A New Parameter Estimation Method for Solute Transport in a Column

To study contaminant transport in groundwater, an essential requirement is robust and accurate estimation of the transport parameters such as dispersion coefficient. The commonly used inverse error function method (IEFM) may cause unacceptable errors in dispersion coefficient estimation using the breakthrough curves (BTCs) data. We prove that the random error in the measured concentrations, which might be described by a normal distribution, would no longer follow the normal distribution after the IEFM transformation. In this study, we proposed a new method using the weighted least squares method (WLSM) to estimate the dispersion coefficient and velocity of groundwater. The weights were calculated based on the slope of the observed BTCs. We tested the new method against other methods such as genetic algorithm and CXTFIT program and found great agreement. This new method acknowledged different characteristics of solute transport at early, intermediate, and late time stages and divided BTCs into three sections for analysis. The developed method was applied to interpret three column tracer experiments by introducing continuous, constant‐concentration of sodium chloride (NaCl) into columns filled with sand, gravel, and sand‐gravel media. This study showed that IEFM performed well only when the observed data points were located in the linear (intermediate time) section of BTCs; it performed poorly when data points were in the early and late time stages. The new WLSM method, however, performed well for data points scattering over the entire BTCs and appeared promising in parameter estimation for solute transport in a column.     

Modeling contaminant transport in homogeneous porous media with fractional advection-dispersion equation

The newly developed Fractional Advection-Dispersion Equation (FADE), which is FADE was extended and used in this paper for modelling adsorbing contaminant transport by adding an adsorbing term. A parameter estimation method and its corresponding FORTRAN based program named FADEMain were developed on the basis of Nonlinear Least Square Algorithm and the analytical solution for one-dimensional FADE under the conditions of step input and steady state flow. Data sets of adsorbing contaminants Cd and NH4+-N transport in short homogeneous soil columns and conservative solute NaCI transport in a long homogeneous soil column, respectively were used to estimate the transport parameters both by FADEMain and the advection-dispersion equation (ADE) based program CXTFIT2.1. Results indicated that the concentration simulated by FADE agreed well with the measured data. Compared to the ADE model, FADE can provide better simulation for the concentration in the initial lower concentration part and the late higher concentration part of the breakthrough curves for both adsorbing contaminants. The dispersion coefficients for ADE were from 0.13 to 7.06 cm2/min, while the dispersion coefficients for FADE ranged from 0.119 to 3.05 cm1.856/min for NaCI transport in the long homogeneous soil column. We found that the dispersion coefficient of FADE increased with the transport distance, and the relationship between them can be quantified with an exponential function. Less scale-dependent was also found for the dispersion coefficient of FADE with respect to ADE.     

微动中多模式面波频散曲线的映射式提取方法

为了避免微动勘探技术中因忽略高阶模式瑞雷波而影响反演精度的不足,提出从微动面波中提取多模式瑞雷波频散曲线的映射式方法.该方法从微动信号入手,首先通过相关法提取多半径台阵的相关系数曲线,然后建立从多条相关系数曲线到多模式瑞雷波频散曲线的映射模型,最后采用分区拟合准则优化实现模型结构,达到提取微动面波中多模式瑞雷波频散曲线的目的.为验证方法的有效性,通过有限差分方法数值计算实际近表面应用中三种常见典型地质结构中的微动信号,采用映射式方法提取微动面波中多模式瑞雷波频散曲线,将提取结果和理论值进行对比分析.结果表明,映射式方法提取微动面波中多模式瑞雷波频散曲线可以满足反演地质结构的要求.     

黏弹性介质中瑞利波频散曲线和衰减系数曲线的反演

瑞利波具有能量大、信噪比高等特点,可以用来反演介质内部的力学信息,近年来在浅层地球物理勘探、深层地震学研究以及超声波无损检测等多个领域都有较广泛的应用。目前大多数瑞利波的应用中都假设介质是弹性的,然而实际中岩石、土壤和金属等介质都在一定程度上体现出了黏弹性。当介质的黏弹性较强时仍然采用弹性假设研究其中瑞利波的反演将增大误差,因此有必要考虑黏弹性介质中的瑞利波反演,但是目前这方面的研究仍不够深入。本文研究黏弹性介质中瑞利波频散曲线和衰减系数曲线的反演问题,给出其在半空间中联合反演的方法,并对该方法的误差进行分析。     

On the methods for determining the transverse dispersion coefficient in river mixing

In this study, the strengths and weaknesses of existing methods for determining the dispersion coefficient in the two-dimensional river mixing model were assessed based on hydraulic and tracer data sets acquired from experiments conducted on either laboratory channels or natural rivers. From the results of this study, it can be concluded that, when the longitudinal dispersion coefficient as well as the transverse dispersion coefficients must be determined in the transient concentration situation, the two-dimensional routing procedures, 2D RP and 2D STRP, can be employed to calculate dispersion coefficients among the observation methods. For the steady concentration situation, the STRP can be applied to calculate the transverse dispersion coefficient. When the tracer data are not available, either theoretical or empirical equations by the estimation method can be used to calculate the dispersion coefficient using the geometric and hydraulic data sets. Application of the theoretical and empirical equations to the laboratory channel showed that equations by Baek and Seo [[3], 2011] predicted reasonable values while equations by Fischer [23] and Boxwall and Guymer (2003) overestimated by factors of ten to one hundred. Among existing empirical equations, those by Jeon et al. [28] and Baek and Seo [6] gave the agreeable values of the transverse dispersion coefficient for most cases of natural rivers. Further, the theoretical equation by Baek and Seo [5] has the potential to be broadly applied to both laboratory and natural channels.     

Estimating longitudinal dispersion in rivers using Acoustic Doppler Current Profilers

The longitudinal dispersion coefficient (D) is an important parameter needed to describe the transport of solutes in rivers and streams. The dispersion coefficient is generally estimated from tracer studies but the method can be expensive and time consuming, especially for large rivers. A number of empirical relations are available to estimate the dispersion coefficient; however, these relations are known to produce estimates within an order of magnitude of the tracer value. The focus of this paper is on using the shear-flow dispersion theory to directly estimate the dispersion coefficient from velocity measurements obtained using an Acoustic Doppler Current Profiler (ADCP). Using tracer and hydrodynamic data collected within the same river reaches, we examined conditions under which the ADCP and tracer methods produced similar results. Since dead zones / transient storage (TS) are known to influence the dispersion coefficient, we assessed the relative importance of dead zones in different stream reaches using two tracer-based approaches: (1) TS modeling which explicitly accounts for dead zones and (2) the advection–dispersion equation (ADE) which does not have separate terms for dead zones. Dispersion coefficients based on the ADE tend to be relatively high as they describe some of the effects of dead zones as well. Results based on the ADCP method were found to be in good agreement with the ADE estimates indicating that storage zones play an important role in the estimated dispersion coefficients, especially at high flows. For the river sites examined in this paper, the tracer estimates of dispersion were close to the median values of the ADCP estimates obtained from multiple datasets within a reach. The ADCP method appears to be an excellent alternative to the traditional tracer-based method if care is taken to avoid spurious data and multiple datasets are used to compute a distance-weighted average or other appropriate measure that represents reach-averaged conditions.     

ABSENCE OF PREFERENTIAL FLOW IN THE PERCOLATING WATERS OF A CONIFEROUS FOREST SOIL

Evidence for the functioning of macropores and the presence of preferential flow in forest soils is equivocal. This is partly because many workers use only one diagnostic technique to indicate whether or not macropore flow occurs. In this paper three lines of evidence are used to suggest that preferential flow does not occur in the percolating waters of a coniferous forest soil under the range of hydrological conditions that prevail in the field. To simulate field conditions, realistic rainfall intensities were used in conservative solute transport experiments on four undisturbed soil columns. A method is described in which breakthrough data can be used to calculate the percentage of antecedent water displaced from a soil column during frontal-type breakthrough experiments. Calculations based on this method using the experimental data show that as little as five percent of the antecedent water was immobile. The simple form of the functional advection–dispersion equation, based on a single value for linear velocity and the dispersion coefficient was fitted to two of the breakthrough curves with reasonable accuracy, further suggesting that preferential flow did not occur in the experiments. Finally, soil moisture characteristic curves were determined for replicate soil samples from the forest soil. The operational water contents of the columns during the breakthrough experiments were compared with the soil moisture characteristics and it was found that pores exerting pressure heads greater than −0·5 kPa did not appear to contribute to flow through the columns, again suggesting an absence of preferential flow. © 1997 by John Wiley & Sons, Ltd.     

Determination of transverse dispersion coefficients from reactive plume lengths

With most existing methods, transverse dispersion coefficients are difficult to determine. We present a new, simple, and robust approach based on steady-state transport of a reacting agent, introduced over a certain height into the porous medium of interest. The agent reacts with compounds in the ambient water. In our application, we use an alkaline solution injected into acidic ambient water. Threshold values of pH are visualized by adding standard pH indicators. Since aqueous-phase acid-base reactions can be considered practically instantaneous and the only process leading to mixing of the reactants is transverse dispersion, the length of the plume is controlled by the ratio of transverse dispersion to advection. We use existing closed-form expressions for multidimensional steady-state transport of conservative compounds in order to evaluate the concentration distributions of the reacting compounds. Based on these results, we derive an easy-to-use expression for the length of the reactive plume; it is proportional to the injection height squared, times the velocity, and inversely proportional to the transverse dispersion coefficient. Solving this expression for the transverse dispersion coefficient, we can estimate its value from the length of the alkaline plume. We apply the method to two experimental setups of different dimension. The computed transverse dispersion coefficients are rather small. We conclude that at slow but realistic ground water velocities, the contribution of effective molecular diffusion to transverse dispersion cannot be neglected. This results in plume lengths that increase with increasing velocity.     

Automatic pickup of arrival time of channel wave based on multi-channel constraints

Accurately detecting the arrival time of a channel wave in a coal seam is very important for in-seam seismic data processing. The arrival time greatly affects the accuracy of the channel wave inversion and the computed tomography (CT) result. However, because the signal-to-noise ratio of in-seam seismic data is reduced by the long wavelength and strong frequency dispersion, accurately timing the arrival of channel waves is extremely difficult. For this purpose, we propose a method that automatically picks up the arrival time of channel waves based on multi-channel constraints. We first estimate the Jaccard similarity coefficient of two ray paths, then apply it as a weight coefficient for stacking the multichannel dispersion spectra. The reasonableness and effectiveness of the proposed method is verified in an actual data application. Most importantly, the method increases the degree of automation and the pickup precision of the channel-wave arrival time.     

Shear dispersion in a fracture with porous walls

We present an analytical expression for the shear dispersion during solute transport in a coupled fracture–matrix system. The dispersion coefficient is obtained in a fracture with porous walls by taking into account an accurate boundary condition at the interface between the matrix and fracture, and the results were compared with those in a non-coupled system. The analysis presented identifies three regimes: diffusion-dominated, transition, and advection-dominated. The results showed that it is important to consider the exchange of solute between the fracture and matrix in development of the shear dispersion coefficient for the transition and advection-dominated regimes. The new dispersion coefficient is obtained by imposing the continuity of concentrations and mass fluxes along the porous walls. The resulting equivalent transport equation revealed that the effective velocity in a fracture increases while the dispersion coefficient decreases due to mass transfer between the matrix and fracture. A larger effective advection term leads to greater storage of mass in the matrix as compared with the classical double-porosity model with a non-coupled dispersion coefficient. The findings of this study can be used for modeling of tracer tests as well as fate, transport, and remediation of groundwater contaminants in fractured rocks.     

带暗柱钢筋砼等肢L形柱轴压比限值调整系数研究

至今,带暗柱的等肢L形柱轴压比限值调整系数尚未得到充分研究,因而限制了其在工程中的应用.为此,针对等肢L形柱,采用非线性全过程数值分析方法,通过C++编制程序,并使用相关实验数据对程序进行了验证;在不同抗震等级、肢高纵筋配筋率及体积配箍率下,计算了带暗柱与不带暗柱钢筋混凝土等肢L形柱的截面曲率延性比,并根据《混凝土异形柱结构技术规程》给出的不同抗震等级下异形柱截面曲率延性比的要求,确定了各抗震等级下带暗柱与不带暗柱的等肢L形柱的轴压比限值及其比值;最后通过拟合分析法及调整系数法确定了带暗柱等肢L形柱轴压比限值的调整系数.     

消除探地雷达数据的子波衰减和频散的反滤波方法

消除探地雷达数据的子波衰减和频散可以很好地提高探地雷达的勘探深度和勘探分辨率.常用的消除探地雷达数据的子波衰减和频散方法为反Q滤波方法.该方法需要利用地下介质的Q参数,但是正确求取地下介质的Q参数很困难.针对这一问题,本文提出了一种消除探地雷达数据的子波衰减和频散的反滤波方法.该方法以地下介质反射系数是随机数为前提,利用地下介质等效滤波器具有最小相位这个特性,通过求取等效滤波器的振幅谱来求取等效滤波器的反滤波器.最后,利用该反滤波器对探地雷达数据进行反滤波,实现消除探地雷达数据的子波衰减和频散.     

Inversion of SASW dispersion curves based on maximum flexibility coefficients in the wave number domain

Spectral analysis of surface waves (SASW) is a nondestructive in-situ testing method that is used to determine stiffness profiles of soil and pavement sites based on dispersion characteristics of Rayleigh-type surface waves.Inversion of the Rayleigh wave dispersion curve of a site provides information on the variation of shear-wave velocity with depth. In the inversion procedures currently used for SASW tests, the field dispersion curve is matched with a theoretical dispersion curve obtained for the fundamental mode of surface wave propagation.In order to overcome difficulties associated with the presence of multi-modes in SASW signals, a new inversion method based on the maximum vertical flexibility coefficient is introduced in this paper. Unlike root-searching methods, the new method easily identifies the predominant propagation modes. In this new approach, the simplex method is used to match field and theoretical dispersion curves automatically. The purpose of this paper is to present the details of the new method and to demonstrate its advantages.     

Quantification of irreversible benzene sorption in sandy materials

Based on a previous study of the irreversible sorption of benzene in sandy aquifer materials, we further investigated a method to quantify an irreversible sorption coefficient of aqueous benzene. Assuming that the rate of irreversible loss from the solution to the sorption sites followed first‐order kinetics, the irreversible sorption coefficient was derived from a kinetic batch sorption test conducted for an appropriate soil‐to‐solution ratio to reflect the flow conditions imposed on a column test. Simulation results revealed that the irreversible sorption coefficient estimated from the kinetic batch test provided a good agreement with the measured data obtained from the column test, indicating that the method proposed in this study can be used to quantify the irreversible sorption coefficient. Copyright © 2004 John Wiley & Sons, Ltd.     

三维VTI介质qP波方程频率空间域有限差分高阶加权算子

波动方程有限差分法是波场模拟的一个重要方法,为解决常规有限差分法存在着数值频散的问题,本文从具有垂直对称轴的三维横向各向同性(VTI)介质频率-空间域qP波动方程出发,在常规差分算子的基础上构造了适合三维VTI介质的频率空间域有限差分优化算子,然后利用最优化理论中的Gauss-Newton法求解了优化算子的系数,使差分方程的相速度与波动方程的相速度尽量吻合,从而在理论上使网格数值频散达到极小,精度对比分析及数值测试表明,有限差分优化算子具有较高的波场数值模拟精度,有效地压制了数值频散现象,为三维VTI介质频率一空间域qP波正演模拟研究提供了理论基础.     

LONGITUDINAL DISPERSION IN OPEN-CHANNEL FLOW

Laboratory experiments on longitudinal dispersion in clear-water and sedimentladen flows are reported. These experiments indicate that the presence of suspended sediment does not have a significant effect on the dispersion process other than its possible effect on the friction factor. Analysis of the writers' and other's data collected in laboratory flumes and natural streams Shows that Taylor's model of longitudinal dispersion based on one-dimensional Fickian diffusion equation with a constant dispersion coefficient, DL, is not suitable for describing the dispersion process in natural streams as DL tends to increase in the downstream direction. Therefore, a similarity analysis of the concentration distributions, on the lines of Day and Wood, has been carried out. Based on dimensional analysis an improved empirical method has been obtained for predicting the concentration-time relation without the use of DL     

Effective dispersion in a chemically heterogeneous medium under temporally fluctuating flow conditions

We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the equilibrium adsorption properties, the corresponding fluctuating retardation factor is modeled as a stationary random space function. The temporal variability of the flow is represented by a stationary temporal random process. Solute spreading is quantified by effective dispersion coefficients, which are derived from the ensemble average of the second centered moments of the normalized solute distribution in a single disorder realization. Using first-order expansions in the variances of the respective random fields, we derive explicit compact expressions for the time behavior of the disorder induced contributions to the effective dispersion coefficients. Focusing on the contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady flow fields, evolves to a disorder-induced macroscopic value (i.e., independent of local dispersion). At the same time, the asymptotic longitudinal dispersion coefficient can decrease. Under certain conditions the contribution to the longitudinal effective dispersion coefficient shows superdiffusive behavior, similar to that observed for transport in s stratified porous medium, before it decreases to its asymptotic value. The presented compact and easy to use expressions for the longitudinal and transverse effective dispersion coefficients can be used for the quantification of effective spreading and mixing in the context of the groundwater remediation based on hydraulic manipulation and for the effective modeling of reactive transport in heterogeneous media in general.     

广义反射-透射系数算法的无量纲化

水平层状介质中瑞利波频散曲线的计算一直是受关注的问题.陈晓非提出的广义反射-透射系数方法虽然具备很好的精确性和稳定性,但是算法中起决定作用的矩阵E存在有量纲元素,并且不同元素之间的数量级差异很大.本文作者通过把广义反射-透射系数算法无量纲化,得到了简洁的瑞利波频散函数的公式体系.分别计算了改进后算法和原算法中矩阵E的最大模元素与最小模元素的比值ε,发现前者的矩阵E中最大模元素与最小模元素最多只相差1个数量级,而后者的矩阵E中最大模元素与最小模元素之间最大达11个数量级的差异,尽管后者可以通过选取变量的单位减小ε的值,但新算法精度更高,从而完善了利用广义反射-透射系数方法求解瑞利波频散曲线问题的理论和算法.     

Macroscopic equations for vapor transport in a multi-layered unsaturated zone

Using the method of homogenization, we present a systematic derivation of the macroscopic equations for air flow and chemical vapor transport in an unsaturated zone with a periodic structure of heterogeneity. The effective specific discharge and hydrodynamic dispersion coefficient are expressible in terms of some cell functions, whose analytical solutions are sought for the simple case of alternate stacking of two strictly plane layers of different properties. For this kind of bi-layered composite, the effects of convection velocity and layer property contrasts on the longitudinal and transverse components of the hydrodynamic dispersion coefficient are investigated.     

瑞雷波多阶模式频散曲线稀疏正则化反演方法研究

目前瑞雷波多阶模式频散曲线反演中仅考虑数据的拟合,缺乏对模型的约束,不能很好地刻画地层间断面的问题,针对此问题,研究了瑞雷波多阶模式频散曲线稀疏正则化反演方法.正演模拟基于广义反射-透射系数法,数值计算上采用一种快速求根方法,与二等分方法相比,能够在很短的时间内达到最优的收敛效果;反演建模时采用L1范数正则化方法对模型...