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- Volume 67, Issue 4, 2019
Geophysical Prospecting - 4 - Rock Physics: from microstructure to seismic signatures, 2019
4 - Rock Physics: from microstructure to seismic signatures, 2019
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Research note: the effect of strain amplitude produced by ultrasonic waves on its velocity
Authors Nazanin Nourifard and Maxim LebedevABSTRACTThe effect of the amplitude of ultrasonic waves propagating through a sample is not often taken into account in laboratory experiments. However, ultrasonic waves can produce relatively large strain inside the sample, and thus change the properties of the sample. To investigate the effect of strain amplitude on the P‐wave velocity, a series of ultrasonic wave propagation experiments were carried out on three different media. All measurements were performed at 1 MHz central frequency and at the strain levels inside propagating waves of ∼3.0 × 10−6 to 6.0 × 10−5 without applying confining pressure to the sample. Strains in the waves were measured by a laser Doppler interferometer upon wave arrival on a free surface of the sample. The ultrasonic velocities were measured by a pair of P‐wave transducers located at the same measuring point as the laser beam of the LDI. The effect of strain on P‐wave velocity varied for different material. The P‐wave velocity was calculated using both a first arrival and a first maximum peak at different applied voltage. The P‐wave velocity remained unchanged for a pure elastic medium (aluminium); however, the velocity increased continuously with the increasing of the strain for polymethylmethacrylate and Gosford sandstone. For Gosford sandstone, velocity increases up to 0.8% with strain increase from 7.0 × 10−6 to 2.0 × 10−5. This effect of velocity increase with the strain induced by an ultrasonic wave can be explained by the in‐elasticity of both the polymethylmethacrylate and Gosford sandstone samples.
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Elastic properties of sands, Part 1: Micro computed tomography image analysis of grain shapes and their relationship with microstructure
Authors Zubair Ahmed and Maxim LebedevABSTRACTElastic properties of an unconsolidated sand are largely dependent on the elastic properties of its constituent grain and the micro‐structure that defines how the grains are arranged within themselves. Coordination number, that is the average number of contacts a grain has with its neighbours, and contact surface area are the two parameters closely related to the microstructure. Moreover, grain shapes and sorting also have substantial influence on these parameters. To calculate these parameters and find any potential relationships with the shape factors, we acquire high‐resolution micro computed tomography images of four mechanically compacted unconsolidated dry sand samples that are of different shape factors and sorting indices. After a comprehensive voxel‐based data processing, we calculate shape factors such as sphericity and roundness of each grain in all samples. Using own algorithm, we then calculate the coordination number and contact surface area. Results show that samples of well‐sorted and higher spherical and rounded grains have higher coordination number and contact surface area than the samples of poorly sorted and lower spherical and rounded grains. Among the poorly sorted samples, coordination number is largely dependent on the fraction of larger grain sizes present in the sample. Inside any given sample, grains of lower sphericity tend to have higher coordination numbers. Moreover, more spherical and rounded grains have greater contact surface area with their neighbours.
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Elastic properties of sands, Part 2: Implementation of contact‐based model to determine the elasticity of the grains from ultrasonic measurements
Authors Zubair Ahmed and Maxim LebedevABSTRACTThe prediction of effective elastic properties of a granular medium using ultrasonic data based on contact models has been studied widely in both laboratory experiments and numerical simulations. In contrast, a calculation of the elastic properties of the constituent grains using similar data by inverting the equations from those models is a rather new concept. To do so, we have developed a controlled experiment technique that includes a uniaxial compaction test and measures ultrasonic velocities of four unconsolidated quartz sand samples with different sorting and grain shapes. We observe that both P‐ and S‐wave velocities are significantly influenced by the microstructure or internal arrangement of the grains. Well sorted and more spherical and rounded samples show higher velocities than the poorly sorted and less spherical and rounded samples. A microstructural parameter – namely coordination number – we have calculated from high resolution micro computed tomography images provides a good match between the model and dynamic effective bulk moduli of the sand pack. Combining this coordination number with a frictional parameter calculated from the measured velocity ratios has been very effective to fit the model with the dynamic effective shear moduli. Using these two key parameters along with the experiment results in the contact model we have been able to obtain the elastic parameters of the quartz sand grains in the sample. Elastic parameters obtained thus are very close to the actual values of the quartz grains found in the literature. This technique can be useful in hard rock mineral exploration where missing core samples or an absence of well logs can be replaced by laboratory measurements of powders to find the elasticity or velocities of the rocks. Moreover, the elastic properties of the solid phase calculated using this technique can be used as input parameters for the fluid substitution and rock physics characterization of unconsolidated reservoir sands.
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Acoustic emission processes occurring during high‐pressure sand compaction
Authors Andrea Muñoz‐Ibáñez, Jordi Delgado‐Martín and Elisa Grande‐GarcíaABSTRACTGranular materials submitted to uniaxial compression undergo pore space reduction due to mechanisms such as particle rearrangement and grain crushing. These changes in the internal structure of the material release energy in the form of elastic waves that can be detected by sensors sensitive to acoustic emission. In this study, Acoustic emission monitoring with a wavelet‐based signal processing technique is used to identify the various mechanisms occurring during high‐pressure sand compaction. Particle movement, grain failure, friction between grains and the surface of the compression cell and intergranular friction are studied. Acoustic emission data recorded during these simplified tests are used to characterize each phenomenon. Wavelet transform analyses allow the identification of useful features, making possible frequency discrimination among sliding, rolling, friction and grain fragmentation processes. For instance, we observe that at low stress, grain flow is characterized by the lowest centroid and peak frequencies, while at greater stresses, intergranular friction and grain fragmentation have the higher values. In the tests performed, the stress–strain evolution and final condition of the tested sand are broadly consistent, irrespective of the condition employed: continuous, stepwise or even variable loading rate or temperature. However, Acoustic emission data manifest much more complex behaviour (including thermal, load‐rate dependency and delayed fragmentation phenomena) than that suggested by stress–strain relationships. At low stress levels, grain flow (sliding/rolling) is a relevant strain‐accommodation mechanism, but so is crushing due to the effect of concentrated forces at the grain contact level. At high stresses, when crushing is generalized, intergranular friction is also a relevant phenomenon due to the increase in the coordination number produced by previous fragmentation.
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Comparison of stress‐dependent geophysical, hydraulic and mechanical properties of synthetic and natural sandstones for reservoir characterization and monitoring studies
ABSTRACTSynthetic rock samples can offer advantages over natural rock samples when used for laboratory rock physical properties studies, provided their success as natural analogues is well understood. The ability of synthetic rocks to mimic the natural stress dependency of elastic wave, electrical and fluid transport properties is of primary interest. Hence, we compare a consistent set of laboratory multi‐physics measurements obtained on four quartz sandstone samples (porosity range 20–25%) comprising two synthetic and two natural (Berea and Corvio) samples, the latter used extensively as standards in rock physics research. We measured simultaneously ultrasonic (P‐ and S‐wave) velocity and attenuation, electrical resistivity, permeability and axial and radial strains over a wide range of differential pressure (confining stress 15–50 MPa; pore pressure 5–10 MPa) on the four brine saturated samples. Despite some obvious physical discrepancies caused by the synthetic manufacturing process, such as silica cementation and anisotropy, the results show only small differences in stress dependency between the synthetic and natural sandstones for all measured parameters. Stress dependency analysis of the dry samples using an isotropic effective medium model of spheroidal pores and penny‐shaped cracks, together with a granular cohesion model, provide evidence of crack closure mechanisms in the natural sandstones, seen to a much lesser extent in the synthetic sandstones. The smaller grain size, greater cement content, and cementation under oedometric conditions particularly affect the fluid transport properties of the synthetic sandstones, resulting in lower permeability and higher electrical resistivity for a similar porosity. The effective stress coefficients, determined for each parameter, are in agreement with data reported in the literature. Our results for the particular synthetic materials that were tested suggest that synthetic sandstones can serve as good proxies for natural sandstones for studies of elastic and mechanical properties, but should be used with care for transport properties studies.
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Acoustic and petrophysical properties of mechanically compacted overconsolidated sands: part 1 – experimental results
Authors Sirikarn Narongsirikul, Nazmul Haque Mondol and Jens JahrenABSTRACTThis paper part one is set out to lay primary observations of experimental compaction measurements to form the basis for rock physics modelling in paper part two. P‐ and S‐wave velocities and corresponding petrophysical (porosity and density) properties of seven unconsolidated natural sands with different mineralogical compositions and textures are reported. The samples were compacted in a uniaxial strain configuration from 0.5 up to 30 MPa effective stresses. Each sand sample was subjected to three loading cycles to study the influence of stress reduction on acoustic velocities and rock physical properties with the key focus on simulating a complex burial history with periods of uplift. Results show significant differences in rock physical properties between normal compaction and overconsolidation (unloaded and reloaded). The differences observed for total porosity, density, and P‐ and S‐wave velocities are attributed to irrecoverable permanent deformation. Microtextural differences affect petrophysical, acoustic, elastic and mechanical properties, mostly during normal consolidation but are less significant during unloading and reloading. Different pre‐consolidation stress magnitudes, stress conditions (isotropic or uniaxial) and mineral compositions do not significantly affect the change in porosity and velocities during unloading as a similar steep velocity–porosity gradient is observed. The magnitude of change in the total porosity is low compared to the associated change in P‐ and S‐wave velocities during stress release. This can be explained by the different sensitivity of the porosity and acoustic properties (velocities) to the change in stress. Stress reduction during unloading yields maximum changes in the total porosity, P‐ and S‐wave velocities of 5%, 25%, and 50%, respectively. These proportions constitute the basis for the following empirical (approximation) correlations: Δϕ ∼ ±5 ΔVP and ΔVP ∼ ±2ΔVS. The patterns observed in the experiments are similar to well log data from the Barents Sea. Applications to rock physics modelling and reservoir monitoring are reported in a companion paper.
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Rock physics modelling based on depositional and burial history of Barents Sea sandstones
Authors Kenneth Bredesen, Per Avseth, Tor Arne Johansen and Richard OlstadABSTRACTUnderstanding how physical properties and seismic signatures of present day rocks are related to ancient geological processes is important for enhanced reservoir characterization. In this paper, we have studied this relationship for the Kobbe Formation sandstone in the Barents Sea. These rocks show anomalous low shear velocities and high VP/VS ratios, which does not agree well with conventional rock physics models for moderately to well consolidated sandstones. These sandstones have been buried relatively deeply and subsequently uplifted 1–2 km. We compared well log data of the Kobbe sandstone with velocity–depth trends modelled by integrating basin modelling principles and rock physics. We found that more accurate velocity predictions were obtained when first honouring mechanical and chemical compaction during burial, followed by generation of micro‐cracks during uplift. We suspect that these micro‐cracks are formed as overburden is eroded, leading to changes in the subsurface stress‐field. Moreover, the Kobbe Formation is typically heterogeneous and characterized by structural clays and mica that can reduce the rigidity of grain contacts. By accounting for depositional and burial history, our velocity predictions become more consistent with geophysical observables. Our approach yields more robust velocity predictions, which are important in prospect risking and net erosion estimates.
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Rock physics model for seismic velocity & fluid substitution in sub‐resolution interbedded sand–shale sequences
Authors Nishank Saxena, Ronny Hofmann, Seán Dolan, Rituparna Sarker, Chen Bao and Stephan GelinskyABSTRACTThe measured geophysical response of sand–shale sequences is an average over multiple layers when the tool resolution (seismic or well log) is coarser than the scale of sand–shale mixing. Shale can be found within sand–shale sequences as laminations, dispersed in sand pores, as well as load bearing clasts. We present a rock physics framework to model seismic/sonic properties of sub‐resolution interbedded shaly sands using the so‐called solid and mineral substitution models. This modelling approach stays consistent with the conceptual model of the Thomas–Stieber approach for estimating volumetric properties of shaly sands; thus, this work connects established well log data‐based petrophysical workflows with quantitative interpretation of seismic data for modelling hydrocarbon signature in sand–shale sequences. We present applications of the new model to infer thickness of sand–shale lamination (i.e., net to gross) and other volumetric properties using seismic data. Another application of the new approach is fluid substitution in sub‐resolution interbedded sand–shale sequences that operate directly at the measurement scale without the need to downscale; such a procedure has many practical advantages over the approach of “first‐downscale‐and‐then‐upscale” as it is not very sensitive to errors in estimated sand fraction and end member sand/shale properties and remains stable at small sand/shale fractions.
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A semi‐empirical approach to model pressure dependence of elastic moduli in granular media accounting for variations of coordination‐number and Poisson‐ratio
Authors Angelo Sajeva, Davide Scarpellini, Pamela Tempone and Simone CapaccioliABSTRACTThe effective medium theory based on the Hertz–Mindlin contact law is the most popular theory to relate dynamic elastic moduli (or elastic velocities) and confining pressure in dry granular media. However, many experimental results proved that the effective medium theory predicts pressure trends lower than experimental ones and over‐predicts the shear modulus. To mitigate these mispredictions, several evolutions of the effective medium theory have been presented in the literature. Among these, the model named modified grain contact theory is an empirical approach in which three parametric curves are included in the effective medium theory model. Fitting the parameters of these curves permits to adjust the pressure trends of the Poisson ratio and the bulk modulus. In this paper, we present two variations of the modified grain contact theory model. First, we propose a minor modification in the fitting function for the porosity dependence of the calibration parameters that accounts for non‐linearity in the vicinity of the critical porosity. Second, we propose a major modification that reduces the three‐step modified grain contact theory model to a two‐step model, by skipping the calibration parameter–porosity fit in the model and directly modelling the calibration parameter–pressure relation. In addition to an increased simplicity (the fitting parameters are reduced from 10 to 6), avoiding the porosity fit permits us to apply the model to laboratory data that are not provided with accurate porosity measurements. For this second model, we also estimate the uncertainty of the fitting parameters and the elastic velocities. We tested this model on dry core measurements from literature and we verified that it returns elastic velocity trends as good as the original modified grain contact theory model with a reduced number of fitting parameters. Possible developments of the new model to add predictive power are also discussed.
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A triple porosity scheme for fluid/solid substitution: theory and experiment
ABSTRACTQuantifying the effects of pore‐filling materials on elastic properties of porous rocks is of considerable interest in geophysical practice. For rocks saturated with fluids, the Gassmann equation is proved effective in estimating the exact change in seismic velocity or rock moduli upon the changes in properties of pore infill. For solid substance or viscoelastic materials, however, the Gassmann theory is not applicable as the rigidity of the pore fill (either elastic or viscoelastic) prevents pressure communication in the pore space, which is a key assumption of the Gassmann equation. In this paper, we explored the elastic properties of a sandstone sample saturated with fluid and solid substance under different confining pressures. This sandstone sample is saturated with octadecane, which is a hydrocarbon with a melting point of 28°C, making it convenient to use in the lab in both solid and fluid forms. Ultrasonically measured velocities of the dry rock exhibit strong pressure dependency, which is largely reduced for the filling of solid octadecane. Predictions by the Gassmann theory for the elastic moduli of the sandstone saturated with liquid octadecane are consistent with ultrasonic measurements, but underestimate the elastic moduli of the sandstone saturated with solid octadecane. Our analysis shows that the difference between the elastic moduli of the dry and solid‐octadecane‐saturated sandstone is controlled by the squirt flow between stiff, compliant, and the so‐called intermediate pores (with an aspect ratio larger than that of compliant pore but much less than that of stiff pores). Therefore, we developed a triple porosity model to quantify the combined squirt flow effects of compliant and intermediate pores saturated with solid or viscoelastic infill. Full saturation of remaining stiff pores with solid or viscoelastic materials is then considered by the lower embedded bound theory. The proposed model gave a reasonable fit to the ultrasonic measurements of the elastic moduli of the sandstone saturated with liquid or solid octadecane. Comparison of the predictions by the new model to other solid substitution schemes implied that accounting for the combined effects of compliant and intermediate pores is necessary to explain the solid squirt effects.
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Dependency of flow and transport properties on aperture distributions and compression states
Authors Joseph H.Y. Ma, Yunyue Elita Li and Arthur ChengABSTRACTFluid conductivity and elastic properties in fractures depend on the aperture geometry – in particular, the roughness of fracture surfaces. In this study, we have characterized the surface roughness with a log‐normal distribution and investigated the transport and flow behaviour of the fractures with varying roughness characteristics. Numerical flow and transport simulations have been performed on a single two‐dimensional fracture surface, whose aperture geometry changes with different variances and correlation lengths in each realization. We have found that conventional measurement of hydraulic conductivity alone is insufficient to determine these two parameters. Transient transport measurements, such as the particle breakthrough time, provide additional constraints to the aperture distribution. Nonetheless, a unique solution to the fracture aperture distribution is still under‐determined with both hydraulic conductivity and transport measurements. From numerical simulations at different compression states, we have found that the flow and transport measurements exhibit different rates of changes with respect to changes in compression. Therefore, the fracture aperture distribution could be further constrained by considering the flow and transport properties under various compression states.
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Contact line friction and surface tension effects on seismic attenuation and effective bulk moduli in rock with a partially saturated crack
Authors Alexander Y. Rozhko and Andreas BauerABSTRACTThe effect of surface phenomena occurring at the interfaces between immiscible fluids and a solid on the seismic attributes of partially saturated rocks has not yet been fully studied. Meanwhile, over the past two decades considerable progress has been made in the physics of wetting to understand effects such as contact line friction, contact line pinning, contact angle hysteresis, and equilibrium contact angle. In this paper, we developed a new rock physics model considering the aforementioned effects on seismic properties of the rock with a partially saturated plane‐strain crack. We demonstrated that for small wave‐induced stress perturbations, the contact line of the interface meniscus will remain pinned, while the meniscus will bulge and change its shape through the change of the contact angles. When the stress perturbation is larger than a critical value, the contact line will move with advancing or receding contact angle depending on the direction of contact line motion. A critical stress perturbation predicted by our model can be in the range of ∼102−104 Pa, that is typical for linear seismic waves. Our model predicts strong seismic attenuation in the case when the contact line is moving. When the contact line is pinned, the attenuation is negligibly small. Seismic attenuation is associated with the hysteresis of loading and unloading bulk moduli, predicted by our model. The hysteresis is large when the contact line is moving and negligibly small when the contact line is pinned. Furthermore, we demonstrate that the bulk modulus of the rock with a partially saturated crack depends also on the surface tension and on the contact angle hysteresis. These parameters are typically neglected during calculation of the effecting fluid moduli by applying different averaging techniques. We demonstrate that contact line friction may be a dominant seismic attenuation mechanism in the low frequency limit (<∼10 Hz) when capillary forces dominate over viscous forces during wave‐induced two‐phase fluid flow.
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Attenuation mechanisms in fractured fluid‐saturated porous rocks: a numerical modelling study
ABSTRACTSeismic attenuation mechanisms receive increasing attention for the characterization of fractured formations because of their inherent sensitivity to the hydraulic and elastic properties of the probed media. Attenuation has been successfully inferred from seismic data in the past, but linking these estimates to intrinsic rock physical properties remains challenging. A reason for these difficulties in fluid‐saturated fractured porous media is that several mechanisms can cause attenuation and may interfere with each other. These mechanisms notably comprise pressure diffusion phenomena and dynamic effects, such as scattering, as well as Biot's so‐called intrinsic attenuation mechanism. Understanding the interplay between these mechanisms is therefore an essential step for estimating fracture properties from seismic measurements. In order to do this, we perform a comparative study involving wave propagation modelling in a transmission set‐up based on Biot's low‐frequency dynamic equations and numerical upscaling based on Biot's consolidation equations. The former captures all aforementioned attenuation mechanisms and their interference, whereas the latter only accounts for pressure diffusion phenomena. A comparison of the results from both methods therefore allows to distinguish between dynamic and pressure diffusion phenomena and to shed light on their interference. To this end, we consider a range of canonical models with randomly distributed vertical and/or horizontal fractures. We observe that scattering attenuation strongly interferes with pressure diffusion phenomena, since the latter affect the elastic contrasts between fractures and their embedding background. Our results also demonstrate that it is essential to account for amplitude reductions due to transmission losses to allow for an adequate estimation of the intrinsic attenuation of fractured media. The effects of Biot's intrinsic mechanism are rather small for the models considered in this study.
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Forced oscillation measurements of seismic wave attenuation and stiffness moduli dispersion in glycerine‐saturated Berea sandstone
Authors Samuel Chapman, Jan V. M. Borgomano, Hanjun Yin, Jerome Fortin and Beatriz QuintalABSTRACTFluid pressure diffusion occurring on the microscopic scale is believed to be a significant source of intrinsic attenuation of mechanical waves propagating through fully saturated porous rocks. The so‐called squirt flow arises from compressibility heterogeneities in the microstructure of the rocks. To study squirt flow experimentally at seismic frequencies the forced oscillation method is the most adequate, but such studies are still scarce. Here we present the results of forced hydrostatic and axial oscillation experiments on dry and glycerine‐saturated Berea sandstone, from which we determine the dynamic stiffness moduli and attenuation at micro‐seismic and seismic frequencies (0.004–30 Hz). We observe frequency‐dependent attenuation and the associated moduli dispersion in response to the drained–undrained transition (∼0.1 Hz) and squirt flow (>3 Hz), which are in fairly good agreement with the results of the corresponding analytical solutions. The comparison with very similar experiments performed also on Berea sandstone in addition shows that squirt flow can potentially be a source of wave attenuation across a wide range of frequencies because of its sensitivity to small variations in the rock microstructure, especially in the aspect ratio of micro‐cracks or grain contacts.
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Compensating elastic transmission losses for P‐wave attenuation estimation from sonic logs
Authors Jiabin Liang, Tobias M. Müller, Genyang Tang and Shangxu WangABSTRACTThe decay of seismic amplitude is caused by a variety of physical phenomena that can be divided broadly into elastic transmission losses (including geometrical spreading, interface transmission losses and scattering attenuation) and intrinsic attenuation, where wave energy is converted into heat due to viscous friction. The so‐called statistical averaging method is currently considered as the most advanced sonic wave attenuation estimation method, and there exist various implementations of this method. But the way elastic transmission losses – that mask the true intrinsic attenuation – are compensated for appears to be an issue and in some cases this correction has been overlooked. In this paper, we revisit the statistical averaging method for intrinsic attenuation estimation with particular focus on the role of elastic transmission losses. Through synthetic examples, we demonstrate the importance of compensating for elastic transmission losses even if the variation of velocity and density with depth is not notable. Our implementation of the method uses finite‐difference simulations thereby providing a versatile and accurate way to generate synthetic seismograms. We use a combination of elastic and viscoelastic finite‐difference simulations to demonstrate the significant error without accurate compensation of the elastic transmission losses. We apply our implementation of the method to sonic waveforms acquired in an exploration well from Browse basin, Australia. The resulting intrinsic attenuation estimates are indeed indicative of gas‐saturated zones identified from petrophysical analysis in which viscous friction are thought to be of importance.
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Water retention effects on elastic properties of Opalinus shale
Authors Alexey Yurikov, Maxim Lebedev, Marina Pervukhina and Boris GurevichABSTRACTShales play an important role in many engineering applications such as nuclear waste, CO2 storage and oil or gas production. Shales are often utilized as an impermeable seal or an unconventional reservoir. For both situations, shales are often studied using seismic waves. Elastic properties of shales strongly depend on their hydration, which can lead to substantial structural changes. Thus, in order to explore shaly formations with seismic methods, it is necessary to understand the dependency of shale elastic properties on variations in hydration. In this work, we investigate structural changes in Opalinus shale at different hydration states using laboratory measurements and X‐ray micro‐computed tomography. We show that the shale swells with hydration and shrinks with drying with no visible damage. The pore space of the shale deforms, exhibiting a reduction in the total porosity with drying and an increase in the total porosity with hydration. We study the elastic properties of the shale at different hydration states using ultrasonic velocities measurements. The elastic moduli of the shale show substantial changes with variations in hydration, which cannot be explained with a single driving mechanism. We suggest that changes of the elastic moduli with variations in hydration are driven by multiple competing factors: (1) variations in total porosity, (2) substitution of pore‐filling fluid, (3) change in stiffness of contacts between clay particles and (4) chemical hardening/softening of clay particles. We qualitatively and quantitatively analyse and discuss the influence of each of these factors on the elastic moduli. We conclude that depending on the microstructure and composition of a particular shale, some of the factors dominate over the others, resulting in different dependencies of the elastic moduli on hydration.
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Static and dynamic stiffness measurements with Opalinus Clay
Authors Serhii Lozovyi and Andreas BauerABSTRACTIn this work, an experimental study was carried out with the aim of reconciling static and dynamic stiffness of Opalinus Clay. The static and dynamic stiffness of core plugs from a shaly and a sandy facies of Opalinus Clay were characterized at two different stress states. The measurements included undrained quasi‐static loading–unloading cycles from which the static stiffness was derived, dynamic stiffness measurement at seismic frequencies (0.5–150 Hz) and ultrasonic velocity measurements (500 kHz) probing the dynamic stiffness at ultrasonic frequencies. The experiments were carried out in a special triaxial low‐frequency cell. The obtained results demonstrate that the difference between static and dynamic stiffness is due to both dispersion and non‐elastic effects: Both sandy and shaly facies of Opalinus Clay exhibit large dispersion, that is, a large frequency dependence of dynamic stiffness and acoustic velocities. Especially dynamic Young's moduli exhibit very high dispersion; between seismic and ultrasonic frequencies they may change by more than a factor 2. P‐wave velocities perpendicular to bedding are by more than 200 m/s higher at ultrasonic frequencies than at seismic frequencies. The static undrained stiffness of both sandy and shaly facies is strongly influenced by non‐elastic effects, resulting in significant softening during both loading and unloading with increasing stress amplitude. The zero‐stress extrapolated static undrained stiffness, however, reflects the purely elastic response and agrees well with the dynamic stiffness at seismic frequency.
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Integrating facies‐based Bayesian inversion and supervised machine learning for petro‐facies characterization in the Snadd Formation of the Goliat Field, south‐western Barents Sea
ABSTRACTSeismic petro‐facies characterization in low net‐to‐gross reservoirs with poor reservoir properties such as the Snadd Formation in the Goliat field requires a multidisciplinary approach. This is especially important when the elastic properties of the desired petro‐facies significantly overlap. Pore fluid corrected endmember sand and shale depth trends have been used to generate stochastic forward models for different lithology and fluid combinations in order to assess the degree of separation of different petro‐facies. Subsequently, a spectral decomposition and blending of selected frequency volumes reveal some seismic fluvial geomorphological features. We then jointly inverted for impedance and facies within a Bayesian framework using facies‐dependent rock physics depth trends as input. The results from the inversion are then integrated into a supervised machine learning neural network for effective porosity discrimination. Probability density functions derived from stochastic forward modelling of endmember depth trends show a decreasing seismic fluid discrimination with depth. Spectral decomposition and blending of selected frequencies reveal a dominant NNE trend compared to the regional SE–NW pro‐gradational trend, and a local E–W trend potentially related to fault activity at branches of the Troms‐Finnmark Fault Complex. The facies‐based inversion captures the main reservoir facies within the limits of the seismic bandwidth. Meanwhile the effective porosity predictions from the multilayer feed forward neural network are consistent with the inverted facies model, and can be used to qualitatively highlight the cleanest regions within the inverted facies model. A combination of facies‐based inversion and neural network improves the seismic reservoir delineation of the Snadd Formation in the Goliat Field.
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