Numerical simulation of three-dimensional saltwater–freshwater fingering instabilities observed in a porous medium

We consider saltwater–freshwater fingering instabilities in a saturated porous medium. In the first part, we present three-dimensional results obtained from a laboratory experiment using non-invasive imaging. In the second part, we define a set of model problems in which the performed laboratory experiments can be ranged in. Due to its highly non-linear behavior and inevitable modeling errors, a detailed numerical reproduction of the physical concentration measurements cannot be expected. Nevertheless, four criteria have been identified, two quantitative and two qualitative, which facilitate a substantiated comparison of the physical experiment and the numerical simulation. With respect to these criteria a high degree of similarity could be observed. The use of these features allows a deeper understanding of the physical processes and the influence of the initial conditions.     

Effects of mechanical layering on volcano deformation

The migration and accumulation of magma beneath volcanoes often causes surface displacements that can be measured by geodetic techniques. Usually, deformation signals are explained using models with uniform mechanical properties. In this paper, we study surface displacements due to magma chamber inflation, using heterogeneous finite element models. We first present a systematic analysis of the influence of mechanical layering, showing that the stiffness contrast significantly affects the entity and the pattern of vertical and radial displacements. Second, as an example we apply the models to interpret ground displacements at Darwin volcano (Galápagos Islands) as revealed by InSAR data in the period 1992–1998. The considered models suggest that geodetic data interpreted using homogeneous models leads to underestimation of the source depth and volume change. Thus, we propose correction factors for the source parameters estimated by homogeneous models, in order to consider a range of variation due to mechanical layering as analysed in this study. The effect of the mechanical heterogeneities affects the correct understanding of geodetic data and also influences the evaluation of a volcanic hazard potential.     

Time-averaged and time-dependent energy-related quantities of harmonic waves in inhomogeneous viscoelastic anisotropic media

The energy–flux vector and other energy-related quantities play an important role in various wave propagation problems. In acoustics and seismology, the main attention has been devoted to the time-averaged energy flux of time-harmonic wavefields propagating in non-dissipative, isotropic and anisotropic media. In this paper, we investigate the energy–flux vector and other energy-related quantities of wavefields propagating in inhomogeneous anisotropic viscoelastic media. These quantities satisfy energy-balance equations, which have, as we show, formally different forms for real-valued wavefields with arbitrary time dependence and for time-harmonic wavefields. In case of time-harmonic wavefields, we study both time-averaged and time-dependent constituents of the energy-related quantities. We show that the energy-balance equations for time-harmonic wavefields can be obtained in two different ways. First, using real-valued wavefields satisfying the real-valued equation of motion and stress–strain relation. Second, using complex-valued wavefields satisfying the complex-valued equation of motion and stress–strain relation. The former approach yields simple results only for particularly simple viscoelastic models, such as the Kelvin–Voigt model. The latter approach is considerably more general and can be applied to viscoelastic models of unrestricted anisotropy and viscoelasticity. Both approaches, when applied to the Kelvin–Voigt viscoelastic model, yield the same expressions for the time-averaged and time-dependent constituents of all energy-related quantities and the same energy-balance equations. This indicates that the approach based on complex-valued representation of the wavefield may be used for time harmonic waves quite universally. This study also shows importance of joint consideration of time-averaged and time-dependent constituents of the energy-related quantities in some applications.     

震电效应在油气勘探开发中的应用

震电效应是流体饱和孔隙介质中客观存在的一种物理现象。开展震电勘探研究是当今地球物理领域的前沿研究课题。笔者基于当前国内外大量室内和野外试验资料，对震电效应及其产生机理、探测方式、勘探应用潜力进行了分析探讨，指出震电效应应用于油气勘探开发，特别是在寻找“剩余油”方面具有广阔的应用前景。     

Sedimentation–consolidation of a double porosity material

This paper studies the sedimentation–consolidation of a double porosity material, such as lumpy clay. Large displacements and finite strains are accounted for in a multidimensional setting. Fundamental equations are derived using a phenomenological approach and non-equilibrium thermodynamics, as set out by Coussy [Coussy, Poromechanics, Wiley, Chichester, 2004]. These equations particularise to three non-linear partial differential equations in one dimensional context. Numerical implementation in a finite element code is currently being undertaken.     

流体饱和多孔介质黏弹性动力人工边界

基于Biot流体饱和多孔介质本构方程，采用平面波和远场散射波经验叠加来反映外行波传播，以经验参数反映人工边界外行波动的衰减和多角度透射特性。在人工边界处分别施加反映固相和液相介质传播效应的弹簧及阻尼来模拟人工边界以外的无限域介质对来自有限域的外行波的能量的吸收作用。从而形成一种流体饱和多孔介质的黏弹性动力人工边界。数值算例表明：边界的精度和稳定性高于现有的黏性边界、黏弹性人工边界及一阶透射边界。     

Analysis of the solid phase stress tensor in multiphase porous media

Conservation equations for mass, momentum, energy, and entropy are formulated for the phases and interfaces of a three‐phase system consisting of a solid and two immiscible fluids. The microscale equations are averaged to the macroscale by integration over a representative elementary volume. Thermodynamic statements for each of the phases and interface entities are also formulated at the microscale and then averaged to the macroscale. This departure from most uses of thermodynamics in macroscale analysis ensures consistency between models and parameters at the two scales. The expressions for the macroscale rates of change of internal energy are obtained by differentiating the derived forms for energy and making use of averaging theorems. These thermodynamic expressions, along with the conservation equations, serve as constraints on the entropy inequality. A linearization of the resulting equations is employed to investigate the theoretical origins of the Biot coefficient that relates the hydrostatic part of the total stress tensor to the normal force applied at the solid surface by the pore fluids. The results here are placed in the context of other formulations and expressions that appear in the literature. Copyright © 2006 John Wiley & Sons, Ltd.     

Upscaling hydraulic conductivity based on the topology of the sub-scale structure

The hydraulic conductivity of heterogeneous porous media depends on the distribution function and the geometry of local conductivities at the smaller scale. There are various approaches to estimate the effective conductivity K_eff at the larger scale based on information about the small scale heterogeneity. A critical geometric property in this ‘upscaling’ procedure is the spatial connectivity of the small-scale conductivities. We present an approach based on the Euler-number to quantify the topological properties of heterogeneous conductivity fields, and we derive two key parameters which are used to estimate K_eff. The required coefficients for the upscaling formula are obtained by regression based on numerical simulations of various heterogeneous fields. They are found to be generally valid for various different isotropic structures. The effective unsaturated conductivity function K_eff (ψ_m) could be predicted satisfactorily. We compare our approach with an alternative based on percolation theory and critical path analysis which yield the same type of topological parameters. An advantage of using the Euler-number in comparison to percolation theory is the fact that it can be obtained from local measurements without the need to analyze the entire structure. We found that for the heterogeneous field used in this study both methods are equivalent.