基于Biot-Squirt方程的波场模拟

Biot流动和喷射流动是含流体多孔隙介质中流体流动的两种重要力学机制,对地震波和声波的传播均产生重要影响. Dvorkin和Nur提出了同时包含Biot流动和喷射流动力学机制的统一的BISQ(Biot-Squirt)模型,基于这一模型,尽管有关弹性波在多孔隙介质中的衰减和频散问题已被广泛研究,然而,基于BISQ波传播方程的波场数值模拟至今仍未见报道. 本文从同时包含两种力学机制的孔隙弹性波方程出发,利用FCT有限差分法对含流体孔隙各向同性介质中的地震波和声波进行了数值模拟,并与基于Biot流动的Biot理论之模拟结果进行比较. 数值模拟结果表明:同时包含Biot流动和喷射流动影响的地震波和声波速度比仅包含Biot流动作用的地震波和声波速度慢,慢P波的衰减比根据Biot理论模拟的慢P波衰减更强.     

Biot流动和喷射流动耦合作用下波传播的FCT紧致差分模拟

本文从含流体多孔隙介质中同时包含Biot流动和喷射流动两种力学机制的BISQ(Biot-Squirt)方程出发,利用FCT(Flux-Corrected Transport)紧致差分方法数值模拟了在Biot流和喷射流共同作用下的波在含流体多孔隙各向同性介质中的传播.通过与仅受Biot流动作用下的波场结果对比,我们研究了...     

基于BISQ模型双相各向同性介质弹性波传播的频率-空间域有限差分模拟

BISQ模型同时包含了合流体孔隙介质中Biot流动和喷射流动两种重要的力学机制.基于BISQ模型的双相各向同性介质弹性波波动方程是一个复变系数偏微分方程组.本文率先建立了该方程的25点频率-空间域有限差分数值解法,在理想相界和黏滞相界情况下,对Biot流动和喷射流动共同作用下的双相各向同性介质中的波传播进行了数值模拟,通过与仅受Biot流动作用下的波场模拟结果的对比,分析了两种机制耦合作用对弹性波传播的影响.同时,本文也研究了波在双层双相各向同性介质分界面处的反射和透射特征.数值模拟结果表明:在Biot流动和喷射流动耦合作用下,双相介质中传播的快P波的速度和振幅都小于仅考虑Biot流动的双相介质中的快P波,且慢P波的衰减也更为强烈,而S波的波速和振幅则无明显差异.这表明局部喷射流动对P波的衰减和频散具有重要影响,而对S波的影响较小;慢P波的强烈衰减使得其在波场快照中无法被观测到,双层双相介质中的波传播现象类似于单相介质的情况.同时本文的研究结果也表明,频率-空间域有限差分法在基于BISQ模型的双相介质中波传播数值模拟中的正确性和有效性,为开展孔隙弹性介质全波形反演问题的研究提供了研究基础.     

双相各向异性介质中弹性波传播有限元方程及数值模拟

基于Biot双相各向异性介质理论和动态问题的哈密顿原理，推导出任意双相各向异性介质中弹性波传播的有限元方程，并给出双相各向异性介质中弹性波有限元方程的数值解法．最后进行有限元法的数值模拟，对双相各向异性介质中弹性波传播特征进行了模拟与分析．       

双相介质中地震波的频率-空间域数值模拟

本文利用优化的25点频率-空间域有限差分算法对基于BISQ模型双相各向同性介质中的地震波进行了数值模拟.通过与经典的Biot模型理论模拟结果进行对比,分析了Biot流动（宏观流体流动）和Squirt流动（微观流体流动）耦合作用对地震波在孔隙介质中传播特性的影响.数值模拟在地震频段进行,结果显示：在理想相界和黏滞相界情况下,Squirt流动机制都比Biot流动机制产生了更大的速度频散和能量衰减.其中,在Biot流动和Squirt流动耦合作用下的快P波的速度和振幅小于仅考虑Biot流动影响下快P波速度和振幅,而且慢P波的衰减也更加强烈.本文还研究了地震波在双层双相各向同性介质分界面处的反射和透射特征,双相介质中波的反射与透射现象类似于单相介质的情况.模拟结果表明,利用优化25点频率-空间域有限差分法模拟双相孔隙介质中的地震波场是可行的,这为开展双相孔隙介质全波形反演问题的研究提供了可能.     

饱和Maxwell流体孔隙介质波传播模型研究

岩石中的弹性波传播特性研究一直是地球物理学研究中的基础科学问题和难点.Biot理论的提出为流固双相介质理论奠定了基础.Biot理论中假设固相、液相的本构关系是线弹性的.而当实际储层中含高黏度的流体时,流体往往表现出一定的非牛顿流体性质.本文主要针对含高黏度流体的孔隙介质,在Biot理论模型中引入线性黏弹性的Maxwell流体本构方程.要通过动态黏度入手,表征非牛顿流体的特性,改进并给出了含高黏度孔隙流体介质的模型.通过数值模拟分析了所提出的模型的特性,并分析了初始黏度和孔隙度参数对模型数值分析结果的影响.最后选取超声波实验数据验证了模型的适用性,结果表明该理论模型的预测结果可较好地反映含高黏度流体孔隙介质的波传播特性.     

含孔隙、裂隙介质弹性波动的统一理论——Biot理论的推广

地球表层的岩石介质往往是即含孔隙又含裂隙,这种现象对弹性波传播产生重要影响．本文在Biot孔隙介质的波动理论基础上,利用该理论中介质在排水（干燥）条件下的弹性模量引入裂隙对弹性性质的影响,并对裂隙在弹性波动作用下的“挤喷流”（squirt flow）效应进行了具体分析,导出了一个描述孔隙、裂隙并存时的弹性波统一理论．该理论既能描述裂隙对介质弹性的影响,又能模拟挤喷效应导致的弹性波衰减和频散,并且指出,这种挤喷效应是由裂隙介质的两个最重要的参数,裂隙密度和纵横比所控制．这一统一理论的另一重要特性是该理论保持了Biot理论的基本特征,即慢速纵波的传播特征及孔隙渗透率的影响．模拟计算结果及与实际数据的对比表明,这一孔隙、裂隙弹性波动的统一理论能较好地描述实际岩石介质中弹性波的传播,从而在地球介质中地震和声波测量中比Biot理论有着更为广泛的应用前景．     

基于BISQ模型的双相介质位移场Green函数

以BISQ模型的波传播方程为基础,研究了弹性波在孔隙各向 同性介质中的传播速度及与流体的Biot流动和喷射流动力学机制的关系,进一步利用场势分 解和δ函数的性质,给出了同时受Biot流动和喷射流动两种动力学机制作用下,两相介 质波场位移在集中力作用下的Green函数,并讨论了喷射流动在Green函数中的表现形式和作用     

气枪激发信号传播的谱元法数值模拟研究

为了研究气枪激发信号的波场,本文利用谱元法对双相介质中波的传播做了数值模拟,分析了波的传播特征.本文主要做了以下工作:(1)研究了使用谱无法(SEM)模拟孔隙弹性介质中波的传播,模拟结果表明,采用谱元法能有效解决双相介质的波场传播模拟问题.(2)验证了Biot理论中慢纵波的存在.双相介质中存在明显的慢纵波,流相波场的慢...     

求解双相和黏弹性介质波传播方程的间断有限元方法及其波场模拟

间断有限元（Discontinuous Galerkin：DG）方法具有低数值频散、网格剖分灵活、能模拟地震波在复杂介质中传播等优点.因此,本文将一种新的DG方法推广到双相和黏弹性等复杂介质的地震波场模拟,发展了求解Biot弹性波方程和D'Alembert介质波动方程的DG方法.首先通过引入辅助变量将Biot双相介质弹性波方程和D'Alembert介质波动方程转化为关于时间-空间的一阶偏微分方程组,然后对该方程组进行DG空间离散,得到半离散化的常微分方程组.最后,对此常微分方程组,应用加权的Runge-Kutta格式进行时间推进计算.数值结果表明,DG方法可以有效地求解Biot双相介质弹性波方程和D'Alembert介质波动方程,并能很好地压制因离散求解波动方程而产生的数值频散,获得清晰的各种地震波震相.     

Transport and fate of nonaqueous phase liquid (NAPL) in variably saturated porous media with evolving scales of heterogeneity

 A stochastic simulation is performed to study multiphase flow and contaminant transport in fractal porous media with evolving scales of heterogeneity. Numerical simulations of residual NAPL mass transfer and subsequent transport of dissolved and/or volatilized NAPL mass in variably saturated media are carried out in conjunction with Monte Carlo techniques. The impact of fractal dimension, plume scale and anisotropy (stratification) of fractal media on relative dispersivities is investigated and discussed. The results indicate the significance of evolving scale of porous media heterogeneity to the NAPL transport in the subsurface. In general, the fractal porous media enhance the dispersivities of NAPL mass plume transport in both the water phase and the gas phase while the influence on the water phase is more significant. The porous media with larger fractal dimension have larger relative dispersivities. The aqueous horizontal dispersivity exhibits a most significant increase against the plume scale.     

平面S波在饱和多孔热弹性介质边界的反射问题研究

针对饱和多孔介质中热弹性波的传播特性问题,基于多孔介质理论和广义的热弹性模型,研究平面S波在饱和多孔热弹性介质边界上的反射问题。以考虑流-固耦合的饱和多孔介质波动方程和热-弹耦合的广义热弹性基本方程出发,建立饱和多孔介质的热-流-固耦合弹性波动模型。通过引入势函数并考虑自由透水和绝热的边界条件,经过理论推导最终给出在饱和多孔热弹性介质边界上的四种反射波的振幅反射率的理论表达式。在此基础上进行数值计算,分别讨论平面S波的入射频率、入射角和热膨胀系数等参数对四种反射波的振幅反射率的影响情况。结果表明:各反射波的振幅反射率分别随频率和热膨胀系数的增大而增大,同时也受到平面S波入射角变化的影响。该结论对于土动力学的理论研究及其相关的工程勘探具有一定的指导意义。     

A fractal model for streaming potential coefficient in porous media

Streaming potential is the result of coupling between a fluid flow and an electric current in porous rocks. The modified Helmholtz–Smoluchowski equation derived for capillary tubes is mostly used to determine the streaming potential coefficient of porous media. However, to the best of our knowledge, the fractal geometry theory is not yet applied to analyse the streaming potential in porous media. In this article, a fractal model for the streaming potential coefficient in porous media is developed based on the fractal theory of porous media and on the streaming potential in a capillary. The proposed model is expressed in terms of the zeta potential at the solid?liquid interface, the minimum and maximum pore/capillary radii, the fractal dimension, and the porosity of porous media. The model is also examined by using another capillary size distribution available in published articles. The results obtained from the model using two different capillary size distributions are in good agreement with each other. The model predictions are then compared with experimental data in the literature and those based on the modified Helmholtz–Smoluchowski equation. It is shown that the predictions from the proposed fractal model are in good agreement with experimental data. In addition, the proposed model is able to reproduce the same result as the Helmholtz–Smoluchowski equation, particularly for high fluid conductivity or large grain diameters. Other factors influencing the streaming potential coefficient in porous media are also analysed.     

A physical–chemical model for the static water retention characteristic of unsaturated porous media

Water retention characteristic or water retention curve (WRC) is an important constitutive feature of porous media, and also meanwhile is an indispensable requirement in hydraulic transport modelling. Previous experiments have indicated that the specific surface area of porous media has effects on the WRC. It has also been observed that a linear relationship generally exists between the air–water interface area and the water saturation within unsaturated porous media. However it seems that no detailed study on their internal linkage with the WRC has been reported yet. This paper, at first gives a review of the development of WRC modelling, then it tries to explain the water retention characteristic according to the physical and chemical behaviours of the phases involved in unsaturated porous media. Using the traditional capillary theory, the volume averaging theorem and the advances in physical chemistry of interfacial surfaces, this paper then derives out a formula which represents the water retention characteristic of porous media. This formula demonstrates the internal linkage of the WRC to the specific surface area of porosities. It also shows agreements with the experimental observations mathematically. Based on this formula, a fitting model is proposed for the static WRC of porous media. Finally, this model is tested to fit the WRC measurements of a wide range of porous materials. Comparison with other main models is presented.     

基于时空守恒元和解元(CE/SE)方法的孔隙介质多相流动计算

将时空守恒元/解元(CE/SE)方法推广到二维孔隙介质多相流问题的数值计算中,采用人工压缩法耦合速度和压力,同时结合杂交粒子水平集方法捕捉物质界面.提出一套完整的二维欧拉型孔隙介质非稳态多相不可压缩黏性流动计算方案.通过对溃坝和液滴在重力作用下的运动和变形问题的数值模拟,验证了方法的精度和有效性.在此基础上,提出了一个新的孔隙介质两相流物理模型——双层流体顶盖驱动方腔流.     

基于临界孔隙度模型的地震波传播

基于岩石物里学中临界孔隙度模型,建立一种简洁的均匀弹性流体饱和孔隙介质模型,进行地震波传播研究.首先定义了构建目标模型的基本力学模型:介绍了全孔隙度区间内基本力学模型和目标孔隙介质的含义,其中基本力学模型除了完全弹性固体模型S和完全弹性流体模型F还包括临界孔隙模型C.然后通过等效力学模型推出了目标力学模型介质本构关系的组分表达形式.文中分别通过直接求取弹性参数的表达形式和运用应力应变关系两种方法得到介质模型的本构关系,进而得到该模型波动方程的组分表达形式.最后对这种介质模型进行了地震波传播的数值模拟,结合模拟结果分析孔隙对地震波传播的影响.     

Reconstruction of porous media using multiple-point statistics with data conditioning

The reconstruction of porous media is of great importance in predicting fluid transport properties, which are widely used in various fields such as catalysis, oil recovery, medicine and aging of building materials. The real three-dimensional structural data of porous media are helpful to describe the irregular topologic structures of porous media. By using multiple-point statistics (MPS) to extract the characteristics of real porous media acquired from micro computed tomography (micro-CT) scanning, the probabilities of structural characteristics of pore spaces are obtained first, and then reproduced in the reconstructed regions. One solution to overcome the anisotropy of training images is to use real 3D volume data as a training image (TI). The CPU cost and memory burden brought up by 3D simulations can be reduced greatly by selecting the optimal multiple-grid template size that is determined by the entropy of a TI. Moreover, both soft data and hard data are integrated in MPS simulation to improve the accuracy of reconstructed images. The variograms and permeabilities, computed by lattice Boltzmann method, of the reconstructed images and the target image obtained from real volume data are compared, showing that the structural characteristics of reconstructed porous media using our method are similar to those of real volume data.     

淤积泥砂对水平地运动作用时刚性坝面动压力的影响

文章基于固体介质，流体介质，液固两相饱和介质的时域显示有限元波动分析方法，研究了可压缩库水条件下淤积泥砂对水平地运动作用时刚性坝面上动压力的影响，研究中分析了作为两相介质处理的淤积泥砂的饱和度、厚度、渗透系数和孔隙率对坝面动压力的影响，还比较了作为流程两相介质，单相固体介质、单相重流体介质处理的不同淤积泥砂层模型间的计算结果差异。     

三维层状孔隙介质中弹性波的一种积分表达式I：理论

孔隙介质弹性波传播理论在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用.而孔隙介质中的弹性波受孔隙度、渗透率、流体黏滞系数等参数的影响,因此研究波场的传播特征将有助于分析和提取这些信息.本文在Biot理论的基础上,针对三维层状孔隙介质模型,利用在合成理论地震图的研究中已经被证实具有稳定、高效且适用范围较广的Luco-Apsel-Chen（LAC）广义反透射方法,给出了弹性波场的一种积分形式的半解析解,可通过数值方法高效、准确地计算层状孔隙介质中的理论波场,所以该积分形式的半解析解可为三维层状孔隙介质波场传播特征的理论数值模拟研究提供一种新的途径和手段.     

横向各向同性多孔介质中的地震波传播

基于各向异性多孔介质中的广义Ｂｉｏｔ理论，导出了横向各向同性多孔介质中波传播的特征方程．指出在多孔介质中有４种类型的频散和耗散波传播：准纵波ＱＰ１（快纵波）、准纵波ＱＰ２（慢纵波）、准横波ＱＳＶ和横渡ＳＨ．文中给出了４种波速度的解析表达式．数值计算频率曲线和衰减曲线与Ｓｃｈｍｉｔｔ（１９８９）用均值处理得到的结果类似．还给出了波传播过程中３种类型准体波之间的耦合系数（或称转换系数）．