套管井应力集中下正交偶极声测井的声弹理论、数值分析与实例

油田受异常地应力作用而损坏的油井绝大部分都是套管井,针对这一实际情况,通过求解套管井应力集中情况下各层介质中应力场的分布,应用摄动积分方法,将裸眼井声弹性方程发展为适用于套管井井孔体系的情况.数值考察了井外无限远单轴水平压应力作用下,声弹方程中各层介质敏感系数和速度-应力系数随频率的变化,及二相互垂直偏振的偶极弯曲波相速度的频散曲线.结果表明,套管井声弹方程中的速度-应力系数主要由地层参数决定,内层介质的贡献较小,其中与三阶弹性模量相对应的项又起决定作用;井孔周围应力集中将引起平行和垂直单轴压应力方向偏振的二弯曲波发生速度分裂,同时随频率的增大两条频散曲线产生交叉,说明这种交叉仍然可用作判断套管井情况下地层各向异性是本征的还是由异常应力诱导的判据,用正交偶极声波测井技术在套管井中无损检测异常地应力仍然可行;但低速地层交叉点将明显向高频区移动,这又是与裸眼井情况重要的不同之处.本文还给出现场实测数据的处理实例,理论结果得到验证.     

横向各向同性地层(VTI)井孔声弹效应对弯曲波的影响

本文发展了建立在地层参考状态为各向同性介质假定下的现行井孔声弹性理论,就井外为横向各向同性面与井轴垂直的、具有9个独立三阶弹性模量的横向各向同性介质(VTI井况),水平面内受双轴应力作用下给出了一个简洁的与井内压力、应力差、应力和以及多极源偏振方位角有关的井孔弯曲波声弹公式,并且导出了平面纵、横波速度的声弹公式.数值考察了弯曲波速度之改变量的灵敏系数随频率的变化、受井外水平双轴应力作用时两种偏振的偶极弯曲波频散曲线以及对应不同方位径向偏振的横波速度.研究结果表明弯曲波声弹公式与5个二阶弹性系数以及7个独立的三阶弹性模量有关;而且由内压引起的井孔弯曲波声弹性公式中的三阶弹性模量仅与6个独立的弹性模量有关.横向各向同性介质井孔弯曲波速度的交叉现象仍是判断地应力存在的标志;一个重要的认识是受双轴应力作用的弯曲波速度变化在低频区主要与c₁₄₄和c₁₅₅两个三阶弹性模量有关,而且此认识与径向偏振的平面横波一致.在缺乏足够实验条件情况下,对VTI情况,以c₁₄₄,c₁₅₅和c₁₂₃三个独立的量进行测量,然后可暂不考虑三阶弹性模量的各向异性,建立简化的应力反演公式.反之,如果已知地层的地应力信息,由简化的声弹公式可以反演三阶弹性模量c₁₄₄,c₁₅₅和c₁₂₃.     

套管井应力集中诱导井周波速各向异性的研究

针对在套管井中应用正交偶极声测井检测地层各向异性和确定异常构造应力的需要, 本文通过求解水平构造应力作用下套管井的应力场分布,应用声弹性理论说明应力集中对套管井井周弹性波速空间分布的影响,分析了波速空间分布对加套管后的正交偶极各向异性声测量的影响.井孔、套管、水泥环和地层系统的复杂性改变了原裸眼井情况地层中的应力场分布,使应力集中的范围明显缩小到井眼附近.对应不同方位径向偏振横波的交叉点向井孔附近移动.横波波速空间分布的方位极值规律发生变化,但纵波波速空间分布的方位极值规律不变,仍能提供最大远场构造应力施加的方向.     

横向各向同性地层井孔伪瑞利波、弯曲波、螺旋波的低频极限速度

在多极源声测井中, 低频弯曲波或螺旋波被广泛应用于测量地层的横波速度. 前人的研究已证明在各向同性地层中井孔伪瑞利波、弯曲波及螺旋波的低频极限速度都等于地层横波速度. 大量的数值计算结果似乎表明此结论在横向各向同性（TI）地层情况下也能成立, 但缺乏理论证明. 本文在井孔平行于TI弹性地层对称轴的模型下, 考察了井内声源激发的波在流-固边界上的反射和透射情况, 阐述了非泄漏模式导波产生的必要条件并讨论了其速度上限值. 我们发现在各向异性参数满足一定条件的TI地层中,导波速度的低频极限值小于沿井孔方向上的横波速度. 通过对井孔导波的频散分析以及对时域全波列的数值模拟, 论证了在这类地层中进行多极源声测井时,不可能根据弯曲波或螺旋波的到达时间准确获取地层的横波速度值.     

偶极子声波测井在双层套管井中激发的声场特征

多层套管井中的套管-水泥以及水泥-地层在径向上的分布较单层套管井界面多且径向分布范围更深.目前还未有针对多层套管井固井质量评价的有效方法,偶极子阵列声波测井具有工作频率低径向探测深的优势,本文通过实轴积分和三维有限差分计算了偶极子声源在不同胶结状况的双层套管井中激发的声场,旨在探讨偶极子阵列声波在双层套管井中评价外层套管和地层之间胶结状况的可行性.计算结果表明,在两层套管之间充填泥浆时,全波波形中可明显观测到地层弯曲波和套管弯曲波,若外层套管和地层之间充填水泥套管弯曲波的慢度明显高于充填泥浆时的慢度值;在外层套管和地层之间胶结的水泥出现缺失,套管弯曲波的频散曲线会处于完全胶结与完全无胶结之间,其变化量与水泥在外层环空的占比近似成线性关系,几乎不受水泥缺失的径向位置影响.由于偶极子声源的指向性,套管弯曲波的响应特征主要受与声源振动指向的方位扇区胶结状况的影响;在两层套管之间充填水泥时,若外层套管和地层之间充填泥浆,仍可观测到套管弯曲波,模拟波列提取的套管弯曲波的频散曲线与解析解计算的频散曲线吻合,两层套管通过水泥胶结在一起,其弯曲振动的传播速度稍有增加,类似单层套管厚度加厚的响应特征.两种模拟方法得到的结果均表明套管弯曲波对外层套管和地层之间的充填介质敏感,验证了偶极子阵列声波测井在双层套管井固井质量评价中应用的可行性.     

套管井声波全波列中地层波的幅度特性

套管井声全渡中的地层波可以检测固井第二界面的水泥胶结质量状况.地层波不仅受地层衰减、套管波干扰等因素影响,更主要受第二界面两侧的声阻抗差值的影响.为此,基于固体介质的声势函数和界面的边界条件,推导了固-固界面纵横波的反射系数和透射系数,以及第一临界角入射情况下反射系数和透射系数的近似公式,并且分析了透射系数与声阻抗之间的关系.数值计算结果发现,地层波幅度随第二界面两侧声阻抗差增大而减小,且这种关系是非线性的.基于临界入射的透射系数,对经过衰减校正和干扰校正的地层波进行声阻抗校正,消除地层声阻抗对地层波幅度影响.使用地层波幅度评价第二界面的水泥胶结状况,并在实际资料处理中见到了好的效果.     

岩石声弹性理论与应用的研究进展

大量岩石实验证明了岩石声弹现象的存在,即岩石的弹性波波速会随着岩石的应力状态的改变而改变,即岩石的声弹性现象.岩石的声弹性现象为地应力无损检测提供了可能.目前许多研究已经分别给出了岩石声弹性的细观和宏观理论,并初步应用到地应力测量方面.为了促进岩石声弹理论的应用,本文总结了岩石声弹性的细观和宏观理论研究及其在地应力测量方面应用研究的进展.     

裸眼井中弹性波传播的非对称模式的数值研究

本文从数值上研究了裸眼井中弹性波传播的非对称模式,给出了合成微地震图和导波（弯曲波）的频散曲线,发现在“硬”地层和“软”地层的井中,导波都是高度频散的,其最大相速度等于地层的横波速度,其截止频率低于对称模式的伪瑞利波的截止频率;在低频（2-3kHz）和长源距（3-4m）的条件下,由非对称的声源（如声偶极子）所产生的微地震图中,初至信号是以横波速度传播的,而以纵波速度传播的信号被抑制。本文的结果对研制横波速度测井仪是有意义的。     

声电效应测井的有限差分模拟

本文研究声电效应测井波场的有限差分模拟算法.忽略井外地层中诱导电磁场对孔隙弹性波的影响,将求解动电耦合波方程组的问题解耦,先计算孔隙弹性波,再计算其诱导电磁场.基于轴对称柱坐标系下的速度-应力交错网格,采用时域有限差分计算井孔流体声波和井外地层孔隙弹性波.将电磁场近似看作似稳场,基于轴对称柱坐标系下的5点式有限差分网格,求解不同时刻的电位Poisson方程,计算诱导电场.结果表明:本文算法可准确模拟频率6.0 kHz的声电效应测井全波;在声波测井频率范围内,电导率、动电耦合系数和动态渗透率的低频近似对伴随电磁场的计算影响不大;地层水平界面导致伴随反射斯通利波的电场和显著的界面电磁波,后者对于探测地层界面具有潜在的应用价值.     

滑移界面表征的套管井声场的理论计算

经典弹性波理论往往在套管与水泥环之间增加一层流体环来模拟套管与水泥环之间胶结差时的测井响应,但流体环的存在,使得套管与水泥环之间缺失了剪切耦合,即使几个微米的厚度,套管波幅度也会明显增大,接近甚至超过自由套管时的30%.因此经典弹性波理论常常无法解释现场测量数据中套管波幅度的渐变现象.实际套管井中胶结界面粗糙或不规则起伏使套管与水泥环界面两侧介质有所接触,往往存在剪切耦合,用剪切刚度和法向刚度表达的滑移界面理论应用到套管与水泥环或水泥环与地层界面的胶结响应,可模拟界面从完全胶结到完全不胶结的过渡状态.通过将滑移界面理论模拟的波结构与在套管与水泥环之间加一层软固体层时的经典弹性波理论模拟的波结构对比,验证了滑移界面理论在模拟水泥胶结时的适用性.滑移界面理论与经典弹性波理论结合分析了水泥不同胶结状态下井孔内外声场的辐射特征,随着界面水泥胶结质量的下降井内接收的套管波以及套管波泄漏到地层中的纵横波幅度逐渐增强,透过井壁辐射到地层中的纵波和横波逐渐降低.将滑移界面理论应用到套管井水泥胶结状况的模拟,弥补了经典弹性波理论在模拟水泥胶结测井响应时的局限性,也为定量刻画水泥环界面的耦合刚度提供了可能...     

Biot dispersion for P‐ and S‐wave velocities in partially and fully saturated sandstones

Ultrasonic compressional‐ and shear‐wave velocities have been measured on 34 samples of sandstones from hydrocarbon reservoirs. The sandstones are all of low clay content, high porosity, and cover a wide range of permeabilities. They were measured dry and brine‐saturated under hydrostatic effective stresses of 10, 20 and 40 MPa. For eight of the sandstones, ultrasonic velocity measurements were made at different partial water saturations in the range from dry to fully saturated. The Gassmann–Biot theory is found to account for most of the changes in velocities at high effective stress levels when the dry sandstones are fully saturated with brine, provided the lower velocities resulting when the dry sandstone initially adsorbs small amounts of moisture are used to determine the elastic properties of the ‘dry’ sandstone. At lower effective stress levels, local flow phenomena due to the presence of open microcracks are assumed to be responsible for measured velocities higher than those predicted by the theory. The partial saturation results are modelled fairly closely by the Gassmann–Biot theory, assuming heterogeneous saturation for P‐waves.     

On correlation between seismic velocity anisotropy and stressesin situ

Seismic velocity anisotropies measured in underground mines are compared within situ stress measurements in these mines. These underground data are also compared with seismic velocity anisotropies observed by large scale seismic sounding conducted from the earth's surface, The velocity anisotropies are about 10% and the data obtained by different methods on different scales and frequencies agree with each other. The directions of largest and smallest velocities coincide with the largest and smallest horizontal stresses, respectively. These results suggest that the direction and magnitude of stresses in potential mining areas could be estimated from velocity anisotropies observed in seismic prospecting of the area.     

Wave‐driven inertial oscillations

Abstract

In a nonrotating system, the shear Reynolds stresses exerted by surface or internal gravity waves vanish on account of the exact quadrature between the horizontal and vertical orbital velocities. It is shown that a rotation of the system induces small in‐phase perturbations, resulting in a mean Reynolds stress which can generate low frequency currents. If both the wave field and the ocean are homogeneous with respect to the horizontal coordinates, the low‐frequency response is an undamped inertial oscillation. If either the wave field or the ocean are weakly inhomogeneous, the oscillation disperses in the vertical and horizontal directions due to phase‐mixing of modes with closely neighboring frequencies. Other effects which produce small frequency shifts also contribute to phase‐mixing, for example the horizontal component of the Coriolis vector and nonlinear interactions with geo‐strophic currents. The analysis is based on operator representations which avoid normal mode decomposition and yield simple integro‐differential operators for each phase‐mixing process. Numerical results are presented for a continuously stratified model typical for a shallow sea (Baltic). The orders of magnitude and qualitative features are in reasonable agreement with observations.     

Measurements of Reynolds stress in a wind-driven lagoonal estuary

Acoustic Doppler current profilers (ADCPs) have been used to measure Reynolds stresses in tidally dominated environments where wave action was minimal. In this paper, we examine observations from a microtidal estuary where the effects of wind stress and surface waves dominate the velocity variance. Reynolds stress measurements in this setting require a technique for addressing surface gravity wave contamination. We present here a method of reducing the effect of wave motion on Reynolds stresses by subtracting coincident observations along the axis of the ADCP beam. Linear wave theory is used to account for the attenuation of wave orbital velocities with depth. Using this method, Reynolds stress values are brought in line with those predicted by drag laws at the surface and bottom. The apparent Reynolds stress that is removed by the along-axis subtraction is shown to be largely due to the interaction of a slight tilt (1°) in the ADCP and the wave orbital velocity. During periods of stronger wind and waves, there is evidence of enhanced near-surface turbulence and momentum flux, presumably due to breaking waves. During these events, our calculated Reynolds stress magnitudes still appear reasonable, although the directions are suspect. We develop a diagnostic technique that clearly demarcates this region when it occurs. Coincident density profile measurements are used with the ADCP data to compute gradient Richardson numbers throughout the water column. Enhanced Reynolds stresses appear to correspond to Richardson numbers less than one. Responsible editor: Alejandro Souza     

山西煤矿矿区井下地应力场分布特征研究

采用煤矿井下专用的小孔径水压致裂地应力测量装置,在山西省的晋城、潞安、汾西、华晋、阳泉、平朔、大同等矿区,完成了160个测点的地应力测量,测点地质条件涵盖了山西省煤矿大部分条件.基于实测数据,分析了地应力与测点埋深的关系,不同深度条件下煤矿矿区井下地应力状态;绘制出山西省煤矿矿区井下地应力分布图,并与震源机制解的分析结果进行了比较,得出山西省煤矿矿区井下地应力场分布特征与变化规律.煤矿井下水平应力总体上随着埋深增加而增大,但由于各矿区地质条件差异较大,导致地应力测试数据离散性也较大;埋深小于250 m的岩层应力状态主要为σ_H>σ_h>σ_V型,埋深处于250~500 m的岩层应力状态以σ_H>σ_V>σ_h型为主,埋深较大的矿区主要为σ_V>σ_H>σ_h型;最大水平主应力与垂直主应力的比值绝大部分集中在0.5~2.0之间,而且随着埋深增加,侧压比呈现减小的趋势,并向1附近集中;最大水平主应力与最小水平主应力的比值主要集中在1.5～2.0之间;平均水平主应力与垂直主应力的比值大多处于0.5～1.5,尤以0.5～1.0之间最多;山西省煤矿矿区从北到南,最大水平主应力方向发生了较大变化.北部最大水平主应力方向为NE,往南发生偏转到NNW;靠东部与西部偏向NW;靠东南部出现了多变的方向.井下实测数据与震源机制解相比在部分区域一致性较好,而在另一些区域存在明显的差异.特别是在受较大地质构造影响的区域,水平主应力方向往往发生明显的扭转和变化.     

重力波在中层大气温度波导中的传播模式研究

本文给出了重力波在中层大气温度波导中的导制传播模型,并在此模型的基础上详细讨论了重力波部分导制传播下的对称模式与非对称模式,导出了不同模式下相应的特征函数和色散方程,进一步用离散的方法对两类色散方程进行了求解;同时还利用二维全隐欧拉格式（FICE）对重力波在温度波导中的传播进行了模拟,模拟的结果也成功地展现了对称与非对称两种传播模式.研究表明,下边界的扰动能量在向上传播进入波导区域后被俘获,形成导制传播.不同周期的初始扰动,在波导内均会形成对称与非对称形式两种模式的导制传播,由于两者的行进速度不一致,最终会引起两种不同模式的分离.数值模拟中重力波的水平行进速度与线性模型预测值非常接近.波导中不同模式下重力波的水平波长与初始扰动的水平波长非常一致,然而波导区域内重力波的频率与初始扰动的频率无关,频率不同的初始扰动会激发出相同频率的重力波对称与非对称导制传播模式.这表明在确定的温度波导中,水平波数才是决定重力波传播特性的决定因素.进一步的分析显示,初始扰动的水平波数-频率分布越接近完全导制传播的色散关系时,温度波导中更易于生成以该种模式部分导制传播的重力波.     

Offset dependence of overburden time-shifts from ultrasonic data

Depletion or injection into a reservoir implies stress changes and strains in the reservoir and its surroundings. This may lead to measurable time-shifts for seismic waves propagating in the subsurface. To better understand the offset dependence of time-shifts in the overburden, we have systematically quantified the time-shifts of three different overburden shales in controlled laboratory tests. These experiments may be viewed as an analogue to the time-shifts recorded from seismic field surveys. For a range of different stress paths, defined as the ratio between the horizontal and the vertical stress changes, the changes of the P-wave velocities in different directions were measured such that the offset dependence of time-shifts for different stress paths could be studied. The time-shifts are stress path dependent, which is particularly pronounced at large offsets. For all stress paths, the time-shifts exhibit a linearly decreasing trend with increasing offset, that is, a negative offset gradient. At zero offset, for which the ray path is normal to the bedding, the time-shifts are similar for all investigated stress paths. The isotropic stress path is associated with the smallest offset gradient of the time-shifts. In contrast, the constant-mean-stress path shows the largest gradient with a flip in the polarity of the time-shifts for the largest offsets. The separate contributions from the strain and velocity changes to the time-shifts were also quantified. The time-shifts for the isotropic stress path are dominated by the contribution from velocity changes at all offsets. In contrast, the strain contributes significantly to the time-shifts at small offsets for the constant-mean-stress path. This shows that the offset dependence in pre-stack seismic data may be a key to understand the changes of subsurface stresses, pore pressure and strain upon depletion or injection. To utilize this knowledge from laboratory experiments, calibrated rock physics models and correlations are needed to constrain the seismic time-shifts and to obtain an adequately updated geological model reflecting the true anisotropic nature of the subsurface. This may have important implications for improved recovery and safety, particularly in mature fields.