含有倾斜薄裂缝孔隙地层中的井孔声场

应用三维交错网格应力-速度有限差分方法,数值模拟了含有倾斜裂缝孔隙介质地层中点声源所激发的井孔声场问题.为满足薄裂缝计算需求,开发了不均匀网格有限差分算法,提高了计算精度及计算速度.利用将孔隙介质方程参数取为流体极限的办法来处理裂缝中的流体,实现了流体-孔隙介质界面处的差分方程统一,使界面处的计算更加灵活方便.在验证了方法正确性的基础上,分别考察了单裂缝宽度、裂缝带宽度、裂缝倾斜角度以及孔隙介质渗透率等参数的变化对井轴上阵列波形的影响并进行了分析.结果表明,声波经过裂缝时可能产生反射横波及斯通利波,后者随裂缝宽度的减小而减小,而前者随裂缝宽度的改变,变化不大,在裂缝很小(20μm)时依然存在;裂缝带的宽度、密度越大,反射斯通利波越强;当裂缝(裂缝带)倾斜时,反射横波消失,但反射斯通利波受裂缝倾斜角度的影响较小;渗透率的改变对斯通利波的衰减影响较为明显.     

Propagation of guided waves in a fluid layer bounded by two viscoelastic transversely isotropic solids

The analysis of Stoneley wave propagation in a fracture is essential for the identification and evaluation of fracture parameters from the borehole Stoneley wave. Also, it is important for many geophysics considerations, e.g. for tremor and long-period events observed in volcanoes and geothermal areas. In this paper, we investigate the guided waves propagation in a fluid layer lying between two viscoelastic vertically transversely isotropic media. The viscoelastic mechanism models the attenuation due to the presence of fluid saturation in the rock. A model based on the superposition of three inhomogeneous partial plane waves: one in the fluid and two heterogeneous waves in the solid is developed. The dispersion equation is obtained for this case. A numerical solution is carried out to obtain the guided wave velocity and attenuation coefficient. The results of this investigation show that there is a strong correlation between the velocity dispersion and attenuation of Stoneley wave and the anisotropic parameters of the medium especially in a sandstone (fast) medium.     

Estimating the permeability of the Nojima Fault Zone by a hydrophone vertical seismic profiling experiment

Abstract A multi-offset hydrophone vertical seismic profiling (VSP) experiment was done in a 747 m deep borehole at Nojima Hirabayashi, Hyogo prefecture, Japan. The borehole was drilled to penetrate the Nojima Fault, which was active in the 1995 Hyogo-ken Nanbu earthquake. The purpose of the hydrophone VSP is to detect subsurface permeable fractures and permeable zones and, in the present case, to estimate the permeability of the Nojima Fault. The analysis was based on a model by which tube waves are generated when incident P-waves compress the permeable fractures (or permeable zones) intersecting the borehole and a fluid in the fracture is injected into the borehole. Permeable fractures (or permeable zones) are detected at the depths of tube wave generation, and fracture permeability is calculated from the amplitude ratio of tube wave to incident P-wave. Several generations of tube waves were detected from the VSP sections. Distinct tube waves were generated at depths of the fault zone that are characterized by altered and deformed granodiorite with a fault gouge, suggesting that permeable fractures and permeable zones exist in the fault zone. Tube wave analysis shows that the permeability of the fault gouge from 624 m to 625 m is estimated to be approximately 2 × 10⁻¹² m².     

Stoneley wave generation by an incident P-wave propagating in the surrounding formation across a horizontal fluid-filled fracture

This study investigates the generation of the low-frequency borehole Stoneley wave (tube wave) by a plane P-wave propagating through the surrounding elastic formation, which is intersected by a fluid-filled fracture. A model is constructed taking into account the dynamic fluid coupling between the borehole interior and the fluid-filled fracture of infinite extent with parallel walls. The basic mechanism of such coupling is due to the contraction of the fracture walls by the incident P-wave, leading to seismic radiation into the fracture. The dynamic fluid flux from the fracture into the borehole interior, and vice versa, is the source of the low-frequency Stoneley wave. An expression for the monopole pressure source, exciting the tube wave, is obtained. The tube-wave equation in the long-wave approximation is derived in the presence of a fluid-filled fracture of infinite extent. Amplitudes and waveforms of Stoneley waves are analysed in the seismic wavelength range for P-wave pulses of various shapes. It is shown that the amplitude and waveform of the Stoneley wave depends significantly on the two dimensionless parameters of the problem: (1) the ratio of the borehole radius to the dominant wavelength of the incident pulse; (2) the ratio of the fracture width to the borehole radius. It is found that the amplitude of the generated Stoneley wave can be of the order of the P-wave amplitude in the borehole fluid. Stoneley waveforms are found to be completely different from those of the incident pulse.     

径向分层TI孔隙介质井孔中激发的模式波的数值研究

横向各向同性介质是地层中普遍存在的一种各向异性介质.本文对径向分层TI孔隙介质包围井孔中激发的斯通利波和弯曲波的传播特性进行了理论计算,发现模式波在低频时更多的是反应原状地层的信息,而随着频率的增加侵入带参数逐渐起控制作用;Biot理论描述的地层衰减比速度更容易受井壁附近地层参数的影响.利用灵敏度曲线定量研究了不同频率下地层各个参数对相速度和衰减系数的贡献大小,主要结果显示模式波的衰减受水平渗透率影响明显,而垂直渗透率的变化对模式波几乎无影响;斯通利波对水平向传播的横波速度比弯曲波的灵敏度高.从单极子和偶极子声源在井孔中激发的全波波形也可发现,声波测井仪器较宽的声源频带和合适的源距设置有利于对不同径向深度上的地层声学参数进行成像.     

Simulation of full-waveform log in saturated cracked formations using Hudson's approach

We study the propagation of elastic waves that are generated in a fluid‐filled borehole surrounded by a cracked transversely isotropic medium. In the model studied the anisotropy and borehole axes coincide. To obtain the effective elastic moduli of a cracked medium we have applied Hudson's theory that enables the determination of the overall properties as a function of the crack orientation in relation to the symmetry axis of the anisotropic medium. This theory takes into account the hydrodynamic mechanism of the elastic‐wave attenuation caused by fluid filtration from the cracks into a porous matrix. We have simulated the full waveforms generated by an impulse source of finite length placed on the borehole axis. The kinematic and dynamic parameters of the compressional, shear and Stoneley waves as functions of the matrix permeability, crack orientation and porosity were studied. The modelling results demonstrated the influence of the crack‐system parameters (orientation and porosity) on the velocities and amplitudes of all wave types. The horizontally orientated cracks result in maximal decrease of the elastic‐wave parameters (velocities and amplitudes). Based on the fact that the shear‐ and Stoneley‐wave velocities in a transversely isotropic medium are determined by different shear moduli, we demonstrate the feasibility of the acoustic log to identify formations with close to horizontal crack orientations.     

含孔隙、裂隙地层随钻多极子声波测井理论

储层岩石中普遍存在孔隙与裂隙,对钻井中的测井声波产生重要影响.基于孔、裂隙介质弹性波理论,导出了随钻声波测井的井孔声场表达式.据此考察了地层裂隙密度与含气饱和度的变化时井孔内随钻多极子模式波（斯通利波、弯曲波和螺旋波）的速度、衰减与灵敏度以及地层纵、横波的响应特征.裂隙密度与含气饱和度对模式波的速度频散与衰减都有影响,且两参数的值越大,影响越大.具体来说,速度对裂隙密度更敏感,而衰减对含气饱和度更敏感.具有"艾里相"特征的随钻偶极和四极子波在地层含气时产生强烈衰减,可以作为判断地层含气的一个明显指示.理论模拟与实际测井数据分析结果符合较好.     

含孔隙、裂隙致密介质中多极子声波的传播特征

非常规油气藏（如致密性地层及蕴藏油气的页岩地层）的重要特征是低孔、低渗,但裂隙或裂缝比较发育.为满足非常规勘探的需求,本文将孔、裂隙介质弹性波传播理论应用于多极子声波测井的井孔声场模拟,重点研究了致密介质中裂隙发育时多极子声波的传播机理以及衰减特征.井孔声场的数值计算结果表明裂隙的存在明显改变了弹性波和井孔模式波的频散、衰减和激发强度,尤其是井壁临界折射纵波的激发谱的峰值随着频率的增加逐渐降低,这与应用经典的Biot理论下的计算结果相反,且裂隙的存在也使得饱含水和饱含气时临界折射纵波激发强度的差异变大.井孔模式波的衰减与地层横波衰减和井壁流体交换有关,井壁开孔边界下致密地层裂隙发育还使得井孔斯通利波和艾里相附近的弯曲波对孔隙流体的敏感性增强,在井壁闭孔边界条件下引起井孔模式波衰减的主要因素是裂隙引起的地层横波衰减造成的,且在截止频率附近弯曲波的衰减与地层的横波衰减一致.数值计算结果为解释非常规油气地层的声学响应特征提供了参考.     

Composite periodic foundation and its application for seismic isolation

This paper proposes a novel multidimensional composite periodic foundation for seismic isolation. The composite periodic foundation achieves multidimensional attenuation by innovative arrangement of periodic structures and taking advantage of the directional attenuation zone of periodic structures. Directional attenuation zones of periodic structures are derived for the in‐plane wave, and the impact of geometrical parameters of the periodic structure on the characteristics of the directional attenuation zones is studied. The effectiveness of the proposed composite periodic foundation is demonstrated through application in seismic isolation for nuclear power plant structures. Harmonic analysis and time history analysis results show that the proposed composite periodic foundation with low‐frequency directional attenuation zones can effectively reduce vibrations of the upper structure in both horizontal and vertical directions.     

裸眼井声波全波测井中纵波和斯通利波的数值研究

本文利用射线展开理论、割线积分技术及留数定理,研究了裸眼井声波全波测井中纵波和斯通利波的性质。下面简要说明数值计算方法。 计算方法 考虑在无限大均匀地层中,有一充满流体的深井。在井轴上放一点状声源,则在井轴上离声源距离为z处的声压为     

CROSS-BOREHOLE OBSERVATION OF MODE CONVERSION FROM BOREHOLE STONELEY WAVES TO CHANNEL WAVES AT A COAL LAYER1

Conversion of borehole Stoneley waves to channel waves was observed in data from a seismic cross-borehole experiment conducted between wellbores penetrating a thin coal layer at 2022 m depth, near Rifle, Colorado. Traveltime moveout observations show that borehole Stoneley waves underwent partial conversion to channel waves at the coal layer. The channel waves were detected directly in an adjacent borehole 35 m away at receiver positions within the coal. Stoneley waves, subsequently produced by partial conversion of channel waves, were also detected at receiver positions located up to 50 m above and below the coal layer in the adjacent borehole. We infer the channel wave to be the first-higher Rayleigh mode by comparing the observed group velocity with theoretically derived dispersion curves. Identifying the conversion between borehole and stratigraphically guided waves is significant because coal penetrated by multiple wells may be detected without placing a transmitter or receiver in the coal itself.     

Azimuthal anisotropy analysis of walkaround vertical seismic profiling vertical seismic profiling: a case study from Saudi Arabia

Understanding fracture orientations is important for optimal field development of fractured reservoirs because fractures can act as conduits for fluid flow. This is especially true for unconventional reservoirs (e.g., tight gas sands and shale gas). Using walkaround Vertical Seismic Profiling (VSP) technology presents a unique opportunity to identify seismic azimuthal anisotropy for use in mapping potential fracture zones and their orientation around a borehole. Saudi Aramco recently completed the acquisition, processing and analysis of a walkaround VSP survey through an unconventional tight gas sand reservoir to help characterize fractures. In this paper, we present the results of the seismic azimuthal anisotropy analysis using seismic traveltime, shear‐wave splitting and amplitude attenuation. The azimuthal anisotropy results are compared to the fracture orientations derived from dipole sonic and image logs. The image log interpretation suggests that an orthorhombic fracture system is present. VSP data show that the P‐wave traveltime anisotropy direction is NE to SW. This is consistent with the cemented fractures from the image log interpretation. The seismic amplitude attenuation anisotropy direction is NW to SE. This is consistent with one of the two orientations obtained using transverse to radial amplitude ratio analysis, with the dipole sonic and with open fracture directions interpreted from image log data.     

孔、裂隙并存地层中的声波测井理论及多极子声场特征

在油、气储层的勘探和开发中观察到的一个现象是储层岩石中普遍存在孔隙和裂隙.随着近年来孔、裂隙介质弹性波动理论的进展,我们可以将此理论应用于测井技术,以此来指导从声波测井中测量孔、裂隙地层的声学参数.本文计算了孔、裂隙地层里充流体井眼中的多极子声场,分析了声场随裂隙介质的两个主要参数(即裂隙密度和裂隙纵横比)的变化特征.井孔声场的数值计算表明裂隙密度可以大幅度地降低井中声波纵、横波的波速和振幅.随着裂隙密度的增加,在测井频段内也可以看到纵、横波速的频散现象(这种频散在孔隙地层中一般是观察不到的).本文还研究了多极子模式波 (即单极的Stoneley波、伪瑞利波以及偶极的弯曲波)随裂隙参数的变化特征.结果表明,这些模式波的振幅激发和速度频散都受裂隙密度的影响.裂隙密度越高影响越大.此外,裂隙还对模式波的传播造成较大的衰减.相对裂隙密度而言,裂隙纵横比是一个频率控制参数,它控制裂隙对声场影响的频率区间.本文的分析结果对裂缝、孔隙型地层的声波测井具有指导意义.     

Modelling the wave phenomena in acoustic and elastic media with sharp variations of physical properties using the grid‐characteristic method

This paper introduces a novel method of modelling acoustic and elastic wave propagation in inhomogeneous media with sharp variations of physical properties based on the recently developed grid‐characteristic method which considers different types of waves generated in inhomogeneous linear‐elastic media (e.g., longitudinal, transverse, Stoneley, Rayleigh, scattered PP‐, SS‐waves, and converted PS‐ and SP‐waves). In the framework of this method, the problem of solving acoustic or elastic wave equations is reduced to the interpolation of the solutions, determined at earlier time, thus avoiding a direct solution of the large systems of linear equations required by the FD or FE methods. We apply the grid‐characteristic method to compare wave phenomena computed using the acoustic and elastic wave equations in geological medium containing a hydrocarbon reservoir or a fracture zone. The results of this study demonstrate that the developed algorithm can be used as an effective technique for modelling wave phenomena in the models containing hydrocarbon reservoir and/or the fracture zones, which are important targets of seismic exploration.     

不规则形状垂直井孔中波传播的2.5维边界元模拟

本文给出了求解声波测井工作中具有任意形状的垂直井孔中波传播的波数域边界元公式。我们将问题看成是垂向均匀的二维介质,并沿垂直方向变换到离散波数域。通过与有限差分计算的频散曲线的比较验证了算法和程序的正确性。边界元方法可以处理任意形状的边界,作为初步应用,我们研究了垂向裂纹对井孔中波传播的影响。     

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.     

Cased borehole effects on downhole seismic measurements1

Both approximate and exact formulations for the interaction of an incident elastic wave with a cased borehole are presented. In the approximate method, simple and explicit formulae are derived for the pressure in fluid at low frequencies. In the exact method, elastic potentials in each annulus are represented as a superposition of fundamental solutions to the Helmholtz equations. Continuity of displacements and stresses across layer boundaries are used to determine unknown coefficients. A global matrix algorithm is employed to compute simultaneously these coefficients in individual layers. Calculations show that, in cased boreholes, the borehole effects on downhole seismic measurements are more significant than in open boreholes. A strong resonance occurs in the fluid for SV-wave incidence from a soft formation. This resonance is prominent even at very high frequencies because the tube-wave velocity is raised well above the formation shear velocity by the steel pipe. At a particular angle of incidence of a plane P-wave, the pressure in the fluid is near zero at low frequencies (the cased borehole screening phenomenon). For hard formations and frequencies above 1 kHz, the cased borehole influence on a downhole geophone measurement is significant, especially at grazing incidence. For soft formations, both the pressure in the fluid and the solid displacement on the borehole wall show strong dependence on frequency and angle of incidence, even at low frequencies.     

Angular and Frequency-Dependent Wave Velocity and Attenuation in Fractured Porous Media

Wave-induced fluid flow generates a dominant attenuation mechanism in porous media. It consists of energy loss due to P-wave conversion to Biot (diffusive) modes at mesoscopic-scale inhomogeneities. Fractured poroelastic media show significant attenuation and velocity dispersion due to this mechanism. The theory has first been developed for the symmetry axis of the equivalent transversely isotropic (TI) medium corresponding to a poroelastic medium containing planar fractures. In this work, we consider the theory for all propagation angles by obtaining the five complex and frequency-dependent stiffnesses of the equivalent TI medium as a function of frequency. We assume that the flow direction is perpendicular to the layering plane and is independent of the loading direction. As a consequence, the behaviour of the medium can be described by a single relaxation function. We first consider the limiting case of an open (highly permeable) fracture of negligible thickness. We then compute the associated wave velocities and quality factors as a function of the propagation direction (phase and ray angles) and frequency. The location of the relaxation peak depends on the distance between fractures (the mesoscopic distance), viscosity, permeability and fractures compliances. The flow induced by wave propagation affects the quasi-shear (qS) wave with levels of attenuation similar to those of the quasi-compressional (qP) wave. On the other hand, a general fracture can be modeled as a sequence of poroelastic layers, where one of the layers is very thin. Modeling fractures of different thickness filled with CO₂ embedded in a background medium saturated with a stiffer fluid also shows considerable attenuation and velocity dispersion. If the fracture and background frames are the same, the equivalent medium is isotropic, but strong wave anisotropy occurs in the case of a frameless and highly permeable fracture material, for instance a suspension of solid particles in the fluid.     

基于简化的Pride理论模拟声电效应测井响应

针对声电效应测井问题，提出了一种全波列数值模拟方法.该方法忽略声电效应测井 时转换电场对声场的影响,并将电场视为似稳场.采用点声源模型，依据Biot理论得出了井外 孔隙介质声场的表达式，运用这些表达式和似稳电场近似方法，导出了声电效应测井时转换 电场的计算公式.在计算出的转换电场波形中，有伴随斯通利波的电场、伴随纵波和横波的 电场、和临界折射电磁波场.在25kHz以下的频率范围内，依据这种方法计算出来的声电转换 波波形与依据完整Pride理论计算的波形一致.