基于Biot-喷射流统一模型Maxwell流体饱和孔隙介质中的弹性波

推广Biot-Tsiklauri声学模型的同时借鉴Dvorkin和Nur的工作,建立了具有任意孔径分布并顾及喷射流动机制的非牛顿流体饱和孔隙介质声学模型,研究了非牛顿流体(Maxwell流体)饱和孔隙介质中的弹性波的衰减和频散特性.着重讨论充孔隙Maxwell流体的非牛顿流效应对弹性波的频散和衰减的影响.研究表明,饱和流体的非牛顿流效应和喷射流动机制均是引起弹性波波频散和衰减的重要因素.依据非牛顿流体(Maxwell流体)饱和各向同性孔隙介质的Biot-喷射流声学模型,喷射流动只影响纵波的频散和衰减,而饱和流体的非牛顿流效应不仅影响纵波,而且还影响横波的频散和衰减.     

孔隙介质中快纵波的衰减特性和动力协调现象

依据Biot理论并采用前人的骨架模量孔隙度关系,计算了弹性波在孔隙介质中的衰减曲线,发现快纵波存在零衰减点.为解释这种现象,分析了孔隙流体相对于骨架运动的特点.结果表明,存在快纵波动力协调介质,快纵波在这种介质中传播时,流体和骨架之间无宏观相对位移,因此无论频率多高,流体粘滞系数多大,快纵波都不衰减.一个引申的结论是,在动力协调的渗透性孔隙介质中,即使存在双电层,快纵波也不产生流动电势.     

流体/准饱和多孔介质中伪Scholte波的传播特性

研究流体/多孔介质界面Scholte波的传播特性对于水下勘探、地震工程等领域具有重要意义.本文基于Biot理论和等效流体模型,采用势函数方法,推导了描述有限厚度流体/准饱和多孔半空间远场界面波的特征方程和位移、孔压计算公式.在此基础上,分别以砂岩和松散沉积土为例,研究了流体/硬多孔介质和流体/软多孔介质两种情况下,可压缩流体层厚度和多孔介质饱和度对伪Scholte波传播特性的影响.结果表明：多孔介质软硬程度显著影响界面波的种类、相速度、位移和水压力分布;有限厚度流体/饱和多孔半空间界面处伪Scholte波相速度与界面波波长和流体厚度的比值有关;孔隙水中溶解的少量气体对剪切波的相速度的影响不大,对压缩波相速度、伪Scholte波相速度和孔隙水压力分布影响显著.     

多尺度波致流非饱和孔隙介质波传播理论研究

弹性波在非饱和孔隙介质中传播时,孔隙流体会发生宏观Biot流、微观喷射流以及由于孔隙流体不同(气、液双相)导致的介(中)观流.将非饱和孔隙介质等效为含液相孔隙流体的背景介质中嵌入含气相孔隙流体的包裹体,在非饱和双重孔隙介质模型基础上,引入微观喷射流,建立了包含宏观、微观和介观三种尺度波至流的非饱和孔隙介质波传播方程.数值分析表明该模型可以更好地预测更宽频带内的波速频散和衰减.     

含少量气泡流体饱和孔隙介质中的弹性波

考虑孔隙流体中含有少量气泡,且气泡在声波作用下线性振动,研究声波在这种孔隙介质中的传播特性.本文先由流体质量守恒方程和孔隙度微分与流体压力微分的关系推导出了含有气泡形式的渗流连续性方程;在处理渗流连续性方程中的气体体积分数时间导数时,应用Commander气泡线性振动理论导出气体体积分数时间导数与流体压强时间导数的关系,进而得到了修正的Biot形式的渗流连续性方程;最后结合Biot动力学方程求得了含气泡形式的位移场方程,便可得到两类纵波及一类横波的声学特性.通过对快、慢纵波的频散、衰减及两类波引起的流体位移与固体位移关系的考察,发现少量气泡的存在对快纵波和慢纵波的传播特性影响较大.     

介观非均匀双相介质中局域流对弹性波传播的影响

针对弹性波衰减与速度频散问题，基于Pride和Berryman的介观非均匀双重孔隙介质理论模型，推导一组用位移表示，另一组用位移及孔压表示的全新形式的耦合动力学方程组，并基于双孔介质模型，推导出弹性波的相速度与逆品质因子的解析式，重点讨论介观尺度下的局域流动对弹性波传播特性的影响.数值算例表明：快波的速度随着频率的增加而迅速增加，且介观流动损失比Biot损失至少高一个数量级；同时局域流对慢波也有着不同程度的影响.证实了局域流是波能损失和相速度频散的主要因素.     

非均匀饱含黏性流体孔隙介质中声波传播及井孔声场分析

声波在饱含流体孔隙介质中的传播特性与流体的黏滞性及孔隙介质的非均匀性密切相关.本文在Biot理论基础上,考虑了孔隙流体的剪切应力及孔隙结构的非均匀性,采用含黏性流体孔隙介质中的波动理论,研究了孔隙介质中四种体波的频散和衰减特性,分析了慢横波对快纵波转换散射的影响,进一步推导了孔隙地层井孔中的模式波及其声场的解析解,研究了非均匀孔隙介质中井孔模式波和波列的特征.研究结果表明,含黏性流体孔隙介质中存在慢横波,慢横波的频散很强,其传播特征受到介质孔隙度、渗透率及孔隙流体黏度的影响.在非均匀孔隙介质中,与慢横波相关的剪切应力平衡过程不仅导致快纵波的频散和衰减,还会影响井孔伪瑞利波及斯通利波的传播特征.本文的工作完善了孔隙介质中声波传播的物理机制,为孔隙地层井孔声波的解释与应用提供了理论指导.     

流体饱和孔隙材料的Biot弹性常数的声学测量

本文研究用声学方法测量流体饱和孔隙介质的Biot4个弹性常数，4个弹性常数主要是通过测量水饱和的孔隙样品中的3种体波速度去计算的（流体压缩系数已知）。为了讨论和验证测量结果，我们还进行了两个实验，一是测量空气饱和样品的切变波速度和纵波速度，并求得框架的体积模量和切变模量；二是测量空气饱和样品中的慢纵波速度，并验证样品曲折度的大小。     

气泡线性振动对含气泡水饱和多孔介质声传播的影响

为了研究孔隙水含少量气泡时多孔介质中波的传播,本文在Biot模型的基础上,将孔隙水中气泡的体积振动融合到多孔介质的孔隙流体渗流连续性方程中,从而得到了考虑气泡体积振动的孔隙流体渗流连续性方程.在此基础上,根据气泡线性振动下气泡瞬时半径和介质背景压力的关系,以及多孔介质运动方程和流体介质运动方程,导出了受气泡影响下多孔介质位移矢量波动方程,建立了非水饱和多孔介质声速频散和衰减预报模型.气泡的存在增大了孔隙水的压缩率,导致含气泡水饱和多孔介质声速的降低.当声波频率等于气泡的共振频率时,在声波激励下,介质呈现高频散,且孔隙水中的气泡产生共振,吸收截面达到最大,使得多孔介质的声衰减也达到最大.文中数值分析验证了上述结论,表明了气泡含量、大小和驱动声场频率是影响声波在含少量气泡的水饱和多孔介质中传播的主要因素.     

基于相场方法的孔隙尺度油水两相流体流动模拟

基于真实岩心颗粒粒径分布，利用过程法构建疏松砂岩油藏的三维孔隙结构模型，利用相场方法建立两相流体流动数学模型并利用有限元方法进行求解，研究驱替速度、流体性质、润湿性对剩余油分布以及采出程度的影响.结果表明：驱替速度的增大和油水粘度比的减小会导致较大的毛管数，进而有利于采出程度的提高；就润湿性而言，水湿条件下毛管力是水驱油的动力，而在油湿条件下是阻力，因此水湿岩心采出程度更高.同时，从孔隙尺度对油水渗流机理及剩余油分布机理进行揭示，结果表明：由于多孔介质的复杂孔隙结构，流体在流经不同孔隙时呈现不同的流动特征，进而对油水两相流整体的压力分布、流速分布造成重要影响.     

A Modified Biot/Squirt Model of Sound Propagation in Water-Saturated Sedment

A modified Biot/Squirt flow model was developed. The difference between MBISQ and BISQ models is the expression for the porosity differential. Numerical analysis shows that the acoustic dispersion predicted by MBISQ is much higher than by BISQ. Investigations of the effects of permeability, viscosity, and squirt flow length on velocity and attenuation indicate that the behavior of MBISQ agrees with that of the BISQ model. The result of sediment acoustic inversion based on MBISQ was more reasonable than the result of BISQ model.     

Viscoelastic BISQ Model for Low-Permeability Sandstone with Clay

A modified BISQ （Blot/Squirt） model for wave propagation in low-permeability sandstone is developed by introducing the viscoelastic mechanism of a porous skeleton into Dvorkin＇s model. The linear viscoelasticity of the Kelvin Voigt constitutive law is employed to describe the stress-strain relation of a solid frame with clay while the ultrasonic waves propagate through the fluid-saturated sandstone. The phase velocity and attenuation of two p-waves are given based on the present BISQ model. The comparisons between numerical results and experimental data indicate that our viscoelastic model is more realistic and feasible for wave propagation in the low-permeability sandstone, especially with clay, than traditional BISQ models.     

Wave-induced fluid flow in random porous media: attenuation and dispersion of elastic waves

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.     

Elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media

This paper studies the elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media with the nonzero boundary slip velocity for pore size distribution. The coefficient bF_m(ω) that measures the deviation from Poiseuille flow friction in such media is presented. Based on this coefficient, we investigate the properties of elastic waves by calculating their phase velocities and attenuation coefficients as functions of frequency and the behaviour of the dynamic permeability. The study shows that the pore size distribution removes oscillations in all physical quantities in the non-Newtonian regime. Consideration of the nonzero boundary slip effect in non-Newtonian (Maxwell) fluid-saturated porous media results in (a) an overall increase of the dynamic permeability, (b) an increase of phase velocities of fast Biot waves and shear waves except in the low frequency domain and an overall increase of phase velocity of slow Biot waves and (c) an overall increase of the attenuation of three Biot waves in the intermediate frequency domain except in the deeply non-Newtonian regime. The study also shows that the attenuation coefficient of slow Biot waves is small in the deeply non-Newtonian regime at higher frequency, which encourages us to detect slow Biot waves in oil-saturated porous rock.     

Elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media

Abstract

This paper studies the elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media with the nonzero boundary slip velocity for pore size distribution. The coefficient bF _m (ω) that measures the deviation from Poiseuille flow friction in such media is presented. Based on this coefficient, we investigate the properties of elastic waves by calculating their phase velocities and attenuation coefficients as functions of frequency and the behaviour of the dynamic permeability. The study shows that the pore size distribution removes oscillations in all physical quantities in the non-Newtonian regime. Consideration of the nonzero boundary slip effect in non-Newtonian (Maxwell) fluid-saturated porous media results in (a) an overall increase of the dynamic permeability, (b) an increase of phase velocities of fast Biot waves and shear waves except in the low frequency domain and an overall increase of phase velocity of slow Biot waves and (c) an overall increase of the attenuation of three Biot waves in the intermediate frequency domain except in the deeply non-Newtonian regime. The study also shows that the attenuation coefficient of slow Biot waves is small in the deeply non-Newtonian regime at higher frequency, which encourages us to detect slow Biot waves in oil-saturated porous rock.     

Bifurcation of the Biot slow wave in a porous medium

The propagation of the Biot slow wave in a fluid-saturated porous medium at low frequencies is investigated by asymptotic methods. It is proven that the Biot wave has a bifurcation behavior depending on its wave number. The bifurcation occurs in a neighborhood of the critical value k(cr), which depends on the permeability of a medium and the viscosity of a fluid. The P2 wave is fully attenuated if its wave number is smaller than k(cr) and it becomes propagatory with wave numbers bigger than k(cr). Asymptotic formulas for the phase velocity and attenuation of the Biot wave are derived.