Materials
2.1.1. Geological settings of the basin
2.1.2. Core sampling
2.2. Methods
2.2.1. X-Ray μtomography 3D localized subsampling
2.2.2. Mineral composition
2.2.3. Thermal analysis
2.2.4. Total porosity calculation
2.2.5. Sample impregnation
2.2.6. Sample surface preparation
2.2.7. Autoradiography
2.2.8. Mercury intrusion porosimetry
2.2.9. Nitrogen adsorption
2.2.10. Nuclear magnetic resonance spectroscopy
2.2.11. Scanning electron microscopy
2.2.12. Image denoizing
Chapter 3. Combination of bulk and imaging techniques
3.1. Correlative coupling of imaging and bulk techniques for quantitative pore network analysis of unconventional shale reservoirs: Vaca Muerta formation, Neuquén basin, Argentina
3.2. Additional measurements on VM samples
3.2.1. Mineral composition
3.2.2. Thermal analysis
3.2.3. Total porosity estimation
3.2.4. Nuclear magnetic resonance spectroscopy
3.2.5. Mercury intrusion porosimetry
3.2.6. Nitrogen adsorption
3.2.7. Autoradiography porosity maps
3.3. Correlation of autoradiography result with bulk measurements
Chapter 4 Multiscale correlation of minerals and porosity distribution
4.1. Integrated multiscale approach
4.2. Correlation of porosity and mineralogy at the core scale (cm-dm)
4.3. Large field mineral mapping from SEM-BSE mosaics
4.3.1. Mosaic reconstruction from individual tiles
4.3.2. Mineral mapping
4.4. 2D correlation of porosity and mineralogy at the grain/small lamina scales (cm-nm)
General conclusions and perspectives
