elastic properties of clay minerals

Clay minerals are the most abundant materials in sedi-mentary basins. The most common—like kaolinite, illite,chlorite, and smectite—are found in various amounts inmudstones and are also often found in clastic and nonclas-tic reservoir rocks. Their presence alters the elastic behav-ior of reservoir rocks significantly as a function of mineraltype, volume and distribution. Thus, two sandstones withthe same clay amount might have different elastic proper-ties due to differences within the clay population. The elas-tic properties of clay minerals are therefore important in rockphysics modeling to understand the seismic and sonic logresponses of shaley sequences and clay-bearing reservoirrocks.

However, the elastic properties of clay minerals are notwell constrained due to their fine-grained nature. Measuringelastic properties of clay minerals from natural mudstonesis extremely difficult and time consuming due to preserva-

tion, physiochemical behavior, and low permeability. A fewmeasurements of clay mineral elastic properties are foundin literature, but there is little agreement between the mea-surements (Table 1). The discrepancy is probably related todifferent experimental techniques that do not account forthe physicochemical behavior of clay minerals. The layercharge and large surface area of clays mean that they inter-act strongly with pore fluids, and extensive heating beforeor during testing may both dehydrate and modify theirstructure and thus their elastic properties. The small grainsize of clays makes it nearly impossible to isolate an indi-vidual grain for direct measurement of rock properties.Therefore, instead of direct measurements, theoretical com-putation, a combination of theoretical and experimentalinvestigations, and the empirical extrapolations of labora-tory measurements has been used to derive elastic proper-ties of clays.

Elastic properties of clay mineralsNAZMUL HAQUE MONDOL, JENS JAHREN and KNUT BJØRLYKKE, University of Oslo, NorwayIVAR BREVIK, StatoilHydro, Trondheim, Norway

758 THE LEADING EDGE JUNE 2008

Table 1. Acoustic and elastic properties of kaolinite and smectite grains found in the literature.

JUNE 2008 THE LEADING EDGE 759

Figure 1. (a) Uniaxial oedometer equipped with acoustic velocity measurement apparatus. (b) Porosity reduction and bulk-density changes inmechanically compacted, brine-saturated (BS) kaolinite aggregates as a function of vertical effective stress. The equation of best fit line and correlationcoefficient (R2) of the bulk density-effective stress relationship for kaolinite (BS) aggregates are shown. (c) Representative waveforms for P- (blue) and S-wave (black) pulses recorded in a clay mixture at 50 MPa effective stress. The first-arrival time picks of P- and S-waves are marked by the red and greenlines, respectively. (d) The extrapolation of lab data of dry and brine-saturated kaolinite and smectite aggregates for effective stresses up to 1000 MPa.Extrapolation shows that clays retain high porosity even at extremely high effective stresses if the compaction process is mechanical. Data of a smectiteaggregate (Chilingarian and Knight, 1960) compacted mechanically at high effective stresses are included for comparison. The best fit lines and correlation coefficient (R2) of porosity-stress relationships of different clay aggregates are shown.

This study estimates the elastic properties of two end-member clay minerals, smectite and kaolinite. They are “endmembers” in the sense that smectite is the most fine-grainedclay found in nature and has a high cation exchange capac-ity and large surface area (700 m2/g), while kaolinite iscoarse-grained and has a much lower cation exchange capac-ity and smaller surface area (10 m2/g) compared to otherclay minerals. Smectite is the volumetrically most abundantdetrital clay mineral in Cenozoic basins world wide.Kaolinite is a common component of well-drained soils inhumid climates, which gets reworked into sandstones andmudstones. In this study, both dry and brine-saturated kaoli-nite and smectite aggregates were compacted mechanicallyin the lab to derive the elastic parameters (bulk and shearmodulus, Young’s modulus, Poisson’s ratio, and the Lameconstantm) of the kaolinite and smectite grains, respectively.The elastic parameters of smectite and kaolinite suggestedin this study are not the direct measurement. The elastic para-meters were deduced from empirical extrapolation of lab

measurements of changes in porosity, density, VP, and Vsduring experimental compaction as a function of increas-ing vertical effective stress. The following steps were per-formed to obtain the elastic properties:

• First, the porosity reduction (w), the changes in bulkdensity (rb), and the compressional (VP) and shear wave(Vs) velocities of dry and brine-saturated kaolinite andsmectite aggregates were measured in the lab as a func-tion of vertical effective stress (Figures 1b and 2). A highstress uniaxial odometer (Figure 1a) cell was used to per-form the mechanical compaction test.

• Next, the measured VP, Vs and rb were used to calculatethe elastic parameters of equivalent dry and brine-sat-urated smectite and kaolinite aggregates.

• Finally, the elastic parameters of smectite and kaolinitegrains were derived from the extrapolation of porosity-elastic moduli relationships to smectite and kaoliniteaggregates with zero porosity (Figures 4 and 5). These

extrapolations assume that the aggregate moduli at zeroporosity represent the equivalent elastic moduli of smec-tite and kaolinite grains, respectively. A polynomialregression of best fit approximation was applied to thedata for the extrapolation (Figures 4 and 5).

The estimated values of elastic moduli may improve byadding more data of compacted smectite and kaolinite aggre-gates at higher effective stresses (stresses higher than themaximum effective stresses applied for this study). Addingsuch tests will only improve the derived moduli margin-ally. This is because the extrapolation of porosity-depthtrends of data found in the lab measurements and data fromChilingarian and Knight (1960) suggest that smectite andkaolinite aggregates will retain a high porosity even atextremely high effective stresses if the compaction processis purely mechanical (i.e. stress driven, Figure 1d). It willtherefore be difficult or impossible to compact smectite andkaolinite aggregates mechanically down to zero porosity. Thecompaction tests show that maintaining brine-saturatedsmectite aggregates at hydrostatic pore pressure is very timeconsuming. This is due to low permeability of the smectiteaggregates; therefore, there is a tendency to develop a highpore pressure (Mondol et al. 2007) during testing of smec-tite. The estimated values of elastic moduli derived from theexperiments were tested by comparing them with an estab-lished shale database (Brevik, 2005) and the lab measure-ments of Han et al. (1986) and Yin (1992). To check thereliability, the estimated elastic moduli values (Table 2) andthe values reported by Vanorio et al. (2003), Wang et al.(2001),and Katahara (1996) were used in effective medium model-ing and in the Gassmann fluid substitution model. The mod-eling results were compared to the shale database found inBrevik.

Materials and methods. Experimental mechanical com-paction tests and velocity measurements of dry and brine-saturated smectite and kaolinite aggregates were performedat the Norwegian Geotechnical Institute (NGI). All experi-ments were performed at room temperature, which wasbetween 190C and 210C. Ahigh-stress uniaxial oedometer (nolateral strain allowed) equipped with acoustic measurementstransducers (Figure 1a) was used to conduct the experiments.The methods used for mechanical compaction and velocitymeasurements have been presented in detail by Mondol etal. (2007; 2008). Oven-dried (600C for 3–4 days) clay powderwas used for the dry tests. For brine-saturated tests, clay slur-ries were prepared by mixing dry clay powder with waterwith a salinity of about 34 000 ppm (parts per million). Toachieve optimal saturation, the brine-saturated slurries wereprepared by thoroughly mixing the clays with water to awater content equal to 1.5 times the liquid limit. The miner-alogical composition of the smectite aggregates is smectite(89%), cristobalite (9%), and quartz (2%), while the miner-alogical composition of the kaolinite aggregates is kaolinite(81%), illite/mica (14%), and microcline (5%). The density ofthe smectite and kaolinite grains were measured in the lab-oratory at 600C (smectite 2.613 g/cc and kaolinite 2.616 g/cc)and 1100C (smectite 2.625 g/cc and kaolinite 2.624 g/cc),respectively, by using an ordinary pycnometer. The poros-ity and bulk density changes as a function of effective stress(Figure 1b) were measured throughout the tests from theexpelled air or brine volume of the dry and brine-saturatedsmectite and kaolinite aggregates, respectively.

The acoustic velocity measurements were performedthroughout the compaction experiments as the effective stresswas increased. The P- and S-wave pulses that traveledthrough the sample to the receiver transducers were recordedby a computer and used to compute acoustic velocity. VP and


Figure 2. Acoustic velocity (both VP and VS) plotted against vertical effective stress of mechanically compacted dry and brine-saturated kaolinite (a and c) and smectite (b and d) aggregates. The differences between VP and VS increase significantly in the brine-saturated state.

Vs were determined by measuring the time taken for anultrasonic pulse to traverse the sample. Traveltimes measuredfrom the reference signals are then compared with measuredspecimen traveltimes for estimating sample velocities. Thereference traveltime measurements were taken with the trans-ducers coupled to each other in head-to-head configuration.Figure 1c shows a representative waveform recorded at 50MPa effective stress for the P- (blue) and S-wave (black)polarization parallel to the stress direction. First arrival timepicks are shown on the waveforms by red (P-wave) andgreen (S-wave) lines (Figure 1c). The estimated experimen-tal errors are ±0.025 MPa or 0.6% in load/stress, ±0.02 mmor ±1.5% in deformation, ±0.005 MPa or ±0.6% in pore pres-

sure, ±50 m/s in VP and ±32 m/s in Vsmeasurements.

Results. The measured VP and Vs areplotted for the dry and brine-saturatedkaolinite and smectite aggregates asfunctions of effective stress and poros-ity and density in Figures 2 and 3,respectively. The dry clay aggregatescompacted less when compared withthe equivalent brine-saturated aggre-gates at the same effective stress. Bothdry and brine-saturated kaoliniteaggregates (Figures 3a and 3c) com-pacted more, compared with smectiteaggregates (Figures 3b and 3d). Thedry kaolinite aggregates compacted toabout 28% porosity at 50 MPa effec-

tive stress (Figure 3a), whereas the dry smectite aggregatesretained a higher porosity (about 45%) at the same effectivestress (Figure 3b). The brine-saturated kaolinite aggregatescompacted to about 10% porosity at 50 MPa effective stress(Figure 3c), while the brine-saturated smectite aggregatesretained a porosity of about 35% at the same stress level(Figure 3d). Published data from Chilingarian and Knightand the extrapolation of our experimental results suggestthat mechanical compaction of clay aggregates down closeto zero porosity is nearly impossible (Figure 1d).

The velocity increases in both dry and brine-saturatedkaolinite and smectite aggregates, as functions of effectivestress, porosity, and density are shown in Figures 2 and 3.


Figure 3. Plots of VP and VS of dry and brine-saturated kaolinite (a) and (c) and smectite (b) and (d) aggregates as functions of mechanical compaction-induced total porosity and bulk density development. The dry clay aggregates (a) and (b) compact less than equivalent brine-saturated aggregates (c)and (d). Smectite aggregates (b) and (d) compacted less and retained higher porosity than kaolinite aggregates (a) and (c) at the same effective stress. Atthe same porosity or bulk density, VP and VS of smectite aggregates are higher than the kaolinite aggregates.

Table 2. The elastic and acoustic properties of kaolinite and smectite grains.


Figure 4. Bulk modulus (a) and shear modulus (b) of brine-saturatedkaolinite (blue circles) and smectite (red circles) aggregates as a functionof total porosity. The elastic parameters of kaolinite and smectite grainswere derived from the extrapolation of the calculated elastic properties ofmechanically compacted brine-saturated kaolinite and smectite aggregates, respectively to zero porosity. The derived bulk and shearmoduli of kaolinite and smectite grains are shown on the y-axis (red andblue crosses). The grey lines show the polynomial fits to the data.Equations of best fit lines and the correlation coefficient (R2) of the relationship between total porosity and the bulk and shear modulus aregiven.

Figure 5. Plots of bulk modulus (a) and shear modulus (b) of dry kaolinite(blue circles) and smectite (red circles) aggregates as a function of totalporosity. The elastic moduli of kaolinite and smectite grains were derivedfrom the extrapolation of the calculated elastic moduli of mechanicallycompacted dry kaolinite and smectite aggregates, respectively, to zeroporosity. The derived bulk and shear moduli of kaolinite and smectitegrains are shown on the y-axis (red and blue crosses). The grey lines showthe polynomial fits to the data. Equations of best fit lines and the correlation co efficient (R2) of the relationship between porosity and thebulk and shear modulus are given.

The difference between VP and Vs was relatively less in dryaggregates (Figures 2a and 2b) compared to the brine-satu-rated state where the difference increased significantly(Figures 2c and 2d). A similar kind of velocity development(both VP and Vs) was observed in both dry kaolinite andsmectite aggregates, respectively, as a function of effectivestress where dry smectite aggregates shows slightly higherVP then the dry kaolinite aggregates. The Vs is nearly iden-tical for both dry kaolinite and smectite aggregates (Figures2a and 2b). The VP and Vs development in both brine-satu-rated kaolinite and smectite aggregates vary compared tothe dry aggregates where both the VP and Vs in kaoliniteaggregates are higher compared to the smectite aggregatesas a function of effective stress (Figures 2c and 2d).

The measured VP, Vs and �b were used to calculate theelastic parameters (K, m, E, � and λ) of the kaolinite and smec-tite aggregates. The calculated elastic parameter of the dryand brine-saturated kaolinite and smectite aggregates areplotted as a function of porosity in Figures 4 and 5. The poly-nomial fit to the data for the relationship between porosityand the elastic parameters was drawn and extrapolated tozero porosity (Figures 4 and 5). The elastic moduli of kaoli-nite and smectite aggregates at zero porosity (marked by y-

axis crosses on Figures 4 and 5) represent the elastic mod-uli of zero-porosity smectite and kaolinite aggregates thatcould correspond theoretically to the elastic moduli of kaoli-nite and smectite grains. The estimated elastic parametersof kaolinite and smectite grains derived from the dry andbrine-saturated kaolinite and smectite aggregates, respec-tively are presented in Table 2. The VP and Vs of individualkaolinite and smectite grains were also estimated by theextrapolation of porosity-velocity relationships to zero poros-ity and are shown in Table 2. The equations of polynomialfits and correlation coefficients of different relationships aregiven in Figures 4 and 5. The elastic parameters of kaolin-ite and smectite grains derived from the dry and brine-sat-urated kaolinite and smectite aggregates differ significantlyand this may be due to the interaction between brine andthe clay minerals. Higher values of VP, K and � are observedfor both kaolinite and smectite grains at brine-saturatedconditions compared to dry conditions. The opposite wereobserved for VS, �, and E where higher values were foundfor the dry state compared to the brine-saturated state (Table2). The � is significantly lower for the dry condition com-pared to the brine-saturated condition for both smectite andkaolinite grains. The Poisson’s ratio of kaolinite and smec-

tite are not suggested for the dry state as the empiricalextrapolation of measured data to zero porosity is unreal-istic. To test the reliability of the estimated bulk and shearmodulus values found in this study, the results were com-pared to a well-defined natural shale database constructedfrom well logs from different parts of the world (Brevik2005), data of Han et al. (1986) and Yin (1992) and additionallab measurements of kaolinite-smectite and kaolinite-siltmixtures (additional lab measurements performed for thisstudy).

Comparison with published data and additional lab mea-surements. Figure 6 shows a comparison of lab measure-ments (this study) and published data of both bulk andshear modulus versus porosity for a variety of mudstones,shales, and shaley sandstones. Both brine-saturated kaoli-nite and smectite aggregates, the additional lab measure-ments of two kaolinite-smectite (80:20 kaolinite-smectiteand 20:80 kaolinite-smectite by weight), and a silt-kaolinite(50:50 by weight) mixture, and published data from Han etal., Yin, and Brevik are included for the comparison. TheBrevik database included 70 wireline logs in sequences ofpure shales. A simple data reduction filter was applied tothe data to pick pure shales. The pure shales were definedas a volumetric clay volume (normalized to the solid vol-ume) of more than 75%. Yin’s data are lab measurements ofbrine-saturated kaolinite powder with particle size rangesfrom 1–4 micrometers. The data from Han et al. are lab mea-surements of 12 cores of shaley sandstones from the Gulf ofMexico that contain 30–50% clays by volume. The bulk andshear modulus of kaolinite and smectite grains estimatedby this study (values derived from the empirical extrapo-lation of data to zero porosity) are shown on the y-axes ofFigures 6a and 6b by the magenta dots.

The lab-derived kaolinite bulk modulus from kaoliniteaggregates agrees reasonably well with the measured bulkmodulus of Yin (1992) for brine-saturated kaolinite (Figure6a), but the shear modulus from Yin (1992) for the same sam-ple shows significantly higher values compared to the labmeasurements (this study) as well as the natural shale data-base from Brevik (Figure 6b). From the comparison, it couldbe stated that the bulk and shear modulus of the brine-sat-urated smectite and kaolinite aggregates represent the upperand lower limits of bulk and shear modulus of natural shalesreported by Brevik. The empirical extrapolation of bulk andshear modulus of brine-saturated smectite and kaoliniteaggregates representing end-member clays encompassnearly the whole range of the data derived from naturalshales. The lab data and its extrapolation represent a muchbetter fit to the upper and lower limits of bulk modulus ofthe natural shale database than to the shear modulus of thesame database (Figures 6a and 6b). Only a few scattered bulkmodulus data points from natural shales fall outside therange suggested by the smectite and kaolinite derived val-ues at low porosity (porosity <5%).

For shear modulus more points fall outside the rangeset up by smectite and kaolinite also at a relatively highporosity level (porosity <15%). The shale database datapoints found outside the limits set up by the smectite andkaolinite bounds may be related to lithology and pore flu-ids, as the outliers represent sand content (Han et al., 1986)and higher resistivity (Brevik, 2005). In nature, it is nearlyimpossible to find mudstones and shales that comprise onlysmectite or kaolinite. Natural mudstones and shales usu-ally contain a mixture of clays, silts, and sands of varyingweight fractions and have different elastic properties com-pared to pure kaolinitic or smectitic mudstones. Therefore,

the data of most natural mudstones and shales should fallin between the data of smectite and kaolinite aggregates, asthese two clay minerals represent the end members clay interms of grain size, cation exchange capacity, and surfacearea. To test the effects of lithology on elastic properties, labmeasurements of three additional well-characterized syn-thetic mudstones (50:50 silt-kaolinite, 80:20 kaolinite-smec-tite, and 20:80 kaolinite-smectite) were included in thecomparison (Figure 6). The bulk and shear moduli of thesethree synthetic mixtures fall in between the upper and lowerlimit represented by the smectite and kaolinite aggregates(Figures 6). As expected, the bulk and shear modulusincrease by adding smectite and silt to the kaolinite aggre-gates, whereas the bulk and shear modulus decrease byadding kaolinite to smectite aggregates (Figures 6a and 6b).The empirical extrapolation of data from the 50:50 kaolin-ite-silt mixture crosses the upper shear modulus limit forpure clays at a low porosity level (Figure 6b). The bulk mod-ulus of the 50:50 kaolinite-silt mixture, however, falls withinthe upper limit restricted by the smectite aggregates (Figure6a). This result suggests that the shear modulus of shalesand mudstones is more sensitive to lithology than the bulkmodulus in the low-porosity range.

From the Brevik database it could be stated that theshear modulus of shales is more sensitive to pore water salin-ity than the bulk modulus at low porosity. The effect ofchemical compaction on bulk and shear modulus may bedifferent, leading to a larger scatter and higher values ofshear modulus than the mechanical extrapolation curves(Figure 6b). Bulk modulus is controlled by the volumetricchanges when the seismic/acoustic wave passes, while theshear modulus is controlled by the frictional couplingbetween the building components (sand, silt, or clay) of ashale, leading to lateral and rotational strain when the seis-mic/acoustic wave passes. We believe that the chemicalcompaction will strongly contribute to these coupling forces,leading to changes in the shear modulus, but not muchchange in volume. The deviation of the shale database(Brevik 2005) from the brine-saturated kaolinite for theporosity-shear modulus relation at porosity less than about20% can be associated with a primary chemical compaction(Figure 6b). The difference is due to the strengthening con-tribution from the chemical compaction on the clay parti-cle to particle forces. This deviation is not seen on the bulkmodulus trends (Figure 6a). Again, the chemical compactionis primarily recognized using shear modulus (or S-wavevelocity), not P-wave (bulk modulus) data.

Effective medium modeling and Gassmann fluid substi-tution. The values of the elastic parameters of kaolinite andsmectite grains suggested in this study show a significantdifference in dry state compared to the brine-saturated state.The VP, K, and λ are higher, but the Vs, �, and E are lowerin the brine-saturated state compared to the dry state forboth kaolinite and smectite grains (Table 2). Differences inclay-brine interaction may explain this fact. A comparisonwith the shale database reported by Brevik shows that thebulk and shear modulus of brine-saturated smectite andkaolinite aggregates, and their extrapolation represent theupper and lower limits to the natural shale database withsome exceptions at low porosity ranges. The values of elas-tic parameters of kaolinite and smectite grains suggested inthis study are somewhere in between the maximum andminimum values reported in the literature (Table 1). Tocheck the consistency of the estimated values, the bulk mod-ulus of kaolinite and smectite aggregates as a function ofporosity was modeled. The estimated bulk modulus values



Figure 6. Comparisons of bulk and shear modulus versus porosity for a group of brine-saturated synthetic and natural mudstones. The extrapolationsof lab data of synthetic clay mixtures are shown by the gray lines. The pure smectite and kaolinite aggregates represent more or less the upper and lowerlimit of the natural shales database presented by Brevik with the exception of upper limit shear modulus at low porosity, where a significant scatter andrelatively higher shear modulus values are observed in the Brevik data set (b). The calculated bulk and shear modulus of two kaolinite-smectite mixtures(20:80 kaolinite-smectite and 80:20 kaolinite-smectite) and a kaolinite-silt mixture (50:50 kaolinite-silt) fall within the upper and lower limits set bykaolinite and smectite with an exception at low porosity (<15%), where the shear modulus of the 50:50 kaolinite-silt mixture shows higher valuesthan the upper limit (b). The bulk modulus of brine-saturated kaolinite aggregates (this study) agree reasonably well (a) with Yin’s data. The shearmodulus of the same sample differs significantly between the two studies with the highest values from the Yin study (b). The low-porosity shaley sandstone shear modulus data from Han et al. show much scatter and higher values than rest of the data (b).


Figure 7. Effective medium modeling of brine-saturated kaolinite aggregates. The modified (weighted) Hashin-Shtrikman upper (HS+, purple) andlower (HS-, magenta) bounds and average (HS avg., pink) were used for modeling. Gassmann fluid substitution was also performed. The modelingresults derived from different values of K and � of kaolinite grains suggested by this study and those of Vanorio et al., Wang et al., and Katahara areshown in plots a–e. The bulk modulus of brine-saturated kaolinite aggregates (blue circles) calculated from the measured VP, Vs, and rb are included inall plots. The results of Gassmann fluid substitution for different K values of kaolinite suggested by this study, Vanorio et al., Wang et al., and Kataharaare shown for comparison. For Gassmann fluid substitution, the bulk modulus of dry kaolinite aggregates was used for the frame bulk modulus (Kframe).

of kaolinite and smectite grains in both dry and brine-sat-urated states (this study) and the values reported byKatahara (1996), Wang et al. (2001) and Vanorio et al. (2003)were used in the effective medium modeling and theGassmann fluid substitution model (Gassmann, 1951). Themodified (weighted) Hashin-Shtrikman (Hashin andShtrikman, 1963) upper (HS+) and lower (HS-) bounds andaverage (HS avg.) were used for the effective medium mod-eling. The shale database found in Brevik was used as a ref-erence for changes in bulk modulus of natural mudstonesand shales as a function of porosity. The modeling resultsare shown in Figures 7–8, respectively.

The values of bulk and shear modulus derived from thebrine-saturated kaolinite aggregates agree reasonably wellwith effective medium modeling (Figure 7a) compared with

the natural shale database from Brevik. The values from thedry kaolinite aggregates (this study) and Vanorio et al. (2003)underpredict (Figures 7b and 7c), and the values from Wanget al. (2001) and Katahara (1996) over-predict the elasticproperties (Figures 7d and 7e) from effective medium mod-eling compared to the shale database in Brevik. Using thevalue Ks=11.8 GPa—the bulk modulus of kaolinite grain esti-mated in this study from the brine-saturated kaolinite aggre-gate—the predicted bulk modulus of Gassmann brinesubstitution agrees surprisingly well with the lab measure-ment of bulk modulus of the brine-saturated kaolinite aggre-gates (Figure 7a). The required values of Kframe (frame bulkmodulus of kaolinite aggregates) for the modeling ofGassmann fluid substitution were taken from the lab mea-surement of dry kaolinite aggregates. The K values of kaoli-


Figure 8. Effective medium modeling of brine-saturated smectite aggregates. The modified (weighted) Hashin-Shtrikman upper (HS+, purple) and lower(HS-, magenta) bounds and average (HS avg., pink) were used for modeling. Gassmann fluid substitution was also performed. The modeling resultsderived from different values of K and � of smectite grains suggested by this study and by Vanorio and Wang et al. are shown in plots a–e, respectively.The bulk modulus of brine-saturated smectite aggregates (red circles) calculated from the measured VP, Vs, and rb are included in all plots. The resultsof Gassmann fluid substitution for different K values of smectite suggested by this study, Vanorio et al. (2003), and Wang et al. (2001) are shown forcomparison. For Gassmann fluid substitution, the bulk modulus of dry smectite aggregates was used for the frame bulk modulus (Kframe).

nite derived from the dry kaolinite aggregates (this study) andVanorio et al. (2003) underestimate (Figures 7b and 7c) andthe values from Wang et al. (2001) and Katahara (1996) over-estimate (Figures 7d and 7e) the bulk modulus of kaoliniteaggregates by the Gassmann brine substitution compared tothe lab measurements.

The effective medium modeling and the prediction ofGassmann brine substitution show more or less similar resultsfor smectite aggregates. The values of bulk and shear modu-lus of smectite derived from the brine-saturated smectiteaggregates predict much better the elastic properties by theeffective medium modeling (Figure 8a) compared to the nat-ural shale database in Brevik. The values from the dry smec-tite aggregates (this study) and Vanorio et al. under-predict(Figures 8b and 8c), while the values from Wang et al. (2001)overpredict (Figure 8d) the elastic properties by the effectivemedium modeling compared to the shale database in Brevik.By using the value Ks=29 GPa, the bulk modulus of a smec-tite grain estimated in this study from the brine-saturatedsmectite aggregates, the predicted bulk modulus of Gassmannbrine substitution agrees very well with the lab measurementof the bulk modulus of the brine-saturated smectite aggregates(Figure 8a). The K values derived from the dry smectite aggre-

gates (this study) and from Vanorio et al. underestimate thebulk modulus of smectite aggregates using Gassmann brinesubstitution compared to the lab measurements (Figures 8band 8c). The Gassmann prediction, which uses the smectitebulk modulus values 63.8 GPa suggested by Wang et al.,agrees fairly well with the lab measurements, though the effec-tive medium modeling overpredicts the bulk modulus ofbrine-saturated smectite aggregates using these values (Figure8d). The required values of Kframe (frame bulk modulus of smec-tite aggregates) for the Gassmann fluid substitution weretaken from the lab measurement of dry smectite aggregates.Using the values of bulk modulus of kaolinite and smectitegrains obtained from this study from the brine-saturated con-dition, we obtain a much better agreement between model pre-diction, lab measurements, and the natural shale database inBrevik.

Conclusions. Elastic properties for smectite and kaolinite havebeen estimated from experimentally compacted smectite andkaolinite aggregates. Significant differences in elastic proper-ties are found for smectite and kaolinite under dry and brine-saturated conditions, respectively. The differences could beexplained by the physicochemical behavior of clay minerals

due to their sensitivity to the chemical composition of the porewater compared to air-filled pores. The values of elasticparameters estimated in this study are shown to be some-where between the maximum and minimum values foundin the literature (Tables 1 and 2). The estimated elastic para-meters of smectite and kaolinite grains represent the upperand lower limits of the natural shale data set found in Brevik2005. The estimated values herein are lower than the theo-retical extrapolations of Katahara (1996) and measurementof clay-epoxy mixtures of Wang et al. (2001) and higher thanthe measurements of cold-pressed and uniaxial stress andkaolinite-water suspension of Vanorio et al. (2003).

Effective medium modeling and Gassmann fluid sub-stitution demonstrate that the bulk and shear modulus ofsmectite and kaolinite grains derived from the experimen-tally compacted brine-saturated smectite and kaoliniteaggregates can be used to predict elastic properties of nat-ural mudstones with known lithology. Clays in rocks are usu-ally saturated, so the elastic moduli derived frombrine-saturated clay aggregates should be more appropri-ate to use in modeling than moduli derived from dry clayaggregates. The elastic moduli deduced from the dry smec-tite and kaolinite aggregates underestimate the elastic mod-uli of natural mudstones; therefore, this is not recommendedin rock physics modeling. The elastic properties of clay min-erals depend to a large extent of the chemical bonds betweencations in the water phase and the charges at the mineralphases. Further research is needed on clay-fluid interac-tions such as surface interactions, interlayer water, natureof pore fluids (salinity, oil and gas saturation), and influ-ence of shape and sizes of clay minerals. Although uncer-tainties exist in extrapolation for deriving the elasticproperties of kaolinite and smectite grains, these data areuseful for modeling and interpretation of seismic and soniclogs responses and studying the seismic properties of claybearing reservoir rocks.

Suggested reading. “Elastic properties of rock-forming min-erals. II. Layered silicates” by Alexandrov and Ryzhova (USSRAcademy of Science and Geophysical Series, 1961). “Burialprocesses and their control on acoustic properties in shales”by Brevik (SEG 2005 Expanded Abstracts). “Relationshipbetween pressure and moisture content of kaolinite, illite, andmontmorillonite clays” by Chilingarian and Knight (AAPGBulletin, 1960). “Effects of porosity and clay content on wavevelocities in sandstones” by Han et al. (GEOPHYSICS, 1986).“Clay mineral elastic properties” by Katahara (SEG 1996Expanded Abstract). “Experimental mechanical compaction ofclay mineral aggregates: Changes in physical properties ofmudstones during burial” by Mondol et al. (Marine andPetroleum Geology, 2007). “Experimental compaction of clays:Relationship between permeability and petrophysical prop-erties of mudstones” by Mondol et al. (Petroleum Geoscience,in press, 2008). “Elastic properties of dry clay mineral aggre-gates, suspensions, and sandstones” by Vanorio et al.(Geophysical Journal International, 2003). “Effective elastic prop-erties of solid clays” by Wang et al. (GEOPHYSICS, 2001).“Elasticity of selected rocks and minerals” by Woeber et al.(GEOPHYSICS; 1963). “Acoustic velocity and attenuation ofrocks: Isotropy, intrinsic anisotropy, and stress inducedanisotropy” by Yin (PhD thesis, Stanford University, 1992).

Acknowledgements. This study is a part of the PETROMAKS (Programmefor the Optimal Management of Petroleum Resources) project,“Quantifying the effects of sediment deposition, compaction and pore fluidon rock properties and seismic signature” funded by the NorwegianResearch Council (NFR). We thank technical staff both at the Departmentof Geosciences, University of Oslo and at the Norwegian GeotechnicalInstitute (NGI) for their assistance during the experimental and analyt-ical work. We also acknowledge our industry partner StatoilHydro foradditional financial support. TLE

Corresponding author: [email protected]


elastic properties of clay minerals

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