Pseudo Rayleigh wave in a partially saturated non-dissipative porous solid

Propagation of surface waves is studied at the pervious boundary of a porous solid saturated with a mixture of two immiscible fluids. An approach, based on continuum mixture theory, is used to derive a secular equation for the propagation of harmonic waves at the stress-free plane surface of this non-dissipative medium. Numerical analysis shows that this secular equation may not represent the propagation of true surface wave in the porous aggregate. Then, this equation is solved numerically for the propagation of pseudo Rayleigh wave or the leaky surface waves. To ensure the existence of pseudo Rayleigh wave, capillary effect between two (wetting and non-wetting) pore-fluids is related to the partial saturation. Effects of porosity and partial saturation coupled with capillary effect are observed on the phase velocity of pseudo Rayleigh waves in sandstone saturated with water-CO₂ mixture.     

Dynamic response of partially sealed circular tunnel in viscoelastic saturated soil

Based on Biot's wave equation, dynamic response of a circular tunnel with partially sealed liner in viscoelastic saturated soil is investigated. By introducing two scalar potential functions, the analytical solutions of stresses, displacements and pore pressure induced by axisymmetric gradually applied step load are derived in Laplace transform domain. Numerical results are obtained by inverting Laplace transform presented by Durbin and used to analyze the influences of partial permeable property of boundary and viscoelastic damping coefficient of soil on dynamic response of the tunnel. It is shown that the attenuation of radial displacement appeared with the increase of viscoelastic damping coefficient of soil, and relative rigidity of liner and soil, and the influence of partial sealing property of boundary on stresses, displacements and pore pressure is remarkable. The available solutions of permeable and impermeable boundary conditions are only two extreme cases of this paper.     

Fully coupled finite element model for dynamics of partially saturated soils

Understanding the response of partially saturated earth structures under various static and dynamic loads is important for the design and construction of economical and safe geotechnical engineering structures. In this study, the numerical approach is used to understand the dynamics of partially saturated soils. The mathematical equations governing the dynamics of partially saturated soils are derived based on the theory of mixtures and implemented within a finite element framework. The stress–strain behavior of the soil is represented by an elasto-plastic constitutive model for unsaturated soil based on bounding surface concept and the moisture-suction behavior is modeled using van Genuchten model. Fully coupled finite element simulations are performed to study the response of partially saturated soil embankment under earthquake loading and validated with centrifuge test results available in the literature. The predicted displacement responses are in good agreement with the measured responses. The pore water pressure, pore air pressure, matric suction, the degree of saturation in various elements and the response of the embankment under different initial moisture content are also discussed.     

OpenGeoSys-Gem: A numerical tool for calculating geochemical and porosity changes in saturated and partially saturated media

Reactive transport codes that use a Gibbs Energy Minimization (GEM) to solve chemical equilibria are uncommon. We present a new coupling of the Richards flow module of the Finite Element (FE) based OpenGeoSys code with the GEM based chemical solver GEMS3K. The coupled code is highly parallelized using an overlapping domain decomposition approach in combination with execution of multiple threads that solve chemical equilibria in parallel. FE reactive transport schemes are often affected by spurious concentration oscillations. We effectively suppress these oscillations with a linearized algebraic flux corrected transport (FCT) algorithm. An application example is presented which investigates the evolution of material interfaces in a deep geological repository for nuclear waste. The example uses all features of the new coupled code: flow and multi-component transport in variably saturated media, and a very complex chemical setup which makes extensive use of (non-linear) solid solution formulations for mineral phases.     

Velocity and attenuation in partially saturated rocks: poroelastic numerical experiments

We use a poroelastic modelling algorithm to compute numerical experiments on wave propagation in a rock sample with partial saturation using realistic fluid distribution patterns from tomography scans. Frequencies are in the range 10 to 500 kHz. The rock is a homogeneous isotropic sandstone partially filled with gas and water, which are defined by their characteristic values of viscosity, compressibility and density. We assume no mixing and that the two different pore-fills occupy different macroscopic regions. The von Kármán self-similar correlation function is used, employing different fractal parameters to model uniform and patchy fluid distributions, respectively, where effective saturation is varied in steps from full gas to full water saturation. Without resorting to additional matrix–fluid interaction mechanisms, we are able to reproduce the main features of the variation in wave velocity and attenuation with effective saturation and frequency, as those of published laboratory experiments. Furthermore, the behaviour of the attenuation peaks versus water saturation and frequency is similar to that of White's model. The conversion of primary P-wave energy into dissipating slow waves at the heterogeneities is shown to be the main mechanism for attenuating the primary wavefield. Fluid/gas patches are shown to affect attenuation more than equivalent patches in the permeability or solid-grain properties.     

Velocity dispersion and fluid substitution in sandstone under partially saturated conditions

The elastic moduli of four sandstone samples are measured at seismic (2?2000 Hz) and ultrasonic (1 MHz) frequencies and water- and glycerin-saturated conditions. We observe that the high-permeability samples under partially water-saturated conditions and the low-permeability samples under partially glycerin-saturated conditions show little dispersion at low frequencies (2?2000 Hz). However, the high-permeability samples under partially glycerin-saturated conditions and the low-permeability samples under partially water-saturated conditions produce strong dispersion in the same frequency range (2?2000 Hz). This suggests that fluid mobility largely controls the pore-fluid movement and pore pressure in a porous medium. High fluid mobility facilitates pore-pressure equilibration either between pores or between heterogeneous regions, resulting in a low-frequency domain where the Gassmann equations are valid. In contrast, low fluid mobility produces pressure gradients even at seismic frequencies, and thus dispersion. The latter shows a systematic shift to lower frequencies with decreasing mobility. Sandstone samples showed variations in V_p as a function of fluid saturation. We explore the applicability of the Gassmann model on sandstone rocks. Two theoretical bounds for the P-velocity are known, the Gassmann–Wood and Gassmann–Hill limits. The observations confirm the effect of wave-induced flow on the transition from the Gassmann–Wood to the Gassmann–Hill limit. With decreasing fluid mobility, the P-velocity at 2–2000 Hz moves from the Gassmann–Wood boundary to the Gassmann–Hill boundary. In addition,, we investigate the mechanisms responsible for this transition.     

Modelling the DC electrical response of fully and partially saturated Permo-Triassic sandstone

Results from a laboratory investigation into the electrical properties of fully and partially saturated Wildmoor Triassic Sandstone have been modelled using the Archie, Waxman–Smits and Hanai–Bruggeman equations. The results demonstrate the limitation of using simple relationships to describe samples when the matrix resistivity ρ_r is not significantly greater than the saturating electrolyte resistivity ρ_w. In these situations Archie's parameters m and n are not accurately determined. Conversely, the more sophisticated Waxman–Smits and Hanai–Bruggeman models provide parameters that better describe the electrical properties of the rock and are able to identify heterogeneity between samples that would otherwise be missed. The ranges of values for matrix resistivity (49 < ρ_r < 161 Ωm) and cementation factor (1.6 < m < 2.1) obtained from the Hanai–Bruggeman model indicate significant variation between samples. Comparison of laboratory‐determined values for cation exchange capacity (0.06 < Q_v < 0.51 meq/mL) and those obtained from the Waxman–Smits model (0.09 < Q_v < 0.55 meq/mL) indicates a very strong correlation, suggesting this model is appropriate for describing the rock. There is good agreement between parameters modelled using fully and partially saturated versions of both the Hanai–Bruggeman and Waxman–Smits equations, indicating that the data are consistent with these models and that the assumptions made are appropriate.     

部分饱和孔隙岩石中声波传播数值研究

利用基于Biot理论的孔隙弹性介质的高阶交错网格有限差分算法,模拟了具有随机分布特征的多种流体饱和岩石中声波在中心频率分别为25,50,75,100kHz时的声场特点. 对于一个由两种成分（气和水）饱和的岩石模型, 假设含不同流体的孔隙介质随机分布在不同的宏观区域,该区域尺度远小于计算的声波波长;组成模型的两种随机分布介质具有相同的固体骨架参数、渗透率和孔隙度,但分别被具有不同压缩性、密度和黏滞系数特性的水和气饱和. 计算和统计分析结果表明,在两种孔隙成分随机分布的部分饱和条件下纵波速度比较复杂,除骨架参数外,其变化主要依赖于中心频率、各种孔隙成分饱和度及饱和介质的速度. 比较该随机分布模型、Gassmann理论模型和White的“气包”模型,发现三种模型得到的纵波速度和衰减规律有较好的定性对应关系. 其次,按照这种随机计算模型的处理方法,本文还首次计算了一个三种流体成分充填饱和的例子,即岩石模型中的孔隙被水、油和气部分饱和,计算时保持模型含水饱和度不变而只改变含油和含气饱和度. 在这种计算条件下,纵波速度随中心频率呈增大的趋势但有起伏变化. 声场快照显示了各种转换波在多种孔隙成分充填（两种和三种孔隙成分）岩石中的声场特征,复杂的水-油-气界面的非均匀分布对声场有重要影响,纵波能量主要转换形成了较为复杂的多种慢纵波和横波.     

Residual deformation characteristics of partially saturated sandy soils subjected to seismic excitation

Multiple series of triaxial tests were carried out on unsaturated sandy soils subjected to irregular seismic excitation. To observe the volume changes of unsaturated soil specimens during undrained loading and subsequent process of drainage, the inner cell was newly installed inside the large triaxial cell. The soil samples tested were recovered from the construction site of a liquefied natural gas storage facility located in Tokyo Bay area. In the tests, the initial conditions of soil specimens were specified with the degrees of saturation S_r of 50, 75 and 100%. The soil specimens were anisotropically consolidated, and subjected to undrained irregular seismic excitation. The time history of irregular seismic excitation was the one obtained from one of the recent earthquakes in Japan. The drainage line was then opened to let the excess pore water drain out of soil specimens. The volume changes and residual shear strains of unsaturated soil specimens thus obtained are presented in the present paper.     

不同压力下部分饱和砂岩纵波衰减的理论及实验研究

深入了解不同压力、频率、流体含量和流体分布对岩石中弹性波传播特性的影响,对指导油气勘探开发具有重要意义.不同尺度下的波致流效应,是声波传播过程中产生速度频散和衰减的重要原因.本文以不同压力下水饱和区域改进的骨架模量为纽带,建立了联合介观尺度斑块饱和效应与微观尺度喷射流效应的部分饱和岩石声学理论模型.开展针对性声学实验,根据不同压力下部分饱和砂岩纵波速度测量数据,确定理论模型中的相关参数,从而实现对不同压力下部分饱和岩石纵波衰减的定量表征.在此基础上,通过理论与实验测量的纵波衰减的对比,分析不同压力、含水饱和度以及频率对岩石纵波衰减的影响.研究结果表明,在较低压力,较高含水饱和度以及较高频段,喷射流效应较强,因此新建模型计算的衰减明显大于斑块饱和模型的衰减.由于新建模型体现了斑块饱和效应与喷射流效应的综合影响,相比于斑块饱和模型,新建模型计算的部分饱和岩石的纵波衰减更接近于实测衰减,但受到岩石自身因素影响,新建模型计算的衰减仍略小于实测衰减.

     

Seismic bearing capacity of strip footing on partially saturated soil using modal response analysis

The present study proposes a novel and simplified methodology to assess the seismic bearing capacity(SBC) of a shallow strip footing by incorporating strength non-linearity arising due to partial saturation of a soil matrix. Furthermore, developed methodology incorporates the modal response analysis of soil layers to assess SBC. A constant matric suction distribution profile has been considered throughout the depth of the soil. The Van Genuchten equation and corresponding fitting parameters have...     

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。     

部分饱和岩石的黏弹性Chapman-Kelvin模型的正演模拟方法研究

在讨论地震波传播理论时, 大部分情况下是把地震波看作弹性波.事实上, 地下介质是非完全弹性介质, 这使得传统的均匀、完全弹性介质理论受到了严重挑战.地震波在裂隙岩石中传播受裂隙系统和流体含量的影响较大, 以往许多关于频变各向异性的理论大多局限于单相流体假设, 但是几乎所有储层中通常被一种以上的流体部分饱和或完全饱和.本文在Chapman理论基础上, 提出了基于部分饱和的黏弹性Chapman-Kelvin模型的正演模拟新方法, 以提高对部分饱和岩石的黏弹性地震波频变各向异性的认识.该方法基于Chapman和Kelvin理论模型, 计算了双相不混溶流体饱和裂隙岩石中的黏弹性波频变各向异性弹性系数的表达式, 提出包含喷射流和斑块效应的统一地震波传播的黏弹性Chapman-Kelvin新模型.通过对新模型进行数值试验, 讨论了无裂缝和存在裂缝两种情况下, 含裂隙储层部分饱和岩石中耦合的喷射流和斑块效应对黏弹性介质频变各向异性的影响.试验结果反映出黏弹性介质下地震波频变各向异性的变化规律, 验证了本文提出的新方法和新模型正确.本文将黏弹性介质各向异性与裂缝中的流体流动参数相联系, 有利于提高对含裂缝储层部分饱和岩石的黏弹性波频变地震各向异性的认识, 以及地震学与油藏工程的结合程度.

     

Bulk moduli and seismic attenuation in partially saturated rocks: hysteresis of liquid bridges effect

A key task of exploration geophysics is to find relationships between seismic attributes (velocities and attenuation) and fluid properties (saturation and pore pressure). Experimental data suggest that at least three different factors affect these relationships, which are not well explained by classical Gassmann, Biot, squirt-flow, mesoscopic-flow and gas dissolution/exsolution models. Some of these additional factors include (i) effect of wettability and surface tension between immiscible fluids, (ii) saturation history effects (drainage versus imbibition) and (iii) effects of wave amplitude and effective stress. We apply a new rock physics model to explain the role of all these additional factors on seismic properties of a partially saturated rock. The model is based on a well-known effect in surface chemistry: hysteresis of liquid bridges. This effect is taking place in cracks, which are partially saturated with two immiscible fluids. Using our model, we investigated (i) physical factors affecting empirical Brie correlation for effective bulk modulus of fluid, (ii) the role of liquids on seismic attenuation in the low frequency (static) limit, (iii) water-weakening effects and (iv) saturation history effects. Our model is applicable in the low frequency limit (seismic frequencies) when capillary forces dominate over viscous forces during wave-induced two-phase fluid flow. The model is relevant for the seismic characterization of immiscible fluids with high contrast in compressibilities, that is, for shallow gas exploration and CO₂ monitoring.     

Comparative review of theoretical models for elastic wave attenuation and dispersion in partially saturated rocks

Saturation of porous rocks with a mixture of two fluids (known as partial saturation) has a substantial effect on the seismic waves propagating through these rocks. In particular, partial saturation causes significant attenuation and dispersion of the propagating waves, due to wave-induced fluid flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. As partial fluid saturation can occur on different length scales, attenuation due to wave-induced fluid flow is ubiquitous. In particular, mesoscopic fluid flow due to heterogeneities occurring on a scale greater than porescale, but less than wavelength scale, is responsible for significant attenuation in the frequency range from 10 to 1000 Hz.Most models of attenuation and dispersion due to mesoscopic heterogeneities imply that fluid heterogeneities are distributed in a periodic/regular way. In 1D this corresponds to periodically alternating layering, in 3D as periodically distributed inclusions of a given shape (usually spheres). All these models yield very similar estimates of attenuation and dispersion.Experimental studies show that mesoscopic heterogeneities have less idealized distributions and that the distribution itself affects attenuation and dispersion. Therefore, theoretical models are required which would simulate the effect of more general and realistic fluid distributions.We have developed two theoretical models which simulate the effect of random distributions of mesoscopic fluid heterogeneities. The first model assumes that one fluid forms a random ensemble of spherical inclusions in a porous medium saturated by the other fluid. The attenuation and dispersion predicted by this model are very similar to those predicted for 3D periodic distribution. Attenuation (inverse quality factor) is proportional to ω at low frequencies for both distributions. This is in contrast to the 1D case, where random and periodically alternating layering shows different attenuation behaviour at low frequencies. The second model, which assumes a 3D continuous distribution of fluid heterogeneities, also predicts the same low-frequency asymptote of attenuation. However, the shapes of the frequency dependencies of attenuation are different. As the 3D continuous random approach assumes that there will be a distribution of different patch sizes, it is expected to be better suited to modelling experimental results. Further research is required in order to uncover how to relate the random functions to experimentally significant parameters.     

Simulation of gaseous diffusion in partially saturated porous media under variable gravity with lattice Boltzmann methods

Liquid distributions in unsaturated porous media under different gravitational accelerations and corresponding macroscopic gaseous diffusion coefficients were investigated to enhance understanding of plant growth conditions in microgravity. We used a single-component, multiphase lattice Boltzmann code to simulate liquid configurations in two-dimensional porous media at varying water contents for different gravity conditions and measured gas diffusion through the media using a multicomponent lattice Boltzmann code. The relative diffusion coefficients (D rel) for simulations with and without gravity as functions of air-filled porosity were in good agreement with measured data and established models. We found significant differences in liquid configuration in porous media, leading to reductions in D rel of up to 25% under zero gravity. The study highlights potential applications of the lattice Boltzmann method for rapid and cost-effective evaluation of alternative plant growth media designs under variable gravity.     

Diagenetic development of unstable and stable magnetization in the St. Bees Sandstone (Triassic) of northern England

Thermal demagnetization of red and drab sandstones from the St. Bees Sandstone shows a wide range of directional stability. After the removal of a metastable secondary magnetization at temperatures up to 300°C red sandstones may show stable or unstable magnetization. Experiments indicate that both the stable and unstable magnetization is carried by coarse haematite particles (specularite).Drab sandstones, which have been subject to reduction and dissolution of haematite are generally unstable but specimens with a stable NRM occur and this must be carried by specularite because the pigment has been removed from these specimens.The stable magnetization is believed to have developed during deposition and early diagenesis by the oxidation of detrital iron oxides. Pole positions correspond to known Triassic poles and there are abundant normal and reversed zones typical of the Lower Triassic.The unstable magnetization of the red sandstones is apparently due to the development of authigenic overgrowths of haematite on the detrital specularites. This phase of authigenesis may have taken place over a long time, and after significant changes in the ambient geomagnetic field resulting in complex magnetizations in individual grains and hence whole rocks.     

Field study of macropore flow processes using tension infiltration of a dye tracer in partially saturated soils

Macropores are important preferential pathways for the migration of water and contaminants through the vadose zone. The objective of this study was to examine small‐scale preferential flow processes during infiltration in macroporous, low permeability soils. A series of tension infiltration tests were conducted using Brilliant Blue dye tracer at two field sites in southwestern Ontario, Canada. The maximum applied pressure head was varied for each test and the resulting dye stain patterns and macropore networks were characterized by excavation, mapping, photography, and image analysis. Worm burrows were the dominant macropore type, with average macropore densities exceeding 400 m^?2 and peak densities of more than 750 m^?2 at 30 cm depth at both sites. Flow in macropores became significant at infiltration pressures > ? 3 cm, with corresponding increases in infiltration rate, soil water content variability (spatially and temporally), and depth of dye staining. The results demonstrated clear evidence for partially saturated macropore flow under porewater tension conditions and the associated importance of macropore–matrix interaction in controlling this flow. Field observations of transient infiltration showed that film and rivulet flow along macropores yielded vertical flow velocities exceeding 40 m d^?1. Simple calculations showed that film flow along the walls and corners of irregularly shaped macropores could explain the observed results. Copyright © 2009 John Wiley & Sons, Ltd.