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。     

Reflection and transmission of attenuated waves at the boundary between two dissimilar poroelastic solids saturated with two immiscible viscous fluids

The phenomenon of reflection and transmission of plane harmonic waves at the plane interface between two dissimilar poroelastic solids saturated with two immiscible viscous fluids is investigated. Both porous media are considered dissipative due to the presence of viscosity in pore‐fluids. Four attenuated (three dilatational and one shear) waves propagate in such a dissipative porous medium. A finite non‐dimensional parameter is used to define the effective connections between the surface‐pores of two media at their common interface. Another finite parameter represents the gas‐share in the saturation of pores. An attenuated wave in a dissipative medium is described through the specification of directions of propagation and maximum attenuation. A general representation of an attenuated wave is defined through its inhomogeneous propagation, i.e., different directions for propagation and attenuation. Incidence of an inhomogeneous wave is considered at the interface between two dissipative porous solids. This results in four reflected and four transmitted inhomogeneous waves. Expressions are derived for the partition of incident energy among the reflected and transmitted waves. Numerical examples are studied to determine the effects of saturating pore fluid, frequency, surface‐pore connections and wave inhomogeneity on the strengths of reflected and transmitted waves. Interaction energy due to the interference of different (inhomogeneous) waves is calculated in both the dissipative porous media to verify the conservation of incident energy.     

非饱和土中剪切S波的传播特性分析

基于对非饱和多孔介质的研究成果,考虑孔隙中的液相和气相的相互影响,研究非饱和土地基中剪切S波的传播特性。通过非饱和土中固相、液相和气相的质量平衡方程、动量平衡方程和非饱和土有效应力原理,建立问题的弹性波动方程,经过理论推导给出非饱和土中剪切S波的弥散特征方程。通过数值算例分析剪切S波的波速和衰减系数随饱和度、频率和固有渗透系数等因素的变化规律。结果表明,剪切S波的波速几乎不受饱和度的影响,但其随着频率的增大而减小,随着固有渗透系数的增大先不变后增大;剪切S波的衰减系数随着饱和度和频率的增加均增大,而随着固有渗透系数的增大先不变后增大最后减小。     

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.     

饱和多孔微极介质的波动方程及其势函数方程

土是由一定尺寸大小颗粒所构成的多孔介质,具有明显的颗粒特性,当土颗粒间的孔隙被流体（如水或油）充满时则成为饱和土.利用微极理论和Biot波动理论的研究成果,把饱和土中多孔固体骨架部分近似地视为微极介质,孔隙中的流体部分视为质点介质,获得饱和多孔微极介质的弹性波动方程.借鉴Greetsma理论,建立了饱和多孔微极介质弹性本构方程力学参数与相应单相介质弹性参数的相互关系,使饱和多孔微极介质弹性波动方程中的物理参数具有明确的物理意义,易于在试验中确定.运用场论理论把饱和多孔微极介质的波动方程简化为势函数方程,建立了饱和多孔微极介质中五种弹性波的弥散方程,数值分析了五种简谐体波在无限饱和多孔微极介质中的传播特性. 结果表明,P1波、P2波和剪切S1波的波速弥散曲线与经典饱和多孔介质基本相同,当频率小于临界频率ω0时旋转纵波θ波和横波S2波不存在,当频率大于临界频率ω0时,θ波和S2波的传播速度随频率增加而减小.     

裂缝、裂隙介质衰减频散研究

为研究裂缝、裂隙介质中波致流引起的衰减,将裂缝看作背景孔隙岩石中非常薄且孔隙度非常高的层状介质,并等价成White周期层状模型.分别考虑不同类型的裂隙和孔隙之间的挤喷流影响,结合改进的Biot方程,推导得到裂缝裂隙介质的刚度与频率的关系.当缝隙中饱含流体时,介质的衰减和速度频散受裂缝、孔隙之间和裂隙、孔隙之间流体流动的显著影响.在低频极限下,裂缝裂隙介质的性质由各向异性Gassmann理论和挤喷流模型获得;而在非常高的频率时,由于缝隙中的压力来不及达到平衡,波致流的影响可忽略.分析表明,裂隙密度主要影响波的衰减,而裂隙纵横比主要控制优势衰减频率和速度显著变化的频率范围;由于不同裂隙的衰减机制不同,衰减和速度频散大小有所差异,但基本趋势相同.     

Elastic properties of saturated porous rocks with aligned fractures

Elastic properties of fluid saturated porous media with aligned fractures can be studied using the model of fractures as linear-slip interfaces in an isotropic porous background. Such a medium represents a particular case of a transversely isotropic (TI) porous medium, and as such can be analyzed with equations of anisotropic poroelasticity. This analysis allows the derivation of explicit analytical expressions for the low-frequency elastic constants and anisotropy parameters of the fractured porous medium saturated with a given fluid. The five elastic constants of the resultant TI medium are derived as a function of the properties of the dry (isotropic) background porous matrix, fracture properties (normal and shear excess compliances), and fluid bulk modulus. For the particular case of penny-shaped cracks, the expression for anisotropy parameter ε has the form similar to that of Thomsen [Geophys. Prospect. 43 (1995) 805]. However, contrary to the existing view, the compliance matrix of a fluid-saturated porous-fractured medium is not equivalent to the compliance matrix of any equivalent solid medium with a single set of parallel fractures. This unexpected result is caused by the wave-induced flow of fluids between pores and fractures.     

基于数字岩心动态应力应变模拟的非均匀孔隙介质波致流固相对运动刻画

地震波传播激发的不同尺度的流固相对运动(宏观、中观和微观)是许多沉积岩地层中地震波频散和衰减的主要原因,然而野外观测和试验测量都难以对非均匀多孔介质孔隙压力弛豫物理过程进行精细刻画.通过数字岩石物理技术,本文建立了三个典型的数字岩心分别用于表征孔隙结构、岩石骨架和斑状饱和流体引起的非均质性,利用动态应力应变模拟技术计算数字岩心的位移和孔隙流体增量图像.通过分析和比较三个数字岩心的位移和孔隙压力增量图像,细致刻画了发生于非均匀含流体多孔介质内的宏观、中观和微观尺度的流固相对运动:1)宏观尺度的波致孔隙流体流动导致波长尺度上数字岩心不同区域的孔隙压力和位移差异;2)中观尺度的流体流动发生在软层与硬层之间、气层与液层之间;3)微观尺度的流体流动发生在孔隙内部或相邻孔隙之间.数值模拟试验也证明基于数字岩心的动态应力应变模拟技术可以从微观尺度上更好的理解波致孔隙流体流动发生的物理机理,从而为建立岩石骨架、孔隙流体、孔隙结构非均质性和弹性波频散-衰减特征的映射关系奠定基础.     

Wavefield simulation in porous media saturated with two immiscible fluids

Wavefields in porous media saturated by two immiscible fluids are simulated in this paper. Based on the sealed system theory, the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation (capillary pressure). So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory. The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported. In our work, wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived. Furthermore, the wavefield and its characteristics are studied using the numerical finite element method. The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band. The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase. More specifically, the displacement decreases with increasing relaxation coefficient.     

两种不同势函数下半空间饱和多孔介质中Rayleigh波求解比较

分别对"考虑两种压缩波和幅值比例系数"和"考虑一种压缩波(P1或P2波)但不考虑幅值比例系数"两种不同势函数下的半空间饱和多孔介质中Rayleigh波求解进行详细推导,理论分析表明"考虑两种压缩波和幅值比例系数"下Rayleigh波求解推导更为严密,与饱和多孔介质中存在两种压缩波的事实相一致。在研究半空间饱和多孔介质中Rayleigh波时应采用"考虑两种压缩波和幅值比例系数"的势函数。     

A novel experimental procedure to investigate the biodegradation of NAPL under unsaturated conditions

Soils need to be thoroughly investigated regarding their potential for the natural attenuation of non-aqueous phase liquids (NAPL). Laboratory investigations truly representative of degradation processes in field conditions are difficult to implement for porous media partially saturated with water, NAPL and air. We propose an innovative protocol to investigate degradation processes under steady-state vadose zone conditions. Experiments are carried out in glass columns filled with a sand and, as bacteria source, a soil from a diesel-fuel-polluted site. Water and NAPL (n-hexadecane diluted in heptamethylnonane (HMN)) are added to the porous medium in a two-step procedure using ceramic membranes placed at the bottom of the column. This procedure results, for appropriate experimental conditions, in a uniform distribution of the two fluids (water and NAPL) throughout the column. In a biodegradation experiment non-biodegradable HMN is used to provide NAPL mass, while keeping biodegradable n-hexadecane small enough to monitor its rapid degradation. Biodegradation is followed as a function of time by measuring oxygen consumption, using a respirometer. Degradative activity is controlled by diffusive transfers in the porous network, of oxygen from the gas phase to the water phase and of n-hexadecane from the NAPL phase to the water phase.     

孔隙介质中波的衰减及其对冲击波的防护作用

孔隙介质对波的衰减极为显著,因此,它能有效降低介质中冲击波的能量。普遍来说,地球浅层介质均可视为孔隙介质,即可作为应对冲击波的天然防护材料,这对大型地下结构的安全防护有着重要的意义。本文通过对大振幅应力脉冲通过水或冰充填的人工节理孔隙介质的测量结果分析,讨论了节理中固相/液相水对爆炸效果的作用。基于双孔隙模型和部分饱和模型计算预测的P波速度以及岩石衰减和频散规律,与实测数据相一致。实验与模型预测均表明,节理中的水和冰对冲击波有较大的衰减,但是充水节理更为明显,且由于填充材料的不同会导致不同的介质性质。因此,在地球介质孔隙节理中充填不同衰减特性材料,可以满足不同情况下的冲击波防护需要。      

Effects of petrophysical parameters on attenuation and dispersion of seismic waves in the simplified poroelastic theory: Comparison between the Biot's theory and viscosity‐extended theory

The simplified macro‐equations of porous elastic media are presented based on Hickey's theory upon ignoring effects of thermomechanical coupling and fluctuations of porosity and density induced by passing waves. The macro‐equations with definite physical parameters predict two types of compressional waves (P wave) and two types of shear waves (S wave). The first types of P and S waves, similar to the fast P wave and S wave in Biot's theory, propagate with fast velocity and have relatively weak dispersion and attenuation, while the second types of waves behave as diffusive modes due to their distinct dispersion and strong attenuation. The second S wave resulting from the bulk and shear viscous loss within pore fluid is slower than the second P wave but with strong attenuation at lower frequencies. Based on the simplified porous elastic equations, the effects of petrophysical parameters (permeability, porosity, coupling density and fluid viscosity) on the velocity dispersion and attenuation of P and S waves are studied in brine‐saturated sandstone compared with the results of Biot's theory. The results show that the dispersion and attenuation of P waves in simplified theory are stronger than those of Biot's theory and appear at slightly lower frequencies because of the existence of bulk and shear viscous loss within pore fluid. The properties of the first S wave are almost consistent with the S wave in Biot's theory, while the second S wave not included in Biot's theory even dies off around its source due to its extremely strong attenuation. The permeability and porosity have an obvious impact on the velocity dispersion and attenuation of both P and S waves. Higher permeabilities make the peaks of attenuation shift towards lower frequencies. Higher porosities correspond to higher dispersion and attenuation. Moreover, the inertial coupling between fluid and solid induces weak velocity dispersion and attenuation of both P and S waves at higher frequencies, whereas the fluid viscosity dominates the dispersion and attenuation in a macroscopic porous medium. Besides, the heavy oil sand is used to investigate the influence of high viscous fluid on the dispersion and attenuation of both P and S waves. The dispersion and attenuation in heavy oil sand are stronger than those in brine‐saturated sandstone due to the considerable shear viscosity of heavy oil. Seismic properties are strongly influenced by the fluid viscosity; thus, viscosity should be included in fluid properties to explain solid–fluid combination behaviour properly.     

含流体孔隙介质中面波的传播特性及应用

基于单相介质中地震波理论的高频面波法已广泛应用于求取浅地表S波的速度.然而水文地质条件表明,普遍的浅地表地球介质富含孔隙.孔隙中充填的流体会显著地影响面波在浅地表的传播,进而造成频散和衰减的变化.本文研究了地震勘探频段内针对含流体孔隙介质边界条件的面波的传播特性.孔隙流体在自由表面存在完全疏通、完全闭合以及部分疏通的情况.孔隙单一流体饱和时,任何流体边界条件下存在R1模式波,与弹性介质中的Rayleigh波类似,相速度稍小于S波并在地震记录中显示强振幅.由于介质的内在衰减,R1在均匀半空间中也存在频散,相速度和衰减在不同流体边界下存在差异.Biot固流耦合系数(孔隙流体黏滞度与骨架渗透率之比)控制频散的特征频率,高耦合系数会在地震勘探频带内明显消除这种差异.介质的迂曲度等其他物性参数对不同流体边界下的R1波的影响也有不同的敏感度.完全闭合和部分疏通流体边界下存在R2模式波,相速度略低于慢P波.在多数条件下,如慢P波在时频响应中难以观察到.但是在耦合系数较低时会显现,一定条件下甚至会以非物理波形式接收R1波的辐射,显示强振幅.浅表风化层低速带存在,震源激发时的运动会显著影响面波的传播.对于接收点径向运动会造成面波的Doppler频移,横向运动会造成面波的时频畸变.孔隙存在多相流体时,中观尺度下不均匀斑块饱和能很好地解释体波在地震频带内的衰减.快P波受到斑块饱和显著影响,R1波与快P波有更明显关联,与完全饱和模型中不同,也更易于等效模型建立.频散特征频率受孔隙空间不同流体成分比例变化的控制,为面波方法探测浅地表流体分布与迁移提供可能性.通常情况孔隙介质频散特征频率较高,标准线性黏弹性固体可以在相对低频的地震勘探频带内等效表征孔隙介质中R1波的传播特征,特别在时域,可在面波成像反演建模中应用.     

含两项不混合/单项黏性流体孔隙介质分界面上反透射系数特征研究

弹性孔隙介质分界面上的反透射系数特征,在岩性划分、流体识别、储层边界判识等方面有重要的应用.本文研究上层为含两项不混合黏性流体孔隙介质、下层为含单项黏性流体孔隙介质分界面上的反透射理论.首先根据两种孔隙介质分界面上的能量守恒得到边界条件,再将波函数、位移、应力与应变关系代入边界条件,推导出完全连通孔隙情况下,第一类纵波入射到孔隙介质分界面上的反透射系数方程.通过建立砂岩孔隙介质模型,分别分析不同孔隙流体类型、不同含油饱和度及不同入射角情况下,各类波的反透射系数特征.研究表明,第二、三类纵波反透射系数数值比第一类纵波小多个数量级,且两者对入射角的变化不敏感,但对孔隙流体性质、含油饱和度的变化较敏感,而横波反透射系数特征恰好与此相反;第一类纵波反透射系数特征比较复杂,入射角、孔隙流体的性质及含油饱和度的变化都对其产生影响.不同孔隙流体弹性物性的差异、孔隙介质中含油饱和度的变化及不同入射角引起垂向和切向应力分量的变化都会影响各类波的反透射系数特征,分析这些特征可以为研究储层含油气性提供理论基础.     

Calculation method of prestack FAGVO and its applications

Frequency attenuation occurs when seismic waves propagate through the porous reservoirs containing hydrocarbons. Current researches on the seismic frequency attenuation mainly focus on the post-stack domain instead of the prestack domain. Here we propose the frequency attenuation gradient vs. offset (FAGVO) based on the amplitude variation with offset and frequency attenuation integral equations. We derive the FAGVO equation that equals to zero in a full-elastic medium and is negative in a viscoelastic medium. FAGVO is affected by the viscosity of the medium, the coefficients of reflection, the frequency variation, and high-frequency attenuation. FAGVO uses the differences of partially stacked data to decrease the interference caused by subsurface strata affecting the frequency attenuation, highlights the frequency attenuation gradient anomalies in hydrocarbon-bearing reservoir pores, and finally realizes the hydrocarbon fluid identification. The method was verified using a two-dimensional wave equation forward model and was found to be cost effective. Furthermore, the method does not require well information, which can be applied in the stage of seismic exploration, especially, in the exploration of a none-well project.     

Acoustic reverberation in a logging tool-borehole-saturated porous medium system

The influence of the elastic and hydrodynamic properties of a rock on the time attenuation coefficient of an acoustic wave, which is reflected from the borehole wall, is considered using the methods of the mechanics of saturated porous media. The calculations were performed for a system consisting of an acoustic logging tool of a finite with a finite diameter, a fluid-filled borehole, and a porous permeable rock. The performed simulation showed that in rocks with a low hydrodynamic permeability, the acoustic-reverberation time is determined by the acoustic impedance of the borehole wall (product of the rock density and the longitudinal-wave velocity in it). In the case of rocks with a permeability of about several hundred millidarcy, the time signal’s attenuation coefficient substantially depends on the rock’s permeability.     

Modulus defect,velocity dispersion and attenuation in partially-saturated reservoirs of Jurassic sandstone,Indus Basin,Pakistan

Partially saturated reservoirs are one of the major sources of seismic wave attenuation, modulus defect and velocity dispersion in real seismic data. The main attenuation and dispersion phenomenon is wave induced fluid flow due to the heterogeneity in pore fluids or porous rock. The identification of pore fluid type, saturation and distribution pattern within the pore space is of great significance as several seismic and petrophysical properties of porous rocks are largely affected by fluid type, saturation and fluid distribution pattern. Based on Gassmann-Wood and Gassmann- Hill rock physics models modulus defect, velocity dispersion and attenuation in Jurassic siliclastic partially-saturated rocks are studied. For this purpose two saturation patterns - uniform and patchy - are considered within the pore spaces in two frequency regimes i.e., lower frequency and higher frequency. The results reveal that at low enough frequency where saturation of liquid and gas is uniform, the seismic velocity and bulk modulus are lower than at higher frequency where saturation of fluid mixture is in the form of patches. The velocity dispersion and attenuation is also modeled at different levels of gas saturation. It is found that the maximum attenuation and velocity dispersion is at low gas saturation. Therefore, the dispersion and attenuation can provide a potential way to predict gas saturation and can be used as a property to differentiate low from high gas saturation.     

Seismic dispersion and attenuation in layered porous rocks with fractures of varying orientations

Wave‐induced fluid flow plays an important role in affecting the seismic dispersion and attenuation of fractured porous rocks. While numerous theoretical models have been proposed for the seismic dispersion and attenuation in fractured porous rocks, most of them neglect the wave‐induced fluid flow resulting from the background anisotropy (e.g. the interlayer fluid flow between different layers) that can be normal in real reservoirs. Here, according to the theories of poroelasticity, we present an approach to study the frequency‐dependent seismic properties of more realistic and complicated rocks, i.e. horizontally and periodically layered porous rock with horizontal and randomly orienting fractures, respectively, distributed in one of the two periodical layers. The approach accounts for the dual effects of the wave‐induced fluid flow between the fractures and the background pores and between different layers (the interlayer fluid flow). Because C₃₃ (i.e., the modulus of the normally incident P‐wave) is directly related to the P‐wave velocity widely measured in the seismic exploration, and its comprehensive dispersion and attenuation are found to be most significant, we study mainly the effects of fracture properties and the stiffness contrast between the different layers on the seismic dispersion and attenuation of C₃₃. The results show that the increasing stiffness contrast enhances the interlayer fluid flow of the layered porous rocks with both horizontal and randomly orienting fractures and weakens the wave‐induced fluid flow between the fractures and the background pores, especially for the layered porous rock with horizontal fractures. The modelling results also demonstrate that for the considered rock construction, the increasing fracture density reduces the interlayer fluid flow while improves the dispersion and attenuation in the fracture‐relevant frequency band. Increasing fracture aspect ratio is found to reduce the dispersion and attenuation in the fracture‐relevant frequency band only, especially for the layered porous rock with horizontal fractures.     

Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence

Wave reflection and refraction in layered media is a topic closely related to seismology, acoustics, geophysics and earthquake engineering. Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials. The system is composed of ideal fluid, porous medium, and underlying elastic solid. By numerical examples, the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed. The results show that the existence of the porous medium, especially in the partially saturated case, may significantly affect the dynamic pressures of the overlying fluid.