Preferred orientation and elastic anisotropy in shales
GEOPHYSICS, VOL. 72, NO. 2 共MARCH-APRIL 2007兲; P. D33–D40, 10 FIGS., 3 TABLES. 10.1190/1.2435966
Preferred orientation and elastic anisotropy in shales
Ivan Lonardelli1, Hans-Rudolf Wenk1, and Y. Ren2
during compaction and diagenesis 共Swan et al., 1989; Schoenberg et al., 1996兲. A quantitative understanding of the texture, and thus the intrinsic contribution of single crystals and their orientation to anisotropy, may help us to better evaluate the effects of the oriented fracture and pore fabric and porosity by comparing calculated and measured elastic properties. Clay minerals are fine grained and poorly crystalline. Conventional analysis with X-ray pole figure goniometry gives only limited information. An X-ray transmission technique has been developed to study the orientation distribution of basal planes of sheet silicates and has been successfully applied to slates 共e.g., Kaarsberg, 1959; Oertel, 1983; Sintubin, 1994b; Ho et al., 1999兲. However, so far, no quantitative 3D crystal orientation distributions 共ODs兲 exist for any clay minerals in shales. Knowledge of the OD is necessary to model the polycrystalline elastic properties in a rigorous and quantitative fashion. Hard X-rays produced at synchrotron sources provide a new method to investigate weakly scattering materials. Advantages are a very intense and highly focused X-ray beam and short wavelength that permit high sample penetration without major absorption. Twodimensional detectors, either charge-coupled device cameras or image plates, are used to record diffraction images. Shales are polyphase materials with many overlapping reflections. Both quantitative phase and texture analyses are necessary to determine the volume fractions and the ODs for each mineral, respectively. The recently developed Rietveld method with texture capabilities has been applied to illite 共Wenk et al., 2007兲 and biomineralized materials 共Lonardelli et al., 2005兲 and has emerged as a powerful tool to extract reliable texture information. Our aim was to investigate texture in two shales with different porosity by hard X-ray synchrotron diffraction measurements and to determine 3D ODs with the Rietveld method. From the OD, we obtained the polycrystalline elastic tensor by averaging single-crystal elastic properties. From those compressional and shear-wave velocities and their texture-related component, anisotropy can be calculated.
ABSTRACT Anisotropy in shales is becoming an important issue in exploration and reservoir geophysics. In this study, the crystallographic preferred orientation of clay platelets that contributes to elastic anisotropy was determined quantitatively by hard monochromatic X-ray synchrotron diffraction in two different shales from drillholes off the coast of Nigeria. To analyze complicated diffraction images with five different phases 共illite/smectite, kaolinite, quartz, siderite, feldspar兲 and many overlapping peaks, we applied a methodology based on the crystallographic Rietveld method. The goal was to describe the intrinsic physical properties of the sample 共phase composition, crystallographic preferred orientation, crystal structure, and microstructure兲 and compute macroscopic elastic properties by averaging single crystal properties over the orientation distribution for each phase. Our results show that elastic anisotropy resulting from crystallographic preferred orientation of the clay particles can be determined quantitatively. This provides a possible way to compare measured seismic anisotropy and texture-derived anisotropy and to estimate the contribution of the low-aspect ratio pores aligned with bedding.
INTRODUCTION The elastic properties of shales are crucial for understanding seismic field measurements in sedimentary basins. The anisotropy of elasticity mainly depends on preferred orientations of rock-forming minerals, single crystal properties, the fracture and pore distribution, and pressure-temperature conditions 共Hornby et al., 1994; Sayers, 1994, 2005兲. Preferred orientation or texture is caused by slow sedimentation of plate-shaped clay minerals that favors orientation of platelets parallel to the sediment surface. This pattern is modified
Manuscript received by the Editor June 13, 2006; revised manuscript received September 5, 2006; published online February 28, 2007. 1 University of California, Department of Earth and Planetary Science, Berkeley, California. E-mail: [email protected]; [email protected]. 2 Argonne National Laboratory, Advanced Photon Source, Argonne, Illinois. E-mail: [email protected]. © 2007 Society of Exploration Geophysicists. All rights reserved.
D33
D34
Lonardelli et al. sions caused by the presence of approximately 15%–20% of silt, particularly in the hard shale. Slabs of 20⫻ 10⫻ 1 mm were cut from core plugs with the long dimension more or less parallel to the bedding plane as well as could be determined macroscopically. It was later determined that, in the case of hard shale, the core plug axis was about 20° off the bedding plane. The samples were then mounted on an aluminum holder for stability. These samples were analyzed on beamline BESSRC 11-ID-C at the Advanced Photon Source 共APS兲 at Argonne National Laboratory on a high-energy beam line with a monochromatic wavelength of 0.107863 Å. Beam size was 1 mm, and sample-to-detector distance was approximately 2 m. The samples were mounted on the metal rod parallel to the vertical axis 共y in Figure 2兲 on a goniometer. Images were recorded using a Mar345 image plate detector 共3450⫻ 3450 pixels兲 at seven different omega tilt angles, rotating the samples around the axis perpendicular to the beam 共y兲 in 10° increments. Images collected at = 30° for both soft and hard shales, with the complete coverage used in the analysis, are shown in Figure 3. The intensity variations along the Debye rings immediately reveal the presence of texture. After data collection, images were converted in FIT2D 共Hammersley, 1998兲 to 16-bit tagged image file format 共TIFF兲 and exported for further processing. A lanthanum hexaboride powder standard was used to calibrate the sample to detector distance and refine instrumental parameters. The TIFF images were entered into the material analysis using diffraction 共MAUD兲 program, a Rietveld code written in Java 共Lutterotti et al., 1997兲. An image manager provides the possibility to interactively set the correct parameters 共e.g., sample/detector distance, ranges for integration, center coordinates, number of spectra兲 to obtain integrated spectra. In this study, the integration was performed over 10° sectors, providing for both samples 36 spectra for each 2D image. Seven images, rotating the sample around in 10° increments from −30° to +30°, provided 7 ⫻ 36 = 252 spectra that were used simultaneously in the Rietveld refinement. The d-range used for the analysis was from 1 to 12 Å. First, instrumental parameters such as the center of the ring, the background parameters 共three for each spectrum兲, and the scale parameters 共one for each image兲 were refined. The scale parameters take into account different absorption and volumes with tilt 共Heidelbach et al., 1999兲. The second step was to extract the correct volumefractions for each phase 共quantitative phase analysis兲 and structuralmicrostructural information concerning lattice parameters and an-
MATERIAL AND EXPERIMENT Two different well-preserved wet shales from a drillhole off the Nigerian coast were provided by Chevron. The first one from a higher level is a soft shale with low density 共 = 2.21 g/cm3兲 and high porosity 共26%兲. The second, from a lower level, is a hard shale, more compacted and lithified, with a higher density 共 = 2.51 g/cm3兲 and lower porosity 共6%兲. The exact location of these shales is Chevron proprietary information. The microstructure for both 共Figure 1兲 reveals a matrix composed of clay minerals and relatively large inclu-
a)
b)
100 µm
100 µm
Figure 1. Microstructures for 共a兲 hard shale and 共b兲 soft shale. Hard shale is characterized by large grains of silt. SEM micrographs, secondary electron image.
y
x z
Sample
Reflected line from {hkl} planes
n 2ϑ
Monochromatic beam
ϑ
{hkl} planes
Beam stop
ω
Detector
Figure 2. Schematic sketch illustrating a X-ray diffraction experiment in transmission geometry. The sample is rotated around the y-axis 共x, y, z define the sample reference system兲 to improve pole figure coverage. The diffraction pattern is recorded with a 2D detector.
a)
b)
Hard shale
I/S (200)
I/S (110) K (001)
y
c)
Soft shale
I/S (200)
I/S (110) K (001)
Coverage
80º 60º 40º 20º z
0º
x
Figure 3. Diffraction images recorded with an image plate detector. Intensity variations along Debye rings are indicative of texture. 共a兲 Hard shale, 共b兲 soft shale, and 共c兲 pole figures coverage provided by seven images at different rotation angles . The reference system for the experiment in transmission geometry is x, y, and z. 共Figure 2兲. An equal area projection.
Preferred orientation in shales isotropic crystallite size 共Popa, 1998兲. The refined values are shownin Table 1. In a last step, a modified EWIMV algorithm related to WIMV 共Matthies and Vinel, 1982兲 and implemented in MAUD was used for texture analysis. This algorithm allows us to calculate ODs for irregular and incomplete pole figure coverage. No sample symmetry was imposed. An example of one selected spectrum from each sample 共soft and hard shale兲 is shown in Figure 4. Notice the extremely complicated
D35
profile with numerous overlapping peaks and the good agreement between experimental data 共dots兲 and the recalculated fit 共solid line兲. In the 2D multiplot that stacks all spectra and displays intensities in gray shades 共Figure 5兲, some reflections are indexed. Here, the difference in texture between the two shales is clearly visible. In particular and contrary to hard shale, the kaolinite 共001兲 diffraction peak in soft shale shows no significant variation in relative intensity because of its very weak texture.
Table 1. Density, porosity, anisotropic crystallite size, and quantitative phase information (in weight percent). The error generated during Rietveld refinement (standard deviation) is shown in parentheses. Crystallite size 共nm兲 Density 共g/cm3兲
Porosity 共%兲
Hard shale
2.51
6
Soft shale
2.21
26
Sample
共100兲
共010兲
共001兲
I/S
Kaolinite
Quartz
Siderite
Feldspar
15.1共7兲 22.4共8兲 26.4共8兲 16.3共9兲
16.5共8兲 20.1共9兲 18.5共12兲 20.1共8兲
3.6共8兲 14.4共6兲 2.7共2兲 11.8共4兲
37共2兲
42共2兲
16.1共1兲
1.9共3兲
2.6共1兲
39共2兲
40共2兲
13.7共6兲
5.4共2兲
1.9共1兲
35
Hard shale
Hard shale
a)
I/S (110) 30
K (001) I/S (200) fit
25
Data
Intensity (count1/2)
a)
I/S Ka I/S Ka
Weight fraction 共%兲
20 I/S Kspar Sid Kaol Quartz
1.0
2.0
3.0
4.0
5.0
2-Theta (º)
Soft shale
I/S (110)
30
K (001)
I/S (110)
K (002)
I/S (200)
b)
Soft shale
I/S (200)
fit
25
20
360º
Data
Intensity (count1/2)
b)
K (001)
270º
I/S Kspar Sid Kaol Quartz
180º 90º 1.0
2.0
3.0
4.0
5.0
0º
2-Theta (º)
1
Figure 4. Example of spectra from 共a兲 hard shale and 共b兲 soft shale. Dots are experimental data, and the solid line is the Rietveld refinement fit. 16.0
2
20.0
3 2-Theta (º)
24.0 28.0 Intensity (count1/2)
4
32.0
5
36.0
Figure 5. Map plots illustrating, with gray shades, intensity variations in 36 spectra from one 2D synchrotron diffraction image. 共a兲 Hard shale and 共b兲 soft shale. Notice that in soft shale the kaolinite line is barely textured. The bottom plot in each image is experimental data, and the top is the Rietveld fit for each sample.
D36
Lonardelli et al.
RESULTS Table 1 shows some information regarding the density and porosity for both shales as well as the volume fractions for each phase obtained with Rietveld refinement. The aim of this work is to quantify texture; thus, illite and smectite are treated as a single mixed-layer phase in both samples 共I/S兲, with a 1:1 ratio 共50% illite, 50% smectite兲 and a Reichweite 共R兲 ordering parameter R1. Each layer is identical and contains an Al-rich and an Al-poor tetrahedral sheet and alternating K-rich and K-poor interlayers 共Stixrude et al., 2002兲. For this phase, we assume a crystal structure of muscovite 共Comodi and Zanazzi, 1995兲 with monoclinic symmetry and space group C2/c 共Hermann-Mauguin convention兲. We are aware of the limitations these assumptions put on interpretations, particularly elastic properties, and we hope this can be refined further in the future. For kaolinite, space group P1 was used 共Young and Hewat, 1988兲. We used MAUD to extract ODs for quartz, feldspar, siderite, I/S, and kaolinite and to export them for further processing in BEARTEX 共Wenk et al., 1998兲. The strength of lattice-preferred orientations 共F2, Bunge, 1985兲, the OD minimum-maximum, and additional texture information are summarized in Table 2. The 共001兲 and 共100兲 pole figures are used for graphic representations 共Figures 6-8兲. For both samples, I/S displays strong preferred orientation 共Figure 6a and b兲. Kaolinite is oriented in hard shale 共Figure 7a兲 but is more or less random in soft shale 共Figure 7b兲. Quartz, feldspar, and siderite are oriented randomly, so pole figures for silt components are not shown. For hard shale 共001兲, pole figures of I/S display a slightly oblique maximum 共Figure 6a兲 with a concentration of 3.01 multiples of a random distribution 共MRD兲. The apparent tilt of approximately 15°20° from the center is caused by the core plug not being exactly perpendicular to the foliation plane. The significant 共001兲 minimum 共also OD minimum兲 of approximately 0.37 MRD tells us that a significant portion of crystallites is randomly oriented. The 共100兲 pole figure for I/S displays a broad girdle with no significant concentrations, indicating the mineral tends to align in a fiber texture rotating freely around the 共001兲 normal. Figure 7a shows 共001兲 and 共100兲 pole figures for kaolinite where the maximum is more than 30° displaced from the I/S maximum. The texture is similar to that observed for I/S, with a larger proportion of crystallites randomly oriented 共minimum 0.5 MRD兲. In the hard shale, the strong texture for both clay minerals 共kaolinite and I/S兲 is also easily recognized by looking at the map plot 共Figure 5a兲. To confirm the tilt of the 共001兲 pole figure maximum relative to I/S, we have extracted the ODs for three additional different regions Table 2. Quantitative texture information for OD and pole figures in multiples of a random distribution (MRD). F2 is the texture strength. F2 Sample phase 共max/min兲 Hard shale I/S Kaolinite Soft shale I/S Kaolinite
OD 共max/min兲
共001兲 共100兲 共max/min兲 共max/min兲
1.43 1.38
4.21/0.28 3.68/0.35
3.01/0.37 2.63/0.50
1.39/0.62 1.30/0.70
1.64 1.03
5.82/0.27 1.38/0.84
4.91/0.33 1.18/0.89
1.45/0.38 1.06/0.94
of the hard shale sample. Figure 8 shows the 共001兲 pole figures for three different spots separated by 3 mm. The results confirm an asymmetric maximum of kaolinite with respect to the foliation plane. In the soft shale, I/S is more strongly aligned than in the hard shale, with 共001兲 poles perpendicular to the foliation plane and a maximum of 4.9 MRD 共Figure 6b兲. The volume fraction of randomly oriented crystallites is similar 共0.33 MRD兲. Although I/S is more textured than in hard shale, kaolinite is nearly randomly oriented with a 共001兲 maximum of approximately only 1.18 MRD 共Figure 7b兲. This result can be confirmed qualitatively by inspecting the map plot in Figure 5, where the variation in intensity along the 共001兲 kaolinite reflection is minimal compared with hard shale. Just to confirm that this unexpected feature is representative of the sample and not a local aberration, several spots were investigated. Figure 9 compares experimental 共001兲 kaolinite lines on several spots for both soft and hard shale, indicating a consistent pattern.
DISCUSSION Hard X-ray synchrotron radiation was used to investigate the preferred orientation of two different shale samples collected at different burial depths. Two-dimensional diffraction images were analyzed with the Rietveld method to provide a quantitative texture characterization from full spectra. Both samples show strong alignment of I/S with 共001兲 planes parallel to the foliation plane. Maximum 共001兲 pole densities are similar to those reported for Zechstein shales 共Sintubin, 1994a; 4–6 MRD兲, Gulf Coast mudstones 共Ho et al., 1995; 2–7 MRD兲, and mudstones from Pennsylvania 共Ho et al., 1995; 2–5 MRD兲 but considerably weaker than muscovite in metamorphic slates 共Oertel and Phakey, 1972; 16 MRD.; Sintubin, 1994b; 5–18 MRD兲. All these previous studies used single peak intensity measurements, which can be unreliable for interlayer clays with diffuse peaks and background uncertainties. Our method relied on full spectra deconvolution. If the ODs and the elastic constants of single crystals for each phase are known, averaging procedures can be applied to evaluate the elastic properties of the polycrystal. Unfortunately, elastic properties of clay minerals are poorly known 共Katahara, 1996兲, and for this study we have used experimental elastic stiffness moduli of muscovite measured with Brillouin scattering 共Vaughan and Guggenheim, 1986兲 and kaolinite elastic constants derived from first-principles studies 共Sato et al., 2005兲. Muscovite is treated as monoclinic, and kaolinite is treated as triclinic. Results for aggregate elastic constants weighted by the OD are shown in Table 3. The Voigt and Reuss values provide upper and lower bounds, assuming uniform strain and uniform stress, respectively, throughout the textured aggregate. A geometric mean averaging is intermediate 共Matthies and Humbert, 1993兲. From aggregate elastic constants obtained by the geometric mean, we calculated phase velocity surfaces 共V p, Vsh, and Vsv兲. Figure 10 gives the 1D profiles of V p and ⌬Vs 共Vsh − Vsv兲 from a position perpendicular to the foliation plane 共0°兲 to the position parallel to the foliation plane 共90°兲. Anisotropies 共in percent兲 for the clay mineral components 共A = 200共Vmax − Vmin兲/共Vmax + Vmin兲兲 are in the range of 10%. From elastic coefficients, we can also calculate Thomsen parameters that are used in exploration seismology 共Thomsen, 1986兲. For the two shales analyzed in this study, anisotropy is moderate 共Table 3兲. This is because by using muscovite elastic moduli for I/S, we assume that any interlayer water is pore water. The elastic anisotropy calculated
Preferred orientation in shales
a)
001
100
3.01
2.26
z y
1.88 1.5 1.12
Pole density (MRD)
2.63
D37 Figure 6. 共100兲 and 共001兲 I/S pole figures recalculated from the OD: 共a兲 hard shale and 共b兲 soft shale. An equal area projection. The pole density scale is in multiples of random distribution 共MRD兲.
0.75 x
b)
0.37 001
100
4.91
3.6 2.95 2.29 1.64
Pole density (MRD)
4.26
0.98 0.33
a)
100
Figure 7. Kaolinite pole figures 共100兲 and 共001兲, recalculated from the OD: 共a兲 hard shale and 共b兲 soft shale. An equal area projection. The pole density is scale in MRD.
001
z y
2.6
2 1.7 x
b)
100
1.4 001
1.1 0.8 0.5
Pole density (MRD)
2.3
D38 Figure 8. 共a兲 I/S and 共b兲 kaolinite 共001兲 pole figures recalculated from the OD for three different spots of the hard shale sample. An equal area projection. The pole density is in MRD.
Lonardelli et al.
a)
Spot 5
Spot 8
Spot 11 I/S z
y
1 cm
x 2.32-0.58 (MRD)
2.49-0.54 (MRD)
Spot 5
b)
3.01-0.37 (MRD)
Spot 8
5 8 11
Spot 11
y
x
Kaolinite
2.62-0.48 (MRD)
Figure 9. The 共001兲 kaolinite peak for hard 共a兲 and soft shale 共b兲. The image shows intensity variation in 36 spectra 共from 0° to 360°兲 from the 2D synchrotron image at = 30° 共tilting angle兲 for each spot analyzed. Notice the different intensity scales for 共a兲 and 共b兲.
a)
2.53-0.50 (MRD)
0º
90º
22
24
2.60-0.50 (MRD)
180º
270º
360º
Spot 5
Spot 8
Spot 11
26
28
30
24
25
Intensity (count1/2)
b)
Spot 5
Spot 8
Spot 11
21
22
23
Intensity (count1/2)
Preferred orientation in shales with this technique comes from the texture of the nonporous material, and the effect of low-aspect ratio pores 共interlayer water兲 aligned with the bedding is neglected. For bulk rock seismic properties, not only does crystal orientation need to be considered but also other contributions to anisotropy in shales, such as oriented fractures, degree of porosity, and water content 共O’Connell and Budiansky, 1976; Crampin, 1981; Hornby et al., 1994; Schoenberg and Sayers, 1995兲. The difference between texture-derived wave-velocity contributions and experimental velocity measurements can be interpreted in terms of direct porosity effects, such as low-aspect ratio pores, preferred orientation of low-aspect ratio pores, and pore interactions 共Ullemeyer et al., 2006兲. Unfortunately, in the case of these samples, no velocity measurements are available. The role of porosity in the development of intrinsic anisotropy described by Wang 共2002兲 共more compacted shales equal a higher de-
D39
gree of anisotropy兲 is only partially confirmed. The I/S in soft shale 共less compacted with 26% of porosity兲 is more strongly aligned than I/S in hard shale 共more compacted with only 6% of porosity兲. However, the rule applies to kaolinite, whereas soft shale the texture is almost random.
CONCLUSIONS
Our study demonstrated the feasibility of extracting orientation distributions of individual mineral components in shales. With the advances in X-ray diffraction methods and Rietveld texture analysis, we are now able to obtain quantitative texture information with a high degree of resolution for complicated multiphase materials. Quantification of the texture-derived contribution to anisotropy of clay minerals in shales opens the possibility to determine a lower limit of anisotropy caused by crystallite orientation and thus advance our understanding of the importance of pores by comparing predicted and measured seisTable 3. Elastic stiffness of I/S and kaolinite aggregates using the geometric mean (Geo), Voigt average (upper limit), Reuss average (lower limit), and mic velocities. With such information, comprecalculated Thomsen anisotropy parameters. The reference single-crystal values hensive models for seismic wave anisotropy in assume monoclinic symmetry for muscovite (Vaughan and Guggenheim, 1986) clay-rich sedimentary rocks can be developed. and triclinic symmetry for kaolinite (Sato et al., 2005). Only the most significant elastic constants are shown.
ACKNOWLEDGMENTS Elastic constants 共GPa兲 Sample/phase Averages Hard shale I/S
Geo Voigt Reuss Geo Voigt Reuss
Kaolinite
Compressional velocity (km/s)
6.2
C13
C66
33.0 41.6 26.9 25.6 41.1 16.7
36.2 37.7 29.3 24.1 34.8 12.9
35.7 44.6 28.7 26.3 41.3 16.9
Geo Voigt Reuss
114.3 99.8 133.9 118.6 91.8 81.9
30.7 39.1 25.1
b)
6 5.8 Illite/smect_hard shale Kaolinite_hard shale Illite/smect_soft shale
5.6 5.4 5.2
0.043 0.036 0.035 0.047 0.038 0.032
␦
␥
0.041 0.005 0.036 0.008 0.033 0.007 0.014 0.039 0.002 0.041 0.006 −0.025
36.9 0.073 0.101 −0.025 45.9 0.065 0.087 −0.026 29.6 0.060 0.090 −0.031
0.35 Illite/smect_hard shale Kaolinite_hard shale Illite/smect_soft shale
0.25 0.2 0.15 0.1 0.05 0
5 4.8
35.9 37.3 29.1
0.3
∆S velocity (km/s)
6.4
111.4 102.7 130.7 121.9 89.5 83.7 79.3 72.5 121.1 112.5 48.1 45.2
C44
0
The project was supported by DOE-BES 共DEFG02-05ER15637兲 and NSF 共EAR-0337006兲. We acknowledge access to the facilities of Beamline 11ID-C at APS ANL. Luca Duranti, Russ Ewy, and Kurt Nihei at Chevron San Ramon kindly supplied the samples. Discussions with them and Seiji Nakagawa 共LBNL兲 are greatly appreciated. Comments by two reviewers and the editor were very helpful for improving the manuscript.
REFERENCES
Soft shale I/S
a)
C33
C11
Thomsen parameters
10
20
30
40
50
60
70
80
90
Angle from bedding-normal sym. axis (º)
–0.05
0
10
20
30
40
50
60
70
80
90
Angle from bedding-normal sym. axis (º)
Figure 10. Calculated seismic velocities for I/S 共hard and soft shale兲 and kaolinite 共hard shale兲. 共a兲 P-waves, 共b兲 ⌬S-waves versus the angle to the bedding plane.
Bunge, H.-J., 1985, Physical properties of polycrystals, in H. R. Wenk, ed., Preferred orientation in deformed metals and rocks: An introduction to modern texture analysis: Academic Press, 507–525. Comodi, P., and P. F. Zanazzi, 1995, High pressure structural study of muscovite: Physics and Chemistry of Minerals, 22, 170–177. Crampin, S., 1981, A review of wave motion in anisotropic and cracked elastic media: Wave Motion, 3, 242–391. Hammersley, A. P., 1998, Fit2D: V99.129 reference manual version 3.1: Internal Report ESRF-98-HA01. Heidelbach, F., C. Riekel, and H.-R. Wenk, 1999, Quantitative texture analysis of small domains with synchrotron X-rays: Journal of Applied Crystallography, 32, 841–849. Ho, N. C., D. R. Peacor, and B. A. Van der Pluijm, 1995, Reorientation mechanisms of phyllosilicates in the mudstone-to-slate transition at Lehigh Gap, Pennsylvania: Journal of Structural Geology, 17, 345–356. ——–, 1999, Preferred orientation of phyllosilicates in Gulf Coast mudstones and relation to the smectite-illite transition: Clays and Clay Minerals, 47, 485– 504. Hornby, B. E., L. M. Schwartz, and J. A. Hudson, 1994, Anisotropic effective-medium modelling of the elastic properties of shales: Geophysics, 59, 1570–1583. Kaarsberg, E. A., 1959, Introductory studies of natural
D40
Lonardelli et al.
and artificial argillaceous aggregates by sound-propagation and X-ray diffraction method: Journal of Geology, 67, 447–472. Katahara, K. W., 1996, Clay mineral elastic properties: 66th Annual International Meeting, SEG, Expanded Abstracts, 1691–1694. Lonardelli, I., H.-R. Wenk, L. Lutterotti, and M. Goodwin, 2005, Texture analysis from synchrotron diffraction images with the Rietveld method: Dinosaur tendon and salmon scale: Journal of Synchrotron Radiation, 12, 354–360. Lutterotti, L., S. Matthies, H.-R. Wenk, A. S. Schultz, and J. W. Richardson Jr., 1997, Combined texture and structure analysis of deformed limestone from time-of-flight diffraction spectra: Journal of Applied Physics, 81, 594–600. Matthies, S., and M. Humbert, 1993, The realization of the concept of a geometric mean for calculating physical constants of polycrystalline materials: Physica Status Solidi, B177, K47–K50. Matthies, S., and G. W. Vinel, 1982, On the reproduction of the orientation distribution function of textured samples from reduced pole figures using the concept of conditional ghost correction: Physica Status Solidi, B112, K111–K114. O’Connell, R., and B. Budiansky, 1976, Seismic velocities in dry and saturated cracked solids: Journal of Geophysical Research, 79, 5412–5426. Oertel, G., 1983, The relationship of strain and preferred orientation of phyllosilicate grains in rocks — Review: Tectonophysics, 100, 413–447. Oertel, G., and P. P. Phakey, 1972, The texture of a slate from Nantille, Caernarvon, North Wales: Texture, 1, 1–8. Popa, N. C., 1998, The hkl dependence of diffraction-line broadening caused by strain and size for all Laue groups in Rietveld refinement: Journal of Applied Crystallography, 31, 176–180. Sato, H., K. Ono, C. T. Johnston, and A. Yamagishi, 2005, First-principles studies on elastic constants of a 1:1 layered kaolinite mineral: American Mineralogist, 90, 1824–1826. Sayers, C. M., 1994, The elastic anisotropy of shales: Journal of Geophysical Research, 99, 767–774. ——–, 2005, Seismic anisotropy of shales: Geophysical Prospecting, 53,
667–676. Schoenberg, M., and C. M. Sayers, 1995, Seismic anisotropy of fractured rock: Geophysics, 60, 204–211. Schoenberg, M., F. Muir, and C. M. Sayers, 1996, Introducing ANNIE: A simple three-parameter anisotropic velocity model for shales: Journal of Seismic Exploration, 5, 35–49. Sintubin, M., 1994a, Clay fabrics in relation to the burial history of shales: Sedimentology, 41, 1161–1169. ——–, 1994b, Phyllosilicate preferred orientation in relation to strain path determination in the lower Paleozoic Stavelot-Venn Massif 共Ardennes, Belgium兲: Tectonophysics, 237, 215–231. Stixrude, L., and D. R. Peacor, 2002, First-principles study of illite-smectite and implications for clay mineral systems: Nature, 420, 165–168. Swan, G., J. Cook, S. Bruce, and R. Meehan, 1989, Strain rate effects in Kimmeridge Bay shale: International Journal of Rock Mechanics and Mining Sciences, 26, 135–149. Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, 1954–1966. Ullemeyer, K., S. Siegesmund, P. N. J. Rasolofosaon, and J. H. Behrmann, 2006, Experimental and texture-derived P-wave anisotropy of principal rocks from the TRANSALP traverse: An aid for the interpretation of seismic field data: Tectonophysics, 414, 97–116. Vaughan, M. T., and S. Guggenheim, 1986, Elasticity of muscovite and its relationship to crystal structure: Journal of Geophysical Research, 91, 4657–4664. Wang, Z., 2002, Seismic anisotropy in sedimentary rocks: Part 2 — Laboratory data: Geophysics, 67, 1423–1440. Wenk, H.-R., I. Lonardelli, H. Franz, K. Nihei, and S. Nakagawa, 2007, Preferred orientation and elastic anisotropy of illite-rich shale: Geophysics, this issue. Wenk, H.-R., S. Matthies, J. Donovan, and D. Chateigner, 1998, BEARTEX, a Windows-based program system for quantitative texture analysis: Journal of Applied Crystallography, 31, 262–269. Young, R. A., and A. W. Hewat, 1988, Verification of the triclinic crystal structure of kaolinite: Clays and Clay Minerals, 36, 225–232.
Preferred orientation and elastic anisotropy in shales
Ivan Lonardelli1, Hans-Rudolf Wenk1, and Y. Ren2
during compaction and diagenesis 共Swan et al., 1989; Schoenberg et al., 1996兲. A quantitative understanding of the texture, and thus the intrinsic contribution of single crystals and their orientation to anisotropy, may help us to better evaluate the effects of the oriented fracture and pore fabric and porosity by comparing calculated and measured elastic properties. Clay minerals are fine grained and poorly crystalline. Conventional analysis with X-ray pole figure goniometry gives only limited information. An X-ray transmission technique has been developed to study the orientation distribution of basal planes of sheet silicates and has been successfully applied to slates 共e.g., Kaarsberg, 1959; Oertel, 1983; Sintubin, 1994b; Ho et al., 1999兲. However, so far, no quantitative 3D crystal orientation distributions 共ODs兲 exist for any clay minerals in shales. Knowledge of the OD is necessary to model the polycrystalline elastic properties in a rigorous and quantitative fashion. Hard X-rays produced at synchrotron sources provide a new method to investigate weakly scattering materials. Advantages are a very intense and highly focused X-ray beam and short wavelength that permit high sample penetration without major absorption. Twodimensional detectors, either charge-coupled device cameras or image plates, are used to record diffraction images. Shales are polyphase materials with many overlapping reflections. Both quantitative phase and texture analyses are necessary to determine the volume fractions and the ODs for each mineral, respectively. The recently developed Rietveld method with texture capabilities has been applied to illite 共Wenk et al., 2007兲 and biomineralized materials 共Lonardelli et al., 2005兲 and has emerged as a powerful tool to extract reliable texture information. Our aim was to investigate texture in two shales with different porosity by hard X-ray synchrotron diffraction measurements and to determine 3D ODs with the Rietveld method. From the OD, we obtained the polycrystalline elastic tensor by averaging single-crystal elastic properties. From those compressional and shear-wave velocities and their texture-related component, anisotropy can be calculated.
ABSTRACT Anisotropy in shales is becoming an important issue in exploration and reservoir geophysics. In this study, the crystallographic preferred orientation of clay platelets that contributes to elastic anisotropy was determined quantitatively by hard monochromatic X-ray synchrotron diffraction in two different shales from drillholes off the coast of Nigeria. To analyze complicated diffraction images with five different phases 共illite/smectite, kaolinite, quartz, siderite, feldspar兲 and many overlapping peaks, we applied a methodology based on the crystallographic Rietveld method. The goal was to describe the intrinsic physical properties of the sample 共phase composition, crystallographic preferred orientation, crystal structure, and microstructure兲 and compute macroscopic elastic properties by averaging single crystal properties over the orientation distribution for each phase. Our results show that elastic anisotropy resulting from crystallographic preferred orientation of the clay particles can be determined quantitatively. This provides a possible way to compare measured seismic anisotropy and texture-derived anisotropy and to estimate the contribution of the low-aspect ratio pores aligned with bedding.
INTRODUCTION The elastic properties of shales are crucial for understanding seismic field measurements in sedimentary basins. The anisotropy of elasticity mainly depends on preferred orientations of rock-forming minerals, single crystal properties, the fracture and pore distribution, and pressure-temperature conditions 共Hornby et al., 1994; Sayers, 1994, 2005兲. Preferred orientation or texture is caused by slow sedimentation of plate-shaped clay minerals that favors orientation of platelets parallel to the sediment surface. This pattern is modified
Manuscript received by the Editor June 13, 2006; revised manuscript received September 5, 2006; published online February 28, 2007. 1 University of California, Department of Earth and Planetary Science, Berkeley, California. E-mail: [email protected]; [email protected]. 2 Argonne National Laboratory, Advanced Photon Source, Argonne, Illinois. E-mail: [email protected]. © 2007 Society of Exploration Geophysicists. All rights reserved.
D33
D34
Lonardelli et al. sions caused by the presence of approximately 15%–20% of silt, particularly in the hard shale. Slabs of 20⫻ 10⫻ 1 mm were cut from core plugs with the long dimension more or less parallel to the bedding plane as well as could be determined macroscopically. It was later determined that, in the case of hard shale, the core plug axis was about 20° off the bedding plane. The samples were then mounted on an aluminum holder for stability. These samples were analyzed on beamline BESSRC 11-ID-C at the Advanced Photon Source 共APS兲 at Argonne National Laboratory on a high-energy beam line with a monochromatic wavelength of 0.107863 Å. Beam size was 1 mm, and sample-to-detector distance was approximately 2 m. The samples were mounted on the metal rod parallel to the vertical axis 共y in Figure 2兲 on a goniometer. Images were recorded using a Mar345 image plate detector 共3450⫻ 3450 pixels兲 at seven different omega tilt angles, rotating the samples around the axis perpendicular to the beam 共y兲 in 10° increments. Images collected at = 30° for both soft and hard shales, with the complete coverage used in the analysis, are shown in Figure 3. The intensity variations along the Debye rings immediately reveal the presence of texture. After data collection, images were converted in FIT2D 共Hammersley, 1998兲 to 16-bit tagged image file format 共TIFF兲 and exported for further processing. A lanthanum hexaboride powder standard was used to calibrate the sample to detector distance and refine instrumental parameters. The TIFF images were entered into the material analysis using diffraction 共MAUD兲 program, a Rietveld code written in Java 共Lutterotti et al., 1997兲. An image manager provides the possibility to interactively set the correct parameters 共e.g., sample/detector distance, ranges for integration, center coordinates, number of spectra兲 to obtain integrated spectra. In this study, the integration was performed over 10° sectors, providing for both samples 36 spectra for each 2D image. Seven images, rotating the sample around in 10° increments from −30° to +30°, provided 7 ⫻ 36 = 252 spectra that were used simultaneously in the Rietveld refinement. The d-range used for the analysis was from 1 to 12 Å. First, instrumental parameters such as the center of the ring, the background parameters 共three for each spectrum兲, and the scale parameters 共one for each image兲 were refined. The scale parameters take into account different absorption and volumes with tilt 共Heidelbach et al., 1999兲. The second step was to extract the correct volumefractions for each phase 共quantitative phase analysis兲 and structuralmicrostructural information concerning lattice parameters and an-
MATERIAL AND EXPERIMENT Two different well-preserved wet shales from a drillhole off the Nigerian coast were provided by Chevron. The first one from a higher level is a soft shale with low density 共 = 2.21 g/cm3兲 and high porosity 共26%兲. The second, from a lower level, is a hard shale, more compacted and lithified, with a higher density 共 = 2.51 g/cm3兲 and lower porosity 共6%兲. The exact location of these shales is Chevron proprietary information. The microstructure for both 共Figure 1兲 reveals a matrix composed of clay minerals and relatively large inclu-
a)
b)
100 µm
100 µm
Figure 1. Microstructures for 共a兲 hard shale and 共b兲 soft shale. Hard shale is characterized by large grains of silt. SEM micrographs, secondary electron image.
y
x z
Sample
Reflected line from {hkl} planes
n 2ϑ
Monochromatic beam
ϑ
{hkl} planes
Beam stop
ω
Detector
Figure 2. Schematic sketch illustrating a X-ray diffraction experiment in transmission geometry. The sample is rotated around the y-axis 共x, y, z define the sample reference system兲 to improve pole figure coverage. The diffraction pattern is recorded with a 2D detector.
a)
b)
Hard shale
I/S (200)
I/S (110) K (001)
y
c)
Soft shale
I/S (200)
I/S (110) K (001)
Coverage
80º 60º 40º 20º z
0º
x
Figure 3. Diffraction images recorded with an image plate detector. Intensity variations along Debye rings are indicative of texture. 共a兲 Hard shale, 共b兲 soft shale, and 共c兲 pole figures coverage provided by seven images at different rotation angles . The reference system for the experiment in transmission geometry is x, y, and z. 共Figure 2兲. An equal area projection.
Preferred orientation in shales isotropic crystallite size 共Popa, 1998兲. The refined values are shownin Table 1. In a last step, a modified EWIMV algorithm related to WIMV 共Matthies and Vinel, 1982兲 and implemented in MAUD was used for texture analysis. This algorithm allows us to calculate ODs for irregular and incomplete pole figure coverage. No sample symmetry was imposed. An example of one selected spectrum from each sample 共soft and hard shale兲 is shown in Figure 4. Notice the extremely complicated
D35
profile with numerous overlapping peaks and the good agreement between experimental data 共dots兲 and the recalculated fit 共solid line兲. In the 2D multiplot that stacks all spectra and displays intensities in gray shades 共Figure 5兲, some reflections are indexed. Here, the difference in texture between the two shales is clearly visible. In particular and contrary to hard shale, the kaolinite 共001兲 diffraction peak in soft shale shows no significant variation in relative intensity because of its very weak texture.
Table 1. Density, porosity, anisotropic crystallite size, and quantitative phase information (in weight percent). The error generated during Rietveld refinement (standard deviation) is shown in parentheses. Crystallite size 共nm兲 Density 共g/cm3兲
Porosity 共%兲
Hard shale
2.51
6
Soft shale
2.21
26
Sample
共100兲
共010兲
共001兲
I/S
Kaolinite
Quartz
Siderite
Feldspar
15.1共7兲 22.4共8兲 26.4共8兲 16.3共9兲
16.5共8兲 20.1共9兲 18.5共12兲 20.1共8兲
3.6共8兲 14.4共6兲 2.7共2兲 11.8共4兲
37共2兲
42共2兲
16.1共1兲
1.9共3兲
2.6共1兲
39共2兲
40共2兲
13.7共6兲
5.4共2兲
1.9共1兲
35
Hard shale
Hard shale
a)
I/S (110) 30
K (001) I/S (200) fit
25
Data
Intensity (count1/2)
a)
I/S Ka I/S Ka
Weight fraction 共%兲
20 I/S Kspar Sid Kaol Quartz
1.0
2.0
3.0
4.0
5.0
2-Theta (º)
Soft shale
I/S (110)
30
K (001)
I/S (110)
K (002)
I/S (200)
b)
Soft shale
I/S (200)
fit
25
20
360º
Data
Intensity (count1/2)
b)
K (001)
270º
I/S Kspar Sid Kaol Quartz
180º 90º 1.0
2.0
3.0
4.0
5.0
0º
2-Theta (º)
1
Figure 4. Example of spectra from 共a兲 hard shale and 共b兲 soft shale. Dots are experimental data, and the solid line is the Rietveld refinement fit. 16.0
2
20.0
3 2-Theta (º)
24.0 28.0 Intensity (count1/2)
4
32.0
5
36.0
Figure 5. Map plots illustrating, with gray shades, intensity variations in 36 spectra from one 2D synchrotron diffraction image. 共a兲 Hard shale and 共b兲 soft shale. Notice that in soft shale the kaolinite line is barely textured. The bottom plot in each image is experimental data, and the top is the Rietveld fit for each sample.
D36
Lonardelli et al.
RESULTS Table 1 shows some information regarding the density and porosity for both shales as well as the volume fractions for each phase obtained with Rietveld refinement. The aim of this work is to quantify texture; thus, illite and smectite are treated as a single mixed-layer phase in both samples 共I/S兲, with a 1:1 ratio 共50% illite, 50% smectite兲 and a Reichweite 共R兲 ordering parameter R1. Each layer is identical and contains an Al-rich and an Al-poor tetrahedral sheet and alternating K-rich and K-poor interlayers 共Stixrude et al., 2002兲. For this phase, we assume a crystal structure of muscovite 共Comodi and Zanazzi, 1995兲 with monoclinic symmetry and space group C2/c 共Hermann-Mauguin convention兲. We are aware of the limitations these assumptions put on interpretations, particularly elastic properties, and we hope this can be refined further in the future. For kaolinite, space group P1 was used 共Young and Hewat, 1988兲. We used MAUD to extract ODs for quartz, feldspar, siderite, I/S, and kaolinite and to export them for further processing in BEARTEX 共Wenk et al., 1998兲. The strength of lattice-preferred orientations 共F2, Bunge, 1985兲, the OD minimum-maximum, and additional texture information are summarized in Table 2. The 共001兲 and 共100兲 pole figures are used for graphic representations 共Figures 6-8兲. For both samples, I/S displays strong preferred orientation 共Figure 6a and b兲. Kaolinite is oriented in hard shale 共Figure 7a兲 but is more or less random in soft shale 共Figure 7b兲. Quartz, feldspar, and siderite are oriented randomly, so pole figures for silt components are not shown. For hard shale 共001兲, pole figures of I/S display a slightly oblique maximum 共Figure 6a兲 with a concentration of 3.01 multiples of a random distribution 共MRD兲. The apparent tilt of approximately 15°20° from the center is caused by the core plug not being exactly perpendicular to the foliation plane. The significant 共001兲 minimum 共also OD minimum兲 of approximately 0.37 MRD tells us that a significant portion of crystallites is randomly oriented. The 共100兲 pole figure for I/S displays a broad girdle with no significant concentrations, indicating the mineral tends to align in a fiber texture rotating freely around the 共001兲 normal. Figure 7a shows 共001兲 and 共100兲 pole figures for kaolinite where the maximum is more than 30° displaced from the I/S maximum. The texture is similar to that observed for I/S, with a larger proportion of crystallites randomly oriented 共minimum 0.5 MRD兲. In the hard shale, the strong texture for both clay minerals 共kaolinite and I/S兲 is also easily recognized by looking at the map plot 共Figure 5a兲. To confirm the tilt of the 共001兲 pole figure maximum relative to I/S, we have extracted the ODs for three additional different regions Table 2. Quantitative texture information for OD and pole figures in multiples of a random distribution (MRD). F2 is the texture strength. F2 Sample phase 共max/min兲 Hard shale I/S Kaolinite Soft shale I/S Kaolinite
OD 共max/min兲
共001兲 共100兲 共max/min兲 共max/min兲
1.43 1.38
4.21/0.28 3.68/0.35
3.01/0.37 2.63/0.50
1.39/0.62 1.30/0.70
1.64 1.03
5.82/0.27 1.38/0.84
4.91/0.33 1.18/0.89
1.45/0.38 1.06/0.94
of the hard shale sample. Figure 8 shows the 共001兲 pole figures for three different spots separated by 3 mm. The results confirm an asymmetric maximum of kaolinite with respect to the foliation plane. In the soft shale, I/S is more strongly aligned than in the hard shale, with 共001兲 poles perpendicular to the foliation plane and a maximum of 4.9 MRD 共Figure 6b兲. The volume fraction of randomly oriented crystallites is similar 共0.33 MRD兲. Although I/S is more textured than in hard shale, kaolinite is nearly randomly oriented with a 共001兲 maximum of approximately only 1.18 MRD 共Figure 7b兲. This result can be confirmed qualitatively by inspecting the map plot in Figure 5, where the variation in intensity along the 共001兲 kaolinite reflection is minimal compared with hard shale. Just to confirm that this unexpected feature is representative of the sample and not a local aberration, several spots were investigated. Figure 9 compares experimental 共001兲 kaolinite lines on several spots for both soft and hard shale, indicating a consistent pattern.
DISCUSSION Hard X-ray synchrotron radiation was used to investigate the preferred orientation of two different shale samples collected at different burial depths. Two-dimensional diffraction images were analyzed with the Rietveld method to provide a quantitative texture characterization from full spectra. Both samples show strong alignment of I/S with 共001兲 planes parallel to the foliation plane. Maximum 共001兲 pole densities are similar to those reported for Zechstein shales 共Sintubin, 1994a; 4–6 MRD兲, Gulf Coast mudstones 共Ho et al., 1995; 2–7 MRD兲, and mudstones from Pennsylvania 共Ho et al., 1995; 2–5 MRD兲 but considerably weaker than muscovite in metamorphic slates 共Oertel and Phakey, 1972; 16 MRD.; Sintubin, 1994b; 5–18 MRD兲. All these previous studies used single peak intensity measurements, which can be unreliable for interlayer clays with diffuse peaks and background uncertainties. Our method relied on full spectra deconvolution. If the ODs and the elastic constants of single crystals for each phase are known, averaging procedures can be applied to evaluate the elastic properties of the polycrystal. Unfortunately, elastic properties of clay minerals are poorly known 共Katahara, 1996兲, and for this study we have used experimental elastic stiffness moduli of muscovite measured with Brillouin scattering 共Vaughan and Guggenheim, 1986兲 and kaolinite elastic constants derived from first-principles studies 共Sato et al., 2005兲. Muscovite is treated as monoclinic, and kaolinite is treated as triclinic. Results for aggregate elastic constants weighted by the OD are shown in Table 3. The Voigt and Reuss values provide upper and lower bounds, assuming uniform strain and uniform stress, respectively, throughout the textured aggregate. A geometric mean averaging is intermediate 共Matthies and Humbert, 1993兲. From aggregate elastic constants obtained by the geometric mean, we calculated phase velocity surfaces 共V p, Vsh, and Vsv兲. Figure 10 gives the 1D profiles of V p and ⌬Vs 共Vsh − Vsv兲 from a position perpendicular to the foliation plane 共0°兲 to the position parallel to the foliation plane 共90°兲. Anisotropies 共in percent兲 for the clay mineral components 共A = 200共Vmax − Vmin兲/共Vmax + Vmin兲兲 are in the range of 10%. From elastic coefficients, we can also calculate Thomsen parameters that are used in exploration seismology 共Thomsen, 1986兲. For the two shales analyzed in this study, anisotropy is moderate 共Table 3兲. This is because by using muscovite elastic moduli for I/S, we assume that any interlayer water is pore water. The elastic anisotropy calculated
Preferred orientation in shales
a)
001
100
3.01
2.26
z y
1.88 1.5 1.12
Pole density (MRD)
2.63
D37 Figure 6. 共100兲 and 共001兲 I/S pole figures recalculated from the OD: 共a兲 hard shale and 共b兲 soft shale. An equal area projection. The pole density scale is in multiples of random distribution 共MRD兲.
0.75 x
b)
0.37 001
100
4.91
3.6 2.95 2.29 1.64
Pole density (MRD)
4.26
0.98 0.33
a)
100
Figure 7. Kaolinite pole figures 共100兲 and 共001兲, recalculated from the OD: 共a兲 hard shale and 共b兲 soft shale. An equal area projection. The pole density is scale in MRD.
001
z y
2.6
2 1.7 x
b)
100
1.4 001
1.1 0.8 0.5
Pole density (MRD)
2.3
D38 Figure 8. 共a兲 I/S and 共b兲 kaolinite 共001兲 pole figures recalculated from the OD for three different spots of the hard shale sample. An equal area projection. The pole density is in MRD.
Lonardelli et al.
a)
Spot 5
Spot 8
Spot 11 I/S z
y
1 cm
x 2.32-0.58 (MRD)
2.49-0.54 (MRD)
Spot 5
b)
3.01-0.37 (MRD)
Spot 8
5 8 11
Spot 11
y
x
Kaolinite
2.62-0.48 (MRD)
Figure 9. The 共001兲 kaolinite peak for hard 共a兲 and soft shale 共b兲. The image shows intensity variation in 36 spectra 共from 0° to 360°兲 from the 2D synchrotron image at = 30° 共tilting angle兲 for each spot analyzed. Notice the different intensity scales for 共a兲 and 共b兲.
a)
2.53-0.50 (MRD)
0º
90º
22
24
2.60-0.50 (MRD)
180º
270º
360º
Spot 5
Spot 8
Spot 11
26
28
30
24
25
Intensity (count1/2)
b)
Spot 5
Spot 8
Spot 11
21
22
23
Intensity (count1/2)
Preferred orientation in shales with this technique comes from the texture of the nonporous material, and the effect of low-aspect ratio pores 共interlayer water兲 aligned with the bedding is neglected. For bulk rock seismic properties, not only does crystal orientation need to be considered but also other contributions to anisotropy in shales, such as oriented fractures, degree of porosity, and water content 共O’Connell and Budiansky, 1976; Crampin, 1981; Hornby et al., 1994; Schoenberg and Sayers, 1995兲. The difference between texture-derived wave-velocity contributions and experimental velocity measurements can be interpreted in terms of direct porosity effects, such as low-aspect ratio pores, preferred orientation of low-aspect ratio pores, and pore interactions 共Ullemeyer et al., 2006兲. Unfortunately, in the case of these samples, no velocity measurements are available. The role of porosity in the development of intrinsic anisotropy described by Wang 共2002兲 共more compacted shales equal a higher de-
D39
gree of anisotropy兲 is only partially confirmed. The I/S in soft shale 共less compacted with 26% of porosity兲 is more strongly aligned than I/S in hard shale 共more compacted with only 6% of porosity兲. However, the rule applies to kaolinite, whereas soft shale the texture is almost random.
CONCLUSIONS
Our study demonstrated the feasibility of extracting orientation distributions of individual mineral components in shales. With the advances in X-ray diffraction methods and Rietveld texture analysis, we are now able to obtain quantitative texture information with a high degree of resolution for complicated multiphase materials. Quantification of the texture-derived contribution to anisotropy of clay minerals in shales opens the possibility to determine a lower limit of anisotropy caused by crystallite orientation and thus advance our understanding of the importance of pores by comparing predicted and measured seisTable 3. Elastic stiffness of I/S and kaolinite aggregates using the geometric mean (Geo), Voigt average (upper limit), Reuss average (lower limit), and mic velocities. With such information, comprecalculated Thomsen anisotropy parameters. The reference single-crystal values hensive models for seismic wave anisotropy in assume monoclinic symmetry for muscovite (Vaughan and Guggenheim, 1986) clay-rich sedimentary rocks can be developed. and triclinic symmetry for kaolinite (Sato et al., 2005). Only the most significant elastic constants are shown.
ACKNOWLEDGMENTS Elastic constants 共GPa兲 Sample/phase Averages Hard shale I/S
Geo Voigt Reuss Geo Voigt Reuss
Kaolinite
Compressional velocity (km/s)
6.2
C13
C66
33.0 41.6 26.9 25.6 41.1 16.7
36.2 37.7 29.3 24.1 34.8 12.9
35.7 44.6 28.7 26.3 41.3 16.9
Geo Voigt Reuss
114.3 99.8 133.9 118.6 91.8 81.9
30.7 39.1 25.1
b)
6 5.8 Illite/smect_hard shale Kaolinite_hard shale Illite/smect_soft shale
5.6 5.4 5.2
0.043 0.036 0.035 0.047 0.038 0.032
␦
␥
0.041 0.005 0.036 0.008 0.033 0.007 0.014 0.039 0.002 0.041 0.006 −0.025
36.9 0.073 0.101 −0.025 45.9 0.065 0.087 −0.026 29.6 0.060 0.090 −0.031
0.35 Illite/smect_hard shale Kaolinite_hard shale Illite/smect_soft shale
0.25 0.2 0.15 0.1 0.05 0
5 4.8
35.9 37.3 29.1
0.3
∆S velocity (km/s)
6.4
111.4 102.7 130.7 121.9 89.5 83.7 79.3 72.5 121.1 112.5 48.1 45.2
C44
0
The project was supported by DOE-BES 共DEFG02-05ER15637兲 and NSF 共EAR-0337006兲. We acknowledge access to the facilities of Beamline 11ID-C at APS ANL. Luca Duranti, Russ Ewy, and Kurt Nihei at Chevron San Ramon kindly supplied the samples. Discussions with them and Seiji Nakagawa 共LBNL兲 are greatly appreciated. Comments by two reviewers and the editor were very helpful for improving the manuscript.
REFERENCES
Soft shale I/S
a)
C33
C11
Thomsen parameters
10
20
30
40
50
60
70
80
90
Angle from bedding-normal sym. axis (º)
–0.05
0
10
20
30
40
50
60
70
80
90
Angle from bedding-normal sym. axis (º)
Figure 10. Calculated seismic velocities for I/S 共hard and soft shale兲 and kaolinite 共hard shale兲. 共a兲 P-waves, 共b兲 ⌬S-waves versus the angle to the bedding plane.
Bunge, H.-J., 1985, Physical properties of polycrystals, in H. R. Wenk, ed., Preferred orientation in deformed metals and rocks: An introduction to modern texture analysis: Academic Press, 507–525. Comodi, P., and P. F. Zanazzi, 1995, High pressure structural study of muscovite: Physics and Chemistry of Minerals, 22, 170–177. Crampin, S., 1981, A review of wave motion in anisotropic and cracked elastic media: Wave Motion, 3, 242–391. Hammersley, A. P., 1998, Fit2D: V99.129 reference manual version 3.1: Internal Report ESRF-98-HA01. Heidelbach, F., C. Riekel, and H.-R. Wenk, 1999, Quantitative texture analysis of small domains with synchrotron X-rays: Journal of Applied Crystallography, 32, 841–849. Ho, N. C., D. R. Peacor, and B. A. Van der Pluijm, 1995, Reorientation mechanisms of phyllosilicates in the mudstone-to-slate transition at Lehigh Gap, Pennsylvania: Journal of Structural Geology, 17, 345–356. ——–, 1999, Preferred orientation of phyllosilicates in Gulf Coast mudstones and relation to the smectite-illite transition: Clays and Clay Minerals, 47, 485– 504. Hornby, B. E., L. M. Schwartz, and J. A. Hudson, 1994, Anisotropic effective-medium modelling of the elastic properties of shales: Geophysics, 59, 1570–1583. Kaarsberg, E. A., 1959, Introductory studies of natural
D40
Lonardelli et al.
and artificial argillaceous aggregates by sound-propagation and X-ray diffraction method: Journal of Geology, 67, 447–472. Katahara, K. W., 1996, Clay mineral elastic properties: 66th Annual International Meeting, SEG, Expanded Abstracts, 1691–1694. Lonardelli, I., H.-R. Wenk, L. Lutterotti, and M. Goodwin, 2005, Texture analysis from synchrotron diffraction images with the Rietveld method: Dinosaur tendon and salmon scale: Journal of Synchrotron Radiation, 12, 354–360. Lutterotti, L., S. Matthies, H.-R. Wenk, A. S. Schultz, and J. W. Richardson Jr., 1997, Combined texture and structure analysis of deformed limestone from time-of-flight diffraction spectra: Journal of Applied Physics, 81, 594–600. Matthies, S., and M. Humbert, 1993, The realization of the concept of a geometric mean for calculating physical constants of polycrystalline materials: Physica Status Solidi, B177, K47–K50. Matthies, S., and G. W. Vinel, 1982, On the reproduction of the orientation distribution function of textured samples from reduced pole figures using the concept of conditional ghost correction: Physica Status Solidi, B112, K111–K114. O’Connell, R., and B. Budiansky, 1976, Seismic velocities in dry and saturated cracked solids: Journal of Geophysical Research, 79, 5412–5426. Oertel, G., 1983, The relationship of strain and preferred orientation of phyllosilicate grains in rocks — Review: Tectonophysics, 100, 413–447. Oertel, G., and P. P. Phakey, 1972, The texture of a slate from Nantille, Caernarvon, North Wales: Texture, 1, 1–8. Popa, N. C., 1998, The hkl dependence of diffraction-line broadening caused by strain and size for all Laue groups in Rietveld refinement: Journal of Applied Crystallography, 31, 176–180. Sato, H., K. Ono, C. T. Johnston, and A. Yamagishi, 2005, First-principles studies on elastic constants of a 1:1 layered kaolinite mineral: American Mineralogist, 90, 1824–1826. Sayers, C. M., 1994, The elastic anisotropy of shales: Journal of Geophysical Research, 99, 767–774. ——–, 2005, Seismic anisotropy of shales: Geophysical Prospecting, 53,
667–676. Schoenberg, M., and C. M. Sayers, 1995, Seismic anisotropy of fractured rock: Geophysics, 60, 204–211. Schoenberg, M., F. Muir, and C. M. Sayers, 1996, Introducing ANNIE: A simple three-parameter anisotropic velocity model for shales: Journal of Seismic Exploration, 5, 35–49. Sintubin, M., 1994a, Clay fabrics in relation to the burial history of shales: Sedimentology, 41, 1161–1169. ——–, 1994b, Phyllosilicate preferred orientation in relation to strain path determination in the lower Paleozoic Stavelot-Venn Massif 共Ardennes, Belgium兲: Tectonophysics, 237, 215–231. Stixrude, L., and D. R. Peacor, 2002, First-principles study of illite-smectite and implications for clay mineral systems: Nature, 420, 165–168. Swan, G., J. Cook, S. Bruce, and R. Meehan, 1989, Strain rate effects in Kimmeridge Bay shale: International Journal of Rock Mechanics and Mining Sciences, 26, 135–149. Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, 1954–1966. Ullemeyer, K., S. Siegesmund, P. N. J. Rasolofosaon, and J. H. Behrmann, 2006, Experimental and texture-derived P-wave anisotropy of principal rocks from the TRANSALP traverse: An aid for the interpretation of seismic field data: Tectonophysics, 414, 97–116. Vaughan, M. T., and S. Guggenheim, 1986, Elasticity of muscovite and its relationship to crystal structure: Journal of Geophysical Research, 91, 4657–4664. Wang, Z., 2002, Seismic anisotropy in sedimentary rocks: Part 2 — Laboratory data: Geophysics, 67, 1423–1440. Wenk, H.-R., I. Lonardelli, H. Franz, K. Nihei, and S. Nakagawa, 2007, Preferred orientation and elastic anisotropy of illite-rich shale: Geophysics, this issue. Wenk, H.-R., S. Matthies, J. Donovan, and D. Chateigner, 1998, BEARTEX, a Windows-based program system for quantitative texture analysis: Journal of Applied Crystallography, 31, 262–269. Young, R. A., and A. W. Hewat, 1988, Verification of the triclinic crystal structure of kaolinite: Clays and Clay Minerals, 36, 225–232.
