Forced oscillation measurements of seismic attenuation in fluid saturated sandstone

Adopting the method of forced oscillation, attenuation was studied in Fontainebleau sandstone (porosity 10%, permeability 10 mD) at seismic frequencies (1–100 Hz). Confining pressures of 5, 10, and 15 MPa were chosen to simulate reservoir conditions. First, the strain effect on attenuation was investigated in the dry sample for 11 different strains across the range 1 × 10^?6–8 × 10^?6, at the confining pressure of 5 MPa. The comparison showed that a strain of at least 5 × 10^?6 is necessary to obtain a good signal to noise ratio. These results also indicate that nonlinear effects are absent for strains up to 8 × 10^?6. For all the confining pressures, attenuation in the dry rock was low, while partial (90%) and full (100%) saturation with water yielded a higher magnitude and frequency dependence of attenuation. The observed high and frequency dependent attenuation was interpreted as being caused by squirt flow.     

Laboratory measurements of seismic attenuation and Young's modulus dispersion in a partially and fully water‐saturated porous sample made of sintered borosilicate glass

We measured the extensional‐mode attenuation and Young's modulus in a porous sample made of sintered borosilicate glass at microseismic to seismic frequencies (0.05–50 Hz) using the forced oscillation method. Partial saturation was achieved by water imbibition, varying the water saturation from an initial dry state up to ～99%, and by gas exsolution from an initially fully water‐saturated state down to ～99%. During forced oscillations of the sample effective stresses up to 10 MPa were applied. We observe frequency‐dependent attenuation, with a peak at 1–5 Hz, for ～99% water saturation achieved both by imbibition and by gas exsolution. The magnitude of this attenuation peak is consistently reduced with increasing fluid pressure and is largely insensitive to changes in effective stress. Similar observations have recently been attributed to wave‐induced gas exsolution–dissolution. At full water saturation, the left‐hand side of an attenuation curve, with a peak beyond the highest measured frequency, is observed at 3 MPa effective stress, while at 10 MPa effective stress the measured attenuation is negligible. This observation is consistent with wave‐induced fluid flow associated with mesoscopic compressibility contrasts in the sample's frame. These variations in compressibility could be due to fractures and/or compaction bands that formed between separate sets of forced‐oscillation experiments in response to the applied stresses. The agreement of the measured frequency‐dependent attenuation and Young's modulus with the Kramers–Kronig relations and additional data analyses indicate the good quality of the measurements. Our observations point to the complex interplay between structural and fluid heterogeneities on the measured seismic attenuation and they illustrate how these heterogeneities can facilitate the dominance of one attenuation mechanism over another.     

Monitoring viscosity changes from time‐lapse seismic attenuation: case study from a heavy oil reservoir

Heating heavy oil reservoirs is a common method for reducing the high viscosity of heavy oil and thus increasing the recovery factor. Monitoring of these viscosity changes in the reservoir is essential for delineating the heated region and controlling production. In this study, we present an approach for estimating viscosity changes in a heavy oil reservoir. The approach consists of three steps: measuring seismic wave attenuation between reflections from above and below the reservoir, constructing time‐lapse Q and Q^?1 factor maps, and interpreting these maps using Kelvin–Voigt and Maxwell viscoelastic models. We use a 4D relative spectrum method to measure changes in attenuation. The method is tested with synthetic seismic data that are noise free and data with additive Gaussian noise to show the robustness and the accuracy of the estimates of the Q‐factor. The results of the application of the method to a field data set exhibit alignment of high attenuation zones along the steam‐injection wells, and indicate that temperature dependent viscosity changes in the heavy oil reservoir can be explained by the Kelvin–Voigt model.     

Quantitative gas saturation estimation by frequency‐dependent amplitude‐versus‐offset analysis

Seismic amplitudes contain important information that can be related to fluid saturation. The amplitude‐versus‐offset analysis of seismic data based on Gassmann's theory and the approximation of the Zoeppritz equations has played a central role in reservoir characterization. However, this standard technique faces a long‐standing problem: its inability to distinguish between partial gas and “fizz‐water” with little gas saturation. In this paper, we studied seismic dispersion and attenuation in partially saturated poroelastic media by using frequency‐dependent rock physics model, through which the frequency‐dependent amplitude‐versus‐offset response is calculated as a function of porosity and water saturation. We propose a cross‐plotting of two attributes derived from the frequency‐dependent amplitude‐versus‐offset response to differentiate partial gas saturation and “fizz‐water” saturation. One of the attributes is a measure of “low frequency”, or Gassmann, of reflectivity, whereas the other is a measure of the “frequency dependence” of reflectivity. This is in contrast to standard amplitude‐versus‐offset attributes, where there is typically no such separation. A pragmatic frequency‐dependent amplitude‐versus‐offset inversion for rock and fluid properties is also established based on Bayesian theorem. A synthetic study is performed to explore the potential of the method to estimate gas saturation and porosity variations. An advantage of our work is that the method is in principle predictive, opening the way to further testing and calibration with field data. We believe that such work should guide and augment more theoretical studies of frequency‐dependent amplitude‐versus‐offset analysis.     

Seismic time–frequency analysis as a robust method to estimate the fluid saturation: A case study of carbonates reservoir,Iran

The propagation of seismic waves through a saturated reservoir compresses the fluid in the pore spaces. During this transition, parts of seismic energy would be attenuated because of intrinsic absorption. Rock physics models make the bridge between the seismic properties and petrophysical reality in the earth. Attenuation is one of the significant seismic attributes used to describe the fluid behaviour in the reservoirs. We examined the core samples using ultrasonic experiments at the reservoir conditions. Given the rock properties of the carbonate reservoir and experiment results, the patchy saturation mechanism was solved for substituted fluid using the theory of modulus frequency. The extracted relationship between the seismic attenuation and water saturation was used in time–frequency analysis. We performed the peak frequency method to estimate the Q factor in the Gabor domain and determined the water saturation based on the computed rock physics model. The results showed how the probable fault in the reservoir has stopped the fluid movement in the reservoir and caused touching the water‐bearing zone through drilling.     

Forced oscillation measurements of seismic wave attenuation and stiffness moduli dispersion in glycerine-saturated Berea sandstone

Fluid 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.     

Seismic dispersion and attenuation in layered porous rocks with fractures of varying orientations

Wave‐induced fluid flow plays an important role in affecting the seismic dispersion and attenuation of fractured porous rocks. While numerous theoretical models have been proposed for the seismic dispersion and attenuation in fractured porous rocks, most of them neglect the wave‐induced fluid flow resulting from the background anisotropy (e.g. the interlayer fluid flow between different layers) that can be normal in real reservoirs. Here, according to the theories of poroelasticity, we present an approach to study the frequency‐dependent seismic properties of more realistic and complicated rocks, i.e. horizontally and periodically layered porous rock with horizontal and randomly orienting fractures, respectively, distributed in one of the two periodical layers. The approach accounts for the dual effects of the wave‐induced fluid flow between the fractures and the background pores and between different layers (the interlayer fluid flow). Because C₃₃ (i.e., the modulus of the normally incident P‐wave) is directly related to the P‐wave velocity widely measured in the seismic exploration, and its comprehensive dispersion and attenuation are found to be most significant, we study mainly the effects of fracture properties and the stiffness contrast between the different layers on the seismic dispersion and attenuation of C₃₃. The results show that the increasing stiffness contrast enhances the interlayer fluid flow of the layered porous rocks with both horizontal and randomly orienting fractures and weakens the wave‐induced fluid flow between the fractures and the background pores, especially for the layered porous rock with horizontal fractures. The modelling results also demonstrate that for the considered rock construction, the increasing fracture density reduces the interlayer fluid flow while improves the dispersion and attenuation in the fracture‐relevant frequency band. Increasing fracture aspect ratio is found to reduce the dispersion and attenuation in the fracture‐relevant frequency band only, especially for the layered porous rock with horizontal fractures.     

Estimating permeability from field measurements of seismic attenuation in fractured chalk

Broadband (100–4000 Hz) cross‐hole seismic data have been acquired at a borehole test site where extensive hydrological investigations have previously been performed, including in situ estimates of permeability. The rock type is homogeneous chalk and fractures and bedding planes have been identified from well logs. High values of seismic attenuation, Q= 22 ≤ 27 ≤ 33, were observed over a 10 m depth interval where fracture permeability values of 20–50 darcy had been recorded. An attempt has been made to separate the attenuation due to scattering and intrinsic mechanisms. The estimated values of intrinsic attenuation, Q= 31 ≤ 43 ≤ 71, have been reproduced using a number of current theories of seismic‐wave propagation and fluid‐flow‐induced seismic attenuation in cracked and fractured media. A model that considers wavelength‐scale pressure gradients is the preferred attenuation mechanism. Model parameters were obtained from the hydro‐geological and seismic data. However, we conclude that it is not possible to use seismic Q to measure rock permeability remotely, principally because of the inherent uncertainties arising from model parameterisations.     

Extension of White's layered model to the full frequency range

The low‐frequency theory of the White model to predict the dispersion and intrinsic attenuation in a single porous skeleton saturated with periodic layers of two immiscible fluids is extended to the full frequency range using the Biot theory. The extension is similar to the Dutta–Odé model for spherical inhomogeneities. Below the layer resonance frequency, the acoustic bulk properties for several gas–water fractions are in good agreement with the original White model. Deviations start to occur at higher frequencies due to the growing importance of resonance phenomena that were neglected in the original White model. The full model predicts significantly higher damping at sonic frequencies than the original White model. We also show that attenuation is significantly dependent on porosity variations. With realistic rock and fluid properties, a maximum attenuation of about 0.3 is found at seismic frequencies.     

Influence of subsurface injection on time‐lapse seismic: laboratory studies at seismic and ultrasonic frequencies

Seismic monitoring of reservoir and overburden performance during subsurface CO₂ storage plays a key role in ensuring efficiency and safety. Proper interpretation of monitoring data requires knowledge about the rock physical phenomena occurring in the subsurface formations. This work focuses on rock stiffness and elastic velocity changes of a shale overburden formation caused by both reservoir inflation induced stress changes and leakage of CO₂ into the overburden. In laboratory experiments, Pierre shale I core plugs were loaded along the stress path representative for the in situ stress changes experienced by caprock during reservoir inflation. Tests were carried out in a triaxial compaction cell combining three measurement techniques and permitting for determination of (i) ultrasonic velocities, (ii) quasistatic rock deformations, and (iii) dynamic elastic stiffness at seismic frequencies within a single test, which allowed to quantify effects of seismic dispersion. In addition, fluid substitution effects connected with possible CO₂ leakage into the caprock formation were modelled by the modified anisotropic Gassmann model. Results of this work indicate that (i) stress sensitivity of Pierre shale I is frequency dependent; (ii) reservoir inflation leads to the increase of the overburden Young's modulus and Poisson's ratio; (iii) in situ stress changes mostly affect the P‐wave velocities; (iv) small leakage of the CO₂ into the overburden may lead to the velocity changes, which are comparable with one associated with geomechanical influence; (v) non‐elastic effects increase stress sensitivity of an acoustic waves; (iv) and both geomechanical and fluid substitution effects would create significant time shifts, which should be detectable by time‐lapse seismic.     

Interaction of multiple courses of wave‐induced fluid flow in layered porous media

Different theoretical and laboratory studies on the propagation of elastic waves in layered hydrocarbon reservoir have shown characteristic velocity dispersion and attenuation of seismic waves. The wave‐induced fluid flow between mesoscopic‐scale heterogeneities (larger than the pore size but smaller than the predominant wavelengths) is the most important cause of attenuation for frequencies below 1 kHz. Most studies on mesoscopic wave‐induced fluid flow in the seismic frequency band are based on the representative elementary volume, which does not consider interaction of fluid flow due to the symmetrical structure of representative elementary volume. However, in strongly heterogeneous media with unsymmetrical structures, different courses of wave‐induced fluid flow may lead to the interaction of the fluid flux in the seismic band; this has not yet been explored. This paper analyses the interaction of different courses of wave‐induced fluid flow in layered porous media. We apply a one‐dimensional finite‐element numerical creep test based on Biot's theory of consolidation to obtain the fluid flux in the frequency domain. The characteristic frequency of the fluid flux and the strain rate tensor are introduced to characterise the interaction of different courses of fluid flux. We also compare the behaviours of characteristic frequencies and the strain rate tensor on two scales: the local scale and the global scale. It is shown that, at the local scale, the interaction between different courses of fluid flux is a dynamic process, and the weak fluid flux and corresponding characteristic frequencies contain detailed information about the interaction of the fluid flux. At the global scale, the averaged strain rate tensor can facilitate the identification of the interaction degree of the fluid flux for the porous medium with a random distribution of mesoscopic heterogeneities, and the characteristic frequency of the fluid flux is potentially related to that of the peak attenuation. The results are helpful for the prediction of the distribution of oil–gas patches based on the statistical properties of phase velocities and attenuation in layered porous media with random disorder.     

Properties of low‐frequency trapped mode in viscous‐fluid waveguides

We derived the velocity and attenuation of a generalized Stoneley wave being a symmetric trapped mode of a layer filled with a Newtonian fluid and embedded into either a poroelastic or a purely elastic rock. The dispersion relation corresponding to a linearized Navier–Stokes equation in a fracture coupling to either Biot or elasticity equations in the rock via proper boundary conditions was rigorously derived. A cubic equation for wavenumber was found that provides a rather precise analytical approximation of the full dispersion relation, in the frequency range of 10^?3 Hz to 10³ Hz and for layer width of less than 10 cm and fluid viscosity below 0.1 Pa· s [100 cP]. We compared our results to earlier results addressing viscous fluid in either porous rocks with a rigid matrix or in a purely elastic rock, and our formulae are found to better match the numerical solution, especially regarding attenuation. The computed attenuation was used to demonstrate detectability of fracture tip reflections at wellbore, for a range of fracture lengths and apertures, pulse frequencies, and fluid viscosity.     

A seismic reflection from isotropic‐fractured fluid‐saturated layer

Average elastic properties of a fluid‐saturated fractured rock are discussed in association with the extremely slow and dispersive Krauklis wave propagation within individual fractures. The presence of the Krauklis wave increases P‐wave velocity dispersion and attenuation with decreasing frequency. Different laws (exponential, power, fractal, and gamma laws) of distribution of the fracture length within the rock show more velocity dispersion and attenuation of the P‐wave for greater fracture density, particularly at low seismic frequencies. The results exhibit a remarkable difference in the P‐wave reflection coefficient for frequency and angular dependency from the fractured layer in comparison with the homogeneous layer. The biggest variation in behaviour of the reflection coefficient versus incident angle is observed at low seismic frequencies. The proposed approach and results of calculations allow an interpretation of abnormal velocity dispersion, high attenuation, and special behaviour of reflection coefficients versus frequency and angle of incidence as the indicators of fractures.     

Seismic Attenuation Computed from GLIMPCE Reflection Data and Comparison with Refraction Results

—Instantaneous frequency matching has been used to compute differential t* values for seismic reflection data from the Great Lakes International Multidisciplinary Program on Crustal Evolution (GLIMPCE) experiment. The differential attenuation values were converted to apparent Q ^?1 models by a fitting procedure that simultaneously solves for the interval Q ^?1 values using non-negative least squares. The bootstrap method was then used to estimate the variance in the interval Q ^?1 models. The shallow Q ^?1 structure obtained from the seismic reflection data corresponds closely with an attenuation model derived using instantaneous frequency matching on seismic refraction data along the same transect. This suggests that the effects of wave propagation and scattering on the apparent attenuation are similar for the two data sets. The Q ^?1 model from the reflection data was then compared with the structural interpretation of the reflectivity data. The highest interval Q ^?1 values (>0.01) were found near the surface, corresponding to the sedimentary rock sequence of the upper Keweenawan. Low Q ^?1 values (<0.0006) are found beneath the Midcontinent rift’s central basin. In addition to structural interpretation, seismic attenuation models derived in this way can be used to correct reflection data for dispersion, frequency and amplitude effects, and allow for improved imaging of the subsurface.     

Quantitative detection of fluid distribution using time-lapse seismic

Although previous seismic monitoring studies have revealed several relationships between seismic responses and changes in reservoir rock properties, the quantitative evaluation of time‐lapse seismic data remains a challenge. In most cases of time‐lapse seismic analysis, fluid and/or pressure changes are detected qualitatively by changes in amplitude strength, traveltime and/or Poisson's ratio. We present the steps for time‐lapse seismic analysis, considering the pressure effect and the saturation scale of fluids. We then demonstrate a deterministic workflow for computing the fluid saturation in a reservoir in order to evaluate time‐lapse seismic data. In this approach, we derive the physical properties of the water‐saturated sandstone reservoir, based on the following inputs: V_P, V_S, ρ and the shale volume from seismic analysis, the average properties of sand grains, and formation‐water properties. Next, by comparing the in‐situ fluid‐saturated properties with the 100% formation‐water‐saturated reservoir properties, we determine the bulk modulus and density of the in‐situ fluid. Solving three simultaneous equations (relating the saturations of water, oil and gas in terms of the bulk modulus, density and the total saturation), we compute the saturation of each fluid. We use a real time‐lapse seismic data set from an oilfield in the North Sea for a case study.     

Measurements of the elastic and anelastic properties of sandstone flooded with supercritical CO2

The aim of this study was to investigate the effects of supercritical CO₂ (scCO₂) injection on the elastic and anelastic properties of sandstone at seismic and ultrasonic frequencies. We present the results of the low‐frequency and ultrasonic experiments conducted on water‐saturated sandstone (Donnybrook, Western Australia) flooded with scCO₂. The sandstone was cut in the direction perpendicular to a formation bedding plane and tested in a Hoek triaxial pressure cell. During the experiments with scCO_2, the low‐frequency and ultrasonic systems and the pump dispensing scCO₂ were held at a temperature of 42°C. The elastic parameters obtained for the sandstone with scCO₂ at seismic (0.1 Hz–100 Hz) and ultrasonic (～0.5 MHz) frequencies are very close to those for the dry rock. The extensional attenuation was also measured at seismic frequencies for the dry, water‐saturated, and scCO₂‐injected sandstones. The applicability of Gassmann's fluid substitution theory to obtained results was also tested during the experiments.     

Seismic attenuation and velocity dispersion in fractured rocks: The role played by fracture contact areas

The presence of fractures in fluid‐saturated porous rocks is usually associated with strong seismic P‐wave attenuation and velocity dispersion. This energy dissipation can be caused by oscillatory wave‐induced fluid pressure diffusion between the fractures and the host rock, an intrinsic attenuation mechanism generally referred to as wave‐induced fluid flow. Geological observations suggest that fracture surfaces are highly irregular at the millimetre and sub‐millimetre scale, which finds its expression in geometrical and mechanical complexities of the contact area between the fracture faces. It is well known that contact areas strongly affect the overall mechanical fracture properties. However, existing models for seismic attenuation and velocity dispersion in fractured rocks neglect this complexity. In this work, we explore the effects of fracture contact areas on seismic P‐wave attenuation and velocity dispersion using oscillatory relaxation simulations based on quasi‐static poroelastic equations. We verify that the geometrical and mechanical details of fracture contact areas have a strong impact on seismic signatures. In addition, our numerical approach allows us to quantify the vertical solid displacement jump across fractures, the key quantity in the linear slip theory. We find that the displacement jump is strongly affected by the geometrical details of the fracture contact area and, due to the oscillatory fluid pressure diffusion process, is complex‐valued and frequency‐dependent. By using laboratory measurements of stress‐induced changes in the fracture contact area, we relate seismic attenuation and dispersion to the effective stress. The corresponding results do indeed indicate that seismic attenuation and phase velocity may constitute useful attributes to constrain the effective stress. Alternatively, knowledge of the effective stress may help to identify the regions in which wave induced fluid flow is expected to be the dominant attenuation mechanism.     

基于常规测井数据的纵波本征衰减估计

地震波本征衰减反映了地层及其所含流体的一些特性,对油气勘探开发有重要意义.已有的理论研究与实验发现,地震频带内的衰减主要与中观尺度(波长与颗粒尺度之间)的斑状部分饱和、完全饱和岩石弹性非均匀性情况下波诱导的局部流体流有关.这种衰减与岩石骨架、孔隙度及充填流体的性质密切相关.本文着重讨论均匀流体分布、斑状或非均匀流体分布两种情况下部分饱和岩石的纵波模量差异.以经典岩石物理理论和衰减机制认识为基础,通过分析低频松弛状态、高频非松弛状态岩石的弹性模量,讨论储层参数(如孔隙度、泥质含量以及含水饱和度等)与纵波衰减之间的确定性关系.上述方法与模型在陆相砂泥岩地层与海相碳酸盐岩地层中的适用性通过常规测井资料得到了初步验证.     

基于Gassmann方程的流体替换方法在珊溪水库地震研究中的应用

引入基于Gassmann方程的流体替换方法,在分析地震波P波速度、波速比与岩石孔隙度和饱和度关系的基础上,应用于珊溪水库地震波速比和P波速度变化特征研究,得到:(1)珊溪水库震中区岩石始终处于接近水饱和的饱水状态,波速比和P波速度"下降-回升"的变化实质上反映了震中区岩石"孔隙度增大(饱和度减小)-饱和度增大"的变化,每一丛地震的波速比由极小值逐渐增大为极大值是由于岩石从不饱和状态变化到饱和状态;(2)根据每一丛地震波速比的变化,计算得到珊溪水库流体扩散率αs=1.06×104 cm2 s-1,该数值与美国南卡罗莱纳水库、巴西Acu水库、广东新丰江水库的流体扩散率基本一致;(3)震源区岩石孔隙度上限值为8.7%~2.0%,该数值与华东勘测设计研究院通过室内岩石物理力学性质试验测定的珊溪水库坝址区新鲜流纹斑岩的孔隙度平均值一致。     

Comparison of P‐wave attenuation models of wave‐induced flow

Wave‐induced oscillatory fluid flow in the vicinity of inclusions embedded in porous rocks is one of the main causes for P‐wave dispersion and attenuation at seismic frequencies. Hence, the P‐wave velocity depends on wave frequency, porosity, saturation, and other rock parameters. Several analytical models quantify this wave‐induced flow attenuation and result in characteristic velocity–saturation relations. Here, we compare some of these models by analyzing their low‐ and high‐frequency asymptotic behaviours and by applying them to measured velocity–saturation relations. Specifically, the Biot–Rayleigh model considering spherical inclusions embedded in an isotropic rock matrix is compared with White's and Johnson's models of patchy saturation. The modeling of laboratory data for tight sandstone and limestone indicates that, by selecting appropriate inclusion size, the Biot‐Rayleigh predictions are close to the measured values, particularly for intermediate and high water saturations.