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Anisotropy of experimentally compressed kaolinite-illite-quartz mixtures

Marco Voltolini1, Hans-Rudolf Wenk1, Nazmul Haque Mondol2, Knut Bjørlykke2, andJens Jahren2

ABSTRACT

The anisotropy of physical properties is a well-known charac-teristic of many clay-bearing rocks. This anisotropy has impor-tant implications for elastic properties of rocks and must be con-sidered in seismic prospecting. Preferred orientation of clay min-erals is an important factor causing anisotropy in clay-bearingrocks such as shales and mudstones that are the main cap rocks ofoil reservoirs. The preferred orientation of clays depends mostlyon the amount of clays and the degree of compaction. To studythe effect of these parameters, we prepared several samples com-pressing �at two effective vertical stresses� a mixture of clays �il-lite and kaolinite� and quartz �silt� with different clay/quartz ra-tios. The preferred orientation of the phases was quantified withRietveld analysis on synchrotron hard X-rays images. Pole fig-ures for kaolinite and illite display a preferred orientation of clay

platelets perpendicular to the compaction direction, increasing instrength with clay content and compaction pressure, althoughquartz particles have a random orientation distribution. Aggre-gate elastic properties can be estimated by averaging the single-crystal properties over the orientation distribution obtained fromthe diffraction data analysis. Calculated P-wave velocity aniso-tropy ranges from 0% �pure quartz sample� to 44% �pure claysample, highly compacted�, but calculated velocities are muchhigher than measured velocities. This is attributed to uncertain-ties about single-crystal elastic properties and oriented mi-cropores and limited grain contacts that are not accounted for inthe model. In this work, we present an effective method to obtainquantitative data helping to evaluate the role of clay percentageand compaction pressure on the anisotropy of elastic propertiesof clay-bearing rocks.

INTRODUCTION

Clay-bearing rocks such as shales and mudstones are very com-mon. They are important because of their association with oil andnatural gas reservoirs �e.g., Awaja and Bhargava, 2006�, and becauseof their role in managing aquifers in dangerous fluids disposal �e.g.,Chadwick et al., 2004�. Their low permeability makes these materi-als excellent natural barriers to fluid flow �Bonin, 1998; Mallants etal., 2001; Bossart et al., 2002�. The understanding and characteriza-tion of properties in clay-bearing rocks is a key issue in both scientif-ic and applied fields. Several authors have studied the relation be-tween effective overburden, stress, porosity, velocity, and rock me-chanical properties �Luo et al. 1998, Pouya et al., 1998; Yang andAplin, 1998; Nygård et al., 2004; Mondol et al., 2007�. Shales candisplay strongly anisotropic properties and this anisotropy is greatlyinfluenced by the alignment of platelet-shaped clay minerals. Duringdeposition, compaction, and diagenesis, clay minerals become ori-

ented perpendicular to the maximum stress direction �Kawamuraand Ogawab, 2004�. Mineralogical changes during chemical di-agenesis also cause significant changes in rock properties aboveabout 70–80 °C related to recrystallization of quartz, the smectite-to-illite transformation, and redistribution of detrital quartz.Anotherchemical process in shales affecting rock physical properties is dis-solution of kaolinite and K-feldspar and precipitation of illite at tem-peratures above 130 °C �Bjørlykke, 1998 and 1999; Kim et al.,1999�. Anisotropic properties of these rocks are linked in part to thepreferred orientation �texture� of clay minerals. Thus a reliablequantitative analysis of the texture is fundamental in understandinganisotropic properties such as seismic velocities.

The anisotropic properties in mudstones and shales becomeevident in seismic prospecting for oil reservoirs �Banik, 1984; Ver-nik and Nur, 1992; Vernik and Liu, 1997�. For this reason, the influ-ence of clays on seismic anisotropy has been studied extensively �Lo

Manuscript received by the Editor 15 January 2008; revised manuscript received 5 June 2008.1University of California, Department Earth and Planetary Science, Berkeley, California, U.S.A. E-mail: voltolini@berkeley.edu; wenk@berkeley.edu.2University of Oslo, Department of Geosciences, Oslo, Norway. E-mail: nazmul.haque@geo.uio.no; knut.bjorlykke@geo.uio.no; jens.jahren@geo.uio.no.

© 2009 Society of Exploration Geophysicists.All rights reserved.

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et al., 1986; Hornby, 1994; Sayers, 1994, 2004, and 2005; Johansenet al., 2004; Vanorio et al., 2003; Bobko and Ulm, 2008�.

Despite the importance of a quantitative analysis of preferred ori-entation in argillaceous rocks, only limited information is available.Poor crystallinity of clay minerals, low scattering power, structuraldisorder, and coexistence of several mineral phases limit the applica-tion of conventional techniques such as X-ray pole-figure goniome-try or electron backscatter diffraction �EBSD�. Nevertheless someresults have been obtained �Sintubin, 1984; Van der Pluijm et al.,1994; Ho et al., 1999; Solum et al., 2003; Aplin et al., 2006�.

In recent years, a new technique for texture analysis has been de-veloped and applied successfully. Synchrotron radiation facilitiesprovide highly focused X-ray beams with high brilliance and energy,permitting analysis of small samples with low scattering power. Theavailability of two-dimensional position-sensitive detectors, such asimage plates or CCD cameras, permits the simultaneous collectionof a 2D diffraction image. The first texture analysis taking advantageof synchrotron radiation was applied to metals �Bäckstrøm et al.,1996; Heidelbach et al., 1999�. A decisive step has been the applica-tion of the Rietveld method �Rietveld, 1969; Young, 1993� with ad-vanced texture-analysis algorithms such as WIMV �Williams-Im-hof-Matthies-Vinel from Matthies and Vinel, 1982� to deconvolutecontinuous diffraction spectra, rather than relying on peak intensi-ties. Availability of the MAUD software �Material Analysis UsingDiffraction, Lutterotti et al., 1999� has made texture analysis fromdiffraction images a comprehensive analytical procedure for a widerange of materials �Ischia et al., 2005; Lonardelli et al., 2005; Wenket al., 2006�. This technique was applied recently to clay samples aswell �Lonardelli et al., 2007; Wenk et al., 2007, Wenk et al., 2008a;Wenk et al., 2008b�.

In the present study, we analyze preferred orientation of kaoliniteand illite in experimentally produced samples with synchrotron hardX-ray diffraction to investigate the influence of clay amounts andcompaction stresses. Compared to the natural samples investigatedpreviously, the new experimental samples have a less complicatedmineralogy and well-defined conditions to identify modeling factorsthat contribute to anisotropy.

SAMPLE PREPARATION AND MEASUREMENTS

Samples analyzed in the present study were prepared by combin-ing clay minerals and quartz. The clay is a mixture of illite, mostlyweathered mica �25% by weight� and kaolinite �75%�, ground to less

than 10 �m. Quartz �silt� particles are less than 40 �m in grain size.The powdered clays were purchased from Potterycraft Ltd., UK.Samples were obtained by mixing different amounts of clay and silt:100%, 75%, 50%, and 25% of clay by weight. We prepared a puresilt sample as well. We mixed the powder with natural salt brine �sa-linity 34,000 ppm� to mimic burial conditions, forming a paste.

Compaction experiments were carried out at the Norwegian Geo-technical Institute �NGI� at the University of Oslo. The brine-satu-rated samples were placed into a high-stress oedometer cell, where auniaxial effective stress �no lateral strain allowed� of 5 MPa and50 MPa was applied on cylindrical samples. In addition, wave ve-locities parallel to the compression direction were measured �Mon-dol et al., 2007�. Two SEM images of the prepared samples �75%clay content, compressed at 5 MPa and 50 MPa� appear in Figure 1.

To obtain suitable samples for the synchrotron measurements,sample fragments �about 2�2�2 cm in extent� were embedded inepoxy resin to obtain an epoxy cylinder �2.5 cm diameter� includingthe clay sample. From these cylinders, 2–3-mm-thick slabs wereprepared by careful cutting and polishing. Kerosene was used as acooling agent in the cutting and polishing operations. These proce-dures were necessary to obtain cohesive samples and to avoid anyclay-water interaction. The pure silt sample compressed at 5 MPawas not coherent enough to prepare a proper sample for analysis.

The diffraction measurements were carried out at the BESSRC11-ID-C beamline at the Advanced Photon Source �APS� of Ar-gonne National Laboratory. The sample slab was mounted on a goni-ometer head, facing the X-ray beam. Wenk et al. �2008b� provides adetailed view of the instrument setup. We used a MAR345 imageplate detector �with a sample-detector distance of about 2 m�. Thewavelength was 0.10738 Å �high energy is advantageous to ensuremaximum sample penetration and minimum absorption�. Beam sizewas 0.5 mm�0.5 mm. Each image is composed of seven measure-ments of 50 s each at different spots, by translating the sample hori-zontally over 2 mm. This improves counting and grain statistics byaveraging over a larger sample volume and keeping the beam sizesmall and thus resolution high. Each sample in our research was tilt-ed around the horizontal axis to collect seven images at different go-niometer tilt angles, from � 45° to 45°, in 15° increments. One im-age covers only one great circle on the pole figure. Coverage is im-proved with images at different tilts �Figure 2�. The coverage shouldbe chosen so that main texture features are represented �such as themaximum of poles to lattice planes �001� for kaolinite�. We chose anelliptically shaped pole figure to illustrate that this is not covered bydata and thus is likely an artifact for the sample produced in axial

compression. Two diffraction images in Figure 3show the variation of intensity with azimuthalong Debye rings that is an expression of texture.

The image datafiles were processed with Fit2Dsoftware �Hammersley, 1998� to refine sample-detector distance, beam center, and detector non-orthogonality. Then images were integrated over10° sectors to obtain 36 diffraction spectra �need-ed to study the azimuthal dependence of peak in-tensities� as shown in Figure 4. Figure 5 �bottom�shows a stack of 36 spectra. This 2D plot high-lights the variation of intensities with azimuth.252 spectra were analyzed simultaneously on a d-spacing range of 1.5–14 Å for each analysis. Thisrange contains a sufficient amount of informationfor the analysis: large d-spacings need to be con-

b)a)

Figure 1. SEM backscattered images of samples containing 75% clay compacted at �a�5 MPa and �b� 50 MPa. Compression axis is indicated by arrows. In �a�, a bigger particleof detrital illite is highlighted �lower arrow�. In �b�, the arrow points toward a quartzgrain.

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sidered with clays and many diffraction peaks are overlapped forlow d-spacings.

Then we used MAUD software for the Rietveld refinement. A Ri-etveld refinement of powder X-ray diffraction data minimizes thedifference between experimental and calculated diffraction data, ac-counting for experimental parameters, sample microstructure, crys-tal structure, and preferred orientation. Input files were created fol-lowing the procedure presented by S. Merkel �2006�. The first step ofthe Rietveld refinement is to determine instrumental parameters byusing a standard material �annealed CeO2 was used�.

We analyzed the samples, taking into account sample-dependentparameters. Sample contribution to peak shapes were calculated us-ing the Popa model �Popa, 1998�. We chose this model to account foreffects of particle size and microstrain because of its ability to takeinto account direction-dependent microstructural effects. TheEWIMV algorithm �derived from WIMV, Matthies and Vinel, 1982�is a tomographic algorithm used in texture analysis and implement-ed in MAUD. It proved to be more efficient than other methods, suchas spherical harmonics, that have limitations especially for low-symmetry materials. Texture analysis using 10° grid cells for the ori-

entation distribution �OD� was conducted without imposing samplesymmetry. Based on intensity variations of all diffraction peaks withazimuth and sample tilt, it is possible to reconstruct OD of the crys-tallites and get quantitative information about preferred orientationpatterns of individual phases �e.g., Matthies et al. 1997�.

In the Rietveld analysis, we used crystal structures of illite fromGualtieri �2000�, kaolinite from Bish and Von Dreele �1989�, andquartz from Kihara �1990�. Nevertheless, a refinement of structure atthe end of the analysis was necessary to obtain the best fit possible.The obtained fits have an average weighted pattern residual �Rwp� of7.1%, which is satisfactory. Figure 4 shows experimental data �dots�and Rietveld fit �line� for a single spectrum. Deviations also areshown below. Figure 5 compares experimental data �bottom� withthe Rietveld fit �top� for a stack of spectra, illustrating that intensityvariations resulting from texture are well reproduced. The kaolinitein the sample was well ordered, and no complex models of disor-dered clay structure were necessary. Refined illite-and-kaolinite lat-tice parameters are listed in Table 1.

EXPERIMENTAL RESULTS

Preferred orientation

As expected, samples with high clay content and higher compac-tion pressure show stronger texture. This is already evident by visualinspection of the raw diffraction images in Figure 3, where two pure-clay samples are shown. The main basal reflection of the illite andkaolinite is marked by arrows to show the strong intensity changewith azimuth that indicates a strong texture, more pronounced in thesample with higher compaction �Figure 3b�.

Basal reflections of the two clay minerals are the most importantbecause they are representative of the large flat surfaces of clayplatelets that display a preferred orientation perpendicular to the ap-plied stress.

We obtained pole figures by exporting orientation distributionsfrom MAUD to Beartex software �Wenk et al., 1998�, where we ap-plied a smoothing filter �10°� before calculating and plotting the polefigures. The pole figures for �001� lattice planes of kaolinite and illitefor all samples are shown in Figure 6. Pole figures are normalizedand express pole densities in multiples of random distribution�MRD�. Even though no sample symmetry has been imposed in the

refinement, the pole figures display more or lessaxial symmetry, consistent with the compressionexperiment. Deviations from axial symmetry insome samples are attributed to incomplete cover-age.As expected, the texture strength is higher forsamples with higher clay content and compactionpressure. Figure 2 illustrates pole-figure coveragefor kaolinite in the sample with 75% clays com-pressed at 50 MPa. In this case, slight deviationsfrom the axial symmetry of the pole figure couldbe from partial pole-figure coverage.

Before advancing to property calculations, weimposed axial symmetry, using the programCSEC �included in Beartex�. Pole figures ob-tained after this procedure are shown in Figure 7.We imposed axial symmetry to be consistent withthe symmetry of the compaction experiment.These pole figures are similar to the ones withoutimposed symmetry. Some quantitative texture

Figure 2. Pole-figure coverage for kaolinite �001� in the sample with75% clay compressed at 50 MPa. Each square corresponds to a sin-gle diffraction profile used in the Rietveld refinement.

a) b)

Figure 3. Diffraction images, obtained with a MAR345 image plate detector, of the pureclay samples compressed at 5 MPa and 50 MPa. The texture of clay phases is evident inazimuthal intensity variations along Debye rings. Arrows highlight two clay basal peaksthat show most clearly the effect of texture in a diffraction image.

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Table 1. Kaolinite and illite lattice parameters used in the refinement (Bish and Von Dreele, 1989; Gualtieri, 2000).

a �Å� b �Å� c �Å� � �°� � �°� � �°�

Kaolinite Bish and Van Dreele 5.1554 8.9448 7.4048 91.700 104.862 89.822

Our experiment 5.153�1� 8.952�2� 7.408�1� 91.968�5� 104.787�4� 89.641�4�

Illite Gualtieri 5.2226 9.0183 20.1430 90 95.67 90

Our experiment 5.207�1� 8.996�2� 20.064�2� 90 94.68�2� 90

Figure 4. Average spectrum of the pure clay samplecompacted at 50 MPa �dots� and the Rietveld fit�line�. Underneath are positions of diffraction linesand deviations between experimental and calculat-ed spectra.

Figure 5. 2D plot of stack of 36 spectra �data fromone image at 0° tilt� for the pure clay sample com-pacted at 50 MPa. The agreement of observed �bot-tom� and calculated �top� data is excellent.

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data extracted after symmetrization are shown in Table 2. Texturepeak widths have been obtained by fitting a cross section of the �001�peak with a Pseudo-Voigt �PV� function, a linear combination ofGaussian �G� and Lorentzian �L� peak functions, with the formula

PV�x� � �L�x,� � � �1 � ��G�x,� � , �1�

in which � is the mixing parameter, � is the full peak width at halfmaximum, and x is the distance from the peak center �in degrees�.Fits were obtained with residual R2 values be-tween 0.98 and 0.99. A simple Gaussian distribu-tion did not provide a satisfactory fit, especiallyfor samples with stronger textures. It is interest-ing to point out that peak gaussianity decreaseswith increasing texture strength. Peak function is16% Gaussian in the sample with higher texturestrength and 81% Gaussian in the sample withlower texture strength. This issue could be impor-tant in the description of preferred orientation ofclay minerals in modeling anisotropic propertiesof clay-bearing rocks. Examples of illite and ka-olinite pole-figure sections are shown in Figure 8.The difference in peak intensities and shapecaused by the different composition is evident.

Figure 9 shows the �100� and �001� pole figuresof two samples, containing 75% clay and 25% siltat 5 MPa and 50 MPa. This figure illustrates that�100� poles of illite and kaolinite are on a girdleperpendicular to the compression direction. Italso documents that quartz pole figures are nearlyrandom. For a better comparison, the pole densityscale is the same for all three mineral species.

Data presented in Table 2 show that texture isstrongest for pure clay samples and for highercompaction pressure. Pure clay at 50 MPa showsstrong maxima for illite and kaolinite, 7.50 MRDand 8.05 MRD, respectively. The maxima arealso quite sharp: full widths at half maximum are32.4° and 39.8°. Texture decreases as clay contentdecreases. As expected, the effective stress ap-plied also has an important role in the develop-ment of texture in our samples. Stress is more ef-fective for samples with high clay content. Illiteand kaolinite show a similar but distinctly differ-ent response to the applied stress, with kaolinitealways somewhat weaker in texture than illite atlow compaction pressure. A possible explanationcould be the difference in size and shape of theminerals. Figure 1a depicts a SEM image of the5 MPa sample containing 75% clay. With highercompression stress �50 MPa�, clay platelets showa stronger preferred orientation �Figure 1b�. Theeffect of quartz particles is also very clear: clayparticles tend to form a layer around larger quartzgrains, with clay platelets parallel to quartz sur-faces. This affects the preferred orientation effectbecause of compaction stress. This effect is visi-ble in the quartz grain shown in Figure 1b. Clayparticles size is not homogeneous: in the SEM

images, particle size ranges from a few hundred nanometers to morethan 10 �m �e.g., the grain highlighted by an arrow in Figure 1a�.

Values of crystallite size obtained by Rietveld refinement usingthe Popa model �which permits consideration of the effect of crystal-lite-size anisotropy�, provided meaningful results for kaolinite: 34-nm size along the c-axis and 71 nm along the b-axis. Values for il-lite are not consistent �140 nm and 115 nm, respectively, for the cand b axes�. The Popa model is not very realistic for sheet silicates

Figure 6. �001� Pole figures of illite and kaolinite for eight samples. Intensity scale is thesame for all pole figures to show differences among the phases and samples. Equal areaprojections. Pole figures are shown in linear contour scale with contour level in multiplesof a random distribution �MRD�.

Figure 7. Pole figures �001� for illite and kaolinite after imposing axial symmetry. The in-tensity scale is the same as in Figure 6.

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with stacking disorder �i.e., translation and rota-tion shifts of the basic layers that cause anisotrop-ic peak broadening in the X-ray powder diffrac-tion profiles� and is used here mainly as a fittingparameter. Stacking disorder is common in clayminerals as documented by TEM investigations�e.g., Bauluz et al., 2002; Kogure and Inoue,2005� or X-ray powder diffraction �Artioli, 1995;Ufer et al. 2004�.

Anisotropy of physical properties

The contribution of individual mineral orienta-tion to bulk anisotropic elastic properties can beestimated by averaging single-crystal elasticproperties over the OD �Bunge, 1985�. Elasticproperties of clay single crystals are difficult tomeasure �Katahara, 1996�, because of the smallcrystallite size. The only direct measurement todate of elastic properties on a single crystal wascarried out on a dickite sample �Prasad et al.,2002� using atomic force acoustic microscopy.An indirect measurement of clay elastic parame-ters is presented by Wang et al. �2001�, wheresome elastic parameters are extrapolated frommeasurement on clay specimens mixed with ep-oxy resin. More recently, elastic properties wereobtained by first-principles calculations �e.g.,Sato et al., 2005�.

We used values obtained from first principles�Sato et al., 2005� for kaolinite, and for illite, val-ues obtained with Brillouin scattering for musco-vite �Vaughan and Guggenheim, 1986�. Forquartz, we used elastic properties obtained byHeyliger et al. �2002� from resonance-ultrasoundspectroscopy measurements.

We averaged single-crystal properties over theOD with the geometric-mean averaging method�Mainprice and Humbert, 1993; Matthies andHumbert, 1993� to obtain polycrystal tensors.

Table 2. Quantitative texture data for illite, kaolinite and quartz.

Illite�001�min

�MRD�

�001�max

�MRD��001� peakFWHM �°�

Kaolinite�001�min

�MRD�

�001�max

�MRD��001� peakFWHM �°�

Quartz�001�min

�MRD�

�001�max

�MRD�

100% clay 5 MPa 0.49 5.26 40.3 0.46 4.11 51.7 — —

50 MPa 0.37 7.50 32.4 0.19 8.05 39.8 — —

75% clay 5 MPa 0.58 3.00 57.2 0.56 2.35 69.4 0.83 1.05

50 MPa 0.51 3.90 49.4 0.45 3.67 56.2 0.84 1.04

50% clay 5 MPa 0.85 1.71 63.2 0.72 1.68 77.0 0.89 1.03

50 MPa 0.61 2.98 54.0 0.54 2.99 57.7 0.88 1.04

25% clay 5 MPa 0.77 2.08 60.3 0.81 1.63 77.5 0.86 1.04

50 MPa 0.73 1.67 96.5 0.69 1.87 79.9 0.89 1.08

0% clay 50 MPa — — — — — — 0.83 1.05

Figure 8. Cross section through symmetrized �001� pole figures, as shown in Figure 7, forillite and kaolinite in samples with 100% and 50% clay, compacted at 50 MPa. Symbolsare data points.

Figure 9. Pole figures for �100� and �001� illite, kaolinite, and quartz in samples contain-ing 75% clay and 25% silt, effective stress 5 MPa and 50 MPa. �001� and �100� pole fig-ures have different intensity scales. Pole figures plotted in equal area projection.

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This seems to be more adequate than other averaging methods likeVoigt and Reuss that provide, respectively, upper and lower bounds�with uniform strain and stress, respectively�. In axially symmetricmaterials, the elastic tensor is reduced to five independent stiffnesscoefficients: C11, C13, C33, C44, and C66 �in Voigt notation�, listed inTable 3 �see also the approach in Cholach and Schmitt, 2006�.

A weighted average �considering volume fractions obtained fromX-ray diffraction data� was calculated from polycrystal tensors foreach mineral phase to obtain the polyphase tensor — a tensor aver-aging the properties of the bulk mineral content of the material. Fi-nally from polyphase tensors we calculated velocity surfaces Vp, Vs1,and Vs2 using Christoffel’s equation. Software to calculate polycrys-tal tensors, polyphase tensors, and wave velocities is included inBeartex. Polyphase Vp �Figure 10a� and �Vs variation �Figure 10b�of samples show increasing anisotropy with texture, i.e., an increaseof the preferred orientation with the increase of clay content andstress.

Numerical values in Table 3 also emphasize the influence of claycontent and compaction pressure to preferred orientation and aniso-tropy with near-isotropy in the pure quartz sample �C11�C33 and

C44�C66�. P-wave anisotropies A � 200�Vmax � Vmin�/�Vmax

� Vmin� range from 0.3% to 44%.Ultrasonic Vp- and Vs-wave velocities parallel to the compaction

stress were measured in the laboratory �receiving transducers had afunctional resonant frequency of 500 kHz� and are listed in Table 4,where they are compared with calculated velocities. We need to em-phasize that calculated velocities do not take into account the contri-bution of cracks and pore distribution. They give an intrinsic valuearising from crystal alignment. Ultrasonic velocities are higher inthe 75% clay sample, probably because of a matrix effect �a strongergrain framework�, in accordance with Marion et al. �1992�.

DISCUSSION

In this study, we describe a method to obtain intrinsic elastic prop-erties of clay-silt mixtures at different compaction pressures from aquantitative-orientation distribution analysis of constituent miner-als. With intrinsic elastic properties we imply the contribution of the

Table 3. Elastic properties of studied samples. Stiffness tensor coefficients for polyphase aggregate assuming axial symmetry(geometric mean), in GPa. Maximum and minimum P-wave velocities (km/s), anisotropy (%), and Thomsen parameters � and� .

C11 C13 C33 C44 C66 VP max VP min VP aniso

100% clay 5 MPa 119.7 16.4 66.7 32.7 48.2 6.6 5.0 29.0 0.3967 0.2793

50 MPa 137.7 14.1 56.1 29.2 55.1 7.1 4.5 44.0 0.7257 0.3838

75% clay 5 MPa 107.8 15.6 79.6 37.2 44.6 6.3 5.4 15.1 0.1772 0.1463

50 MPa 113.0 15.6 75.6 35.8 46.3 6.5 5.3 19.9 0.2467 0.1756

50% clay 5 MPa 100.9 13.6 88.9 40.1 43.2 6.1 5.7 6.3 0.0676 0.0595

50 MPa 104.8 12.6 85.0 39.3 44.9 6.2 5.6 10.4 0.1165 0.0799

25% clay 5 MPa 98.3 10.6 94.0 42.3 43.6 6.0 5.9 2.2 0.0231 0.0154

50 MPa 99.3 10.8 92.2 42.0 43.9 6.1 5.8 3.7 0.0384 0.0307

0% clay 50 MPa 97.2 8.0 96.5 44.1 44.6 6.0 6.0 0.3 0.0038 � 0.0016

a) b)

Figure 10. Calculated polyphase �a� VP and �b� �VS velocity plots for all samples studied.

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mineral phases only, without taking into account parameters such asporosity �amount, pore-size distribution and aspect ratio, pore con-tent, etc.�, crystal-size distribution, or particle connectivity. Cholachand Schmitt �2006� employ a similar approach to shales — they ap-ply different theoretical lattice-preferred orientation models, fromanisotropic to fully isotropic, using a Gaussian distribution of thecrystal platelets in the material.

This method works well for metals �e.g., Bunge, 1985� and igne-ous and metamorphic rocks �e.g., Barruol and Kern, 1996� but obvi-ously the situation is more complicated for shales. Figure 11 com-pares calculated and experimental P-wave velocities. Both illustratethe systematic changes with clay content and compaction pressure,but calculated velocities are about twice as high as those measured.Similar discrepancies have been recorded for natural shales �e.g.,Wenk et al., 2008b�.

The simplified model that does not take porosity into accountgives overestimated velocities. However, it still provides a usefulbasis to develop more sophisticated models that can include porosi-ty-related parameters �Han et al., 1986; Klimentos and McCann,1990; Klimentos, 1991; Sams andAndrea, 2001; Bayuk et al., 2007�,fracture distribution �Schoenberg and Sayers, 1995; Sayers, 1998�,and saturation �e.g., Pham et al., 2002�. An additional factor thatmust be considered in comparing modeled velocities to measuredvalues is the wave frequency �Sams et al., 1997; Batzle et al., 2001�.The problem of developing a reliable model for elastic properties ofclay-bearing rocks, taking into account all factors that can contributeto anisotropy, is still a topic of major interest �Sayers, 2005; Bayuk etal., 2007�. Reliable quantitative-orientation distributions of mineralphases are a critical ingredient for these models. Synchrotron hardX-ray diffraction has proven to be an effective method to providethis information.

From values listed in Table 2, we can see that compaction pressureand clay amount are important factors that favor preferred orienta-tion, but a considerable amount of preferred orientation is alreadypresent in the sample with lowest compaction pressure and clay per-centage: 2.08 MRD and 1.63 MRD for illite and kaolinite �001� max-ima, respectively. These values are very close to the sample with thesame clay percentage but compressed at 50 MPa. If we comparethese two samples with the pure-clay samples, we can see that com-paction pressure has little effect in samples with a low clay percent-age, probably because the framework of silt or sand grains carries

most of the stress. The compaction effect is much stronger in sam-ples with higher clay content: at 50 MPa, pole-figure maxima forpure-clay phases are 7.50 MRD and 8.05 MRD for illite and kaolin-ite, respectively, at 50 MPa. However at 5 MPa, maxima valuesdrop to 5.26 MRD and 4.11 MRD. It is noteworthy that for all sam-ples, except for pure clay and 50 MPa, the �001� minimum is close to0.5 MRD or higher, indicating that a large number of crystallites arerandomly oriented. One can see that this is plausible by looking atthe microstructure with many bent and obliquely oriented particles�Figure 1�.

Values for illite and kaolinite differ slightly: illite seems to be lessinfluenced by compaction stress. A possible explanation of this be-havior could be that the illite used in the mixture is detrital mica,which is stiffer elastically than kaolinite and has a larger grain size.For authigenic illite, we would expect the opposite behavior with astronger preferred orientation of kaolinite that was observed in natu-ral shales �Wenk et al. 2008a; Wenk et al., 2008b�.

Polyphase velocities calculated from the data collected with thediffraction experiment display significant anisotropy �Table 3�. Forthe material studied, the Vp anisotropy reaches its maximum in thepure-clay sample compacted at higher pressure, where a 44% aniso-tropy is estimated with a 4.5 km/s velocity parallel to the compres-sion axis and 7.1 km/s perpendicular to it �i.e., in the direction per-pendicular to the layering in a transversely isotropic medium�. In thesame sample, shear-wave-splitting �Vs is 1.23 km/s. Samples witha low clay amount show weak but distinct anisotropic properties�2.2% and 3.7% Vp anisotropy for 5 MPa and 50 MPa effectivestress, respectively�.

The differences between measured �unfortunately only parallel tothe compression axis� and calculated wave velocities are evident inFigure 11 for P-waves. The difference between calculated and mea-sured velocities is large because pores and crack effects are very im-portant for both acoustic velocities and anisotropy �Brace, 1965;Walsh, 1995; Kern, 1978�. Intrinsic values calculated from preferredorientation alone are not realistic for the low-pressure regime, whereporosity and cracks are significant factors. Also our model does nottake into account matrix effects: this can explain the discrepancy il-lustrated in Figure 11. Our calculated values are upper limits foracoustic velocities.

Table 4. P- and S-wave velocities parallel to the compression direction, measured in the high-stress oedometer and calculatedfrom the polyphase tensor obtained from preferred orientation data.

Measured velocities Calculated velocities

VP �km/s� VS �km/s� VP �km/s� VS �km/s�

5 MPa 50 MPa 5 MPa 50 MPa 5 MPa 50 MPa 5 MPa 50 MPa

100% clay 1.849 2.866 0.500 1.132 5.00 4.58 3.50 3.31

75% clay 1.888 3.014 0.541 1.316 5.46 5.32 3.73 3.66

50% clay 1.760 2.851 0.512 1.263 5.78 5.65 3.88 3.84

25% clay 1.694 2.689 0.447 1.117 5.95 5.89 3.99 3.98

0% clay 1.594 2.276 0.365 0.838 — 6.03 — 4.08

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To summarize the anisotropic properties, we plotted Vp max ver-sus Vp min in Figure 12a. This graph shows clearly the increasing an-isotropy of samples from isotropy �100% silt� to very strong aniso-tropy. Figure 12b illustrates a plot of Thomsen parameters �Thom-sen, 1986� with

� � �C11 � C33�/2C33 �2�

and � � ��C13 � C55�2 � �C33 � C55�2�/2C33�C33 � C55� ,

�3�

where Cij are elastic stiffness coefficients. It also shows the strongvariation of elastic properties, with the data points arranged in a lin-ear fashion. Values obtained follow the trend presented for othershales by Wenk et al. �2008a� and Wenk et al. �2008b�. If we considermeasured Thomsen parameters in clay-bearing rocks presented inthe literature �e.g., Wang, 2002; Best et al., 2007�, we see strong vari-ation of and depending on sample composition and microstruc-ture. Shale properties can be very different from sample to sample.Mineralogical composition �and single grain properties� and thesample burial history can affect a number of important factors great-ly, such as microstructure and mineral preferred orientation. Thesefactors contribute to the great variability of anisotropy parametersmeasured in shales. The sample containing 100% clay and subject to50 MPa effective stress can be considered close to an upper limit forclay-bearing rocks: values reported in literature are usually lower,but this is not surprising because natural samples are not generallypure clay and can be less compacted. �In this pa-per, it is clear that the clay percentage plays a keyrole in anisotropy for these materials.� In Figure12b, an average of values from measured samplesof hard shales �from Wang, 2002�, is plotted as acomparison. This average value follows the trendpresented here, but we must keep in mind thatthere is a wide range of Thomsen parameters with ranges from 0.011 to 0.326 and ranges from� 0.170 to 0.242 �Wang, 2002�. As expected,sands and shaly sands are usually less anisotrop-ic.

From preferred orientation, it is possible to cal-culate an estimate of the compaction strain in thesystem. We follow March’s approach for the pre-ferred orientation of originally random-orientedrigid platelets embedded in a viscous matrixwhen the composite is homogeneously strained�March, 1932�. The original March model has

been modified for compaction, i.e., with a volume change �Oerteland Curtis, 1972�. The compaction strain c is related to the maxi-mum platelet pole density, �max, by c � �max

�1/2 � 1. We applied thismodel to our samples and compared experimental and calculatedvalues �Table 5�. To calcu-late the March strain, we used �001� pole

Table 5. Sample vertical displacement and measured and estimated (from kaolinite-preferred orientation) strain values andmeasured porosity.

Sample height �mm� Measured strain March strain Measured porosity �vol %�

0 MPa 5 MPa 50 MPa 5 MPa 50 MPa 5 MPa 50 MPa 5 MPa 50 MPa

100% clay 26.88 11.52 8.83 � 0.57 � 0.67 � 0.51 � 0.65 31.92 11.21

75% clay 26.83 12.71 10.31 � 0.53 � 0.62 � 0.35 � 0.48 34.20 18.83

50% clay 27.42 13.83 11.33 � 0.50 � 0.59 � 0.23 � 0.42 31.10 15.89

25% clay 25.51 15.39 13.18 � 0.40 � 0.48 � 0.22 � 0.27 35.88 25.28

0% clay 20.18 14.56 12.87 � 0.28 � 0.36 — — 37.65 29.47

Figure 11. P-waves velocities calculated at 0° and 90° from the com-pression axis and measured parallel to the compression direction.Samples at 50 MPa are displayed with solid symbols, samples at5 MPa with empty symbols.

a) b)

Figure 12. �a� VP max/VP min plot and �b� Thomsen parameters and plot. The averagevalue of less porous “hard shales” obtained by Wang �2001� is plotted as a comparison.

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densities for kaolinite, dominant clay phase. Calculated and mea-sured values are in good agreement for the pure-clay sample, butwith the introduction of silt in the system we can see that strains areunderestimated. The application of this method seems unreliableinsamples with high silt percentages, probably because the initial as-sumption of homogeneous deformation cannot be applied — the siltdoes not deform homogeneously.

CONCLUSION

Synchrotron X-ray diffraction, combined with the Rietveld meth-od for data analysis, proved to be a very effective analytical tech-nique to obtain quantitative texture information about clay compos-ites, even in samples consisting of several mineral phases. Now thismethod is available for a wide range of applications to determine mi-crostructural characteristics of clay-rich rocks. The preferred orien-tation patterns of experimentally compressed illite, kaolinite, andquartz mixtures show increasing texture strength as a function ofclay content and compaction stress. This can be used to better under-stand the alignment of crystallites in fine-grained sediments.

Based on preferred orientation data, intrinsic acoustic-wave ve-locities have been calculated for the aggregate by averaging. Veloci-ty anisotropies for Vp range from 0% for pure silt to 44% for the pureclay sample compressed at 50 MPa, which is comparable toanisotropies reported in the literature. Samples with high sand andsilt contents are nearly isotropic with respect to P- and S-wave veloc-ity at all stress conditions. However, the calculated velocities arehigher than those measured in the laboratory because our model doesnot take into account factors such as pore geometry and distributionor grain contacts. Nevertheless, quantitative texture information isan intrinsic ingredient for a comprehensive model of anisotropicproperties of clay-bearing rocks.

The experiments illustrate that the degree of anisotropy in mud-stones is a function of the primary composition and compaction andthus relevant for understanding sedimentary facies.

ACKNOWLEDGMENTS

Comments by reviewers and the editor have been valuable in im-proving the manuscript. We acknowledge access to the facilities ofbeamline 11-ID-C atAPSANL and Yang Ren for assistance with theexperiments. The project was supported by the U.S. Department ofEnergy Office of Basic Energy Sciences �DE-FG02-05ER15637�and the National Science Foundation �EAR-0337006�. Compactionexperiments were supported by the Research Council of Norway�NFR� under the PETROMAKS �Programme for the Optimal Man-agement of Petroleum Resources� project: Quantifying the Effectsof Sediment Deposition, Compaction, and Pore Fluids on RockProperties and Seismic Signatures. We would like to thank ToralvBerre, Gudmund Havstad, Mufak Naoroz, and many other technicalstaff of the Norwegian Geotechnical Institute �NGI� and the Univer-sity of Oslo, Department of Geosciences, for their assistance duringthe experimental work. We also acknowledge StatoilHydro for addi-tional financial support.

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