孔隙介质弹性波频散—衰减理论模型

储层地球物理学中,孔隙介质的各类弹性波模型常用于了解地层岩石物理性质.本文介绍了含油、气、水等物质的多相孔隙介质弹性波频散和衰减研究进展,给出了流体饱和与部分饱和孔隙介质中波传播的物理模型综述.根据孔隙介质中的固、流体分布情况,从相关基础理论和实验研究工作等方面出发,在宏观、微观和介观尺度上对流体替换、Biot孔隙力学、喷射流、Biot喷射流(BISQ)、等效球体癍块饱和、双重孔隙介质局部流动等现有主要合流体孔隙介质速度频散和衰减理论进行了回顾.研究表明,应力松弛过程是弹性波频散和衰减的基本机理,该过程由平衡特征时间刻画.该特征时间与孔隙介质的渗透率、流体粘性和体积模量紧密相关.当波频较低时,特征时间小于波周期,压力平衡得以发生,可以用等效流体模型描述波速;反之,当波频较高时,局部压差始终保持较高水平。整个骨架体积模量升高,等效模型面临困难,发展出斑块饱和模型.在分析了各类模型理论框架适用性以及所面临困难后,我们对未来研究方向给出了一些有意义的探讨.     

介观尺度孔隙流体流动作用对纵波传播特征的影响研究——以周期性层状孔隙介质为例

介观尺度孔隙流体流动是地震频段岩石表现出较强速度频散与衰减的主要作用.利用周期性层状孔隙介质模型,基于准静态孔弹性理论给出了模型中孔隙压力、孔隙流体相对运动速度以及固体骨架位移等物理量的数学解析表达式,同时利用Biot理论将其扩展至全频段条件下,克服了传统White模型中介质分界面处流体压力不连续的假设. 在此基础上对准静态与全频段下模型介质中孔隙压力、孔隙流体相对运动速度变化形式及其对弹性波传播特征的影响进行了讨论,为更有效理解介观尺度下流体流动耗散和频散机制提供物理依据.研究结果表明,低频条件下快纵波孔压在介质层内近于定值,慢纵波通过流体扩散改变总孔隙压力, 随频率的增加慢波所形成的流体扩散作用逐渐减弱致使介质中总孔压逐渐接近于快纵波孔压,在较高频率下孔压与应力的二次耦合作用使总孔压超过快纵波孔压.介质中孔隙流体相对运动速度与慢纵波形成的流体相对运动速度变化形式一致;随频率的增加孔隙流体逐渐从排水的弛豫状态过渡到非弛豫状态,其纵波速度-含水饱和度变化形式也从符合孔隙流体均匀分布模式过渡到斑块分布模式,同时介质在不同含水饱和度下的衰减峰值与慢纵波所形成的孔隙流体相对流动速度具有明显的相关性.     

中低孔渗储层岩石弹性参数的流体敏感性研究(英文)

本文从WXS凹陷中低孔渗储层岩石声波实验出发,以岩样的纵横波速度和密度为基础数据,求取出一系列的弹性参数,包括纵横波波速比、纵波波阻抗、横波波阻抗、泊松比、拉梅常数、剪切模量、体积模量、杨氏模量,等等。在前人的孔隙流体识别究基础上,综合相关理论和实验分析,构建了一个新的流体识别因子F。以饱和流体岩石弹性参数及其组合参数的相对变化量Ag/w和Ao/w为定量指标,评价各流体识别因子的流体识别效果,并采用交会图技术进行了验证。新流体敏感因子在传统较难分辨的孔隙流体"水"和"油"的区别上具有良好效果,有利于提高中低孔渗储层流体识别的成功率。     

基于Kelvin-Voigt黏弹性骨架的含非饱和流体孔隙介质BISQ模型(英文)

本文综合考虑了在波传播过程中孔隙介质的三种重要力学机制——"Biot流动机制一squirt流动机制-固体骨架黏弹性机制",借鉴等效介质思想,将含水饱和度引入波动力学控制方程,并考虑了不同波频率下孔隙流体分布模式对其等效体积模量的影响,给出了能处理含粘滞性非饱和流体孔隙介质中波传播问题的黏弹性Biot/squirt(BISQ)模型。推导了时间-空间域的波动力学方程组,由一组平面谐波解假设,给出频率-波数域黏弹性BISQ模型的相速度和衰减系数表达式。基于数值算例分析了含水饱和度、渗透率与频率对纵波速度和衰减的影响,并结合致密砂岩和碳酸盐岩的实测数据,对非饱和情况下的储层纵波速度进行了外推,碳酸盐岩储层中纵波速度对含气饱和度的敏感性明显低于砂岩储层。     

含混合裂隙、孔隙介质的纵波衰减规律研究

地下多孔介质中的孔隙类型复杂多样,既有硬孔又有扁平的软孔.针对复杂孔隙介质,假设多孔介质中同时含有球型硬孔和两种不同产状的裂隙(硬币型、尖灭型裂隙),当孔隙介质承载载荷时,考虑两种不同类型的裂隙对于孔隙流体压力的影响,建立起Biot理论框架下饱和流体情况含混合裂隙、孔隙介质的弹性波动方程,并进一步求取了饱和流体情况下仅由裂隙引起流体流动时的含混合裂隙、孔隙介质的体积模量和剪切模量,随后,在此基础上讨论了含混合裂隙、孔隙介质在封闭条件下地震波衰减和频散的高低频极限表达式.最后计算了给定模型的地震波衰减和频散,发现地震波衰减曲线呈现"多峰"现象,速度曲线为"多频段"频散.针对该模型分析讨论了渗透率参数、裂隙纵横比参数以及流体黏滞性参数对于地震波衰减和频散的影响,表明三个参数均为频率控制参数.     

地层模量分解及在流体识别中的应用

储层流体识别是确定油气水分布,合理布设井位,提高钻井成功率的关键之一.本文基于流体饱和孔隙介质岩石物理模型,对地震反演的地层体积模量进行分解,获得孔隙流体体积模量,并依据油、气、水(尤其是气-油、气-水)模量的显著差异进行识别.文中简要分析了Gassmann模型和Kuster-Toksz模型的特征,详细讨论了孔隙形态和饱和度对弹性模量的影响,提出了联合Kuster-Toksz方程和Gassmann方程的体积模量分解方法.该方法通过Kuster-Toksz方程从测井数据中反演地层骨架固体和干骨架的弹性模量,再利用Gassmann方程对地层体积模量进行分解,既考虑了孔隙形态,又充分利用了Gassmann方程的易用性.理论模型结果表明方法是可行的.方法应用于西部地区某气田,流体识别与地层含气性预测结果与钻井基本一致,进一步证实了方法的有效性.     

基于流体弹性阻抗反演的储层含油气性识别方法

流体弹性阻抗反演是一种能将反映储层流体效应的敏感参数从弹性波阻抗数据体中直接求取出来的地震反演方法.该方法不仅具有抗噪性、直观性强的特点,而且有效地避免了间接提取流体因子存在的累积误差问题.在双相介质理论和岩石物理实验指导下对岩石固液效应解耦,构建出凸显孔隙流体效应的流体等效体积模量参数,并推导了其流体弹性波阻抗方程,最后综合利用地质、测井和地震资料,完成对埕岛地区下第三系不整合圈闭储层的含流体检测,进一步明确了该地区含油气储层物性横向变化的认识,具有良好的实际应用效果.     

基于孔隙弹性理论探讨根据地下水观测资料求解Skempton系数B的方法

在孔隙弹性理论中,Skempton系数B是流体压强、应力、断层等的几何形态和密封性的函数,它反映了孔隙度和孔隙流体压缩系数的特性和含水层的封闭程度,是孔隙弹性理论中的重要参数。B值一般用于计算由地震引起的与孔隙弹性理论相关的应力变化,主要用于库仑破裂应力的计算。对于活动断层来说,B值与本征摩擦系数μ一样难以确定。本文在介绍并总结近几十年来B值的理论研究的同时,重点介绍基于孔隙弹性理论从地下流体观测资料中获取井孔原位条件下B值的方法、目前在获取方法上存在的争议及其在库仑破裂应力计算中的具体应用。     

多相岩石弹性特征的试验研究及其在地层评价中的一些应用

弹性特征是岩石的基本物理特征 ,是弹性波传播和岩石力学问题分析的基础。岩石是矿物的集合体 ,是典型的多相混合介质。岩石的性质不仅取决于构成岩石的固相和流体的特征 ,还与固 -流两相的排列方式有关。本文将岩石视为多相体 ,从其各组成相的弹性特征和组成相之间的相互作用着手研究岩石的弹性特征。1　开展了多相岩石固相体积模量的试验测试　　利用“不套封”压缩试验测试了砂岩、花岗岩和熔融氧化硅的固相体积模量。测试结果表明 ,砂岩的固相体积模量可在 3 8Gpa左右发生较大变化 ,与岩石固相的组成成分和胶结物的构造位置等因素有关…     

流体体积模量计算方法研究

Wood模型、Patchy模型、Domenico模型及Brie的经验公式是常用的流体体积模量计算模型,目前低孔低渗或致密储层一般采用Brie的经验公式来计算流体体积模量.通过深入研究这几种模型,计算出流体体积模量的上下界,将上下界分别带入Gassmann方程反推出Brie干岩石剪切模量模型指数值范围,从指数范围内寻找一个最优值,使得纵横波预测误差最小,这个最优值即为剪切模型中的指数值.Brie剪切模型中采样点的指数值为固定值,将该固定值表示为随深度变化的变量,优化了Brie干岩石模量的计算方法.将优化后的Brie干岩石模型与Gassmann方程相结合反推出流体的体积模量.本文对Weyburn油田常规储层、胜利油田低孔低渗储层及苏里格气田致密储层进行研究,得出如下结论:(1)流体体积模量除了受各相流体的体积模量、含水饱和度、压力的影响外,还与孔隙的连通程度有关,即在有效压力不大的情况下,流体体积模量随含水饱和度的变化规律主要是连通性决定的;(2)低孔低渗、致密储层流体体积模量岩石物理模型与常规储层有很大的区别,Wood模型适用于常规储层流体体积模量的计算,而Wood模型和Domenico模型相结合的形式适用于低孔低渗和致密储层流体体积模量的计算.     

Effective bulk modulus of the pore fluid at patchy saturation

We explore a package of parallel porous layers, each filled with a different fluid. Assume that this package is sampled by an elastic wave with the wavelength much larger than the thickness of an individual layer. Also assume that the layers are hydraulically isolated from each other, meaning that the diffusion length is smaller than that of the individual layer. This assumption is relevant to a patchy saturation scenario. Suppose that we wish to conduct the fluid substitution operation on this package treated as a single porous elastic body. What is the effective bulk modulus of the pore fluid to be used in this operation that will result in the same elastic modulus as computed by Backus averaging the individual moduli of the layers? We address this question analytically by assuming that the porosity, dry frame, and the mineral matrix properties of the individual layers are the same for all layers. The only difference between the layers is the pore fluid. We find that the resulting effective bulk modulus of the fluid thus derived falls between the arithmetic and harmonic averages of the fluid bulk moduli in the layers. It can be approximated by a linear combination of these two bounds where the weights are 0.50 and 0.50 or 0.75 for the arithmetic average and 0.25 for the harmonic average, depending on the elastic moduli of the dry frame, the mineral, and the pore fluids. This solution also provides a relation between the effective bulk modulus of the pore fluid in the system under examination and water saturation to be used in the fluid substitution operation at a coarse spatial scale.     

Effect of fracture fill on frequency‐dependent anisotropy of fractured porous rocks

In fractured reservoirs, seismic wave velocity and amplitude depend on frequency and incidence angle. Frequency dependence is believed to be principally caused by the wave‐induced flow of pore fluid at the mesoscopic scale. In recent years, two particular phenomena, i.e., patchy saturation and flow between fractures and pores, have been identified as significant mechanisms of wave‐induced flow. However, these two phenomena are studied separately. Recently, a unified model has been proposed for a porous rock with a set of aligned fractures, with pores and fractures filled with two different fluids. Existing models treat waves propagating perpendicular to the fractures. In this paper, we extend the model to all propagation angles by assuming that the flow direction is perpendicular to the layering plane and is independent of the loading direction. We first consider the limiting cases through poroelastic Backus averaging, and then we obtain the five complex and frequency‐dependent stiffness values of the equivalent transversely isotropic medium as a function of the frequency. The numerical results show that, when the bulk modulus of the fracture‐filling fluid is relatively large, the dispersion and attenuation of P‐waves are mainly caused by fractures, and the values decrease as angles increase, almost vanishing when the incidence angle is 90° (propagation parallel to the fracture plane). While the bulk modulus of fluid in fractures is much smaller than that of matrix pores, the attenuation due to the “partial saturation” mechanism makes the fluid flow from pores into fractures, which is almost independent of the incidence angle.     

Analytical approximations of bulk and shear moduli for dry rock based on the differential effective medium theory

Differential effective medium theory has been applied to determine the elastic properties of porous media. The ordinary differential equations for bulk and shear moduli are coupled and it is more difficult to obtain accurate analytical formulae about the moduli of dry porous rock. In this paper, in order to decouple these equations we first substitute an analytical approximation for the dry‐rock modulus ratio into the differential equation and derive analytical solutions of the bulk and shear moduli for dry rock with three specific pore shapes: spherical pores, needle‐shaped pores and penny‐shaped cracks. Then, the validity of the analytical approximations is tested by integrating the full differential effective medium equation numerically. The analytical formulae give good estimates of the numerical results over the whole porosity range for the cases of the three given pore shapes. These analytical formulae can be further simplified under the assumption of small porosity. The simplified formulae for spherical pores are the same as Mackenzie's equations. The analytical formulae are relatively easy to analyse the relationship between the elastic moduli and porosity or pore shapes and can be used to invert some rock parameters such as porosity or pore aspect ratio. The predictions of the analytical formulae for experimental data show that the formulae for penny‐shaped cracks are suitable to estimate the elastic properties of micro‐crack rock such as granite, they can be used to estimate the crack aspect ratio while the crack porosity is known and also to estimate the crack porosity evolution with pressure if the crack aspect ratio is given.     

Elastic moduli of dry rocks containing spheroidal pores based on differential effective medium theory

Differential effective medium (DEM) theory is applied to determine the elastic properties of dry rock with spheroidal pores. These pores are assumed to be randomly oriented. The ordinary differential equations for bulk and shear moduli are coupled and it is more difficult to obtain accurate analytical formulae about the moduli of dry porous rock. In this paper, we derive analytical solutions of the bulk and shear moduli for dry rock from the differential equations by applying an analytical approximation for dry-rock modulus ratio, in order to decouple these equations. Then, the validity of this analytical approximation is tested by integrating the full DEM equation numerically. The analytical formulae give good estimates of the numerical results over the whole porosity range. These analytical formulae can be further simplified under the assumption of small porosity. The simplified formulae for spherical pores (i.e., the pore aspect ratio is equal to 1) are the same as Mackenzie's equations. The analytical formulae are relatively easy to analyze the relationship between the elastic moduli and porosity or pore shapes, and can be used to invert some rock parameters such as porosity or pore aspect ratio. The predictions of the analytical formula for the sandstone experimental data show that the analytical formulae can accurately predict the variations of elastic moduli with porosity for dry sandstones. The effective elastic moduli of these sandstones can be reasonably well characterized by spheroidal pores, whose pore aspect ratio was determined by minimizing the error between theoretical predictions and experimental measurements. For sandstones the pore aspect ratio increases as porosity increases if the porosity is less than 0.15, whereas the pore aspect ratio remains relatively stable (about 0.14) if the porosity is more than 0.15.     

Monitoring fluid substitution in rock samples from noise correlation

An alternative laboratory technique to measure the elastic constants of solid samples, based on the analysis of the cross‐correlation spectra of the vibratory response of randomly excited short solid cylinders, has been recently proposed. The aim of this paper is to check the ability of the technique called passive ultrasonic interferometry to monitor fluid substitution in different rock samples. Velocity variations due to fluid substitution are easily measured if the wave attenuation in the fluid‐saturated rock is not too large (typically in rocks with few cracks or microfractures). The experimental results are in agreement with the predictions of Biot–Gassmann poroelastic theory. The effect of substituting water with a stiffer saturating fluid, such as ethylene glycol, is to increase the overall bulk modulus of the rock, without any substantial effect on shear modulus. Furthermore, the experimental results compare well with those obtained independently with conventional pulse‐transmission technique using ultrasonic transducers. However, the measured pulse‐transmission bulk moduli are slightly larger than the corresponding measured ultrasonic interferometry moduli, with the deviation increasing with increasing fluid viscosity. This can be explained by dispersion due to wave‐induced flow of the viscous fluid since pulse‐transmission experiments involve higher frequencies than ultrasonic interferometry experiments.     

Fluid‐dependent shear‐wave splitting in fractured media

Azimuthal anisotropy in rocks can result from the presence of one or more sets of partially aligned fractures with orientations determined by the stress history of the rock. A shear wave propagating in an azimuthally anisotropic medium splits into two components with different polarizations if the source polarization is not aligned with the principal axes of the medium. For vertical propagation of shear waves in a horizontally layered medium containing vertical fractures, the shear‐wave splitting depends on the shear compliance of the fractures, but is independent of their normal compliance. If the fractures are not perfectly vertical, the shear‐wave splitting also depends on the normal compliance of the fractures. The normal compliance of a fluid‐filled fracture decreases with increasing fluid bulk modulus. For dipping fractures, this results in a decrease in shear‐wave splitting and an increase in shear‐wave velocity with increasing fluid bulk modulus. The sensitivity of the shear‐wave splitting to fluid bulk modulus depends on the interconnectivity of the fracture network, the permeability of the background medium and on whether the fracture is fully or partially saturated.     

基于反演基质矿物模量和多约束条件的双相介质AVO正演方法（英文）

基于双相介质理论的AVO正演技术是储层性质描述和流体预测的有效技术手段之一,但是输入参数中基质矿物模量的准确性和双相介质模型的的合理性极大地影响双相介质AVO正演效果。因此,本文采用基于流体因子的基质矿物模量反演方法,自适应反演基质矿物体积模量。引入具有岩石物理意义的多约束条件,使得流体替换技术制作的双相介质模型具有岩石物理意义。保证获得的双相介质AVO特征反映实际地层响应,真实可靠。通过不同岩性岩样的对比分析,说明反演方法的优越性和准确性。同时LH地区实际资料应用,获得孔隙度和流体饱和度等重要岩性参数变化时双相介质AVO特征,特别是不同储层孔隙度在同一入射角对应快纵波和横波反射系数幅值的大小差异和突变角差异是分辨储层孔隙度大小的依据。     

Fluid-dependent shear-wave splitting in a poroelastic medium with conjugate fracture sets

The dependence of shear‐wave splitting in fractured reservoirs on the properties of the filling fluid may provide a useful attribute for identifying reservoir fluids. If the direction of wave propagation is not perpendicular or parallel to the plane of fracturing, the wave polarized in the plane perpendicular to the fractures is a quasi‐shear mode, and therefore the shear‐wave splitting will be sensitive to the fluid bulk modulus. The magnitude of this sensitivity depends upon the extent to which fluid pressure can equilibrate between pores and fractures during the period of the deformation. In this paper, we use the anisotropic Gassmann equations and existing formulations for the excess compliance due to fracturing to estimate the splitting of vertically propagating shear waves as a function of the fluid modulus for a porous medium with a single set of dipping fractures and with two conjugate fracture sets, dipping with opposite dips to the vertical. This is achieved using two alternative approaches. In the first approach, it is assumed that the deformation taking place is quasi‐static: that is, the frequency of the elastic disturbance is low enough to allow enough time for fluid to flow between both the fractures and the pore space throughout the medium. In the second approach, we assume that the frequency is low enough to allow fluid flow between a fracture set and the surrounding pore space, but high enough so that there is not enough time during the period of the elastic disturbance for fluid flow between different fracture sets to occur. It is found that the second approach yields a much stronger dependence of shear‐wave splitting on the fluid modulus than the first approach. This is a consequence of the fact that at higher wave frequencies there is not enough time for fluid pressure to equilibrate and therefore the elastic properties of the fluid have a greater effect on the magnitude of the shear‐wave splitting.     

基于微观孔隙结构特征的速度频散和衰减模拟

孔隙尺度的喷射流流动是引起地震波速度频散和衰减的重要机制之一.目前,大多数喷射流模型仅考虑硬孔隙与微裂隙之间的局部流动,而忽略了具有不同孔隙纵横比微裂隙间的喷射流作用.为了研究各种类型孔隙间的流体流动效应,本文对经典喷射流模型进行了扩展,通过结合等效介质理论和孔隙结构模型,根据从干燥岩石超声速度-压力曲线中提取的微裂隙孔隙纵横比分布,求取出岩石中各种微裂隙的体积压缩系数,并在此基础上,利用孔隙空间的压力松弛效应对微裂隙间的喷射流效应进行了模拟,并运用Biot理论描述了硬孔隙间的宏观流动效应.扩展后的理论模型不仅考虑了微裂隙与硬孔隙间的局部流动、硬孔隙与硬孔隙间的Biot宏观流,还加入了微裂隙与微裂隙间的喷射流作用,且模型的高、低频极限始终与Mavko-Jizba理论和Gassmann方程保持一致.模型应用分析发现,对于砂岩和大部分致密灰岩样品,扩展模型均能给出与超声实验测量数据吻合良好的估计结果.此外,扩展模型预测的速度频散及衰减表明,喷射流机制在地震和测井频段发挥着重要作用,其速度频散曲线由低频至高频呈逐渐增大趋势,不具有明显的快速变化特征,与经典频散曲线形态存在显著差异;在低有效压力下,频散和衰减程度较大,喷射流机制发挥主要作用,而随着有效压力的增加,Biot宏观流机制开始占主导,频散和衰减程度逐渐减小.