TY - JOUR
AU - Shuai, Da
AB - Summary The presence of clay minerals can alter the elastic behaviour of reservoir rocks significantly as the type of clay minerals, their volume and distribution, and their orientation control the shale's intrinsic anisotropic behaviours. Clay minerals are the most abundant materials in shale, and it has been proven extremely difficult to measure the elastic properties of natural shale by means of a single variable (in this case, the type of clay minerals), due to the influences of multiple factors, including water, TOC content and complex mineral compositions. We used quartz, clay (kaolinite, illite and smectite), carbonate and kerogen extract as the primary materials to construct synthetic shale with different clay minerals. Ultrasonic experiments were conducted to investigate the anisotropy of velocity and mechanical properties in dry synthetic and natural shale as a function of confining pressure. Velocities in synthetic shale are sensitive to the type of clay minerals, possibly due to the different structures of the clay minerals. The velocities increase with confining pressure and show higher rate of velocity increase at low pressures, and P-wave velocity is usually more sensitive than S-wave velocity to confining pressure according to our results. Similarly, the dynamic Young's modulus and Poisson's ratio increase with applied pressure, and the results also reveal that E11 is always larger than E33 and ν31 is smaller than ν12. Velocity and mechanical anisotropy decrease with increasing stress, and are sensitive to stress and the type of clay minerals. However, the changes of mechanical anisotropy with applied stress are larger compared with the velocity anisotropy, indicating that mechanical properties are more sensitive to the change of rock properties. Geomechanics, Acoustic properties, Wave propagation 1 INTRODUCTION Shales constitute over 75 per cent of the rock in sedimentary basins (Jones & Wang 1981) and can be cap rocks for hydrocarbon bearing reservoirs (Sayers 1994; Aplin & Larter 2005). The increasing significance of shale gas plays has demonstrated a need for deeper understanding of shale behaviour. Shales display significant seismic anisotropy, and failing to account for this can cause errors in petrophysical analysis, seismic data processing and interpretation, and hydraulic fracturing. Natural shale exhibits two common types of anisotropy in stiffness: stress induced and inherent. Stress-induced anisotropy predominates in granular soils in which particle reorientation and rearrangement occurs under stress rotation (Oda et al. 1985; Gurevich et al.2011). Anisotropic in-situ stresses could also produce stress-induced anisotropy in a deposited shale. Inherent anisotropy is a physical characteristic intrinsic to the material and independent of external loads (Wong et al. 2008) and is attributed to the depositional environment and mineral fabric of the soil or rock mass (Casagrande & Carrillo 1944). The intrinsic anisotropic behaviours of shale are mainly due to four factors: the clay minerals alignment parallel to bedding (Vernik & Liu 1997; Hornby 1998; Sondergeld et al.2000; Wenk et al.2007; Sarout & Guéguen 2008; Sayers 2013); the content and maturation level of kerogen, and the bedding-parallel lamination of organic material (Vernik 1993, 1994; Vernik & Landis 1996; Vanorio et al. 2008; Sondergeld & Rai 2011; Ahmadov et al. 2012); as well as platelet shaped pores aligned roughly parallel to the bedding plane (Vernik & Nur 1992; Vasin et al. 2013). Previous research on shale anisotropy was focused mainly on velocity anisotropies (Jones & Wang 1981; Yin 1992; Vernik & Liu 1997; Hornby et al. 1994; Wang 2002) and attenuation anisotropy (Yin 1992; Best et al. 2007; Piane et al. 2014; Zhubayev et al. 2016). However, measurements of elastic modulus for complete determination of the five elastic constants and their anisotropy, despite being critical to hydraulic fracture propagation in shale, have been very limited (Wong et al. 2008; Sayers 2010; Thomsen 2013). The economic production of shale gas depends on hydraulic fracturing. The mechanical properties of shale (including but not limited to Young's modulus E, and Poisson's ratio ν) are among the most important factors affecting hydraulic fracture propagation. Characterizing these organic- rich shales can be challenging, as these rocks vary quite significantly (Passey et al. 2010). Due to anisotropy, Young's modulus and Poisson's ratio are related with angle to the symmetry axis (Sayers 2013; Sone & Zoback 2013; Yan et al. 2016). Understanding the anisotropy of these mechanical parameters is important for determining the variation of minimum horizontal stress with depth and for designing optimal patterns of hydraulic fractures for economic production from low-permeability gas shale reservoirs. However, the complexity of mineral components, water-phobic character, and high brittleness of natural shale make it more complicated for samples preparation, as well as for measuring the anisotropy of shale. Clay minerals are hydrous aluminium silicates and are classified as phyllosilicates, or layer silicates. All layer silicates are constructed from two modular units: a sheet of corner-linked tetrahedra and a sheet of edge-linked octahedra. These sheets can have different unbalanced layer charges depending on the clay type (Pal-Bathija et al. 2008; Sayers 2014). Several attempts have been made to obtain the elastic modulus of clay, by both theoretical and experimental investigations; Katahara (1996) derived effective elastic properties of clays by theoretical computations, Vanorio et al. (2003) measured acoustic velocities of clay powder in dry compacted form, and Ortega et al. (2007) suggested using nano- and microindentation techniques to measure anisotropic moduli of clay minerals. Clay minerals are one of the major components of shale, and they tend to align parallel to bedding planes during compaction (Katahara 1996; Hornby 1998; Voltolini et al.2009). The presence of clay minerals can alter the elastic properties and anisotropy of rocks significantly, as a function of mineral type, volume and distribution (Bayuk et al. 2007; Mondol 2008); to further complicate the situation there are more than 400 different types of clays. Two shales with the same clay amount might have different elastic properties, due to differences in the proportions of different clay minerals. Consequently, knowing the elastic properties of shales with different type of clay mineral is imperative to fully understanding the seismic and acoustic properties of a reservoir and its sealing rocks. In this paper, we present new data on dynamic mechanical properties and anisotropy (including Young's modulus E and Poisson's ratio ν), obtained from synthetic shales with different type of clay minerals (kaolinite, illite and smectite) and natural shale. In order to reduce the number of multiple variables, such as water content and clay content, we use quartz, clay (kaolinite, illite and smectite), carbonate, and kerogen extract as the primary materials for sample preparation. Synthetic shales with different clay minerals were prepared using the cold-pressing method, by applying uniaxial effective stress (200 MPa) with no lateral strain at ambient temperature for over 100 hr. Confining pressure experiments were performed at room temperature, to obtain both P- and S-wave velocities of synthetic shale and natural shale, and we present the measured velocities at ultrasonic frequency of samples as a function of confining pressure and with respect to the symmetry axis. The elastic stiffness tensor C is calculated from the Christoffel equations (Cheadle et al. 1991), and finally the anisotropy of velocity and mechanical properties are quantified, based on Thomsen (1986). 2 SAMPLE PREPARATION AND MEASUREMENTS 2.1 Sample preparation and description Natural shale is a kind of sedimentary rock with layers composed of fine particles. The most common—like clasolite, clay minerals, organic minerals—are found in various amounts in shale. The mineral components of natural shale are very complex and vary greatly with different origins. Natural shale samples (particularly well-preserved, drilled core samples), are extremely difficult to obtain for laboratory research, due to their high brittleness. Multiple tests must be carried out on one sample, and some samples are discarded after destructive testing. We therefore produced synthetic shale samples to simulate natural shale by using the cold pressing method (Voltolini et al. 2009; Gong et al. 2016; Luan et al. 2016). Compared with natural shales, our synthetic shale samples are relatively simple to duplicate, have controllable of porosity and permeability; and can be constructed with single variation of any mixture ratio, to avoid the uncertainties due to multiparameter variability in natural shale. Shale composition was categorized with respect to its quartz, clay, carbonate, and organic content based on statistical analysis of several shale samples from the US, Canada, and China. These four types of material constitute more than 95 per cent of shale, and are responsible for its major properties. Therefore, the samples analysed in this study were prepared by combining quartz, calcite and different types of clay minerals (kaolinite, illite and smectite), and all of these particle sizes were less than 0.004 mm. As shown in Fig. 1, scanning electron microscopy (SEM) was used to estimate the particle distribution of clay powder; the clay particles have plate-like structures with large surface areas. Real kerogen, extracted from natural sedimentary rocks, was used to represent organic matter in the synthetic shale and to ensure that its properties were consistent with the natural shale. The powder was mixed together in a ball mill to ensure a homogeneous composition, and then mixed with liquid adhesives (less than 5 per cent by weight) to mimic burial conditions, forming a paste. We can find liquid adhesives (salt brine or epoxy resin) are used frequently in the construction of synthetic sample (Voltolini et al. 2009; Ding et al. 2014; Luan et al. 2016). Because the diagenesis of rocks are long and complex processes that generally include chemical changes and various physical, such as cementation, compaction, metasomatism, crystallization and biochemical reactions in the sediments. In this study, an A/B double component unsaturated epoxy resin (YY-505) was chosen, to simulate cementation of diagenesis in rocks. Its operable time is 2–3 hr and full curing time is approximately 24 hr, which can ensure full curing in the process of pressure consolidation. Its impact strength is 32–34 kJ m−2, peel strength is 30–32 kN m-1, and mould shrinkage is less than 0.5 per cent, which meant the synthetic samples experienced little deformation after curing. The material parameters of the synthetic shale samples are given in Table 1 . Figure 1. View largeDownload slide The microstructure of clay powder. (a) SEM image of kaolinite powder. (b) SEM image of illite powder. (c) SEM image of smectite powder. Figure 1. View largeDownload slide The microstructure of clay powder. (a) SEM image of kaolinite powder. (b) SEM image of illite powder. (c) SEM image of smectite powder. Table 1. Material parameters of synthetic shale. Sample  Kaolinite (wt%)  Illite (wt%)  Smectite (wt%)  Quartz (wt%)  Calcite (wt%)  Kerogen (wt%)  Adhesive (wt%)  Pressure (MPa)  K  30  /  /  41  16  9  4  200  I  /  30  /  41  16  9  4  200  S  /  /  30  41  16  9  25  200  Sample  Kaolinite (wt%)  Illite (wt%)  Smectite (wt%)  Quartz (wt%)  Calcite (wt%)  Kerogen (wt%)  Adhesive (wt%)  Pressure (MPa)  K  30  /  /  41  16  9  4  200  I  /  30  /  41  16  9  4  200  S  /  /  30  41  16  9  25  200  View Large A defined amount of the paste mixture was placed in a specially designed mould, and the pressure was loaded on after a certain amount of mixture had been laid to mould at each time. The sample could be removed from the mould after undergoing a uniaxial effective stress (200 MPa) with no lateral strain at ambient temperature for over 100 hr. Fig. 2(a) shows the process of pressure consolidation and synthetic shale sample after demoulding is shown in Fig. 2(b). Using this method, we produced three sets of synthetic shale samples with different types of clay minerals: kaolinite (K), illite (I), smectite (S). The porosity of samples was generally less than 10 per cent, and the density varied between 2.54 and 2.66 g cm−3. On the microscale, the particles of synthetic shale are arranged directionally at perpendicular bedding planes, and the SEM analyses show that the synthetic and natural shale share high similarity in the microstructure (Fig. 3). Acoustic testing of the samples also suggests the validity of transverse isotropic (verified transverse isotropic, VTI, assuming horizontal layering) in consideration of our samples. Figure 2. View largeDownload slide (a) The process of pressure consolidation. (b) A primary synthetic shale sample after demoulding. Figure 2. View largeDownload slide (a) The process of pressure consolidation. (b) A primary synthetic shale sample after demoulding. Figure 3. View largeDownload slide Scanning electron micrograph of parallel symmetry axis. (a) SEM image of natural shale. (b) SEM image of synthetic shale K. (c) SEM image of natural shale Y. (d) SEM image of synthetic shale S. Figure 3. View largeDownload slide Scanning electron micrograph of parallel symmetry axis. (a) SEM image of natural shale. (b) SEM image of synthetic shale K. (c) SEM image of natural shale Y. (d) SEM image of synthetic shale S. Homogeneity is one of the most significant factors in measuring the effectiveness of a synthetic shale model. To test the homogeneity, we used transducers to test five points in the X-direction (marked as A, B, C, D and E) and also five points in the Z-direction (marked as a, b, c, d and e), as shown in Fig. 4. The X-direction is perpendicular to the symmetry axis, and the Z-direction is parallel to the symmetry axis. Taking the P- wave of cuboid sample S as an example, the sample length in X-direction is 7.11 cm and Z-direction is 5.19 cm. And the start time T0 of system is 1 us. The differences in waveform and arrival time were compared, as shown in Fig. 5. The arrival time indicates the wave velocity, and the waveform indicates the internal microstructure of the sample. Each point showed high conformance in terms of the arrival times and peak and trough amplitudes, confirming the homogeneity of the synthetic samples. Figure 4. View largeDownload slide Schematic diagram of the test method for homogeneity. Figure 4. View largeDownload slide Schematic diagram of the test method for homogeneity. Figure 5. View largeDownload slide Waveform of P-wave of cuboid sample S in the directions (a) parallel and (b) perpendicular to the symmetry axis; five points were tested in each orientation. The sample length in the Z-direction (parallel to the symmetry axis) is 5.19 cm and the X-direction (perpendicular to the symmetry axis) is 7.11 cm. Figure 5. View largeDownload slide Waveform of P-wave of cuboid sample S in the directions (a) parallel and (b) perpendicular to the symmetry axis; five points were tested in each orientation. The sample length in the Z-direction (parallel to the symmetry axis) is 5.19 cm and the X-direction (perpendicular to the symmetry axis) is 7.11 cm. To verify the reliability of synthetic shale, we also prepared natural shale samples for the same experiment. Natural shale samples in this study were collected from the Sichuan Basin, and are named ‘N’. The volumetric compositions of the natural samples were determined by combining results from powder X-ray diffraction analysis. The quartz content was approximately 40 per cent and clay content was approximately 35 per cent, calcite and dolomite were approximately 7.7 per cent and 8.8 per cent, respectively. In addition, there were a small amount of potash feldspar, pyrite and other minerals. The organic matter content was approximately 3.7 per cent. The porosity of our natural sample was approximately 5.3 per cent and the bulk density was approximately 2.69 g cm−3. Fig. 3(a) shows the microstructure of natural shale. 2.2 Experimental setup and measurements To study the anisotropic behaviours of synthetic shale, we prepared four sets of cylindrical samples (diameter 2.5 cm, length 5 cm). The samples were cut at different angles with respect to the symmetry axis. From each sample, we produced cores perpendicular (90°), parallel (0°) and at 45° to the symmetry axis, and the axis of the symmetry is perpendicular to the bedding plane. Samples were oriented with respect to the S-wave polarization direction in a way similar to that described by Lo et al. (1986) to ensure simultaneous measurements of the traveltime of P-, SH- and SV-modes of propagation (Fig. 6). In Fig. 6, the thin lines indicate the bedding plane or lamination; Arrows indicate the directions of wave propagation and polarization. For transverse isotropic (TI) media, five independent elastic constants Cij are needed to characterize anisotropy (Thomsen 1986). Three sets of synthetic shale samples (named K, I and S) and one set of natural shale samples (named N) were used to study ultrasonic anisotropy, and therefore, twelve cores were prepared for measurement. Figure 6. View largeDownload slide Scheme of sample preparation and velocity measurements in shales. The thin lines indicate the bedding plane or lamination; arrows indicate the directions of wave propagation and polarization. Figure 6. View largeDownload slide Scheme of sample preparation and velocity measurements in shales. The thin lines indicate the bedding plane or lamination; arrows indicate the directions of wave propagation and polarization. Shale samples used for the ultrasonic experiments under confining pressure, were inserted into a rubber jacket and the jacketed samples were then placed between ultrasonic P- or S-wave transducers, as shown in Fig. 7(a); a schematic illustration of experimental setup is shown in Fig. 7(b). The transducer diameter was 2.5 cm, and the dominant frequency was 0.5 MHz. The black marks on the two transducers could be aligned which should align the polarized shear waves. As shown in Fig. 7(a), the only spot that the wire overlaps was at the location where the wire was twisted, which could ensure equal pressure all the way around the circumference, and could seal well. The acoustic assembly was placed into a confining apparatus. All experiments were performed at room temperature. Figure 7. View largeDownload slide (a) 1-inch velocity transducer with sample. Arrow points the black mark, which on both transducers shows the polarization of shear waves. (b) Experimental setup used to measure P- wave and S- wave velocities at different stress conditions. Figure 7. View largeDownload slide (a) 1-inch velocity transducer with sample. Arrow points the black mark, which on both transducers shows the polarization of shear waves. (b) Experimental setup used to measure P- wave and S- wave velocities at different stress conditions. Fig. 8 shows an example of recorded signals for the synthetic sample K parallel to the symmetry axis (0°) at low (2 MPa) and intermediate (12 MPa) confining pressures. The dry core waveforms display a strong effect of confining pressure, visible in both the arrival time and amplitude of the signal for a propagation direction parallel to the symmetry axis. As shown in Fig. 8, both P-wave and S-wave (fast and slow) waveforms could be obtained at the same time, and the difference between fast and slow S-wave could be ignored because there was no polarization in the Z (0°) direction. For S-wave splitting in the Z (0°) direction, we checked the difference between fast and slow S-wave in 360° direction on the cuboid sample, the results show that the difference can be ignored. Confining pressures of up to 40 MPa were applied, and in this way, both P- and S-wave velocities of samples were obtained by the pulse transmission technique. Figure 8. View largeDownload slide Typical waveforms recorded signals for the synthetic sample K parallel to the symmetry axis (0°) at low (2 MPa) and intermediate (12 MPa) confining pressure. Figure 8. View largeDownload slide Typical waveforms recorded signals for the synthetic sample K parallel to the symmetry axis (0°) at low (2 MPa) and intermediate (12 MPa) confining pressure. 3 THEORY Shale samples can be well considered as TI media with an axis of rotational symmetry aligned perpendicular to the bedding plane. The TI media have five independent elastic stiffnesses Cij. As shown in Fig. 4, taking the axis Z as the axis with the rotational symmetry, the stiffness matrix can be written as:   \begin{equation}C = \left[ {\begin{array}{@{}*{6}{c}@{}} {{C_{11}}}&{{C_{12}}}&{{C_{13}}}&{}&{}&{}\\ {{C_{12}}}&{{C_{11}}}&{{C_{13}}}&{}&{}&{}\\ {{C_{13}}}&{{C_{13}}}&{{C_{33}}}&{}&{}&{}\\ {}&{}&{}&{{C_{44}}}&{}&{}\\ {}&{}&{}&{}&{{C_{44}}}&{}\\ {}&{}&{}&{}&{}&{{C_{66}}} \end{array}} \right].\end{equation} (1) For VTI media, there are only five independent elastic constants, since C12 = C11 − 2C66. Elastic constants of shale can be calculated based on the Christoffel equations by appropriately measuring five elastic wave velocities (Cheadle et al. 1991; Mah & Schmitt 2001a), as shown below:   \begin{equation}{C_{11}} = \rho V_{{\rm{P}}(90^\circ )}^2,\end{equation} (2)  \begin{equation}{C_{33}} = \rho V_{{\rm{P}}(0^\circ )}^2,\end{equation} (3)  \begin{equation}{C_{44}} = \rho V_{{\rm{SV}}(0^\circ )}^2,\end{equation} (4)  \begin{equation}{C_{66}} = \rho V_{{\rm{SH}}(90^\circ )}^2,\end{equation} (5)  \begin{eqnarray} {C_{13}} {=} - {C_{44}} {+} \sqrt {\bigg({C_{11}} {+} {C_{44}} - 2\rho V_{{\rm{P}}(45^\circ )}^2\bigg)\bigg({C_{33}} {+} {C_{44}} - 2\rho V_{{\rm{P}}(45^\circ )}^2\bigg)},\!\!\!\!\! \nonumber\\ \end{eqnarray} (6)where ρ is bulk density; VP(90°) and VSH(90°) represent the P- wave and S-wave velocities of shale propagating perpendicular to the symmetry axis; VP(0°) and VSV(0°) represent the P- wave and S-wave velocities of synthetic shale propagating parallel to the symmetry axis; and VP(45°) represents the P-wave velocity of samples at 45°to the symmetry axis. Note that eqs (2)–(6) for conversion of the observed wave velocities to the elastic stiffness constants assume ‘phase’ velocities, that is, velocities that would be observed for a plane wave. The phase velocity differs from the group velocity through the material (Kebaili & Schmitt 1997). It is important to make this distinction because these two velocities would not necessarily be the same in a given direction in an anisotropic material (Wong et al. 2008). However, the traveltimes measured in laboratory experiments should represent phase velocities if the ratio of core sample height to transducer width is less than 3 (Dellinger & Vernick 1994; Wong et al. 2008). Since the ratios used in our tests are approximately 2, we are confident that phase velocities were measured in our experiment. Thomsen (1986) proposed the anisotropy parameters to describe velocity anisotropy, as shown by the following equations:   \begin{equation}\varepsilon = \frac{{{C_{11}} - {C_{33}}}}{{2{C_{33}}}},\end{equation} (7)  \begin{equation}\gamma = \frac{{{C_{66}} - {C_{44}}}}{{2{C_{44}}}},\end{equation} (8)  \begin{equation}\delta = \frac{{{{({C_{13}} + {C_{44}})}^2} - {{({C_{33}} - {C_{44}})}^2}}}{{2{C_{33}}({C_{33}} - {C_{44}})}}.\end{equation} (9) Finally, substituting the values Cij in eqs (7)–(9), we can obtain the anisotropic parameters. Young's Modulus and Poisson's Ratio are basic parameters for describing the mechanical properties of material. For VTI media, as in horizontally layered shales, the concepts of Young's modulus and Poisson's ratio can be straightforwardly extended to VTI media using Hooke's law (King 1964; Christensen & Zywicz 1990; Gautam 2004; Gautam & Wong 2006). Their relationships with the elastic constants are described by the following equations:   \begin{equation}{E_{33}} = \frac{{{C_{33}}({C_{11}} - {C_{66}}) - C_{13}^2}}{{{C_{11}} - {C_{66}}}},\end{equation} (10)  \begin{equation} {E_{11}} = \frac{{4{C_{66}}\big({C_{33}}({C_{11}} - {C_{66}}) - C_{13}^2\big)}}{{{C_{11}}{C_{33}} - C_{13}^2}},\end{equation} (11)  \begin{equation}{\nu _{31}} = \frac{{{C_{13}}}}{{2({C_{11}} - {C_{66}})}},\end{equation} (12)  \begin{equation}{\nu _{12}} = \frac{{{C_{33}}({C_{11}} - 2{C_{66}}) - C_{13}^2}}{{{C_{11}}{C_{33}} - C_{13}^2}},\end{equation} (13)  \begin{equation}{\nu _{13}} = \frac{{2{C_{13}}{C_{66}}}}{{{C_{11}}{C_{33}} - C_{13}^2}}.\end{equation} (14) 4 EXPERIMENTAL RESULTS Ultrasonic velocity was measured from the first P- wave or S-wave arrival time and the height of the sample. Relative errors in the velocity estimates were calculated and were found to be no larger than 1 per cent. This method provides relatively simple yet stable and accurate measurements of ultrasonic velocity, and is also a valid approach for comparative purposes. Elastic stiffness tensors C of samples were calculated based on the Christoffel equations by measuring the five elastic wave velocities (Cheadle et al. 1991). In particular, we checked the accuracy of C13 in our four sets of samples. The dynamic Young's modulus and dynamic Poisson's ratio of samples, which can be straightforwardly extended to VTI media using Hooke's Law (King 1964; Christensen & Zywicz 1990). Finally, we quantified the velocity and mechanical anisotropy based on the definition of Thomsen (1986). 4.1 Ultrasonic velocity The measured velocities along three directions are summarized in Tables 2 –5. Both P- and S-wave velocities in different directions increase with the applied differential pressure in all samples, as shown in Tables 2–5. The effects of compliant crack and/or pore closure can be also seen from velocity measurements at different applied stresses. Fig. 9 shows both P- wave and S-wave velocities for the four sets of samples as a function of confining pressure. The behaviour observed for the four sets of samples tested is relatively consistent, which shows that synthetic shale shares high similarity with natural shale. Besides, the velocity behaviour of the samples is similar to many other observations of TI media with VP(90°) > VP(45°) > VP(0°) (Sarout et al. 2007; Johnston & Christensen 2012). Moreover, the velocity in our synthetic shale are relatively lower than velocities in natural shale, because the synthetic samples are made by the cold-press method, so that the velocities could not be too large even at extremely high stresses, due to the compaction process is pure mechanical. Figure 9. View largeDownload slide Both P- and S-wave velocities correspond to the cylindrical samples perpendicular (90°), parallel (0°), and 45° to the symmetry axis of synthetic shales K (triangles), I (squares), S (circles) and natural shale N (diamonds), respectively. Figure 9. View largeDownload slide Both P- and S-wave velocities correspond to the cylindrical samples perpendicular (90°), parallel (0°), and 45° to the symmetry axis of synthetic shales K (triangles), I (squares), S (circles) and natural shale N (diamonds), respectively. Table 2. Both P- and S-wave velocities as a function of confining pressure of synthetic shale K. Confining pressure  VP(0°)  VP(45°)  VP(90°)  VSV(0°)  VSH(90°)  (MPa)            0  2024  2437  2714  1452  1620  3  2116  2509  2780  1494  1657  5  2145  2532  2795  1511  1665  8  2200  2580  2840  1539  1690  10  2243  2614  2871  1561  1710  12  2295  2661  2911  1597  1736  15  2354  2715  2951  1635  1757  18  2424  2766  2992  1660  1777  20  2455  2795  3018  1671  1786  23  2529  2858  3069  1701  1805  25  2560  2889  3091  1722  1815  27  2589  2911  3106  1741  1826  30  2642  2951  3140  1764  1846  33  2684  2990  3173  1787  1863  35  2711  3010  3188  1803  1874  37  2744  3029  3204  1811  1883  40  2783  3069  3242  1836  1904  Confining pressure  VP(0°)  VP(45°)  VP(90°)  VSV(0°)  VSH(90°)  (MPa)            0  2024  2437  2714  1452  1620  3  2116  2509  2780  1494  1657  5  2145  2532  2795  1511  1665  8  2200  2580  2840  1539  1690  10  2243  2614  2871  1561  1710  12  2295  2661  2911  1597  1736  15  2354  2715  2951  1635  1757  18  2424  2766  2992  1660  1777  20  2455  2795  3018  1671  1786  23  2529  2858  3069  1701  1805  25  2560  2889  3091  1722  1815  27  2589  2911  3106  1741  1826  30  2642  2951  3140  1764  1846  33  2684  2990  3173  1787  1863  35  2711  3010  3188  1803  1874  37  2744  3029  3204  1811  1883  40  2783  3069  3242  1836  1904  View Large Table 3. Both P- and S-wave velocities as a function of confining pressure of synthetic shale S. Confining pressure  VP(0°)  VP(45°)  VP(90°)  VSV(0°)  VSH(90°)  (MPa)            0  2445  2908  3245  1765  1950  3  2495  2950  3285  1785  1967  5  2526  2971  3302  1797  1976  8  2544  2989  3318  1810  1985  10  2565  3006  3328  1824  1991  12  2583  3021  3340  1835  1998  15  2605  3038  3353  1848  2006  18  2628  3055  3367  1860  2015  20  2649  3072  3380  1873  2023  23  2667  3088  3390  1887  2029  25  2685  3105  3400  1903  2035  27  2700  3118  3410  1913  2041  30  2712  3131  3418  1925  2046  33  2725  3143  3428  1934  2052  35  2737  3156  3436  1946  2057  37  2746  3164  3441  1952  2059  40  2754  3172  3445  1960  2062  Confining pressure  VP(0°)  VP(45°)  VP(90°)  VSV(0°)  VSH(90°)  (MPa)            0  2445  2908  3245  1765  1950  3  2495  2950  3285  1785  1967  5  2526  2971  3302  1797  1976  8  2544  2989  3318  1810  1985  10  2565  3006  3328  1824  1991  12  2583  3021  3340  1835  1998  15  2605  3038  3353  1848  2006  18  2628  3055  3367  1860  2015  20  2649  3072  3380  1873  2023  23  2667  3088  3390  1887  2029  25  2685  3105  3400  1903  2035  27  2700  3118  3410  1913  2041  30  2712  3131  3418  1925  2046  33  2725  3143  3428  1934  2052  35  2737  3156  3436  1946  2057  37  2746  3164  3441  1952  2059  40  2754  3172  3445  1960  2062  View Large Table 4. Both P- and S-wave velocities as a function of confining pressure of synthetic shale I. Confining pressure  VP(0°)  VP(45°)  VP(90°)  VSV(0°)  VSH(90°)  (MPa)            0  2702  3100  3423  1840  2055  3  2761  3158  3475  1878  2084  5  2774  3170  3485  1888  2090  8  2809  3203  3513  1912  2107  10  2828  3220  3526  1924  2114  12  2845  3236  3539  1936  2122  15  2874  3262  3561  1951  2133  18  2904  3287  3578  1971  2143  20  2924  3305  3592  1983  2151  23  2952  3329  3613  2002  2165  25  2966  3341  3621  2010  2169  27  2980  3353  3630  2018  2174  30  3004  3376  3648  2037  2185  33  3024  3396  3664  2053  2195  35  3032  3404  3671  2058  2199  37  3041  3413  3679  2063  2203  40  3062  3432  3693  2077  2211  Confining pressure  VP(0°)  VP(45°)  VP(90°)  VSV(0°)  VSH(90°)  (MPa)            0  2702  3100  3423  1840  2055  3  2761  3158  3475  1878  2084  5  2774  3170  3485  1888  2090  8  2809  3203  3513  1912  2107  10  2828  3220  3526  1924  2114  12  2845  3236  3539  1936  2122  15  2874  3262  3561  1951  2133  18  2904  3287  3578  1971  2143  20  2924  3305  3592  1983  2151  23  2952  3329  3613  2002  2165  25  2966  3341  3621  2010  2169  27  2980  3353  3630  2018  2174  30  3004  3376  3648  2037  2185  33  3024  3396  3664  2053  2195  35  3032  3404  3671  2058  2199  37  3041  3413  3679  2063  2203  40  3062  3432  3693  2077  2211  View Large Table 5. Both P- and S-wave velocities as a function of confining pressure of natural shale N. Confining pressure  VP(0°)  VP(45°)  VP(90°)  VSV(0°)  VSH(90°)  (MPa)            0  3806  4141  4548  2467  2797  3  3838  4167  4566  2486  2807  5  3859  4184  4576  2500  2813  8  3878  4200  4590  2510  2821  10  3897  4217  4604  2522  2829  12  3915  4232  4617  2532  2837  15  3929  4243  4625  2539  2842  18  3940  4253  4633  2545  2845  20  3953  4264  4640  2552  2848  23  3960  4271  4648  2554  2851  25  3971  4280  4653  2563  2855  27  3981  4288  4658  2568  2857  30  3990  4295  4664  2573  2860  33  4000  4303  4668  2579  2862  35  4005  4307  4670  2584  2864  37  4011  4312  4674  2587  2866  40  4015  4315  4675  2590  2867  Confining pressure  VP(0°)  VP(45°)  VP(90°)  VSV(0°)  VSH(90°)  (MPa)            0  3806  4141  4548  2467  2797  3  3838  4167  4566  2486  2807  5  3859  4184  4576  2500  2813  8  3878  4200  4590  2510  2821  10  3897  4217  4604  2522  2829  12  3915  4232  4617  2532  2837  15  3929  4243  4625  2539  2842  18  3940  4253  4633  2545  2845  20  3953  4264  4640  2552  2848  23  3960  4271  4648  2554  2851  25  3971  4280  4653  2563  2855  27  3981  4288  4658  2568  2857  30  3990  4295  4664  2573  2860  33  4000  4303  4668  2579  2862  35  4005  4307  4670  2584  2864  37  4011  4312  4674  2587  2866  40  4015  4315  4675  2590  2867  View Large Fig. 9 also shows that velocities of our samples increase with confining pressure, which can be explained by the closure of compliant cracks and pores under pressure. However, the velocity gradient in the stress domain (∂V/∂σ) differs for the three orientations at a given stress. Further examination suggests that the highest rate of change in velocity occurs for the P-wave propagating parallel to the symmetry axis, whereas the velocity gradient is the lowest at perpendicular to the symmetry axis. For example, in sample I (Fig. 9), with confining pressure ranging from 0 to 40 MPa, VP(0°) increases approximately 13.3 per cent from 2706 to 3062 m s−1, and VP(90°) increases approximately 7.9 per cent from 3423 to 3693 m s−1. These results are indicative of preferential alignments of shale minerals and microcracks. We also note that P-wave velocity is usually more sensitive than the S-wave velocity to confining pressure according to our results. Taking natural sample N as an example, with confining pressure ranging from 0 to 40 MPa, VP(0°) increases approximately 5.6 per cent from 3806 to 4015 m s−1 and VSV(0°) increases approximately 5 per cent from 2467 to 2590 m s−1, VP(90°) increases approximately 2.8 per cent from 4548 to 4675 m s−1 and VSH(90°) increases approximately 2.5 per cent from 2797 to 2867 m s−1. The velocity increase in the synthetic samples is greater than those in natural shale, which can be attributed to the characteristic of synthetic shale. The porosity of synthetic samples are larger than most natural shale (7–10 per cent for synthetic samples), this is because the extrapolation of porosity–depth trends of data found in the lab measurements and data from Chilingarian & Knight (1960) suggest that smectite and kaolinite aggregates will retain a high porosity even at extremely high stresses if the compaction process is purely mechanical. Therefore, at the same confining pressure, the velocity increases in synthetic samples are greater compared with natural shale due to ‘high porosity’ of synthetic shale. As shown in Fig. 9, the measured velocities of synthetic shale are sensitive to the type of clay minerals, and follow the sequence I > S > K, and the velocity increase in sample K is most obvious in our synthetic shale, which might be explained by the porosity of sample K is the largest and sample I is the lowest, which caused by the different volume change of three sets of synthetic samples in the process of pressure consolidation. All these difference of velocity and porosity of three sets of synthetic samples might be due to the different structures of the clay minerals. 4.2 Velocity anisotropy The velocity behaviour of the synthetic samples resembles that found in many observations of natural shale (Vernik & Liu 1997; Wang 2002; Wong et al. 2008). Ultrasonic velocities of the samples for both P- and S-waves propagating perpendicular to the symmetry axis are higher than those parallel to the symmetry axis (Fig. 9). The VP/VS ratios for the three different sets of samples are shown in Fig. 10, as functions of confining pressure for two different orientations of the cylindrical samples with respect to the confining pressure. As shown in Fig. 10, almost all VP/VS ratio are less than 1.7, and both VP/VS ratio in the 0° direction and 90° direction increase with confining pressure. The following inequality (eq. 15) is generally observed for VP/VS ratio in our synthetic shale and natural shale, which agrees well with previous observations (Zhubayev et al. 2016).   \begin{equation}{V_{\rm{P}}}_{(0^\circ )}/{V_{\rm{S}}}_{(0^\circ )} < {V_{\rm{P}}}_{(90^\circ )}/{V_{\rm{S}}}_{(90^\circ )}.\end{equation} (15) Figure 10. View largeDownload slide VP/VS ratio as a function of confining pressure correspond to the cylindrical samples parallel (0°) and perpendicular (90°) to the symmetry axis of synthetic shale K (triangles), I (squares), S (circles) and natural shale N (diamonds), respectively. Figure 10. View largeDownload slide VP/VS ratio as a function of confining pressure correspond to the cylindrical samples parallel (0°) and perpendicular (90°) to the symmetry axis of synthetic shale K (triangles), I (squares), S (circles) and natural shale N (diamonds), respectively. The velocity anisotropy (in terms of ε, γ, δ) of our samples under different stress conditions were calculated from the measured velocity by using eqs (7)–(9), and the results are shown in Fig. 11, which shows that the degree of P-wave and S-wave velocity anisotropy can be as large as 0.39 and 0.14, respectively. Values of the anisotropy parameter δ of our samples are all positive and can be as large as 0.59. The values of these velocity anisotropy parameters for the four sets of samples differ pronouncedly at the same applied stress. Some of these differences can be explained by structure differences and compositional variations of the different clay minerals. We also find that these anisotropy parameters, especially S-wave velocity anisotropy γ, decrease with increasing of stress and are sensitive to stress and lithology. The variation in velocity with increasing of stress could be primarily attributed to crack closure mechanisms, which become independent of the stress magnitude at high stress. Consequently, under deeper subsurface conditions where most cracks are considered closed, the velocity anisotropy should be less sensitive to the stress magnitude. The change of S-wave velocity anisotropy with applied stress are greater than those found for P-waves (compare ε and γ in Fig. 11). This can be explained by the closure of microcracks and compliant pores, which exert a stronger effect on P-wave anisotropy, and is a direct observation of changes in Thomsen's parameters due to changes in rock properties (e.g. crack density, porosity and permeability). Note that three synthetic shales in this paper display a δ > ε relation, which agree well with the previous observations (Yin 1992; Darrel & Douglas 2006; Sarout & Guéguen 2008; Nadri et al. 2011). This behaviour can be explained by statement that the crack-induced anisotropy is typically characterized by the inequality ε > δ > 0 in dry shale, whereas in oil-saturated shale the inequality ε > δ > 0 applies (Vernik 1993). Figure 11. View largeDownload slide Velocity anisotropy as a function of confining pressure correspond to synthetic shale K (triangles), I (squares), S (circles) and natural shale N (diamonds). Figure 11. View largeDownload slide Velocity anisotropy as a function of confining pressure correspond to synthetic shale K (triangles), I (squares), S (circles) and natural shale N (diamonds). 4.3 Mechanical properties and anisotropy Dynamic Young's modulus and Poisson's ratios under different stress conditions were derived from the anisotropy data set that contains complete sets of stiffness constants by using eqs (10)–(13), which are precisely correct for VTI media. As shown in Fig. 12, the dynamic Young's modulus E and Poisson's ratio ν of synthetic shale and natural shale increase with increasing applied pressure. The small increasing trend is reasonable because the shale is heavily over-consolidated, that is, the deformations occurring during hydrostatic compression are small. It should be noted that the increases of dynamic Young's modulus and Poisson's ratios parallel to the symmetry axis are larger than those perpendicular to the symmetry axis. Taking synthetic sample S as an example, with confining pressure ranging from 0 to 40 MPa, E33 increases approximately 26.5 per cent and E11 increase approximately 12.2 per cent; ν31 increase approximately 2.5 per cent andν12 increase approximately 2 per cent. These behaviours suggesting that bedding parallel microcracks are getting closed. Furthermore, E11 is always larger than E33 (E11 > E33), which agrees well with previous observations (Higgins et al. 2008; Suarez-Rivera et al.2009; Sayers 2010), since VTI rocks are harder in the horizontal direction than in the vertical direction (Yan et al. 2012, 2016). For Poisson's ratio ν of our samples, ν31 is smaller than ν12. These results indicate that the Young's modulus E and Poisson's ratio ν of synthetic shale display anisotropic behaviour. It should be noted that an obvious increase in Poisson's ratios of sample K is seen between 10 and 25 MPa, especially ν31. This might can be explained by the ‘high porosity’ of sample K, which means grain contact stiffening and also stiffening of the crystal structure need larger stress. Figure 12. View largeDownload slide Dynamic Young's modulus and Poisson's ratios as a function of confining pressure correspond to synthetic shale K (triangles), I (squares), S (circles) and natural shale N (diamonds). Figure 12. View largeDownload slide Dynamic Young's modulus and Poisson's ratios as a function of confining pressure correspond to synthetic shale K (triangles), I (squares), S (circles) and natural shale N (diamonds). To describe the differences between values of Young's modulus E and Poisson's ratio ν parallel to the symmetry axis and those perpendicular to the symmetry axis, we define ΔE and Δν as follows:   \begin{equation}\Delta E = \frac{{{E_{11}} - {E_{33}}}}{{{E_{33}}}},\end{equation} (16)  \begin{equation}\Delta \nu = \frac{{{\nu _{12}} - {\nu _{31}}}}{{{\nu _3}_1}}.\end{equation} (17) The mechanical anisotropy (the anisotropy of Young's modulus E and Poisson's ratio ν) of our samples as a function of confining pressure was calculated by using eqs (16) and (17). As shown in Fig. 13, the degree of Young's modulus and Poisson's ratios anisotropy can be as large as 0.8 and 0.6, respectively. These mechanical anisotropy parameters also for these four sets of samples differ pronouncedly at the same applied stress. We also find that these anisotropy parameters decrease with the increase of stress and are sensitive to stress and the type of clay minerals, especially ΔE. Similar to the velocity anisotropy, these mechanical anisotropy parameters become independent of the stress magnitude at the highest stresses, which could be primarily attributed to crack closure mechanisms, so that both the velocity and mechanical properties are less sensitive to the stress magnitude under deeper subsurface conditions where most cracks are considered closed. By comparing the velocity anisotropy and mechanical anisotropy, we can find the changes of mechanical anisotropy (i.e. the anisotropy of Young's modulus and Poisson's ratio) with applied stress are larger than those of velocity anisotropy, indicating that mechanical properties are more sensitive to the change of rock properties. Figure 13. View largeDownload slide Mechanical anisotropy ΔE and Δν as a function of confining pressure correspond to synthetic shale K (triangles), I (squares), S (circles) and natural shale N (diamonds). Figure 13. View largeDownload slide Mechanical anisotropy ΔE and Δν as a function of confining pressure correspond to synthetic shale K (triangles), I (squares), S (circles) and natural shale N (diamonds). 5 DISCUSSIONS In this paper, the dynamic Young's modulus were derived from the anisotropy data set that contains complete sets of stiffness constants, which are precisely correct for VTI media. However, these true dynamic Young's modulus cannot be calculated in many cases, because the stiffness constant C13 is not determined due to limited sample availability. In this case, an approximate value of Young's modulus could be calculated from isotropic equations (18) and (19), which is described as apparent Young's modulus by Thomsen (2013) and Sone & Zoback (2013). According to eqs (18) and (19), the apparent Young's modulus of our samples perpendicular and parallel to the symmetry axis can be obtained by using the P- and S-wave modulus perpendicular and parallel to the symmetry axis, respectively. Using the anisotropy dataset that contains complete sets of stiffness constants for our samples by using eqs (10) and (11), we calculated the true dynamic Young's modulus perpendicular and parallel to the symmetry axis, respectively:   \begin{equation}E_{33}^{{\rm{apparent}}} = \frac{{{C_{44}}(3{C_{33}} - 4{C_{44}})}}{{{C_{33}} - {C_{44}}}},\end{equation} (18)  \begin{equation}E_{11}^{{\rm{apparent}}} = \frac{{{C_{66}}(3{C_{11}} - 4{C_{66}})}}{{{C_{11}} - {C_{66}}}}.\end{equation} (19) As shown in Fig. 14, we compare the true and apparent dynamic Young's modulus in the vertical and horizontal directions, the plot shows a good agreement between each other. For the vertical samples (axes of sample parallel to the symmetry axis), the agreement is within 13 per cent, and the agreement is within 3 per cent for the horizontal direction (axes of sample perpendicular to the symmetry axis). The true dynamic Young's modulus and the apparent dynamic Young's modulus show positive correlation in our samples; linear regression analysis gives the following expression:   \begin{equation}{E_{true}} = A * {E_{apparent}} + B.\end{equation} (20) Figure 14. View largeDownload slide The true dynamic Young's modulus versus apparent dynamic Young's modulus correspond to the cylindrical samples (a) parallel and (b) perpendicular to the symmetry axis of synthetic shale K (triangles), I (squares), S (circles) and natural shale N (diamonds). The black and grey lines show one-to-one correspondence and 10 per cent differences. Figure 14. View largeDownload slide The true dynamic Young's modulus versus apparent dynamic Young's modulus correspond to the cylindrical samples (a) parallel and (b) perpendicular to the symmetry axis of synthetic shale K (triangles), I (squares), S (circles) and natural shale N (diamonds). The black and grey lines show one-to-one correspondence and 10 per cent differences. This relationship between the true dynamic Young's modulus and the apparent dynamic Young's modulus is not only found in our samples, but also in natural shales, the measured values also show good linearity and consistent relationship, and the fitting coefficient is approximately equal to one (Sone & Zoback 2013). 6 CONCLUSIONS Using the cold pressure method, we made three sets of synthetic shale samples with different clay minerals, and one set of natural shale samples was prepared for comparison. Ultrasonic experiments were conducted to study ultrasonic anisotropy in dry synthetic and natural samples as a function of applied confining pressure. The SEM pictures and experimental results confirm that synthetic shale has a stable construction process and shares highly similar characteristics with natural shale. The experimental results show that the types of clay minerals have a significant influence on the velocity and mechanical anisotropy. Structure difference and compositional variations of clay minerals may explain some of these behaviours. The measured velocities of synthetic shale are sensitive to the type of clay minerals and follow the sequence I > S > K; the velocity increase for K is most obvious, which might be due to the different structures of the clay minerals. Besides, the velocities of samples increase with applied pressure, and higher rates of velocity increase are observed at lower pressures (<15 MPa), moreover P-wave velocity is usually more sensitive than the S-wave velocity to confining stress according to our results. Similarly, the dynamic Young's modulus E and Poisson's ratio ν increase with applied pressure, and the results also reveal that E11 is always larger than E33 and ν31 is smaller than ν12. In our observations, the degree of velocity anisotropy can be as large as 0.40, and the anisotropic degree of Young's modulus and Poisson's ratio can be as large as 0.8 and 0.61, respectively. These anisotropy parameters decrease with increasing stress, and are sensitive to stress and the type of clay minerals. The changes of P-wave velocity anisotropy with applied stress are larger than those found from S-wave. 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TI - Dynamic mechanical properties and anisotropy of synthetic shales with different clay minerals under confining pressure
JF - Geophysical Journal International
DO - 10.1093/gji/ggx537
DA - 2018-03-01
UR - https://www.deepdyve.com/lp/oxford-university-press/dynamic-mechanical-properties-and-anisotropy-of-synthetic-shales-with-vROO3e20FM
SP - 2003
EP - 2015
VL - 212
IS - 3
DP - DeepDyve
ER -