Calculating Groundwater Response Times for Flow in Heterogeneous Porous Media

Predicting the amount of time required for a transient groundwater response to take place is a practical question that is of interest in many situations. This time scale is often called the response time. In the groundwater hydrology literature, there are two main methods used to calculate the response time: (1) both the transient and steady‐state groundwater flow equations are solved, and the response time is taken to be amount of time required for the transient solution to approach the steady solution within some tolerance; and (2) simple scaling arguments are adopted. Certain limitations restrict both of these approaches. In this study, we outline a third method, based on the theory of mean action time. We derive the governing boundary value problem for both the mean and variance of action time for confined flow in two‐dimensional heterogeneous porous media. Importantly, we show that these boundary value problems can be solved using widely available software. Applying these methods to a test case reveals the advantages of the theory of mean action time relative to standard methods.     

基于Comsol的饱和多孔介质动力方程的数值模拟及应用

两相饱和多孔介质的动力响应问题在地震工程领域具有重要的研究意义,由于涉及到固相和液相的动力耦合,使得该问题的求解尤为复杂。本文利用Comsol在求解多场耦合问题上的优点,针对Biot饱和多孔介质u-U耦合形式下的波动方程特征,经过一系列微分算子运算和矩阵变换得到导数形式下的波动方程,基于Comsol Multiphysics提供的广义偏微分方程模式对变形后的波动方程进行求解,并把改进后的无限元边界应用到无限域动力问题的模拟中。通过与饱和多孔介质动力响应的解析解进行对比,验证模型求解技术的可行性和正确性,并在此基础上讨论饱和土地基中空沟隔振效果与饱和土体参数孔隙率、泊松比的关系。通过研究分析,可以为饱和土地基中空沟隔振设计提供一些有价值的参考。     

Inhomogeneous Harmonic Plane Waves in Viscoelastic Anisotropic Media

In viscoelastic media, the slowness vector p of plane waves is complex-valued, p = P + iA. The real-valued vectors P and A are usually called the propagation and the attenuation vector, repectively. For P and A nonparallel, the plane wave is called inhomogeneousThree basic approaches to the determination of the slowness vector of an inhomogeneous plane wave propagating in a homogeneous viscoelastic anisotropic medium are discussed. They differ in the specification of the mathematical form of the slowness vector p. We speak of directional specification, componental specification and mixed specification of the slowness vector. Individual specifications lead to the eigenvalue problems for 3 × 3 or 6 × 6 complex-valued matrices.In the directional specification of the slowness vector, the real-valued unit vectors N and M in the direction of P and A are assumed to be known. This has been the most common specification of the slowness vector used in the seismological literature. In the componental specification, the real-valued unit vectors N and M are not known in advance. Instead, the complex-valued vactorial component p of slowness vector p into an arbitrary plane with unit normal n is assumed to be known. Finally, the mixed specification is a special case of the componental specification with p purely imaginary. In the mixed specification, plane represents the plane of constant phase, so that N = ±n. Consequently, unit vector N is known, similarly as in the directional specification. Instead of unit vector M, however, the vectorial component d of the attenuation vector in the plane of constant phase is known.The simplest, most straightforward and transparent algorithms to determine the phase velocities and slowness vectors of inhomogeneous plane waves propagating in viscoelastic anisotropic media are obtained, if the mixed specification of the slowness vector is used. These algorithms are based on the solution of a conventional eigenvalue problem for 6 × 6 complex-valued matrices. The derived equations are quite general and universal. They can be used both for homogeneous and inhomogeneous plane waves, propagating in elastic or viscoelastic, isotropic or anisotropic media. Contrary to the mixed specififcation, the directional specification can hardly be used to determine the slowness vector of inhomogeneous plane waves propagating in viscoelastic anisotropic media. Although the procedure is based on 3 × 3 complex-valued matrices, it yields a cumbersome system of two coupled equations.     

An Experimenting Field Approach for the Numerical Solution of Multiphase Flow in Porous Media

In this work, we apply the experimenting pressure field technique to the problem of the flow of two or more immiscible phases in porous media. In this technique, a set of predefined pressure fields are introduced to the governing partial differential equations. This implies that the velocity vector field and the divergence at each cell of the solution mesh can be determined. However, since none of these fields is the true pressure field entailed by the boundary conditions and/or the source terms, the divergence at each cell will not be the correct one. Rather the residue which is the difference between the true divergence and the calculated one is obtained. These fields are designed such that these residuals are used to construct the matrix of coefficients of the pressure equation and the right‐hand side. The experimenting pressure fields are generated in the solver routine and are fed to the different routines, which may be called physics routines, which return to the solver the elements of the matrix of coefficients. Therefore, this methodology separates the solver routines from the physics routines and therefore results in simpler, easy to construct, maintain, and update algorithms.     

Flow Characteristics of Microbubble Suspensions in Porous Media as an Oxygen Carrier

Microbubble suspensions were generated as an oxygen carrier for aerobic biodegradation, and their flow characteristics in porous media were investigated. Commercial surfactants including sodium dodecyl sulfate (SDS), and dodecylethyldimethylammonium bromide (DEDAB), saponin (a natural surfactant), and collagen (a protein hydrolysate) were examined as base materials for generating microbubble suspensions. Among them, 2×CMC (critical micellar concentration) of SDS, DEDAB, and saponin developed microbubble suspensions with the highest gas hold‐up and half‐drainage time. Visualization of the flow patterns in sand showed that the microbubble suspensions were separated into a liquid and gas phase directly after injection, showing much faster movement of liquid phase flow. The gas front of the microbubble suspensions flowed in a plug‐flow manner, particularly in cases of SDS and DEDAB. The experimental results from both homogeneous and heterogeneous cells confirmed that the microbubble flow could overcome the heterogeneity in porous media. However, the plug‐flow characteristics and flow propagation of the microbubble suspensions to the low‐permeability zone was accompanied by a large pressure drop, which needs to be considered for future field application.     

非均匀TI介质P-SV波传播交错网格高阶有限差分数值模拟

给出了在非均匀横向各向同性(TI)介质情况下,四阶时间精度、高阶空间精度的一阶速度-应力P-SV波的波动方程交错网格有限差分解法.首先根据一阶速度(应力)波动方程把速度(应力)对时间的一阶和三阶导数转换为应力(速度)对空间的导数,从而在使用四阶时间精度有限差分格式计算某一时刻的波场时只需要前面两个时间步的波场值;然后在空间上采用高阶有限差分格式以提高数值模拟的精度.数值模拟结果和实测垂直地震剖面(VSP)记录符合得很好,说明该方法是可行的.     

各向异性双相介质弹性波场褶积算法数值模拟

从各向同性介质中波场数值模拟的褶积微分算子法出发,推导出了各向异性双相介质中波场传播数值计算的褶积新算法.将常见的二阶微分Biot波动方程用等效的一阶速度—应力双曲方程表示,其中未知的波场向量包括固相和流体的速度分量和应力分量,由此对方程的时间项使用交错网格差分方法计算,而对空间项则采用褶积微分算法进行求解.对各向异性双相介质在单层介质模型和双层介质模型中的波场特征进行了研究.研究的结果显示,在两层介质分界面上当地震波产生反射时能观测到两类纵波和横波,并且在衰减系数大的介质里慢纵波很难见到.     

Second-Order and Higher-Order Perturbations of Travel Time in Isotropic and Anisotropic Media

The partial derivatives of travel time with respect to model parameters are referred to as perturbations. Explicit equations for the second-order and higher-order perturbations of travel time in both isotropic and anisotropic media are derived. The perturbations of travel time and its spatial derivatives can be calculated by simple numerical quadratures along rays.     

两相介质波动问题显式有限元方法稳定性研究

基于动力反应递推计算格式传递矩阵的性质,进行了饱和两相介质波动问题时域显式有限元方法稳定性问题的研究。定义了综合考虑各种影响因素的稳定性判别指标——传递因子;研究了稳定性影响因素,包括时间步长、空间步距和渗透系数取值的作用规律;给出了方法稳定性的实用判别准则。研究结果表明:时间步长、空间步距和渗透系数取值都对饱和两相介质波动问题的时域显式有限元方法的稳定性有较为显著的影响。随着时间步长的增大,方法的稳定性降低;随着空间步距的增大,方法的稳定性增加;当渗透系数取值增大时,方法的稳定性增加。     

A flexible nonlinear modelling framework for nonstationary generalized extreme value analysis in hydroclimatology

Parameters in a generalized extreme value (GEV) distribution are specified as a function of covariates using a conditional density network (CDN), which is a probabilistic extension of the multilayer perceptron neural network. If the covariate is time or is dependent on time, then the GEV‐CDN model can be used to perform nonlinear, nonstationary GEV analysis of hydrological or climatological time series. Owing to the flexibility of the neural network architecture, the model is capable of representing a wide range of nonstationary relationships. Model parameters are estimated by generalized maximum likelihood, an approach that is tailored to the estimation of GEV parameters from geophysical time series. Model complexity is identified using the Bayesian information criterion and the Akaike information criterion with small sample size correction. Monte Carlo simulations are used to validate GEV‐CDN performance on four simple synthetic problems. The model is then demonstrated on precipitation data from southern California, a series that exhibits nonstationarity due to interannual/interdecadal climatic variability. Copyright © 2009 Her Majesty the Queen in right of Canada. Published by John Wiley & Sons, Ltd.     

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 5. Single-Fluid-Phase Transport

This work is the fifth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are used to develop models that describe species transport and single-fluid-phase flow through a porous medium system in varying physical regimes. Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces are developed. Two different approaches are presented, one that makes use of a momentum equation for each entity along with constitutive relations for species diffusion and dispersion, and a second approach that makes use of a momentum equation for each species in an entity. The alternative models are developed by relying upon different approaches to constrain an entropy inequality using mass, momentum, and energy conservation equations. The resultant constrained entropy inequality is simplified and used to guide the development of closed models. Specific instances of dilute and non-dilute systems are examined and compared to alternative formulation approaches.     

利用三维非均匀不稳定渗流场的数值解求解垂直井与水平井的联合开采

用差分的方法给出了三维非均匀不稳定渗流方程的离散方程组，将配斯曼（Peaceman）方程拓展成能够被用于同时求解垂直井与水平井联合开采问题的形式，利用迭代解法求解差分方程和配斯曼方程所组成的方程组，并以实际层状不均匀介质为例计算了其压强的空间分布。     

介质随机扰动条件下的层析反演算法

在层析成像中,介质的随机扰动将对反演精度有很大影响.本文在反演迭代过程中,通过自相关平滑算法,将先验约束由单纯的均值拓展为模型方差、相关系数等统计参数,实现了随机介质的分布特征对层析反演的先验约束,有利于压制高频干扰,提高层析成像的精度.岩溶区洞穴探测的工程实例表明,在传统层析反演算法无法获得合理解释的情况下,采用自相关平滑算法仍能获得合理的地质剖面.     

A computational procedure for the implementation of equivalent linearization in finite element analysis

This paper deals with the practical implementation of the statistical equivalent linearization method (EQL) in conjunction with general FE‐analysis to evaluate non‐linear structural response under random excitation. A computational procedure is presented which requires the non‐linear part of the system to be subdivided into suitable sub‐domains (elements). Each element is independently linearized using only a minimum number of co‐ordinates. A local co‐ordinate system is introduced using linear transformations of the global (master) degrees of freedom. Restoring forces and non‐linear constitutive laws are defined by the local co‐ordinates of each element. The linearization coefficients are further transformed back to establish the global linearized system. The procedure has, on one hand, the ability to use any desired linearization criterion and, on the other hand, it can be combined with highly developed procedures to determine the response of arbitrary large FE‐models. To illustrate the applicability of the procedure, two different non‐linear systems are analysed under bi‐directional earthquake excitation. Copyright © 2000 John Wiley & Sons, Ltd.     

多孔介质中甲烷水合物边界的CT图像识别技术

采用X射线计算机断层扫描(X-CT)技术观测多孔介质中天然气水合物的生成和分解过程,具有实时、直观和无损等优点。由于颗粒物边缘图像容积效应和X-CT分辨率的限制,多孔介质体系中不同物质的边界域难以确定,从而影响对多孔介质中水合物赋存状态的准确判断。利用Matlab平台图像处理软件中的开闭运算、多值化、梯度图像提取和边缘检测等方法,对实验获得的多孔介质中甲烷水合物的CT图像进行优化处理,获得了更清晰的图像,可有效地提高多孔介质中不同物质边界域的识别效果,有利于准确判断甲烷水合物在多孔介质中的赋存状态。     

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 8. Interface and Common Curve Dynamics

This work is the eighth in a series that develops the fundamental aspects of the thermodynamically constrained averaging theory (TCAT) that allows for a systematic increase in the scale at which multiphase transport phenomena is modeled in porous medium systems. In these systems, the explicit locations of interfaces between phases and common curves, where three or more interfaces meet, are not considered at scales above the microscale. Rather, the densities of these quantities arise as areas per volume or length per volume. Modeling of the dynamics of these measures is an important challenge for robust models of flow and transport phenomena in porous medium systems, as the extent of these regions can have important implications for mass, momentum, and energy transport between and among phases, and formulation of a capillary pressure relation with minimal hysteresis. These densities do not exist at the microscale, where the interfaces and common curves correspond to particular locations. Therefore, it is necessary for a well-developed macroscale theory to provide evolution equations that describe the dynamics of interface and common curve densities. Here we point out the challenges and pitfalls in producing such evolution equations, develop a set of such equations based on averaging theorems, and identify the terms that require particular attention in experimental and computational efforts to parameterize the equations. We use the evolution equations developed to specify a closed two-fluid-phase flow model.     

Coupling of a Column System with ICP‐MS for the Characterisation of Colloid‐mediated Metal(loid) Transport in Porous Media

In this work a coupling method for the characterisation of colloid‐mediated transport of the metal(loid) species in porous media was developed. For this transport experiments quartz sand was used as column packing material and the synthetic three‐layer clay mineral laponite as model colloid. The determination of colloids was conducted by means of UV detection. The quantification of the metal(loid) ions was carried out in two different ways: (1) The fractions collected at the column outlet were analysed with an inductively coupled plasma mass spectrometer (ICP‐MS) (offline measurements); (2) the column system was directly coupled with ICP‐MS (online measurements). In the column experiments the influence of laponite colloids on the transport of Cu, Pb, Zn, Pt and As species was investigated. In the offline experiments as a consequence of dilution during sample preparation no metal(loid) species at the column outlet could be found. Unlike this the breakthrough of all metal(loid)s could be detected under the same experimental column conditions in the coupling experiments. This coupling technique offers the online detection of the metal species and colloidal particles with high resolution even at low concentrations and without any time‐consuming preparation. The coupling experiments have shown that the laponite particles accelerate the transport of the cationic metals. For anionic metal(loid) species no influence of laponite on their transport behaviour was found.