组分孔隙介质模型及其地震波传播理论研究
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摘要
现代油气勘探的发展要求更多地了解地下介质的物性信息,包含地下介质物性信息的介质模型及其地震波传播理论是油气和水合物地震勘探的理论基础,其中孔隙介质模型及其地震波传播理论是当前油气和水合物勘探领域研究的热点。开展这方面的理论研究对于油气、水合物勘探具有理论意义和实用价值。
孔隙介质模型及其地震波传播理论研究的核心内容就是建立孔隙介质的等效弹性性质与组分的弹性性质之间的关系模型。通过剖析前人的孔隙介质模型,本文发现多相孔隙介质的等效弹性性质就是组分的弹性性质加权叠加的结果,这个思想构成组分孔隙介质模型的理论基础。
基于组分加权的建模思想和微观力学的一些原理,本文围绕组分孔隙介质模型及其地震波传播理论开展了一系列研究,主要包含以下一些内容:
首先,基于线弹性各向同性组分孔隙介质模型的基本假设以及应力和应变组分关系方程,推导出等效弹性矩阵与组分弹性矩阵的组分关系方程以及等效弹性模量与组分弹性模量的组分关系方程;分析弹性模量的组分关系方程,指出组分加权系数是组分孔隙介质模型的核心内容;借鉴线弹性各向同性均匀固体单相介质的地震波传播理论研究的基本思路,提出线弹性各向同性组分孔隙介质的地震波传播理论。
其次,结合组分模型的系数张量对角化条件与Hashin-Shtrikman弹性模量边界,提出四个新的等效弹性模量估算公式,弥补了Hashin-Shtrikman边界估算等效剪切模量的不足;对比组分模型与Biot-Gassmann方程,提出两个模型的转换关系以及流体饱和介质弹性模量的组分表达,指出框架弹性模量的组分加权系数的物理意义以及固结和非固结孔隙岩石的框架弹性模量组分模型表述的特点,并就饱水和饱气岩石以及流体替换问题的组分加权系数与孔隙度的关系进行讨论。再次,结合弹性模量组分关系方程与正交基函数理论,推导组分加权系数的正交条件;基于正交条件,提出组分加权系数为孔隙度二次多项式时正交组分加权系数的构造方法以及正交组分加权系数适用范围的拓展方法;结合临界孔隙度理论,提出一个基于两个状态分界点的组分模型实例;比较组分模型的计算结果与前人关于砂岩弹性模量的实验结果,证明了组分孔隙介质模型理论的合理性。最后,基于各向异性应力和应变组分关系方程,推导各向异性组分孔隙介质模型的弹性矩阵和弹性模量组分关系方程,并对弹性模量组分加权模式进行分析;参照Kelvin介质,提出弹性与黏弹性各向同性组分孔隙介质模型的对应规则,推导出黏弹性各向同性双相组分孔隙介质模型的本构方程和弹性模量组分关系方程,并讨论相速度、衰减因数和品质因子的组分表述。
组分孔隙介质模型以组分加权的形式凸现了组分弹性性质对于宏观等效弹性性质的贡献,为研究孔隙介质与其组分之间的弹性性质关系模式提供了一个思路,也为解决海洋天然气水合物的储量估算问题奠定了一定的基础。
Understanding the elastic properties of underground rocks is the requirement of modern oil-gas seismic explorations, which are based on media models and seismic wave propagation theories concerning the elastic properties of subsurface rocks, in which the porous medium model, along with its seismic wave propagation theory, is concerned by many researchers in the field of oil-gas and hydrate explorations. Studies on this subject have great academic significance and applied value for the oil-gas and hydrate explorations.
The object of these studies about the porous medium and its seismic wave propagation theory is to obtain the relationships of effective elastic properties between the porous medium and its constituents. With a comprehensive analysis of all the available literature on this subject, it can be found the effective elastic properties of the multi-phase porous medium is a summation of all constituents’elastic properties weighted by their corresponding weighting coefficients. Some researches on the constituent porous medium model and its seismic wave propagation theory are carried out based on this idea and some principles of micro-mechanics, and some key points of these studies are listed below.
First, based on those assumptions of the linear elastic and isotropic constituent porous medium model, the constituent equation of effective elastic matrix and constituent elastic matrices, and also the constituent equations of effective elastic moduli and constituent elastic moduli are derived from the average stress and average strain relations between the porous medium and its constituents. Different expressions of the constituent equations of elastic moduli are presented and analyzed, and it can be found that the constituent weighting coefficient plays a very important role in the studies of the constituent model. The theory of seismic wave propagation in the constituent medium is derived on the basis of investigations of the basic points of the linear elastic and isotropic homogenous solid single-phase medium model and its seismic wave propagation theory.
Second, combined the diagonalizing conditions of coefficient tensors of the constituent model with the Hashin-Shtrikman bounds, four new formulas of effective elastic modulus are derived to make up for the shortcomings of the Hashin-Shtrikman bounds in the estimation of the effective shear modulus. Based on some comparisons between the constituent model and the Biot-Gassmann equations, the constituent expressions of elastic moduli of a fluid-saturated multi-phase medium and its frame areobtained in order to find the physical meaning of the frame weighting coefficients and the feature of the frame moduli expressions of consolidated and unconsolidated porous rocks. Following the comparison it discusses the weighting coefficients of bulk moduli of rocks saturated with water or gas and the problem of fluid substitution.
Third, the conditions fulfilled by orthogonal constituent weighting coefficients are derived after the theory of orthogonal basis functions is introduced into the constituent model. When these coefficients are quadratic functions of the porosity, specific constituent orthogonal weighting coefficients are derived from these orthogonal conditions along with a discussion about how to extend the applicable range of the constituent orthogonal weighting coefficients in the orthogonal coordinates. Based on the combination of the theory of critical porosity and the constituent model, it presents a specific example of the constituent model that includes two transforming points. The reasonability of above-mentioned theories is shown by comparison of theoretical calculations and measured data on effective elastic moduli of clean sandstone or sandstone analogs saturated with pure water.
Last, Based on the average stress and strain relations between the anisotropic porous medium and its anisotropic or isotropic constituents, the constituent equation of effective elastic matrix and constituent elastic matrices, and the constituent equations of effective elastic moduli and constituent elastic moduli of the anisotropic constituent model are derived along with a discussion about the weighting pattern of elastic moduli. The correspondence principle between elastic and viscoelastic isotropic constituent porous medium model is derived on the basis of analyses of the Kelvin medium model, and then the constitutive equation and the constituent equations of elastic moduli, and constituent expressions of phase velocity, attenuation coefficient and quality factor are obtained with the aid of this principle.
The weighting expressions of the constituent porous medium model in this paper clearly demonstrate the contribution of all constituents to the effective elastic properties of the porous medium, and this model not only provide an idea for the studies on elastic property patterns between the porous medium and its constituents, but also provide a foundation for solving the problem of storage estimation of marine gas hydrate.
孔隙介质模型及其地震波传播理论研究的核心内容就是建立孔隙介质的等效弹性性质与组分的弹性性质之间的关系模型。通过剖析前人的孔隙介质模型,本文发现多相孔隙介质的等效弹性性质就是组分的弹性性质加权叠加的结果,这个思想构成组分孔隙介质模型的理论基础。
基于组分加权的建模思想和微观力学的一些原理,本文围绕组分孔隙介质模型及其地震波传播理论开展了一系列研究,主要包含以下一些内容:
首先,基于线弹性各向同性组分孔隙介质模型的基本假设以及应力和应变组分关系方程,推导出等效弹性矩阵与组分弹性矩阵的组分关系方程以及等效弹性模量与组分弹性模量的组分关系方程;分析弹性模量的组分关系方程,指出组分加权系数是组分孔隙介质模型的核心内容;借鉴线弹性各向同性均匀固体单相介质的地震波传播理论研究的基本思路,提出线弹性各向同性组分孔隙介质的地震波传播理论。
其次,结合组分模型的系数张量对角化条件与Hashin-Shtrikman弹性模量边界,提出四个新的等效弹性模量估算公式,弥补了Hashin-Shtrikman边界估算等效剪切模量的不足;对比组分模型与Biot-Gassmann方程,提出两个模型的转换关系以及流体饱和介质弹性模量的组分表达,指出框架弹性模量的组分加权系数的物理意义以及固结和非固结孔隙岩石的框架弹性模量组分模型表述的特点,并就饱水和饱气岩石以及流体替换问题的组分加权系数与孔隙度的关系进行讨论。再次,结合弹性模量组分关系方程与正交基函数理论,推导组分加权系数的正交条件;基于正交条件,提出组分加权系数为孔隙度二次多项式时正交组分加权系数的构造方法以及正交组分加权系数适用范围的拓展方法;结合临界孔隙度理论,提出一个基于两个状态分界点的组分模型实例;比较组分模型的计算结果与前人关于砂岩弹性模量的实验结果,证明了组分孔隙介质模型理论的合理性。最后,基于各向异性应力和应变组分关系方程,推导各向异性组分孔隙介质模型的弹性矩阵和弹性模量组分关系方程,并对弹性模量组分加权模式进行分析;参照Kelvin介质,提出弹性与黏弹性各向同性组分孔隙介质模型的对应规则,推导出黏弹性各向同性双相组分孔隙介质模型的本构方程和弹性模量组分关系方程,并讨论相速度、衰减因数和品质因子的组分表述。
组分孔隙介质模型以组分加权的形式凸现了组分弹性性质对于宏观等效弹性性质的贡献,为研究孔隙介质与其组分之间的弹性性质关系模式提供了一个思路,也为解决海洋天然气水合物的储量估算问题奠定了一定的基础。
Understanding the elastic properties of underground rocks is the requirement of modern oil-gas seismic explorations, which are based on media models and seismic wave propagation theories concerning the elastic properties of subsurface rocks, in which the porous medium model, along with its seismic wave propagation theory, is concerned by many researchers in the field of oil-gas and hydrate explorations. Studies on this subject have great academic significance and applied value for the oil-gas and hydrate explorations.
The object of these studies about the porous medium and its seismic wave propagation theory is to obtain the relationships of effective elastic properties between the porous medium and its constituents. With a comprehensive analysis of all the available literature on this subject, it can be found the effective elastic properties of the multi-phase porous medium is a summation of all constituents’elastic properties weighted by their corresponding weighting coefficients. Some researches on the constituent porous medium model and its seismic wave propagation theory are carried out based on this idea and some principles of micro-mechanics, and some key points of these studies are listed below.
First, based on those assumptions of the linear elastic and isotropic constituent porous medium model, the constituent equation of effective elastic matrix and constituent elastic matrices, and also the constituent equations of effective elastic moduli and constituent elastic moduli are derived from the average stress and average strain relations between the porous medium and its constituents. Different expressions of the constituent equations of elastic moduli are presented and analyzed, and it can be found that the constituent weighting coefficient plays a very important role in the studies of the constituent model. The theory of seismic wave propagation in the constituent medium is derived on the basis of investigations of the basic points of the linear elastic and isotropic homogenous solid single-phase medium model and its seismic wave propagation theory.
Second, combined the diagonalizing conditions of coefficient tensors of the constituent model with the Hashin-Shtrikman bounds, four new formulas of effective elastic modulus are derived to make up for the shortcomings of the Hashin-Shtrikman bounds in the estimation of the effective shear modulus. Based on some comparisons between the constituent model and the Biot-Gassmann equations, the constituent expressions of elastic moduli of a fluid-saturated multi-phase medium and its frame areobtained in order to find the physical meaning of the frame weighting coefficients and the feature of the frame moduli expressions of consolidated and unconsolidated porous rocks. Following the comparison it discusses the weighting coefficients of bulk moduli of rocks saturated with water or gas and the problem of fluid substitution.
Third, the conditions fulfilled by orthogonal constituent weighting coefficients are derived after the theory of orthogonal basis functions is introduced into the constituent model. When these coefficients are quadratic functions of the porosity, specific constituent orthogonal weighting coefficients are derived from these orthogonal conditions along with a discussion about how to extend the applicable range of the constituent orthogonal weighting coefficients in the orthogonal coordinates. Based on the combination of the theory of critical porosity and the constituent model, it presents a specific example of the constituent model that includes two transforming points. The reasonability of above-mentioned theories is shown by comparison of theoretical calculations and measured data on effective elastic moduli of clean sandstone or sandstone analogs saturated with pure water.
Last, Based on the average stress and strain relations between the anisotropic porous medium and its anisotropic or isotropic constituents, the constituent equation of effective elastic matrix and constituent elastic matrices, and the constituent equations of effective elastic moduli and constituent elastic moduli of the anisotropic constituent model are derived along with a discussion about the weighting pattern of elastic moduli. The correspondence principle between elastic and viscoelastic isotropic constituent porous medium model is derived on the basis of analyses of the Kelvin medium model, and then the constitutive equation and the constituent equations of elastic moduli, and constituent expressions of phase velocity, attenuation coefficient and quality factor are obtained with the aid of this principle.
The weighting expressions of the constituent porous medium model in this paper clearly demonstrate the contribution of all constituents to the effective elastic properties of the porous medium, and this model not only provide an idea for the studies on elastic property patterns between the porous medium and its constituents, but also provide a foundation for solving the problem of storage estimation of marine gas hydrate.
引文
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