Elastic properties of clay minerals

Elastic properties of clay minerals NAZMUL HAQUE MONDOL, JENS JAHREN and KNUT BJØRLYKKE, University of Oslo, Norway IVAR BREVIK, StatoilHydro, Trondheim, Norway

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 in mudstones and are also often found in clastic and nonclastic reservoir rocks. Their presence alters the elastic behavior of reservoir rocks significantly as a function of mineral type, volume and distribution. Thus, two sandstones with the same clay amount might have different elastic properties due to differences within the clay population. The elastic properties of clay minerals are therefore important in rock physics modeling to understand the seismic and sonic log responses of shaley sequences and clay-bearing reservoir rocks. However, the elastic properties of clay minerals are not well constrained due to their fine-grained nature. Measuring elastic properties of clay minerals from natural mudstones is extremely difficult and time consuming due to preserva-

tion, physiochemical behavior, and low permeability. A few measurements of clay mineral elastic properties are found in literature, but there is little agreement between the measurements (Table 1). The discrepancy is probably related to different experimental techniques that do not account for the physicochemical behavior of clay minerals. The layer charge and large surface area of clays mean that they interact strongly with pore fluids, and extensive heating before or during testing may both dehydrate and modify their structure and thus their elastic properties. The small grain size of clays makes it nearly impossible to isolate an individual grain for direct measurement of rock properties. Therefore, instead of direct measurements, theoretical computation, a combination of theoretical and experimental investigations, and the empirical extrapolations of laboratory measurements has been used to derive elastic properties of clays.

Table 1. Acoustic and elastic properties of kaolinite and smectite grains found in the literature. 758

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Figure 1. (a) Uniaxial oedometer equipped with acoustic velocity measurement apparatus. (b) Porosity reduction and bulk-density changes in mechanically compacted, brine-saturated (BS) kaolinite aggregates as a function of vertical effective stress. The equation of best fit line and correlation coefficient (R2) of the bulk density-effective stress relationship for kaolinite (BS) aggregates are shown. (c) Representative waveforms for P- (blue) and Swave (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 green lines, 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 smectite aggregate (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 endmember clay minerals, smectite and kaolinite. They are “end members” in the sense that smectite is the most fine-grained clay found in nature and has a high cation exchange capacity and large surface area (700 m2/g), while kaolinite is coarse-grained and has a much lower cation exchange capacity and smaller surface area (10 m2/g) compared to other clay minerals. Smectite is the volumetrically most abundant detrital clay mineral in Cenozoic basins world wide. Kaolinite is a common component of well-drained soils in humid climates, which gets reworked into sandstones and mudstones. In this study, both dry and brine-saturated kaolinite and smectite aggregates were compacted mechanically in the lab to derive the elastic parameters (bulk and shear modulus, Young’s modulus, Poisson’s ratio, and the Lame constant m) of the kaolinite and smectite grains, respectively. The elastic parameters of smectite and kaolinite suggested in this study are not the direct measurement. The elastic parameters were deduced from empirical extrapolation of lab

measurements of changes in porosity, density, VP, and Vs during experimental compaction as a function of increasing vertical effective stress. The following steps were performed to obtain the elastic properties: • First, the porosity reduction (w), the changes in bulk density (rb), and the compressional (VP) and shear wave (Vs) velocities of dry and brine-saturated kaolinite and smectite aggregates were measured in the lab as a function of vertical effective stress (Figures 1b and 2). A high stress uniaxial odometer (Figure 1a) cell was used to perform the mechanical compaction test. • Next, the measured VP, Vs and rb were used to calculate the elastic parameters of equivalent dry and brine-saturated smectite and kaolinite aggregates. • Finally, the elastic parameters of smectite and kaolinite grains were derived from the extrapolation of porosityelastic moduli relationships to smectite and kaolinite aggregates with zero porosity (Figures 4 and 5). These JUNE 2008

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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.

extrapolations assume that the aggregate moduli at zero porosity represent the equivalent elastic moduli of smectite and kaolinite grains, respectively. A polynomial regression of best fit approximation was applied to the data for the extrapolation (Figures 4 and 5). The estimated values of elastic moduli may improve by adding more data of compacted smectite and kaolinite aggregates at higher effective stresses (stresses higher than the maximum effective stresses applied for this study). Adding such tests will only improve the derived moduli marginally. This is because the extrapolation of porosity-depth trends of data found in the lab measurements and data from Chilingarian and Knight (1960) suggest that smectite and kaolinite aggregates will retain a high porosity even at extremely high effective stresses if the compaction process is purely mechanical (i.e. stress driven, Figure 1d). It will therefore be difficult or impossible to compact smectite and kaolinite aggregates mechanically down to zero porosity. The compaction tests show that maintaining brine-saturated smectite aggregates at hydrostatic pore pressure is very time consuming. This is due to low permeability of the smectite aggregates; therefore, there is a tendency to develop a high pore pressure (Mondol et al. 2007) during testing of smectite. The estimated values of elastic moduli derived from the experiments were tested by comparing them with an established shale database (Brevik, 2005) and the lab measurements of Han et al. (1986) and Yin (1992). To check the reliability, the estimated elastic moduli values (Table 2) and the values reported by Vanorio et al. (2003), Wang et al.(2001), and Katahara (1996) were used in effective medium modeling and in the Gassmann fluid substitution model. The modeling results were compared to the shale database found in Brevik. 760

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Materials and methods. Experimental mechanical compaction tests and velocity measurements of dry and brinesaturated smectite and kaolinite aggregates were performed at the Norwegian Geotechnical Institute (NGI). All experiments were performed at room temperature, which was between 190C and 210C. A high-stress uniaxial oedometer (no lateral strain allowed) equipped with acoustic measurements transducers (Figure 1a) was used to conduct the experiments. The methods used for mechanical compaction and velocity measurements have been presented in detail by Mondol et al. (2007; 2008). Oven-dried (600C for 3–4 days) clay powder was used for the dry tests. For brine-saturated tests, clay slurries were prepared by mixing dry clay powder with water with a salinity of about 34 000 ppm (parts per million). To achieve optimal saturation, the brine-saturated slurries were prepared by thoroughly mixing the clays with water to a water content equal to 1.5 times the liquid limit. The mineralogical composition of the smectite aggregates is smectite (89%), cristobalite (9%), and quartz (2%), while the mineralogical composition of the kaolinite aggregates is kaolinite (81%), illite/mica (14%), and microcline (5%). The density of the smectite and kaolinite grains were measured in the laboratory 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 porosity and bulk density changes as a function of effective stress (Figure 1b) were measured throughout the tests from the expelled air or brine volume of the dry and brine-saturated smectite and kaolinite aggregates, respectively. The acoustic velocity measurements were performed throughout the compaction experiments as the effective stress was increased. The P- and S-wave pulses that traveled through the sample to the receiver transducers were recorded by a computer and used to compute acoustic velocity. VP and

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 compactioninduced 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. At the same porosity or bulk density, VP and VS of smectite aggregates are higher than the kaolinite aggregates.

sure, ±50 m/s in VP and ±32 m/s in Vs measurements. Results. The measured VP and Vs are plotted for the dry and brine-saturated kaolinite and smectite aggregates as functions of effective stress and porosity and density in Figures 2 and 3, respectively. The dry clay aggregates compacted less when compared with the equivalent brine-saturated aggregates at the same effective stress. Both dry and brine-saturated kaolinite aggregates (Figures 3a and 3c) compacted more, compared with smectite aggregates (Figures 3b and 3d). The Table 2. The elastic and acoustic properties of kaolinite and smectite grains. dry kaolinite aggregates compacted to about 28% porosity at 50 MPa effecVs were determined by measuring the time taken for an tive stress (Figure 3a), whereas the dry smectite aggregates ultrasonic pulse to traverse the sample. Traveltimes measured retained a higher porosity (about 45%) at the same effective from the reference signals are then compared with measured stress (Figure 3b). The brine-saturated kaolinite aggregates specimen traveltimes for estimating sample velocities. The compacted to about 10% porosity at 50 MPa effective stress reference traveltime measurements were taken with the trans- (Figure 3c), while the brine-saturated smectite aggregates ducers coupled to each other in head-to-head configuration. retained a porosity of about 35% at the same stress level Figure 1c shows a representative waveform recorded at 50 (Figure 3d). Published data from Chilingarian and Knight MPa effective stress for the P- (blue) and S-wave (black) and the extrapolation of our experimental results suggest polarization parallel to the stress direction. First arrival time that mechanical compaction of clay aggregates down close picks are shown on the waveforms by red (P-wave) and to zero porosity is nearly impossible (Figure 1d). green (S-wave) lines (Figure 1c). The estimated experimenThe velocity increases in both dry and brine-saturated tal errors are ±0.025 MPa or 0.6% in load/stress, ±0.02 mm kaolinite and smectite aggregates, as functions of effective or ±1.5% in deformation, ±0.005 MPa or ±0.6% in pore pres- stress, porosity, and density are shown in Figures 2 and 3. 762

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Figure 4. Bulk modulus (a) and shear modulus (b) of brine-saturated kaolinite (blue circles) and smectite (red circles) aggregates as a function of total porosity. The elastic parameters of kaolinite and smectite grains were derived from the extrapolation of the calculated elastic properties of mechanically compacted brine-saturated kaolinite and smectite aggregates, respectively to zero porosity. The derived bulk and shear moduli of kaolinite and smectite grains are shown on the y-axis (red and blue 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 are given.

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 total porosity. The elastic moduli of kaolinite and smectite grains were derived from the extrapolation of the calculated elastic moduli of mechanically compacted dry kaolinite and smectite aggregates, respectively, to zero porosity. The derived bulk and shear moduli of kaolinite and smectite grains are shown on the y-axis (red and blue crosses). The grey lines show the polynomial fits to the data. Equations of best fit lines and the correlation co efficient (R2) of the relationship between porosity and the bulk and shear modulus are given.

The difference between VP and Vs was relatively less in dry aggregates (Figures 2a and 2b) compared to the brine-saturated 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 and smectite aggregates, respectively, as a function of effective stress where dry smectite aggregates shows slightly higher VP then the dry kaolinite aggregates. The Vs is nearly identical for both dry kaolinite and smectite aggregates (Figures 2a and 2b). The VP and Vs development in both brine-saturated kaolinite and smectite aggregates vary compared to the dry aggregates where both the VP and Vs in kaolinite aggregates are higher compared to the smectite aggregates as a function of effective stress (Figures 2c and 2d). The measured VP, Vs and
b were used to calculate the elastic parameters (K, m, E,  and λ) of the kaolinite and smectite aggregates. The calculated elastic parameter of the dry and brine-saturated kaolinite and smectite aggregates are plotted as a function of porosity in Figures 4 and 5. The polynomial fit to the data for the relationship between porosity and the elastic parameters was drawn and extrapolated to zero porosity (Figures 4 and 5). The elastic moduli of kaolinite and smectite aggregates at zero porosity (marked by y-

axis crosses on Figures 4 and 5) represent the elastic moduli of zero-porosity smectite and kaolinite aggregates that could correspond theoretically to the elastic moduli of kaolinite and smectite grains. The estimated elastic parameters of kaolinite and smectite grains derived from the dry and brine-saturated kaolinite and smectite aggregates, respectively are presented in Table 2. The VP and Vs of individual kaolinite and smectite grains were also estimated by the extrapolation of porosity-velocity relationships to zero porosity and are shown in Table 2. The equations of polynomial fits and correlation coefficients of different relationships are given in Figures 4 and 5. The elastic parameters of kaolinite and smectite grains derived from the dry and brine-saturated kaolinite and smectite aggregates differ significantly and this may be due to the interaction between brine and the clay minerals. Higher values of VP, K and  are observed for both kaolinite and smectite grains at brine-saturated conditions compared to dry conditions. The opposite were observed for VS, , and E where higher values were found for the dry state compared to the brine-saturated state (Table 2). The  is significantly lower for the dry condition compared to the brine-saturated condition for both smectite and kaolinite grains. The Poisson’s ratio of kaolinite and smecJUNE 2008

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tite are not suggested for the dry state as the empirical extrapolation of measured data to zero porosity is unrealistic. To test the reliability of the estimated bulk and shear modulus values found in this study, the results were compared to a well-defined natural shale database constructed from well logs from different parts of the world (Brevik 2005), data of Han et al. (1986) and Yin (1992) and additional lab measurements of kaolinite-smectite and kaolinite-silt mixtures (additional lab measurements performed for this study). Comparison with published data and additional lab measurements. Figure 6 shows a comparison of lab measurements (this study) and published data of both bulk and shear modulus versus porosity for a variety of mudstones, shales, and shaley sandstones. Both brine-saturated kaolinite and smectite aggregates, the additional lab measurements of two kaolinite-smectite (80:20 kaolinite-smectite and 20:80 kaolinite-smectite by weight), and a silt-kaolinite (50:50 by weight) mixture, and published data from Han et al., Yin, and Brevik are included for the comparison. The Brevik database included 70 wireline logs in sequences of pure shales. A simple data reduction filter was applied to the data to pick pure shales. The pure shales were defined as a volumetric clay volume (normalized to the solid volume) of more than 75%. Yin’s data are lab measurements of brine-saturated kaolinite powder with particle size ranges from 1–4 micrometers. The data from Han et al. are lab measurements of 12 cores of shaley sandstones from the Gulf of Mexico that contain 30–50% clays by volume. The bulk and shear modulus of kaolinite and smectite grains estimated by this study (values derived from the empirical extrapolation of data to zero porosity) are shown on the y-axes of Figures 6a and 6b by the magenta dots. The lab-derived kaolinite bulk modulus from kaolinite aggregates agrees reasonably well with the measured bulk modulus of Yin (1992) for brine-saturated kaolinite (Figure 6a), but the shear modulus from Yin (1992) for the same sample shows significantly higher values compared to the lab measurements (this study) as well as the natural shale database from Brevik (Figure 6b). From the comparison, it could be stated that the bulk and shear modulus of the brine-saturated smectite and kaolinite aggregates represent the upper and lower limits of bulk and shear modulus of natural shales reported by Brevik. The empirical extrapolation of bulk and shear modulus of brine-saturated smectite and kaolinite aggregates representing end-member clays encompass nearly the whole range of the data derived from natural shales. The lab data and its extrapolation represent a much better fit to the upper and lower limits of bulk modulus of the natural shale database than to the shear modulus of the same database (Figures 6a and 6b). Only a few scattered bulk modulus data points from natural shales fall outside the range suggested by the smectite and kaolinite derived values at low porosity (porosity