Elastic Ani Sot Ropy of Shale

8/6/2019 Elastic Ani Sot Ropy of Shale

1/7324 The Leading Edge March 2011

SPECIAL SECTION: S h a l e sS h a l e sSPECIAL SECTION: S h a l e s

Accompanying the resource potential o gas shales is a newinterest in understanding the physical and petrophysicalproperties o shales. Shale by geochemical or stratigraphic

measures is arguably the most common lithology encounteredin sedimentary basins. Despite this, shales remain littlestudied while engineers and explorationists ocused onconventional reservoirs. Geophysicists did this knowingull well that oten a refection coecient rom a reservoirwas controlled by the shale properties o the cap rock. Wecompensated or this ignorance by arguing that shales aredeposited in deepwater environments in which lateral andvertical changes are slow and thereore inconsequential. We urther compounded this ignorance by assuming thatthe shales were isotropic. An example o the consequenceso this ignorance was clearly documented by Margesson

and Sondergeld (1999). Engineers share culpability or thisignorance too, since most o the drilling problems occur inshales and most o the lithologies drilled through to reach thetarget reservoirs are shales; however, shales were rarely sampledunless a problem was encountered. Shales are now universallyrecognized as being anisotropic. Laboratory measurementsare key to dening symmetries and magnitudes o anisotropyand indicate that weak anisotropy (dened here to be lessthan 10% in V

Pand V

S) is the exception and not the rule.

Measurement o elastic anisotropy typically requiresknowledge o the symmetry and orientation o principal axes.omographic approaches with multiply redundant observa-

tions allow one to simultaneously deduce the anisotropicsymmetry and magnitude o the elastic constants (Dellinger,unpublished work). Te practical challenges to measuringeven simple transverse isotropy are ormidable. First, shalesare chemically and mechanically unstable and are oten rac-tured which makes suitably sized core recovery a challenge.Only the stronger, more stable shales are recovered and mea-sured. Tis is compounded by the act that shale oten arrivesdesiccated ater protracted periods in storage.

Te most common approach to shale characterization is toassume a symmetry, extract oriented plugs, and measure thephase velocities corresponding to specic elastic constants.For transverse isotropy (I) symmetry this requires extrac-

tion o horizontal, vertical, and 45 core plugs with respect tobedding, and measurements o compressional and polarizedshear velocities to provide the ve required elastic constants.Te measurement conguration is shown schematically inFigure 1.

Note that there are three measures o C44

which providea test o the assumed symmetry. Te method outlined byWang (2002) is similar but signicantly reduces the infuenceo sample heterogeneity. For a I medium, Tomsen (1986)parameterized the ve elastic constants as described below:

CARL H. SONDERGELDandCHANDRA S. RAI, University of Oklahoma

and are the compressional and shear velocities perpen-dicular to bedding. and are the P-wave and S-wave an-isotropies, the ractional dierence between the ast and slowvelocities, and is a parameter which controls the slownessor velocity surace at polar angles to the principal direction.Te three-plug method provides a redundancy in the mea-surements o C

44which provides a test o the validity o the

I assumption. We tested the validity o the I assumptionthrough direct measurements on Floyd Shale samples at vari-ous azimuthal angles. Sometimes insucient data have beenpresented in legacy publications to check this assumption.We report legacy data at ace value.

An example: Anisotropy o the Floyd Shale

Te Floyd Shale is a potential but to date uneconomic gas-shale prospect in Alabama. Exploratory cores taken by Brownand Wagner provided an opportunity to measure anisotropy

o the Floyd Shale. A number o these measurements have

Figure 1. Tree-plug measurement schematic. P-wave phase velocitiesprovide C

11, C

33and C

13while the polarized S-wave velocities provide

C44

and C66

. Note that the two orthogonal shear velocities measuredon the vertical plug and the shear velocity polarized perpendicularlyto bedding on the horizontal plug provide redundant measures o C

44

(Figure rom Wang, 2002).


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measured phase velocities with Tomsens (solid lines) andBerrymans (dashed line) theories or phase velocity subjectto assumptions o weak and strong anisotropy (Figure 5). We simply inserted the measured values or and in theTomsen expression and the values o C

ijin the Berryman

expression to calculate the predicted phase velocities. Te twoTomsen curves result rom calculating using the C

13val-

ues obtained on the 45 and 60 plugs. Te values measuredparallel and perpendicular to bedding are also plotted. TeBerryman ormulation provides much better agreement withthe observations than Tomsens, but expectedly so, since it

does not assume weak anisotropy.

been presented by Sakar et al., (2008). We extracted one-inch plugs at various azimuthal (Figure 2) and polar (Figure4) angles rom a 4-inch diameter whole core. Te plugs weremachined into right circular cylinders with ends ground fatand polished. A series o plugs was also extracted in the con-ventional manner, parallel, perpendicular and 45 to bed-ding. Additional plugs were extracted at polar angles o 15and 60 with respect to bedding and a series o horizontalplugs taken at 45 azimuthal angles were extracted (Figure2). Te azimuthal plugs were used to evaluate the I sym-metry. Te polar plugs provide phase velocities or the cal-culation o C

13rom these orientations. Tese velocities are

used to evaluate the weak (Tomsen) and strong (Berryman,2008) phase-velocity approximations. Both ormulationsallow the calculation o phase velocities at any polar angle.However, the Tomsen (Equation 16a) ormulation requiresthe magnitude o anisotropies be small, specically



S h a l e s

Weak anisotropy

Stemming rom the seminal work o Tomsen in 1986, thecommunity has been quick to embrace the concept o anisot-ropy and its embodiment as weak anisotropy. Weak anisot-ropy is understood to mean that the magnitudes o and are less than 10%. Unortunately, the reality is that anisot-ropy in shale is not weak but strong, not only exceeding 10%but approaching 5060%. A summary o measurements oand are presented in Figure 6. Tere are over 150 measure-ment compiled in this plot. Te diamonds represent mea-surements made in our laboratory while the circles are values

taken rom the literature. We nd a unctional relationshipbetween and to be while Wang ound . suneyama and Mavko (2005) report theollowing relationship or sands and shales based on log data:. Te intercepts are consistently near zero,where they should be, and the slopes appear to vary some-what but are close to 1.

Te values o and equal to 10% are dened by thedashed vertical and horizontal lines. Te implication o thesedata is that we cannot model phase velocities using the linearapproximation based weak anisotropy.

Causes o anisotropy

Tere are multiple causes o anisotropy in shales; these in-clude alignment o clay platelets, organic matter, stresses, andractures. Work by Hornby (1998) suggested that compac-tion resulted in increased clay particle alignment (modeledas an isotropic component) which consequently increasedanisotropy. In support, he argued that density increases withcompaction and thereore should be correlated with anisot-ropy in shales. Sayers (1994, 2008) considers the deormationand shape o the pore space in shales as a control on anisotro-py. Johnston and Christensen (1994, 1995) developed a rela-tion between basal plane intensities o clays in well-induratedshales determined through X-ray diraction and anisotropy

the greater the strength o the basal plane intensities, the

greater the measured anisotropy. Work by Vernik and Nur(1992) and Sondergeld et al. (2000) suggests that anisotropyincreased with organic matter content. Increasing organiccontent would decrease density and hence produce an eectopposite to compaction. Te existence o interparticle mi-crocracks is unresolved since most observations are made ondesiccated and poorly preserved core samples. Recent SEMwork on ion-milled samples is revealing the microstructuraldetails o shales and showing that shale systems are much

more complicated than our simple intuitive conceptual mod-

VP

VS

gm/cc km/s km/s

Shale 2.42 3.06 1.49 0.256 0.481 0.051

Sand 2 2.95 1.48 0 0 0

Table 1.Measured properties or sand and shale used in generatingFigure 7.

Figure 5. Comparison o predicted and measured phase velocities inFloyd Shale. Te solid line and short dashed lines use the Tomsenphase-velocity ormula or weak anisotropy while the long dashed lineuses Berrymans expression or strong anisotropy. Te better agreementis clearly with the Berryman ormulation.

Figure 6.A compilation o measures o and on shales. Tesedata are taken rom available literature values (circles) as well asmeasurements made recently on gas shales (diamonds). Te reddashed lines defne the boundary o values o 10%. Over 95% othe measured values exceed this value, convincingly demonstratingthat weak anisotropy is the exception and not the rule. A 1:1 line isalso plotted or reerence as well as a least-squares ft. Te reerences

indicated with an * provided values used in this plot.

Figure 7. Te calculated Backus response or mixtures o sand andshale layers having the properties given in able 1. A concentration o0 represents 100% sand while a value o 1 represents 100% shale.



S h a l e s

els. Clay platelets are highly organized on a local level andare a complex o crystals and rather lenticular pores (Son-dergeld et al., 2010). Previous imaging capabilities producedimages rom ractured suraces which show grain pull-outsand not true interparticle pores (Sayers, 2008). Tese obser-vations spurred conceptual models which do not capture thecomplexity o shale structures. Using Sayers theory, we ndthat values o the ratio o BN/B rom 0.2 to 0.8 cover thebreadth o data plotted in Figure 6 and that a value o 0.4 tsthe data best. A value o about 0.35 produces a 1:1 relation-ship between and . Further observations reveal the organicmatter to have porosities in excess o 50%. Te existence oporosity in organic matter changes the generic 2:1 conversiono weight percent OC to volume percent. Lower organicmatter densities suggest organic volumes are greater thanpreviously thought. Te undamental properties o clays andorganics remain poorly dened and estimated values spanconsiderable ranges (Prasad, 2002), hampering theoreticalmodeling o shale systems.

Anisotropy is a generic characteristic o almost all crystalsymmetry classes. Te organization o these minerals at somescale partially controls the apparent anisotropy o shales.

In addition, simple composites o isotropic materials withwelded boundaries result in overall anisotropic elastic behav-ior. Composites o anisotropic and isotropic materials withwelded boundaries result in a system which can possess evenstronger elastic anisotropy. Te magnitude o anisotropy isdependent in a predictable way on the volumetric concentra-tion o the constituents. Tis has implications or determin-ing the net to gross in a sand-shale sequence. Assuming theproperties or sand and shale presented in able 1, we canuse a simple Backus average (Backus, 1962) to estimate whatvarious concentrations o these components would do to theoverall anisotropy.

Shale anisotropy has multiple causes which complicate

the interpretation o anisotropy measurements made onshales. Scale thereore is an inherent issue with anisotropymeasurements. We would thereore anticipate a variation inobserved anisotropy with the scale o observation, that is,anisotropy measurements on small core plugs may not sensewhat a logging tool does at the meter scale or what a seismic wavelength senses at tens to hundreds o meters. However,consistency among measurement scales would suggest aniso-tropic homogeneity.

Above (Figure 8) is a picture o a small (1.8 0.744 1.129 mm) shale sample used or ultrasound resonance mea-surements o anisotropic elastic properties (Leisure, 2008,personal communication). Te results are compared in able2 to core measurements made on three 1-inch diameter by1-inch long core plugs and measurements determined rom adipole sonic log run over the same depth interval rom wherethe cores and resonance sample were recovered.

Te values presented in able 2 suggest the anisotropyobserved in this section o the shale is homogeneous over therange o scales sampled (i.e., rom mm to tens o centime-ters). Such comparisons are rare, statistically insignicant butcertainly enticing and suggestive.

Pressure and efective pressure dependencies

Many conventional reservoirs are overpressured and sealed

c33 c44 c11 c66 c13 c12

Lab 30.4 12.5 49.9 20.2 11.8 9.6

Dipole 36 15 55 20.5 10 14

Rus-2 27.1 15.1 53.8 17.1 12.7 12.7

Table 2. Comparison o elastic constants made on shale samples andderived rom a dipole log. Elastic constants are given in GPa.Note thatthe dipole was run in a deviated portion o the wellbore (Plona, 200,

personal communication).

Figure 8.A resonant ultrasound sample o Barnett Shale used to measure the anisotropic elastic constants.


5/7March 2011 The Leading Edge 329

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Figure 10. Computed values o P-wave, , and S-wave, ,anisotropies in Woodord (W) and Haynesville (H) gas shales asa unction o confning pressure, P

con. Te pressure dependence

o Woodord Shale anisotropy diers markedly rom that o theHaynesville Shale. We attribute this to the microstructural dierence(Sondergeld et al., 2010).

Figure 11.Measured compressional-wave speeds in vertical,horizontal, and 45 gas shale plugs saturated and pressurized withnitrogen. Tese are plots o P-wave velocities at constant dierentialpressure (P

d= 500 psi). Te horizontal slopes suggest = 1 or the

horizontal and 45 plugs. Te slope in the vertical plug is causedby the longer pore-pressure equilibration times due to the lowerpermeability perpendicular to bedding.

Figure 9. Compressional velocities measured on horizontal, 45, andvertical plug samples rom Woodord (W) and Haynesville (H) gasshales as a unction o confning pressure, P

con. Te Woodord Shale

displays much less pressure-dependence than the Haynesville Shale.

by shales. A ew gas-shale reservoirs are highly overpressured.Tus the eect o pressure and overpressure on shale behav-ior becomes o interest. I the reservoir is overpressured, thepore pressure is in excess o an equivalent hydrostat to that

depth, implying there is an impermeable barrier bearing thegradient o this transition rom normal to overpressure. Inother lithologies, this topic has been studied extensively;Zimmerman (1991) gives an excellent treatment o the topic.Te mechanical behavior o the overpressured system obeysthe eective pressure law:

where Pe

is the eective pressure, Pcon

is the conning pres-sure, P

poreis the pore pressure and is the Biot coecient.

is an empirical constant which has static and dynamic deni-tions and has been measured, depending on the property, to

be both greater and less than 1. While the exact value o

can be critical, or our discussion, the undamental questionis: Do velocities in shale obey the eective pressure law? I so,velocity perturbations induced by excess pore pressure can beused to detect and estimate pore pressures in shales. Hornby(1998) demonstrated that two shales appear to obey the e-ective pressure law through direct measurements on brine-saturated North Sea shales. Hornby (1994) ound that pore-pressure equilibration times are very long in these laboratoryexperiments. We have carried out similar measurements on a

suite o gas shale samples rom the Woodord and Haynesvilleshales. Te measured compressional velocities are presentedin Figure 9 and the computed P-wave and S-wave anisotro-pies are plotted in Figure 10 as a unction o conning pres-sure. In accord with the observations by Rai and Hanson(1998), resh and well-preserved shales show little pressuredependence; we observe this velocity behavior in the Wood-ord shale (Figure 9). However, the pressure dependence ovelocity in the Haynesville shale is strong; this is normallyinterpreted as a maniestation o desiccation cracks parallel tobedding. However, detailed scanning electron microscopy oion-milled samples reveals the microstructure o the Haynes-

ville is dominated by intrinsic slot-like micropores whichimpart this pressure dependence (Sondergeld et al., 2010).Predictably, this pressure dependency is also observed in thepressure dependence o the anisotropic parameters and .Te consequence o these observations is that the Haynes-ville is more likely to display a strong pressure signature upondepletion than the Woodord, making seismic a potentialmanagement tool to monitor compartmentalization or by-passed gas.

Figure 11 shows measurements o P-wave velocities onhorizontal, vertical and 45 core plugs as a unction o conn-ing pressure with constant dierential pressure. Dierentialpressure was maintained at 500 psi. Nitrogen is the pressuriz-

ing fuid. Increasing and decreasing pressure tests are shown.



S h a l e s

Clearly, the compressional velocities in the horizontal and45 plugs show a simple dierential pressure-dependence.Te vertical plug appears to obey a similar behavior but theresponse is not exactly as fat as that or the other plugs. Tesimple explanation is that, with the horizontal and 45 plugs,the fuid has access parallel to the bedding planes while theaccess is across the bedding planes or the vertical plug. Te

pore pressure equilibration time or the vertical plug withoutthe screening employed by Hornby (1994) is much longer.Given these limitations, these measurements suggest that thecompressional velocities in shale obey the eective pressurelaw. Tus overpressured shales should display diagnostic ve-locity changes. Equivalently, these signatures can be used tomap untapped, isolated or compartmentalized zones.

Summary and conclusions

Limited core measurements on shales suggest a good start-ing anisotropic model or the lithology is I symmetry andthat the magnitude o the anisotropy is large (2050%);

thus, weak anisotropic assumptions should not be used inmodeling shales. Berrymans ormulation should be used tomodel phase velocities when anisotropy is strong. Tere ex-ists a strong correlation between and and this correlationcan be interpreted in terms o the ratio o normal and shearcompliances between clay platelets (Sayers, 1994, 2008) butno correlation between either or and . Tat is to say,i you know either or , you can predict the other withcondence. Intrinsic anisotropy and pressure-dependence ovelocities in shales are oten masked by inadequate preser-vation ater post recovery. However, SEM studies indicatethat microstructural dierences in shales are responsible orpressure dependencies o velocities and anisotropies. Pore-pressure studies suggest shales obey the eective pressurelaw when proper pore-pressure equilibration times are em-ployed. On geological time scales, we expect this behavior tobe observed. Progress in rening our understanding o shalesand shale anisotropy requires more and better controlledmeasurements as well as access to resh and preserved cores.Heretoore, most authors report measurements, but not mea-surement conditions (i.e., core saturation or equilibrationtime between measurements).

ReerencesBackus, G. E., 1962, Long-wavelength elastic ansiotropy produced by

horizontal layering: Journal o Geophysical Research, 67, no. 11,44274440, doi:10.1029/JZ067i011p04427.

Berryman, J. G., 2008, Exact seismic velocities or transversely isotro-pic media and extended Tomsen ormulas or stronger anisotro-pies: Geophysics, 73, no. 1, D1D10, doi:10.1190/1.2813433.

Hornby, B. E., 1994, Te elastic properties o shale: Ph.D. thesis,Cambridge University.

Hornby, B. E., 1998, Experimental laboratory determination o the dy-namic elastic properties o wet, drained shales: Journal o Geophys-ical Research, 103, B12, 2994529964, doi:10.1029/97JB02380.

Johnston, J. E. and N. I. Christensen, 1994, Elastic constants and ve-locity suraces o indurated ansiotropic shales: Surveys in Geophys-

ics, 15, no. 5, 481494, doi:10.1007/BF00690171. Johnston, J. E. and N. I. Christensen, 1995, Seismic anisotropy o

shales: Journal o Geophysical Research, 100, B4, 59916003,doi:10.1029/95JB00031.

Lo, ., K. B. Coyner, and M. N. oksz, 1986, Experimental de-termination o elastic anisotropy o Berea sandstone, Chicopeeshale and Chelmsord granite: Geophysics, 51, no. 1, 164171,doi:10.1190/1.1442029.

Margesson, R. W. and C. H. Sondergeld, 1999, Anisotropy and am-plitude versus oset: a case history rom the West o Shetlands, inA. J. Fleet and S. A. R. Boldy, eds., Petroleum geology o northwestEurope: Geological Society London, 635643.

Prasad, M., M. Kopycinska, U. Rabe and W. Arnold, 2002, Mea-surement o Youngs modulus o clay minerals using atomic orceacoustic microscopy: Geophysical Research Letters, 29, 8, 13-1-13-4.

Rai, C. S. and K. E. Hanson, 1998, Shear-wave velocity anisotropyin sedimentary rocks: A laboratory study: Geophysics, 53, no. 6,800806, doi:10.1190/1.1442515.

Sakar, M., C. S. Rai, and C. H. Sondergeld, 2008, A petrophysicalstudy o Floyd shale: AAPG Annual Convention.

Sayers, C. M., 1994, Te elastic anisotrophy o shales: Journal o Geo-physical Research, 99, B1, 767774, doi:10.1029/93JB02579.

Sayers, C. M., 2008, Te eect o low aspect ratio pores on the seismicanisotropy o shales: 78th Annual International Meeting, SEG,Extended Abstracts, 2606-2611.

Sondergeld, C. H., C. S. Rai, R. W. Margesson, and K. J. Whidden,2000, Ultrasonic measurements o anisotropy on Kimmeridgeshale: 70th Annual International Meeting, SEG, Expanded Ab-stracts, 18581861.

Sondergeld, C. H., R. J. Ambrose, C. S. Rai, and J. Moncrei, 2010,Micro-structural studies o gas shales: SPE paper 131771.

Tomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, no. 10,19541966, doi:10.1190/1.1442051.

suneyama, F., and G. Mavko, 2005, Velocity anisotropy estimationor brine-saturated sandstone and shale: Te Leading Edge, 24, no.9, 882888, doi:10.1190/1.2056371.

Vernik, L. and A. Nur, 1992, Ultrasonic velocity and anisotropyo hydrocarbon source rocks: Geophysics, 57, no. 5, 727735,doi:10.1190/1.1443286.

Wang, Z., 2002, Seismic anisotropy in sedimentary rocks, part 1: Asingle-plug laboratory method: Geophysics, 67, no. 5, 14151422,doi:10.1190/1.1512787.

Zimmerman, R. W., 1991, Compressibility o sandstones: Elsevier.Data reerences Hornby, B. E., 1994, Te elastic properties oshale: Ph.D. thesis, Cambridge University.

Hornby*, B. E., 1998, Experimental laboratory determina-tion o the dynamic elastic properties o wet, drained shales:

Journal o Geophysical Research, 103, B12, 2994529964,doi:10.1029/97JB02380.

Jakobsen*, M. and A. Johansen, 2000, Anisotropy approximationsor mudrocks: A seismic laboratory study: Geophysics, 65, no. 6,17111725, doi:10.1190/1.1444856.

Johnston*, J. E. and N. I. Christensen, 1994, Elastic constants andvelocity suraces o indurated ansiotropic shales: Surveys in Geo-physics, 15, no. 5, 481494, doi:10.1007/BF00690171.

Johnston*, J. E. and N. I. Christensen, 1995, Seismic anisotropy oshales: Journal o Geophysical Research, 100, B4, 59916003,doi:10.1029/95JB00031.

Jones*, L. E. A., and H. F. Wang, 1981, Ultrasonic velocities in Cre-


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Elastic Ani Sot Ropy of Shale