多孔介质声学模型与多极源声电效应测井和多极随钻声测井的理论与数值研究
|
摘要
本文研究了弹性波在孔隙介质的 Biot-Tsiklauri 模型和 BISQ 模型下的传
播特点；进行了多极声电效应测井响应及偏心点源声电效应测井响应的理论与
数值研究；对弹性地层和可渗地层情况，进行了随钻声测井响应的理论和数值
研究。
深入研究孔隙介质中弹性波的传播机制是理解孔隙介质中各种波动现象的
前提之一。Biot 理论奠定了孔隙介质的声学基础并得到广泛的应用。然而，有
许多实际的孔隙岩石，Biot 理论对声波的频散和衰减不能较好地给出解释。有
一种认识是，Biot 理论没有顾及喷射流流动效应。Biot 流动和喷射流动被认为
是含流体多孔隙介质中流体流动的两种重要力学机制,对孔隙介质中弹性波的
传播均产生重要的影响。本文研究了 Dvorkin 和 Nur 提出的 BISQ(Biot-Squirt)
模型中慢纵波的基本特点、特征喷射流长度对平面波在流体与孔隙介质边界上
的折反射、特征喷射流长度对井孔声导波传播的影响。给出了 BISQ 模型中的慢
纵波速度和衰减的低频近似公式，这一公式在低频给出了很好地近似值，并直
观地反映了慢纵波速度和衰减与介质参数特别是特征喷射流长度的关系。慢纵
波在流体与孔隙介质的边界上可产生更大的渗流。基于多孔介质 BISQ 模型可以
预测，无粘流体饱和孔隙岩石中不存在喷射流机制；顾及喷射流机制的粘滞流
体饱和孔隙岩石中不会发生“动力协调”现象。与没考虑喷射流效应的折反射
系数对比表明在折反射问题中喷射流机制的影响是明显的。顾及喷射流机制后，
单极、偶极、和四极声源激发的井孔各类导波的衰减都增大，但它们的频散特
性几乎不受喷射流的影响。这一特点表明，利用井孔导波拾取岩石中的特征喷
射流长度是可能的，为确定这一岩石独立参数提供一个新的途径。
此外，针对孔隙岩石饱含的石油呈现非牛顿流效应引起人们的关注，本文
发展了 Biot-Tsiklauri 模型，给出顾及孔径分布具有非零滑移速度边界的非牛
顿流体饱和孔隙介质声学模型,研究了在此孔隙介质中弹性波的传播特点。在非
牛顿流体饱和孔隙介质中考虑非零滑移速度边界的影响表明(a)动态渗透率全
面增加(b)除相对低频区外第一类纵波和横波的相速度增加，第二类纵波的相速
度在所有频率范围全面增加。除深度非牛顿流区域外，在中间频率域三种波的
衰减全面增加。研究也表明在较高频率的深度非牛顿流的第二类纵波的衰减系
163
摘要
数很小，这也激励我们在油储孔隙岩石中探测第二类纵波。
为模拟多极声源激发的声电效应测井响应，本文从 Pride 耦合弹性波-电磁
波方程组出发，导出无源均匀孔隙介质中多极声电耦合波的通解表达式。导出
多极点声源在井中激发声波时，井内声场和电磁场的计算公式、地层中耦合声
场和电磁波场的计算公式。利用声场-电磁场的边界条件确定井内外波场的系
数，利用波场的表达式模拟多极源声电效应测井响应曲线，研究井孔转换电磁
场的基本特性，考察部分介质参数对转换电磁场的影响。与点源激发不同，井
轴上的偶极声源或四极声源发射声波时，声场具有非轴对称性，在地层中耦合
的伴随电磁波也具有非轴对称性，电磁场在井内以横电场(TE)和横磁场(TM)的
混合模式传播。在井内除了可记录到反射声场还可记录到通过井壁转换而来的
电磁场的 6 个分量，这与对称源激发只能记录到 3 个分量不同。
数值模拟表明当位于井轴上的多极点声源发射声波时，在井内不仅接受到
来自地层的声波，还可以接收到两类电磁场。一类是在井内流体与地层界面井
壁上产生的临界折射电磁波，几乎同时到达阵列接收器，称电磁首波；另一类
是表观速度具有声波速度的电(磁)场，是地层中伴随声波的局域电(磁)场。井
中接收到的转换电磁场的强弱，不仅取决于地层的动电耦合系数，还取决于波
的传播特性和井孔的波导效应。对于单极点源发射时，井内偏离井轴可接收的
电磁场只有Ez ，Er和Hθ ；而偶极源和四极源发射声波时，井内可接收到电磁
场的六个分量，这对于井内转换电场信息的接收和利用是大有益处的。从电声
比可以看出，单极斯通利波、偶极弯曲波及四极螺旋波的电声转换系数具有相
同的数量级。纵波电声比总是最大，结果在声压全波图中幅度较小的纵波，在
伴随的电磁场全波中很容易辨别。单独改变渗透率时，电声比的变化并不明显。
地层水矿化度增大时，电磁场的幅度变小。
声源偏心是一个没有轴对称的问题，井内声、电场和井外声电耦合场都要
进行多极波场展开。针对单极点声源偏离井轴情况，导出井内声场、电磁场及
井外均匀孔隙地层中声电耦合波场的表达式，数值模拟了偏心点声源声电测井
响应，研究了偏心对转换电磁场的影响。为模拟偏心电声测井，导出了垂直电
偶极子偏心时井内电磁场的计算公式。数值结果表明，用有限极多级场叠加可
以描述偏心声源激发时的声电效应响应。需要顾及多级项的多少，取决于声源
的激发频率的高低，偏心的大小，和井外波场声电转换的频率响应特性。声源
的偏心对轴向电场的电磁首波影响很小。这一研究为理论上和实验上进一步深
入认识和利用声电效应测井响应是有意义的。
多极源和偏心点源
This thesis developed Biot-Tsiklauri model and investigated the properties of
elastic waves in generalized Biot-Tsiklauri model and BISQ model, and studied the
properties of acoustoelectric well logging and acoustic logging while drilling in both
the impermeable and permeable formation excited by multipole acoustic sources.
Elastic waves propagation measurements are useful and convenient tools for
investigating the inner properties of fluid-saturated porous media. In the theory of
elastic waves propagation through porous media, acoustic velocity and attenuation in
sediments and porous rocks are related to physical properties of the material.
Understanding of the whole mechanism involved in acoustic energy dissipation and
velocity dispersion during the passage of an elastic wave is an important and
interesting problem of acoustics and geophysics.
Biot’s theory has been a successful tool for interpreting experimental data, and
applied in sciences as diverse as geophysics. However, there are many examples of
real earth materials for which Biot’s theory does not seem to explain the dispersion
and attenuation very well. Various additions and corrections to Biot’s theory have
been attempted. As a matter of fact, in real fluid saturated rocks with thin cracks, Biot
and squirt-flow mechanisms coexist and dominate the dispersion and attenuation. The
united Biot and squirt flow mechanism model is presented by Dvorkin and Nur
(1993). From then on, this model has been drawing much attention. Since the strong
attenuation of slow waves in porous media, it is difficult to be detected, so that people
usually underestimate the effect of slow waves. Actually, slow waves will play
important roles in converted waves on the interface of porous rock with other medium
and the conversion mechanism of seismoelectric field. In this paper, the slow
compressional wave (P2-wave) in porous media based on BISQ model is investigated.
The low frequency approximate expression for velocity and attenuation of P2-wave is
presented. Comparing with Biot model, BISQ model predicts that: the attenuation of
P2 waves is very large at low frequency and decrease with characteristic squirt flow
length (R) increasing, the velocity low frequency limit is not zero and decrease with
R increasing, the ratio of pore fluid-displacement and bulk-displacement is similar to
167
英文摘要 abstract
attenuation and phase is different from that of Biot model; The seepage flow induced
by P2 wave at the fluid-porous media interface is more large than that of Biot model.
Two conclusions are induced from BISQ model: there is no squirt mechanism in
in-viscid fluid-saturated porous media and there is no “dynamic compatibility”
phenomenon in viscid fluid-saturated porous media. The effect of squirt flow on the
reflection and refraction coefficients predicted by BISQ model is noticeable. The
effects of the characteristic squirt flow length on the acoustic guided waves
propagation in borehole is also investigated. The numerical simulation of full
waveforms shows that the characteristic squirt flow length influence on the amplitude
of mode waves. Attenuations of Stoneley waves, pseudo-Rayleigh waves, flexural
waves, screw waves and higher modes are enhanced due to the exist of the
characteristic squirt flow, however velocity dispersion of those guided waves is nearly
independent of the characteristic squirt flow. We may use this property to estimate the
characteristic squirt flow length by attenuation coefficients of the guided waves from
acoustical logging data.
For a classic Newtonian fluid, Biot’s theory can be used to describe interaction of
fluid-saturated solid with the sound. But for oil and other hydrocarbons often
exhibiting significant non-Newtonian behavior, they are not proper again. As a step
forward, the novelty in the present work is to combine models of Tsiklarui which
introduced non
播特点；进行了多极声电效应测井响应及偏心点源声电效应测井响应的理论与
数值研究；对弹性地层和可渗地层情况，进行了随钻声测井响应的理论和数值
研究。
深入研究孔隙介质中弹性波的传播机制是理解孔隙介质中各种波动现象的
前提之一。Biot 理论奠定了孔隙介质的声学基础并得到广泛的应用。然而，有
许多实际的孔隙岩石，Biot 理论对声波的频散和衰减不能较好地给出解释。有
一种认识是，Biot 理论没有顾及喷射流流动效应。Biot 流动和喷射流动被认为
是含流体多孔隙介质中流体流动的两种重要力学机制,对孔隙介质中弹性波的
传播均产生重要的影响。本文研究了 Dvorkin 和 Nur 提出的 BISQ(Biot-Squirt)
模型中慢纵波的基本特点、特征喷射流长度对平面波在流体与孔隙介质边界上
的折反射、特征喷射流长度对井孔声导波传播的影响。给出了 BISQ 模型中的慢
纵波速度和衰减的低频近似公式，这一公式在低频给出了很好地近似值，并直
观地反映了慢纵波速度和衰减与介质参数特别是特征喷射流长度的关系。慢纵
波在流体与孔隙介质的边界上可产生更大的渗流。基于多孔介质 BISQ 模型可以
预测，无粘流体饱和孔隙岩石中不存在喷射流机制；顾及喷射流机制的粘滞流
体饱和孔隙岩石中不会发生“动力协调”现象。与没考虑喷射流效应的折反射
系数对比表明在折反射问题中喷射流机制的影响是明显的。顾及喷射流机制后，
单极、偶极、和四极声源激发的井孔各类导波的衰减都增大，但它们的频散特
性几乎不受喷射流的影响。这一特点表明，利用井孔导波拾取岩石中的特征喷
射流长度是可能的，为确定这一岩石独立参数提供一个新的途径。
此外，针对孔隙岩石饱含的石油呈现非牛顿流效应引起人们的关注，本文
发展了 Biot-Tsiklauri 模型，给出顾及孔径分布具有非零滑移速度边界的非牛
顿流体饱和孔隙介质声学模型,研究了在此孔隙介质中弹性波的传播特点。在非
牛顿流体饱和孔隙介质中考虑非零滑移速度边界的影响表明(a)动态渗透率全
面增加(b)除相对低频区外第一类纵波和横波的相速度增加，第二类纵波的相速
度在所有频率范围全面增加。除深度非牛顿流区域外，在中间频率域三种波的
衰减全面增加。研究也表明在较高频率的深度非牛顿流的第二类纵波的衰减系
163
摘要
数很小，这也激励我们在油储孔隙岩石中探测第二类纵波。
为模拟多极声源激发的声电效应测井响应，本文从 Pride 耦合弹性波-电磁
波方程组出发，导出无源均匀孔隙介质中多极声电耦合波的通解表达式。导出
多极点声源在井中激发声波时，井内声场和电磁场的计算公式、地层中耦合声
场和电磁波场的计算公式。利用声场-电磁场的边界条件确定井内外波场的系
数，利用波场的表达式模拟多极源声电效应测井响应曲线，研究井孔转换电磁
场的基本特性，考察部分介质参数对转换电磁场的影响。与点源激发不同，井
轴上的偶极声源或四极声源发射声波时，声场具有非轴对称性，在地层中耦合
的伴随电磁波也具有非轴对称性，电磁场在井内以横电场(TE)和横磁场(TM)的
混合模式传播。在井内除了可记录到反射声场还可记录到通过井壁转换而来的
电磁场的 6 个分量，这与对称源激发只能记录到 3 个分量不同。
数值模拟表明当位于井轴上的多极点声源发射声波时，在井内不仅接受到
来自地层的声波，还可以接收到两类电磁场。一类是在井内流体与地层界面井
壁上产生的临界折射电磁波，几乎同时到达阵列接收器，称电磁首波；另一类
是表观速度具有声波速度的电(磁)场，是地层中伴随声波的局域电(磁)场。井
中接收到的转换电磁场的强弱，不仅取决于地层的动电耦合系数，还取决于波
的传播特性和井孔的波导效应。对于单极点源发射时，井内偏离井轴可接收的
电磁场只有Ez ，Er和Hθ ；而偶极源和四极源发射声波时，井内可接收到电磁
场的六个分量，这对于井内转换电场信息的接收和利用是大有益处的。从电声
比可以看出，单极斯通利波、偶极弯曲波及四极螺旋波的电声转换系数具有相
同的数量级。纵波电声比总是最大，结果在声压全波图中幅度较小的纵波，在
伴随的电磁场全波中很容易辨别。单独改变渗透率时，电声比的变化并不明显。
地层水矿化度增大时，电磁场的幅度变小。
声源偏心是一个没有轴对称的问题，井内声、电场和井外声电耦合场都要
进行多极波场展开。针对单极点声源偏离井轴情况，导出井内声场、电磁场及
井外均匀孔隙地层中声电耦合波场的表达式，数值模拟了偏心点声源声电测井
响应，研究了偏心对转换电磁场的影响。为模拟偏心电声测井，导出了垂直电
偶极子偏心时井内电磁场的计算公式。数值结果表明，用有限极多级场叠加可
以描述偏心声源激发时的声电效应响应。需要顾及多级项的多少，取决于声源
的激发频率的高低，偏心的大小，和井外波场声电转换的频率响应特性。声源
的偏心对轴向电场的电磁首波影响很小。这一研究为理论上和实验上进一步深
入认识和利用声电效应测井响应是有意义的。
多极源和偏心点源
This thesis developed Biot-Tsiklauri model and investigated the properties of
elastic waves in generalized Biot-Tsiklauri model and BISQ model, and studied the
properties of acoustoelectric well logging and acoustic logging while drilling in both
the impermeable and permeable formation excited by multipole acoustic sources.
Elastic waves propagation measurements are useful and convenient tools for
investigating the inner properties of fluid-saturated porous media. In the theory of
elastic waves propagation through porous media, acoustic velocity and attenuation in
sediments and porous rocks are related to physical properties of the material.
Understanding of the whole mechanism involved in acoustic energy dissipation and
velocity dispersion during the passage of an elastic wave is an important and
interesting problem of acoustics and geophysics.
Biot’s theory has been a successful tool for interpreting experimental data, and
applied in sciences as diverse as geophysics. However, there are many examples of
real earth materials for which Biot’s theory does not seem to explain the dispersion
and attenuation very well. Various additions and corrections to Biot’s theory have
been attempted. As a matter of fact, in real fluid saturated rocks with thin cracks, Biot
and squirt-flow mechanisms coexist and dominate the dispersion and attenuation. The
united Biot and squirt flow mechanism model is presented by Dvorkin and Nur
(1993). From then on, this model has been drawing much attention. Since the strong
attenuation of slow waves in porous media, it is difficult to be detected, so that people
usually underestimate the effect of slow waves. Actually, slow waves will play
important roles in converted waves on the interface of porous rock with other medium
and the conversion mechanism of seismoelectric field. In this paper, the slow
compressional wave (P2-wave) in porous media based on BISQ model is investigated.
The low frequency approximate expression for velocity and attenuation of P2-wave is
presented. Comparing with Biot model, BISQ model predicts that: the attenuation of
P2 waves is very large at low frequency and decrease with characteristic squirt flow
length (R) increasing, the velocity low frequency limit is not zero and decrease with
R increasing, the ratio of pore fluid-displacement and bulk-displacement is similar to
167
英文摘要 abstract
attenuation and phase is different from that of Biot model; The seepage flow induced
by P2 wave at the fluid-porous media interface is more large than that of Biot model.
Two conclusions are induced from BISQ model: there is no squirt mechanism in
in-viscid fluid-saturated porous media and there is no “dynamic compatibility”
phenomenon in viscid fluid-saturated porous media. The effect of squirt flow on the
reflection and refraction coefficients predicted by BISQ model is noticeable. The
effects of the characteristic squirt flow length on the acoustic guided waves
propagation in borehole is also investigated. The numerical simulation of full
waveforms shows that the characteristic squirt flow length influence on the amplitude
of mode waves. Attenuations of Stoneley waves, pseudo-Rayleigh waves, flexural
waves, screw waves and higher modes are enhanced due to the exist of the
characteristic squirt flow, however velocity dispersion of those guided waves is nearly
independent of the characteristic squirt flow. We may use this property to estimate the
characteristic squirt flow length by attenuation coefficients of the guided waves from
acoustical logging data.
For a classic Newtonian fluid, Biot’s theory can be used to describe interaction of
fluid-saturated solid with the sound. But for oil and other hydrocarbons often
exhibiting significant non-Newtonian behavior, they are not proper again. As a step
forward, the novelty in the present work is to combine models of Tsiklarui which
introduced non
引文
Arntsen B?rge and Carcione J.M., 2001,Short Note: Numerical simulation of the Biot slow wave
in water-saturated Nivelsteiner Sandstone, Geophysics, 66,890-896.
Aron, J., Chang, S.K., Codazzi.D., et.al.,1997,Real-time sonic logging while drilling in hard and
soft rocks.,SPWLA.
巴音贺希格,2001,无限 Biot 双相介质中水平流体层声波场的理论分析和数值计算,吉林大学
硕士学位论文.
Beresnev, I.A, Johnson, P.A., 1994,Elastic-wave stimulation of oil production: A review of
methods and results, Geophysics, 59,1000-1017.
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