Vectorized simulation of groundwater flow and contaminant transport using analytic element method and random walk particle tracking

Groundwater contaminant transport processes are usually simulated by the finite difference (FDM) or finite element methods (FEM). However, they are susceptible to numerical dispersion for advection‐dominated transport. In this study, a numerical dispersion‐free coupled flow and transport model is developed by combining the analytic element method (AEM) with random walk particle tracking (RWPT). As AEM produces continuous velocity distribution over the entire aquifer domain, it is more suitable for RWPT than FDM/finite element methods. Using the AEM solutions, RWPT tracks all the particles in a vectorized manner, thereby improving the computational efficiency. The present model performs a convolution integral of the response of an impulse contaminant injection to generate concentration distributions due to a permanent contaminant source. The RWPT model is validated with an available analytical solution and compared to an FDM solution, the RWPT model more accurately replicates the analytical solution. Further, the coupled AEM‐RWPT model has been applied to simulate the flow and transport in hypothetical and field aquifer problems. The results are compared with the FDM solutions and found to be satisfactory. The results demonstrate the efficacy of the proposed method.     

On different numerical inverse Laplace methods for solute transport problems

Numerical inversion is required when Laplace transform cannot be inverted analytically by manipulating tabled formulas of special cases. However, the numerical inverse Laplace transform is generally an ill-posed problem, and there is no universal method which works well for all problems. In this study, we selected seven commonly used numerical inverse Laplace transform methods to evaluate their performance for dealing with solute transport in the subsurface under uniform or radial flow condition. Such seven methods included the Stehfest, the de Hoog, the Honig–Hirdes, the Talbot, the Weeks, the Simon and the Zakian methods. We specifically investigated the optimal free parameters of each method, including the number of terms used in the summation and the numerical tolerance. This study revealed that some commonly recommended values of the free parameters in previous studies did not work very well, especially for the advection-dominated problems. Instead, we recommended new values of the free parameters for some methods after testing their robustness. For the radial dispersion, the de Hoog, the Talbot, and the Simon methods worked very well, regardless of the dispersion-dominated or advection-dominated situations. The Weeks method can be used to solve the dispersion-dominated problems, but not the advection-dominated problems. The Stehfest, the Honig–Hirdes, and the Zakian methods were recommended for the dispersion-dominated problems. The Zakian method was efficient, while the de Hoog method was time-consuming under radial flow condition. Under the uniform flow condition, all the methods could present somewhat similar results when the free parameters were given proper values for dispersion-dominated problems; while only the Simon method, the Weeks method, and the de Hoog method worked well for advection-dominated problems.     

Data-based modelling approach for variable density flow and solute transport simulation in a coastal aquifer

Data-based models, namely artificial neural network (ANN), support vector machine (SVM), genetic programming (GP) and extreme learning machine (ELM), were developed to approximate three-dimensional, density-dependent flow and transport processes in a coastal aquifer. A simulation model, SEAWAT, was used to generate data required for the training and testing of the data-based models. Statistical analysis of the simulation results obtained by the four models show that the data-based models could simulate the complex salt water intrusion process successfully. The selected models were also compared based on their computational ability, and the results show that the ELM is the fastest technique, taking just 0.5 s to simulate the dataset; however, the SVM is the most accurate, with a Nash-Sutcliffe efficiency (NSE) ≥ 0.95 and correlation coefficient R ≥ 0.92 for all the wells. The root mean square error (RMSE) for the SVM is also significantly less, ranging from 12.28 to 77.61 mg/L.     

基于PML边界条件的二阶电磁波动方程GPR时域有限元模拟

完全匹配层(PML)作为一种稳定高效的吸收边界条件,广泛应用于基于一阶电磁波动方程的探地雷达(GPR)数值模拟中.为解决基于二阶电磁波动方程的GPR数值模拟的吸收边界问题,本文借鉴二阶弹性波动方程的PML边界条件构建思想,提出了一种适合二阶电磁波动方程GPR时域有限元模拟的PML边界条件.从二阶电磁波动方程出发,基于复拉伸坐标变换,推导了PML算法的频域表达式;通过合理构造辅助微分方程,得到了PML算法的时域表达式,并以变分形式(弱形式)加载到GPR时域有限元方程中,实现了PML边界条件在二阶电磁波动方程GPR时域有限元模拟中的应用.在此基础上,对比了无边界条件、Sarma边界条件和PML边界条件下均匀模型的波场快照、单道波形、时域反射误差和能量衰减曲线,结果表明:PML边界条件的吸收效果要远优于Sarma边界条件,具有近似零反射系数.一个复杂介质模型的正演模拟验证了PML边界条件在非均匀地电结构中电磁波传播模拟的良好吸收效果.     

Data assimilation methods for estimating a heterogeneous conductivity field by assimilating transient solute transport data via ensemble Kalman filter

An ensemble Kalman filter (EnKF) is developed to identify a hydraulic conductivity distribution in a heterogeneous medium by assimilating solute concentration measurements of solute transport in the field with a steady‐state flow. A synthetic case with the mixed Neumann/Dirichlet boundary conditions is designed to investigate the capacity of the data assimilation methods to identify a conductivity distribution. The developed method is demonstrated in 2‐D transient solute transport with two different initial instant solute injection areas. The influences of the observation error and model error on the updated results are considered in this study. The study results indicate that the EnKF method will significantly improve the estimation of the hydraulic conductivity field by assimilating solute concentration measurements. The larger area of the initial distribution and the more observed data obtained, the better the calculation results. When the standard deviation of the observation error varies from 1% to 30% of the solute concentration measurements, the simulated results by the data assimilation method do not change much, which indicates that assimilation results are not very sensitive to the standard deviation of the observation error in this study. When the inflation factor is more than 1.0 to enlarge the model error by increasing the forecast error covariance matrix, the updated results of the hydraulic conductivity by the data assimilation method are not good at all. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical simulation of transport and sequential biodegradation of chlorinated aliphatic hydrocarbons using CHAIN_2D

Microbiological degradation of perchloroethylene (PCE) under anaerobic conditions follows a series of chain reactions, in which, sequentially, trichloroethylene (TCE), cis‐dichloroethylene (c‐DCE), vinylchloride (VC) and ethene are generated. First‐order degradation rate constants, partitioning coefficients and mass exchange rates for PCE, TCE, c‐DCE and VC were compiled from the literature. The parameters were used in a case study of pump‐and‐treat remediation of a PCE‐contaminated site near Tilburg, The Netherlands. Transport, non‐equilibrium sorption and biodegradation chain processes at the site were simulated using the CHAIN_2D code without further calibration. The modelled PCE compared reasonably well with observed PCE concentrations in the pumped water. We also performed a scenario analysis by applying several increased reductive dechlorination rates, reflecting different degradation conditions (e.g. addition of yeast extract and citrate). The scenario analysis predicted considerably higher concentrations of the degradation products as a result of enhanced reductive dechlorination of PCE. The predicted levels of the very toxic compound VC were now an order of magnitude above the maximum permissible concentration levels. Copyright © 1999 John Wiley & Sons, Ltd.     

An adaptive hybrid EnKF-OI scheme for efficient state-parameter estimation of reactive contaminant transport models

Reactive contaminant transport models are used by hydrologists to simulate and study the migration and fate of industrial waste in subsurface aquifers. Accurate transport modeling of such waste requires clear understanding of the system’s parameters, such as sorption and biodegradation. In this study, we present an efficient sequential data assimilation scheme that computes accurate estimates of aquifer contamination and spatially variable sorption coefficients. This assimilation scheme is based on a hybrid formulation of the ensemble Kalman filter (EnKF) and optimal interpolation (OI) in which solute concentration measurements are assimilated via a recursive dual estimation of sorption coefficients and contaminant state variables. This hybrid EnKF-OI scheme is used to mitigate background covariance limitations due to ensemble under-sampling and neglected model errors. Numerical experiments are conducted with a two-dimensional synthetic aquifer in which cobalt-60, a radioactive contaminant, is leached in a saturated heterogeneous clayey sandstone zone. Assimilation experiments are investigated under different settings and sources of model and observational errors. Simulation results demonstrate that the proposed hybrid EnKF-OI scheme successfully recovers both the contaminant and the sorption rate and reduces their uncertainties. Sensitivity analyses also suggest that the adaptive hybrid scheme remains effective with small ensembles, allowing to reduce the ensemble size by up to 80% with respect to the standard EnKF scheme.     

The impact of boundary on the fractional advection–dispersion equation for solute transport in soil: Defining the fractional dispersive flux with the Caputo derivatives

The inherent heterogeneity of geological media often results in anomalous dispersion for solute transport through them, and how to model it has been an interest over the past few decades. One promising approach that has been increasingly used to simulate the anomalous transport in surface and subsurface water is the fractional advection–dispersion equation (FADE), derived as a special case of the more general continuous time random walk or the stochastic continuum model. In FADE, the dispersion is not local and the solutes have appreciable probability to move long distances, and thus reach the boundary faster than predicted by the classical advection–dispersion equation (ADE). How to deal with different boundaries associated with FADE and their consequent impact is an issue that has not been thoroughly explored. In this paper we address this by taking one-dimensional solute movement in soil columns as an example. We show that the commonly used FADE with its fractional derivatives defined by the Riemann–Liouville definition is problematic and could result in unphysical results for solute transport in bounded domains; a modified method with the fractional dispersive flux defined by the Caputo derivatives is presented to overcome this problem. A finite volume approach is given to numerically solve the modified FADE and its associated boundaries. With the numerical model, we analyse the inlet-boundary treatment in displacement experiments in soil columns, and find that, as in ADE, treating the inlet as a prescribed concentration boundary gives rise to mass-balance errors and such errors could be more significant in FADE because of its non-local dispersion. We also discuss a less-documented but important issue in hydrology: how to treat the upstream boundary in analysing the lateral movement of tracer in an aquifer when the tracer is injected as a pulse. It is shown that the use of an infinite domain, as commonly assumed in literature, leads to unphysical backward dispersion, which has a significant impact on data interpretation. To avoid this, the upstream boundary should be flux-prescribed and located at the upstream edge of the injecting point. We apply the model to simulate the movement of Cl⁻ in a tracer experiment conducted in a saturated hillslope, and analyse in details the significance of upstream-boundary treatments in parameter estimation.     

A quasi three-dimensional model for flow and transport in unsaturated and saturated zones: 1. Implementation of the quasi two-dimensional case

A quasi three-dimensional (QUASI 3-D) model is presented for simulating the subsurface water flow and solute transport in the unsaturated and in the saturated zones of soil. The model is based on the assumptions of vertical flow in the unsaturated zone and essentially horizontal groundwater flow. The 1-D Richards equation for the unsaturated zone is coupled at the phreatic surface with the 2-D flow equation for the saturated zone. The latter was obtained by averaging 3-D flow equation in the saturated zone over the aquifer thickness. Unlike the Boussinesq equation for a leaky-phreatic aquifer, the developed model does not contain a storage term with specific yield and a source term for natural replenishment. Instead it includes a water flux term at the phreatic surface through which the Richards equation is linked with the groundwater flow equation. The vertical water flux in the saturated zone is evaluated on the basis of the fluid mass balance equation while the horizontal fluxes, in that equation, are prescribed by Darcy law. A 3-D transport equation is used to simulate the solute migration. A numerical algorithm to solve the problem for the general quasi 3-D case was developed. The developed methodology was exemplified for the quasi 2-D cross-sectional case (QUASI2D). Simulations for three synthetic problems demonstrate good agreement between the results obtained by QUASI2D and two fully 2-D flow and transport codes (SUTRA and 2DSOIL). Yet, simulations with the QUASI2D code were several times faster than those by the SUTRA and the 2DSOIL codes.     

探地雷达检测公路结构层隐含裂缝实用方法研究

本文在简要介绍探地雷达基本原理的基础上,详细介绍了作者最近完成的“多层均匀层状介质中的垂直裂缝对雷达波场响应的数值模拟和物理模拟实验研究”成果,通过与实际的公路工程检测结果对比,三者表现出很好的一致性. 研究结果表明,采用探地雷达检测公路结构层中的隐含裂缝,理论条件是充分的,实践上是可行的,检测方法本身实用性较大,检测结果直观、可靠.     

利用热-孔隙流体耦合有限元数值模拟研究干热岩开发温度下降过程——以青海共和盆地恰卜恰地区干热岩开发为例

水力压裂是干热岩(HDR)开发最常用到的压裂方式, 水力压裂形成的裂缝网络为增强地热系统的运行(EGS)提供了高渗透率的人工储层.本文在系统总结前人关于共和盆地水力压裂实验、数值模拟资料和现场水力压裂监测结果的基础上, 引入了离散裂缝网络(DFN), 利用多物理场模拟软件COMSOL Multiphysics建立了共和盆地恰卜恰地区干热岩开采过程中的二维裂缝-基质热-孔隙流体耦合模型, 并讨论了裂缝开度和基质渗透率对干热岩开采温度下降过程的影响.结果表明, 裂缝网络是流体运移的主要通道.温度下降和早期压力变化范围沿着裂缝延伸, 并向周围被裂缝分割的基质扩展.裂缝开度和基质渗透率是影响干热岩地热开采过程中温度下降的重要因素.当裂缝开度越大时, 流体运移范围就越大, 储层温度和产出水温下降就越快, 储层下降范围就越广, 热突破时间和运行寿命就越短.当基质渗透率越大时, 越有利于流体进入基质进行热量交换, 越容易从干热岩中提取热量, 产出水温下降越快, 运行寿命越短.

     

Using the extended finite element method for simulation of transient well leakage in multilayer aquifers

The extended finite element (XFEM) is applied to the problem of transient leakage from abandoned or free-flowing artesian wells in perforated aquifer-aquitard systems. To more accurately capture the singularities in potentiometric head at the wells, the standard linear finite element basis is locally augmented with asymptotic analytical solutions which enable more accurate calculations of leakage rates between aquifers. Highly accurate flux estimates are obtained without the need for higher mesh resolution near wells. Simulations are carried out to test both the accuracy and convergence properties of the XFEM implementation, and the XFEM results are compared to those of a high-resolution standard finite element model. It is seen that for the type of singularity-driven problem posed here, the standard FEM is unable to resolve leakage rates without very fine discretization, but that the XFEM performs robustly with fewer degrees of freedom. The impact of aquifer geometric heterogeneity on leakage rates is assessed and seen to be an important factor in determining total leakage. It is demonstrated that the XFEM may be a valuable tool in many water resources applications where small-scale effects can impact global system behavior.     

碳酸盐岩洞穴型储层双侧向测井数值模拟和响应特征(英文)

洞穴型碳酸盐岩地层具有显著的非均质性和测井预测难度大的特点,如何利用双侧向测井对识洞穴进行准确识别与定量评价,是当前的一个研究难点与热点。利用数值模拟方法计算电测井响应,可为洞穴识别与评价提供理论依据。本文根据双侧向测井原理,采用有限元素法,研究了球状洞穴模型的测井响应特征,并考察了不同尺寸的洞穴对电测井响应的影响;然后,系统研究了不同充填程度的洞穴模型的测井响应,得出了电阻率与充填程度之间的关系;最后,研究了洞穴中充填泥质、灰质、砾岩和砂泥岩薄互层等多种充填物的测井响应特征。研究结果对碳酸盐岩洞穴型储层的识别与评价具有较高的应用价值和研究意义。     

三维各向异性裂缝介质正演模拟的三种交错网格适应性比较及Lebedev方法的改进

研究了三维各向异性裂缝介质的正演模拟的三种不同有限差分法,即标准交错网格（SSG）、旋转交错网格（RSG）和Lebedev方法（LS）,详细对比分析这三种交错网格方法在模拟复杂各向异性介质的优势与局限.提出一种新的改进方法,简化了LS有限差分法在任意各向异性介质中的正演模拟.为了模拟三维大规模复杂各向异性介质的地震响应,提出一个优化的正演模拟计算流程：将模型参数分为模型介质参数和模型构造参数.该计算流程适用于三种有限差分法中的任何一种.使用LS方法实现任意三维各向异性裂缝介质地震响应的三维全波场模拟,通过使用三种不同的有限差分模拟方法进行二维和三维模型数值模拟试验,验证了所提出方法有效.

     

含环状天线槽正交方位随钻电磁波测井仪器三维有限体积法数值模拟

针对由多环状天线槽构成的方位随钻电磁波测井仪器真实结构,基于柱坐标系下耦合势Helmholtz方程和三维有限体积法研究建立一套相应的三维电磁响应数值模拟算法.首先,采用柱坐标系下三维不规则Yee氏交错网格对计算区域进行剖分,保证了钻铤表面附近的剖分网格与非光滑刻槽钻铤表面同形;并利用电场延拓边界条件逼近钻铤表面的理想电...     

Perfectly matched layer boundary conditions for the second-order acoustic wave equation solved by the rapid expansion method

We derive a governing second-order acoustic wave equation in the time domain with a perfectly matched layer absorbing boundary condition for general inhomogeneous media. Besides, a new scheme to solve the perfectly matched layer equation for absorbing reflections from the model boundaries based on the rapid expansion method is proposed. The suggested scheme can be easily applied to a wide class of wave equations and numerical methods for seismic modelling. The absorbing boundary condition method is formulated based on the split perfectly matched layer method and we employ the rapid expansion method to solve the derived new perfectly matched layer equation. The use of the rapid expansion method allows us to extrapolate wavefields with a time step larger than the ones commonly used by traditional finite-difference schemes in a stable way and free of dispersion noise. Furthermore, in order to demonstrate the efficiency and applicability of the proposed perfectly matched layer scheme, numerical modelling examples are also presented. The numerical results obtained with the put forward perfectly matched layer scheme are compared with results from traditional attenuation absorbing boundary conditions and enlarged models as well. The analysis of the numerical results indicates that the proposed perfectly matched layer scheme is significantly effective and more efficient in absorbing spurious reflections from the model boundaries.     

Outburst susceptibility assessment of moraine‐dammed lakes in Western Himalaya using an analytic hierarchy process

Glacier retreat results in the formation and expansion, and sometimes outburst, of moraine‐dammed lakes worldwide. Sudden outburst floods from such lakes have caused enormous damage to settlements and infrastructure located downstream. Such lakes located in the Himalayan region are highly prone to outburst floods due to climatic conditions and geotectonic settings. In this study, multi‐temporal Landsat images from 2002–2014, digital elevation models (DEMs), geomorphic analysis and modelling were used to assess the changes in glacial lakes and the outburst susceptibility of moraine‐dammed lakes in the Chandra–Bhaga basin of the north‐western Indian Himalaya. An inventory of lakes was developed using satellite data, thematic maps and ground‐based investigations for the Chandra–Bhaga basin. The total area of all glacial lakes (size >5000 m²) increased by 47% from 2002 to 2014, with a pronounced increase of 57% for moraine‐dammed lakes. Sixteen moraine‐dammed lakes were identified and assessed for outburst susceptibility using the analytic hierarchy process (AHP). Forty‐one reported glacial lake outburst flood (GLOF) events from moraine‐dammed lakes in Himalayan regions were analysed, culminating in the identification of 11 critical factors for assessing outburst susceptibility using the AHP, including those related to the lake area and change, surrounding terrain characteristics, dam geometry, regional seismicity and rainfall history. The past three GLOF events in the Himalayan region were used to validate the method and to classify moraine‐dammed lakes as having very high, high, medium or low outburst susceptibility. Eight lakes classified as very high and high outburst susceptibility should be further investigated in detail. The proposed AHP‐based approach is suitable for first‐order identification of critical lakes for prioritising future detailed investigation and monitoring of moraine‐dammed glacial lakes in the Himalayan region. Copyright © 2017 John Wiley & Sons, Ltd.     

我国深地资源电磁探测新技术研究进展

诸多研究表明我国深部资源潜力巨大,但目前的开发开采深度普遍停留在500 m以浅,开展"攻深探盲"是构建国家资源安全体系的有效途径.应用最先进的科学技术手段,提取深部地质信息,已成为我国当前地球物理科学研究的发展方向.作为地球物理学的重要分支,电磁法是矿产资源探查的主体手段之一.在分析我国现阶段航空、地面及海洋电磁探测技术进展的基础上,本文重点说明了极低频电磁法（简称WEM法）,多通道瞬变电磁法（简称MTEM）和电性源短偏移瞬变电磁法（简称SOTEM）等电磁探测新技术.WEM法建立一套包括岩石层、大气层和电离层在内的全空间电磁传播理论,通过新研制的观测系统,获取地下10 km的地电信息;MTEM方法是地下埋深4 km目标体精细勘查的有效手段;SOTEM实现地下1.5 km深度范围内目标体的精细探测.通过多种电磁探测技术组合,可实现地下10 km深度范围内多尺度探测,达到"望远镜+放大镜+显微镜"探测效果.同时,本文指出进一步研发与新方法配套的装备、资料处理技术和大数据人工智能识别等将是我国电磁法未来的发展方向.