THE EFFECT OF CEMENTATION ON THE SEISMIC PROPERTIES OF SANDSTONE:

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1 THE EFFECT OF CEMENTATION ON THE SEISMIC PROPERTIES OF SANDSTONE: Xavier Du Bernard, Manika Prasad, Michael Reinstaedtler * 1. INTRODUCTION Composition and cementation are two major parameters that control the elastic properties of granular media. The different types of cement found in sandstones depend on their depositional and burial environments. In this paper, we consider how the type of cement and the stiffness of the bond determine the strength and seismic properties of the rock. It is well recognized that P- and S-wave velocities in rocks samples reduce with clay content, when the clay is load-bearing 1. This reduction in velocity is mainly due to the low elastic moduli in clay minerals. For example, the Young s modulus of a clay mineral, dickite can be as low as 6 GPa 2. Although it has been long recognized that contact micromechanics play a major role in governing wave propagation in granular media, a direct relation between the impedance of different types of contacts in sandstones and the elastic moduli of the rock is largely unknown. We have analyzed three types of contact zones in sandstones using optical microscopy, Scanning Electron Microscopy (SEM), Scanning Acoustic Microscopy (SAM), and compared these observations to measurements of elastic moduli as functions of pressure using ultrasonic pulse transmission experiments in the laboratory. A quantitative analysis of the contact impedance is presented using SAM. Traditionally, SEM and optical microscopy are used to characterize microstructure. By using SAM in conjunction with these traditional techniques, we were able to identify the contacts zones and measure their contact stiffnesses in terms of elastic impedance. The aim of this study was to quantify and compare impedance changes corresponding with quartz quartz cements and quartz clay cements in sandstones and their effects on the seismic properties. Such analyses will allow us to gain an understanding of the contact mechanism controls on wave propagation and their predictions from indirect seismic measurements. * Manika Prasad, Geophysics Department, Stanford University, Stanford, CA 9435, USA, Xavier Du Bernard, Laboratoire de Géophysique Interne et Tectonophysique (UMR 5559), BP 53X, 3841 Grenoble cedex 9, France. Michael Reinstaedtler, Fraunhofer-Institute for Nondestructive Testing (IZFP), University, Bldg. 37, D Saarbrücken, Germany. 1

2 2 DU BERNARD ET AL. 2. EXPERIMENTAL METHODS We have used scanning acoustic microscopy (SAM) at 1 GHz to measure impedance in various rocks. The instrument operated at 1 GHz. SAM can be best understood in geophysical terms as microscopic analogs to side-scan sonar and reflection seismic mapping 3. C-scans of surface and subsurface features were used to study impedance changes in the sample quantitatively 4,5. By making a gray scale calibration using materials of known impedance, the acoustic images of the sandstones were evaluated for impedance variations as functions of cementation strength 6. A set of standard materials was selected to calibrate the gray scale of the instrument to known impedance values. The expected impedance in the unknown sample lay within the impedance values of the standard materials. The procedure is describes in detail in Prasad et al., The gray scale variations in the unknown image were determined from the calibration plot of reflection coefficient versus impedance based on a least-square fit. Approximately 1-15% error is to be expected due to instrumental drift, especially if calibrations are not performed often or if the sample has large variations in surface topography. Figure 1 shows the reflection coefficient versus impedance plot for the standard samples used in this study along with values for common rock-forming minerals. Expected variations in the impedance of reservoir rocks lie between 1.5 Mrayls (water) and 37 Mrayls (pyrite). Two sets of calibration standards were used to map the impedance variations in the rock samples, a low (8 1.5 Mrayls) and a high ( Mrayls) impedance group. Reflection Coefficient Low impedance AS 2 S 3 Acrylic Polycarbonate HDPE Polystyrene LDPE High impedance Copper Titanium Silicon Aluminum Glass Magnesium Impedance (MRayls) Figure 1. Reflection coefficient values plotted versus impedance for the materials used for gray scale calibration. Two sets were used, the softer plastic materials covered the lower impedance values. Metals and glasses covered the upper impedance range (from Prasad et al., 22 6 ). P- and S-wave velocities (Vp and Vs, respectively) were also measured as functions of pressure on room-dry core plugs. The pulse transmission technique was used for the measurements 7. The experimental setup consists of a digital oscilloscope and a pulse generator. The sample was jacketed with rubber tubing to isolate it from the confining pressure medium. PZT-crystals mounted on steel endplates were used to generate P- and S- waves. The principal frequency was about 1 MHz for P and 7 MHz for S-waves. A high viscosity-bonding medium (Panametrics SWC) was used to bond the endplates to the sample. The experimental configuration allowed simultaneous measurements of P- and S-waves at various confining pressures up to 3 MPa. Travel time was measured after digitizing each

3 CEMENT STIFFNESS IN SANDSTONES 3 trace with 124 points at a time sweep of 5 µs, thus allowing a time resolution of about 5 ns (=.2% velocity error). Total error in velocity measurement is estimated to be around 1% due to operator error in picking first arrival. The system delay time was measured by taking headto-head time at 2 MPa. The travel-time calibration was confirmed by measuring an aluminum cylinder at different pressures. We used an SEM equipped with an EDAX thin-window energy dispersive x-ray detector to determine the composition of the cement. 3. SAMPLES AND PETROPHYSICAL CONSIDERATIONS We present here results of SAM analyses on sandstone samples to demonstrate the applicability of quantitative scanning acoustic microscopy for determining cementation strengths. Table 1 gives a list of the samples along with their main petrophysical characteristics and composition. The samples used were either thin-sections with the final polish made with.1 µm polishing powder (for SAM) or 25.4 mm diameter core plugs (for Vp and Vs measurements). The samples for this study came from a variety of environments. They were chosen to represent different cementation textures of quartz quartz, quartz clay, and a mixture of both. These samples allowed us to analyze the effect of cement stiffness on pressure - velocity relations. Table 1. Petrophysical properties of the samples used for this study Sample Clay content (%) Porosity (%) Permeability (md) Cement composition Composition Boise < Quartz Arkose Berea Clay and quartz Quartz arenite Nubian Clay Quartz arenite The petrophysical properties of sedimentary rocks at depth depend largely on their sedimentation history and their evolution from deposition to compaction and cementation during burial. As sediments are deposited and they undergo compaction, their porosity decreases and velocity increases with depth. Cementation and pore-filling events cause the porosity and velocity trends to deviate from the normal. Once cementation occurs, the sediment develops a frame that resists compaction and porosity reduction proceeds at a reduced rate. The increase in sediment-frame stiffness due to cementation also causes an abrupt increase in velocity. The absolute increase in velocity depends on the stiffness of the cementing material. The strength of the cement controls any further mechanical compaction behavior of the sediment. Thus, the compliance of contact cements sandstones is an important factor in studying their velocity and its dependence on pressure 8,9. It has been observed that clay minerals in sandstones can affect wave velocities considerably 1. Velocity is lower in sandstones containing clay than in those without clay. Figure 2 shows the changes in P-wave velocity as a function of porosity in sandstones with

4 4 DU BERNARD ET AL. varying amounts of clay content. At the same porosity, velocity decreases as clay content in the sandstones increases. Clay content Vp (km/s) Porosity Figure 2. P-wave velocity (V P ) variation as a function of porosity in sandstones. The data are color coded according to clay content. The color bar on the right gives clay content corresponding to each color. At the same porosity, velocity decreases with increasing clay content 1. The effect of clay minerals on wave propagation in glass is shown in Figure 3 6. Addition of a clay layer to glass discs dampens waves significantly. The signals displayed show signal damping after applying a.5 mm thick clay layer in the contact region between the glass discs. The effect is more pronounced in the S-waves than in the P-waves. The amplitudes of both signals, in particular that of the S-signal decrease significantly. In this work, we have tried to quantify the grain boundary cement strength in terms of impedance using SAM in a micrometer-scale sample. We then compare this cement strength to the velocity of a cm-scale sample and show how quantifying microstructure as impedance variations can help understand the effects of cement stiffness in sandstones receiver 19.6 mm with clay layer with couplant -25 w ith clay layer -5 w ith couplant.5 mm sender Figure 3. P- and S-waves through glass discs as shown on the right. Gray lines depict signals traveling through glass only and black lines represent signals through two glass discs separated by a.5mm layer of clay 6. Signals deteriorate on addition of clay to the contact area between the glass discs. The shear wave marked by a thin black line was made with the transducers at cross-polar position to ascertain shear arrival (thick black line).

5 CEMENT STIFFNESS IN SANDSTONES 5 4. RESULTS Figure 4 illustrates the velocity pressure relations for the three sandstones. The upper row shows results from the ultrasonic experiments and the lower row shows impedance textures. Starting first with the ultrasonic results, velocity values are highest in the Boise sandstone followed by Berea sandstone. The Nubian sandstone has lowest velocity. Although velocity increases with pressure, at 25 MPa Vp in Nubian sandstone is much lower than in the other two samples. The pressure dependence of velocity and porosity gives an indication of the mechanical strength of the samples. Boise sandstone does not show much change in velocity (about 1%) and porosity (less than 2%) with pressure. In contrast, the Nubian sandstone with lowest velocity amongst the three shows maximum change in velocity (about 2%) and porosity (about 6%). The Berea sandstone with a mixed cement lies between the two extremes, very stiff (Boise) and very compliant (Nubian). An examination of the microimpedances provides the reason for the velocity differences between the sandstones and the velocity variations with pressure for each sample. In Boise sandstone, the impedance of the cement is comparable to that of the grains resulting in a very stiff composite. In both other cases, the stiffness of the clay cement is much lower and so the composite is weaker and deforms more with pressure. Vp (km/s) Berea Boise Nubian Vp change (%) Nubian Berea Boise Porosity change (%) Nubian Berea Boise Pressure (MPa) Pressure (MPa) Pressure (MPa) 2 µm 312 µm 1 µm Figure 4. Top: P-wave velocity, V P (left), Vp-change (middle) and porosity change (right) as functions of pressure in Boise (strar), Berea (open circles), and Nubian (gray circles) sandstones measured in cm-sized core-plugs. Bottom: Microstructure and impedance variations imaged with acoustic microscopy in Boise (left), Berea (middle), and Nubian (right) sandstones. Impedance contrast is low between the grains and the cement region in Boise sandstone whereas it is quite significant in the Berea sandstone. In the Nubian sandstone, there is a large zone of low

6 6 DU BERNARD ET AL. impedance between adjacent grains. This low impedance is reflected in the low P-wave velocity and the large change in velocity with pressure. We now compare the impedance values obtained from the ultrasonic experiments on cmsized samples and from scanning acoustic microscopy on a micrometer scale in Table 2. The ultrasonic impedance was calculated from P-wave velocity measurements and density. The micro-impedance values, given only for the contact zone, were determined by using the calibrated gray scale made with standard materials of known impedance. In Table 2, we also present calculations for impedance of clay and quartz cements and for sandstones with clay cement (as an analog for Berea and Nubian sandstones) and with quartz cement (as an analog for Boise sandstone). These calculations were made using the cementation model 9. In our calculations, we took the Young s modulus of clay as 6 GPa and its Poisson s ratio as.3 2. For the three sandstones, the impedance values obtained from the ultrasonic experiments and those calculated by the cementation model are quite similar. Although the calculation does not take into account the grain size, the roughness and the geometry of contact, these results lead us to conclude that the nature of cement is one of the major parameter controlling the seismic properties of detrital sedimentary rocks. Consistent with observations, the ultrasonic velocity in Berea and in Nubian sandstone is better modeled using clay cement while quartz cement allows a more accurate estimation of velocity for the Boise sandstone. Table 3. Impedance values of the sandstones from ultrasonic and acoustic microscopy measurements. Note that impedance of quartz = 15.9 and of clay 9. Sample Porosity (%) Ultrasonic impedance Cement impedance Cement impedance normalized by quartz Calculated impedance Boise Berea Nubian CONCLUSIONS We have shown how quantitative acoustic microscopy can be used for petrophysical studies of reservoir rocks. The gray scale of acoustic microscopy images is calibrated with materials of known impedance. Variations of micro-impedance values in unknown samples can be determined by comparing the gray scale of their images with the calibration values. In the sandstones, quantitative acoustic microscopy results showed significant changes in microstructural impedance of the cement. In our case study of sandstones with varying types of cements, quantitative acoustic microscopy helps to interpret and understand the impedance variations as functions of cement strength. The differences in cement impedance at a micrometer scale can explain the impedance of a cm-sized sample obtained from the ultrasonic experiments. Our observations reveal that 1. The quartz cement in Boise sandstone has higher impedance than the kaolinite cement in Berea and Nubian sandstones. 2. The cement impedance controls velocities, elastic moduli, and Poisson s ratio of the sandstones.

7 CEMENT STIFFNESS IN SANDSTONES 7 3. The cement impedance also controls the amount of strain in a rock as it is subjected to pressure. Such studies will help By relating different types of cement and their stiffness to the seismic properties of the whole rock, our results indicate how nature and properties of cement are important to estimate the strength of a granular rock. In the future, it would be interesting to include new type of cement, in particular carbonate, in order to complete the survey of cements in sandstones. With more examples, it could be possible to derive a clear and useful relationship linking wave velocities to the amount and composition of cement. 6. ACKNOWLEDGEMENTS X.B. s was supported by IFP and he is grateful to I. Moretti and B. Colletta for their confidence. M.P.'s work was performed under the auspices of National Science Foundation (Grant No. EAR 7433) and Department of Energy (Award No. DE-FC26-1BC15354). The acoustic microscopy was performed at the Fraunhofer-Institute for Nondestructive Testing (IZFP) in Saarbrücken, Germany. We thank Walter Arnold for critical discussions, comments and help. 7. REFERENCES 1. D. Han, A. Nur, and F. D. Morgan, Effect of porosity and clay content on wave velocities of sandstones, Geophysics: 51: , M. Prasad, M. Kopycinska, U. Rabe, and W. Arnold, Measurement of Young s modulus of clay minerals using Atomic Force Acoustic Microscopy, Goephys. Res. Lett., 29, #8, , M. Prasad, Mapping impedance microstructures in rocks with acoustic microscopy, The Leading Edge: 2: , S. Hirsekorn, and S. Pangraz, Materials characterization with the acoustic microscope, Appl. Phys. Lett.: 64: , S Hirsekorn,. S. Pangraz, G. Weides, and W. Arnold, Measurement of elastic impedance with high spatial resolution using acoustic microscopy, Appl. Phys. Lett., 67: , M. Prasad, M. Reinstaedtler, and W. Arnold, Quantitative acoustic microscopy: Applications to petrophysical studies of reservoir rocks: Acoustical Imaging, 26, Kluver Publications, , M. Prasad, G. Palafox, and A. Nur, Velocity and Attenuation Characteristics of Daqing sandstones: Effects of permeability on velocity and attenuation anisotropy: AGU Fall Meeting, EOS, v. 8, M. Prasad, Correlating Permeability with Velocity using Flow Zone Indicators: Geophysics, 68, #1, , J. Dvorkin, J., A. Nur, and H. Z. Yin, Effective properties of cemented granular-materials: Mechanics of Materials, 18, , 1994.