Stochastic analysis of the effect of spatial variability of diffusion parameters on radionuclide transport in a low permeability clay layer

Most studies that incorporate subsurface heterogeneity in groundwater flow and transport models only analyze and simulate the spatial variability of hydraulic conductivity. Heterogeneity of the other flow and transport parameters are usually neglected. This approach is often justified, but there are, however, cases in which disregarding the heterogeneity of the other flow and transport parameters can be questionable. In low permeability media, for instance, diffusion is often the dominant transport mechanism. It therefore seems logical to incorporate the spatial variability of the diffusion parameters in the transport model. This study therefore analyses and simulates the spatial variability of the effective diffusion coefficient and the diffusion accessible porosity with geostatistical techniques and incorporates their heterogeneity in the transport model of a low permeability formation. The formation studied was Boom clay (Belgium), a candidate host rock for the deep geological disposal of high-level radioactive waste. The calculated output radionuclide fluxes of this model are compared with the fluxes calculated with a homogeneous model and a model with a heterogeneous hydraulic conductivity distribution. This analysis shows that the heterogeneity of the diffusion parameters has a much larger effect on the calculated output radionuclide fluxes than the heterogeneity of hydraulic conductivity in the low permeability medium under study.     

基于流网单元的污染物优势运移数值模型

垃圾填埋场滤出液、入侵海水、核废物及生产生活废水等污染物随地下水的迁移威胁人类生存。地下水渗流的随机性导致溶质运移问题更加复杂。根据流网特点,利用流线与水头等势线对求解域进行离散,基于质量守恒原理建立流网单元内溶质浓度求解的隐式有限体积差分格式。基于多孔介质孔隙流速分布规律,利用蒙特卡洛法建立流管单元随机流速场进行溶质运移过程的数值模拟,最后根据数值模拟和模型试验的结果对比,验证了数值模拟方法的准确性。基于流网单元的数值模型中沿流线方向的物质交换由对流和扩散共同作用,而流管间的物质交换只有扩散作用,因此,可在不使用弥散系数下进行污染物运移的模拟。引入随机方法确定流管内流速为研究非均匀流场中染污物的优势迁移提供了新的思路。     

非均质介质中地下水流动与溶质运移模拟——问题与挑战

对大空间尺度和长时间跨度的地下水流动及污染物质运移进行预测的需求, 使水文地质研究面临异乎寻常的挑战.这些需求来自于对核废料地质储放方法的安全性评价、地下水污染状况评价及其治理方案的选择.流动系统的非均质性是地下水流动及物质运移模拟中最主要的困难之一, 这种困难来自对非均质系统进行特征描述(通过原位观测实现)、概念化及模拟.评述了非均质介质中流动运移模拟的一些重要问题与挑战, 讨论了解决的途径.讨论的主题包括: 动力流动的沟道化, 示踪剂穿透曲线, 裂隙岩石中流体流动的多尺度, 观测的不同尺度, 模拟、预测与非均质性以及系统特征描述和预测性模拟的分析.      

含水层非均质性不同刻画方法对地下水流和溶质运移预测的影响

为探讨含水层非均质性不同刻画方法对地下水流和溶质运移预测的影响,基于非均质含水层砂箱实验,分别用传统等效均质模型、克立金插值和水力层析刻画含水层渗透系数场,并探讨了先验信息对水力层析结果的影响.将不同方法估算的渗透系数场用以预测地下水流和溶质运移过程,以此判断不同方法估算结果的优劣,分析含水层非均质性对地下水流和溶质运移的影响.结果表明:与克立金插值法相比,水力层析法可以更好地刻画含水层非均质性,较准确地预测地下水流和溶质运移过程;钻孔岩心渗透系数样本值作为先验信息可以提高水力层析法估算结果的精度;传统等效均质模型无法准确预测地下水流和溶质运移过程.含水层非均质性的增强将导致溶质污染羽分布形态和运移路径的空间变异性增强,并且优势通道直接决定溶质的分布及运移路径.      

Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium)

Sedimentological processes often result in complex three-dimensional subsurface heterogeneity of hydrogeological parameter values. Variogram-based stochastic approaches are often not able to describe heterogeneity in such complex geological environments. This work shows how multiple-point geostatistics can be applied in a realistic hydrogeological application to determine the impact of complex geological heterogeneity on groundwater flow and transport. The approach is applied to a real aquifer in Belgium that exhibits a complex sedimentary heterogeneity and anisotropy. A training image is constructed based on geological and hydrogeological field data. Multiple-point statistics are borrowed from this training image to simulate hydrofacies occurrence, while intrafacies permeability variability is simulated using conventional variogram-based geostatistical methods. The simulated hydraulic conductivity realizations are used as input to a groundwater flow and transport model to investigate the effect of small-scale sedimentary heterogeneity on contaminant plume migration. Results show that small-scale sedimentary heterogeneity has a significant effect on contaminant transport in the studied aquifer. The uncertainty on the spatial facies distribution and intrafacies hydraulic conductivity distribution results in a significant uncertainty on the calculated concentration distribution. Comparison with standard variogram-based techniques shows that multiple-point geostatistics allow better reproduction of irregularly shaped low-permeability clay drapes that influence solute transport.     

Using Multiple-Point Geostatistics for Tracer Test Modeling in a Clay-Drape Environment with Spatially Variable Conductivity and Sorption Coefficient

This study investigates the effect of fine-scale clay drapes on tracer transport. A tracer test was performed in a sandbar deposit consisting of cross-bedded sandy units intercalated with many fine-scale clay drapes. The heterogeneous spatial distribution of the clay drapes causes a spatially variable hydraulic conductivity and sorption coefficient. A fluorescent tracer (sodium naphthionate) was injected in two injection wells and ground water was sampled and analyzed from five pumping wells. To determine (1) whether the fine-scale clay drapes have a significant effect on the measured concentrations and (2) whether application of multiple-point geostatistics can improve interpretation of tracer tests in media with complex geological heterogeneity, this tracer test is analyzed with a local three-dimensional ground-water flow and transport model in which fine-scale sedimentary heterogeneity is modeled using multiple-point geostatistics. To reduce memory needs and calculation time for the multiple-point geostatistical simulation step, this study uses the technique of direct multiple-point geostatistical simulation of edge properties. Instead of simulating pixel values, model cell edge properties indicating the presence of irregularly shaped surfaces are simulated using multiple-point geostatistical simulations. Results of a sensitivity analysis show under which conditions clay drapes have a significant effect on the concentration distribution. Calibration of the model against measured concentrations from the tracer tests reduces the uncertainty on the clay-drape parameters. The calibrated model shows which features of the breakthrough curves can be attributed to the geological heterogeneity of the aquifer and which features are caused by other processes.     

孔隙尺度多孔介质流体流动与溶质运移高性能模拟

深入探究孔隙尺度下的流体流动特性和溶质运移规律对石油开采、农田养分管理、地下水污染修复有着重要意义。以人工构建的多孔介质结构和同步辐射X射线显微CT扫描的土壤团聚体(分辨率3.7μm)为研究对象,在空间节点数多达64 000 000的情况下,基于格子Boltzmann模型和GPU并行技术计算得到多孔介质流体运动和溶质运移过程的关键参数,并据此探究多孔介质空间异质性对水力学特性的影响。通过对3组不同结构的多孔介质比较发现,结构复杂程度最高的土壤样品和不规则堆叠的圆球结构的渗透率在100 mD(即10^-13m^2)量级,远低于规则堆叠的圆球结构(>20 000 mD);土壤的迂曲度为1.40~1.60,明显高于规则堆叠的圆球结构。研究结果表明,渗透率大的样品具有较小的迂曲度,这与结构的空间异质性有较强的关系;土壤的渗透率和迂曲度呈现各向异性;在水力梯度一定的前提下,渗透率较大的样品,纵向弥散系数也较大;同时,结构的异质性也会影响溶质的穿透曲线。本研究提出的模拟方法可在土壤结构中进行高效的水流运动和溶质运移模拟,可用于土壤多孔介质在孔隙尺度下的水力学特性研究。     

Numerical modeling of contaminant transport in a stratified heterogeneous aquifer with dipping anisotropy

The combined influence of dip angle and adsorption heterogeneity on solute transport mechanisms in heterogeneous media can be understood by performing simulations of steady-state flow and transient transport in a heterogeneous aquifer with dipping anisotropy. Reactive and non-reactive contaminant transport in various types of heterogeneous aquifer is studied by simulations. The hydraulic conductivity (K) of the heterogeneous aquifer is generated by HYDRO_GEN with a Gaussian correlation spectrum. By considering the heterogeneity of the adsorption distribution coefficient (K _d), a perfect negative correlation between lnK and lnK _d is obtained by using the spherical grains model. The generated K and K _d are used as input to groundwater flow and transport models to investigate the effects of dipping sedimentary heterogeneity on contaminant plume evolution. Simulation results showed that the magnitude of the dip angle strongly controls the plume evolution in the studied anisotropic and heterogeneous aquifer. The retarded average pore-water velocity (v/R) of the adsorption model significantly controls the horizontal spreading of the plume. The bottom plume is intensively retarded in the zones between the dipping lenses of lower hydraulic conductivity and the no-flow bottom boundary. The implications of these findings are very important for the management of contaminated heterogeneous aquifers.     

Simulation of nitrate transport and wastewater seepage in groundwater flow system

Groundwater quantity and quality modeling is one approach for optimal use of available water resources in arid and semiarid regions. This study was conducted to simulate flow treatment and nitrate transport on Shahrekord aquifer using three-dimensional solute transport model and geographical information system. Hydraulic conductivity, specific yield and recharge values in flow simulation process and effect molecular diffusion coefficient, longitudinal dispersivity and distribution coefficient in quality model were calibrated. 120 water samples during July 2007 to June 2008 were collected monthly from 10 wells and measurements of nitrate were carried out. The results show that the developed model is successfully used to simulate flow path and nitrate transport in saturated porous media. The highest values of nitrate occur along Bahram–Abad village and the surroundings. The groundwater quality in the area represents a complex system, which is affected by different factors of pollution, such as urban wastewater and leaching of agricultural lands.     

北京市朝阳区沙子营垃圾污染物在潜水含水层中迁移规律的现场模拟实验

选择北京平原区水文地质、环境地质等方面都比较典型的沙子营垃圾堆放场,建立了其水文地质模型。在充分收集资料、分析得出部分计算所需参数后,采用现场弥散实验、勘查取样测试等方法,求得了该含水层的弥散系数等参数;用二维非稳定流溶质运移方程对污染物在此含水层中的迁移扩散规律、速度和污染范围等进行了模拟计算;采用现场钻探、取样测试分析等方法,评价了该含水层的实际污染状况。实验模拟计算和现场调查结果表明:污染物在潜水含水层中的运移规律遵循二维非稳定流场中的溶质运移方程,污染物在潜水含水层中的运移速度约为86.25m/a,迁移扩散主要发生在地下水流向上,侧向扩散宽度极小,是地下水流向上的1/17。     

孔隙尺度多孔介质流体流动与溶质运移高性能模拟

深入探究孔隙尺度下的流体流动特性和溶质运移规律对石油开采、农田养分管理、地下水污染修复有着重要意义。以人工构建的多孔介质结构和同步辐射X射线显微CT扫描的土壤团聚体（分辨率3.7 μm）为研究对象，在空间节点数多达64 000 000的情况下，基于格子Boltzmann模型和GPU并行技术计算得到多孔介质流体运动和溶质运移过程的关键参数，并据此探究多孔介质空间异质性对水力学特性的影响。通过对3组不同结构的多孔介质比较发现，结构复杂程度最高的土壤样品和不规则堆叠的圆球结构的渗透率在100 mD（即10^-13m²）量级，远低于规则堆叠的圆球结构（>20 000 mD）；土壤的迂曲度为1.40~1.60，明显高于规则堆叠的圆球结构。研究结果表明，渗透率大的样品具有较小的迂曲度，这与结构的空间异质性有较强的关系；土壤的渗透率和迂曲度呈现各向异性；在水力梯度一定的前提下，渗透率较大的样品，纵向弥散系数也较大；同时，结构的异质性也会影响溶质的穿透曲线。本研究提出的模拟方法可在土壤结构中进行高效的水流运动和溶质运移模拟，可用于土壤多孔介质在孔隙尺度下的水力学特性研究。     

含水层层状非均质对地下水流系统的影响

区域尺度上含水层非均质具有复杂的结构性和随机性,难以准确刻画,造成非均质对区域地下水流系统的影响机制研究不够深入。本文以鄂尔多斯盆地白垩系地下水流系统为研究实例,选择典型剖面,采用剖面二维随机数值模拟方法,通过对比不同非均质刻画方法下地下水流场的变化,探讨含水层层状非均质对地下水流系统的影响机制。结果显示,均质条件下模型各向异性（含水层水平和垂向渗透系数比值Kh/Kv）取值为1000时,地下水流场与实际条件较为接近;非均质条件下,渗透系数方差取值0.91,水平相关长度取值5000 m,Kh/Kv取值150时,接近实际条件。研究表明,在大尺度地下水流模拟研究中,采用水平相关长度、渗透系数方差和各向异性值三个变量生成的随机场能很好地刻画含水层的层状非均质特征及其对水流系统的影响控制作用。由于含水层不同尺度层状非均质的叠加效应,采用均质各向异性介质等效概化含水层层状非均质性会造成等效各向异性值偏大失真的效应。     

Influence of temporal fluctuations and spatial heterogeneity on pollution transport in porous media

The combined influence of temporal fluctuations and spatial heterogeneity on non-reactive solute transport mechanisms in porous media can be understood by performing simulations of steady and unsteady flow and transport in heterogeneous media. The study focuses on issues such as the degree of heterogeneity, correlation length, separation of the combined effects of temporal and spatial variations, and ergodicity conditions under unsteady flow conditions. It is shown that the effect of temporal variations on solute transport is masked by the strong effect of spatial heterogeneity. There is no obvious difference in plume shape between steady and unsteady flow conditions; the first and the second spatial moments of the plume of the unsteady-state flow condition fluctuate around the steady-state flow condition with the same period of oscillations as the input signal at small storage coefficient (S????0.001). At a relatively high standard deviation in hydraulic conductivity and a small storage coefficient, the unsteady flow condition sharpens the temporal variations in macrodispersion coefficients. The magnitude of the longitudinal macrodispersion coefficient under unsteady flow condition is almost doubled at the maximum values. However, the transverse macrodispersion coefficient fluctuates around zero. The Kubo number and Peclet number ranges are 1.2?C64 and 10?C250, respectively.     

纵向弥散作用与渗透介质非均质性定量关系的模拟研究

在地下水污染模拟预报中,弥散参数是很难确定的一个模型参数。因实验室小尺度弥散规律一般不能用于大尺度弥散过程,而野外示踪试验却耗资大、周期长,限制了其实用性。文中利用随机数值模拟手段、基于随机理论的蒙特卡罗方法及序贯高斯模拟技术来生成渗透系数随机场,并研究渗透系数对数场的方差、相关长度以及变异函数类型在不同尺度上对纵向弥散度的影响,进而建立纵向弥散度与随机分布渗透系数场的方差和相关长度的统计定量关系,并与Gelhar理论计算结果进行比较。数值模拟结果表明,经过一定迁移距离后纵向弥散度与随机分布渗透系数对数场的方差和相关长度具有良好的线性统计关系,与Gelhar理论公式表达的关系类型类似。但对于较大的方差,纵向弥散度模拟结果明显大于Gelhar理论计算值,而对于较大相关长度在迁移距离不很大时,纵向弥散度模拟结果明显小于Gelhar理论计算值。本研究可为野外大尺度地下水污染预报模型中水动力弥散参数的确定提供方法借鉴。     

Sensitivity Analysis of a Combined Groundwater Flow and Solute Transport Model Using Local-Grid Refinement: A Case Study

Combining groundwater flow models with solute transport models represents a common challenge in groundwater resources assessments and contaminant transport modeling. Groundwater flow models are usually constructed at somewhat larger scales (involving a coarser discretization) to include natural boundary conditions. They are commonly calibrated using observed groundwater levels and flows (if available). The groundwater solute transport models may be constructed at a smaller scale with finer discretization than the flow models in order to accurately delineate the solute source and the modeled target, to capture any heterogeneity that may affect contaminant migration, and to minimize numerical dispersion while still maintaining a reasonable computing time. The solution that is explored here is based on defining a finer grid subdomain within a larger coarser domain. The local-grid refinement (LGR) implemented in the Modular 3D finite-difference ground-water flow model (MODFLOW) code has such a provision to simulate groundwater flow in two nested grids: a higher-resolution sub-grid within a coarse grid. Under the premise that the interface between both models was well defined, a comprehensive sensitivity and uncertainty analysis was performed whereby the effect of a parameter perturbation in a coarser-grid model on transport predictions using a higher-resolution grid was quantified. This approach was tested for a groundwater flow and solute transport analysis in support of a safety evaluation of the future Belgian near-surface radioactive waste disposal facility. Our reference coarse-grid groundwater flow model was coupled with a smaller fine sub-grid model in two different ways. While the reference flow model was calibrated using observed groundwater levels at a scale commensurate with that of the coarse-grid model, the fine sub-grid model was used to run a solute transport simulation quantifying concentrations in a hypothetical well nearby the disposal facility. When LGR coupling was compared to a one-way coupling, LGR was found to provide a smoother flow solution resulting in a more CPU-efficient transport solution. Parameter sensitivities performed with the groundwater flow model resulted in sensitivities at the head observation locations. These sensitivities identified the recharge as the most sensitive parameter, with the hydraulic conductivity of the upper aquifer as the second most sensitive parameter in regard to calculated groundwater heads. Based on one-percent sensitivity maps, the spatial distribution of the observations with the highest sensitivities is slightly different for the upper aquifer hydraulic conductivity than for recharge. Sensitivity analyses were further performed to assess the prediction scaled sensitivities for hypothetical contaminant concentrations using the combined groundwater flow and solute transport models. Including all pertinent parameters into the sensitivity analysis identified the hydraulic conductivity of the upper aquifer as the most sensitive parameter with regard to the prediction of contaminant concentrations.     

考虑矿层渗透系数非均质性和不确定性的砂岩型铀矿地浸采铀过程随机模拟与分析

砂岩型铀矿矿层渗透系数普遍具有空间非均匀性,但受试验和分析手段制约,非均匀渗透系数难以准确刻画,导致地浸采铀过程预测出现偏差,限制了地浸采铀过程精细化管控。针对该问题提出一种矿层非均匀参数分布随机表征方法,在此基础上,开展水盐耦合数值随机模拟,揭示不同渗透系数空间分布条件下,群井抽注所引起的溶浸剂储层内部迁移过程和影响范围。在内蒙古某铀矿床应用结果显示：沿区域地下水流方向渗透系数增加,有利于注入溶浸剂疏散;相反,溶浸剂易出现聚集效应。利用水位监测数据对模型边界条件进行识别与验证后,在均质假设条件下溶浸剂扩散速率为210 m2/d,20 a开采周期波及范围为1.53 km2;考虑矿层非均质性和参数不确定性,预测溶浸剂扩散速率为191～228 m2/d,波及范围为1.47～1.74 km2。相比于均质假设,溶浸剂扩散速率和波及范围不确定性显著,分别为17.62%和17.65%。考虑渗透系数非均质性和不确定性,使得溶浸剂迁移转化行为预测结果更具代表性,可为合理制定地浸采铀方案提供更加可靠的依据。     

Non-Darcian flow in low-permeability media: key issues related to geological disposal of high-level nuclear waste in shale formations

In clay or other low-permeability media, water flow becomes non-Darcian and characterized by the non-linear relationship between water flux and hydraulic gradient. This work is devoted to addressing a number of key issues related to geological disposal of high-level nuclear waste in clay/shale formations. It is demonstrated that water flow velocity in the damaged zone (often considered as a potential preferential advection paths in a repository) surrounding the tunnel is extremely small, as a result of non-Darcian flow behavior, such that solute transport is dominated by diffusion, rather than advection. The finding is also consistent with the often-observed existence of persistent abnormal pressures in shale formations. While relative permeability is the key parameter for modeling the unsaturated flow process, without incorporating non-Darcian flow behavior, significant errors can occur in the determination of relative permeability values from traditional measurement methods. An approach for dealing with temperature impact on non-Darcian flow and a formulation to calculate non-Darcian water flux in an anisotropic medium are presented, taking into consideration that a geological repository is subject to temperature evolution in the near field as a result of heat generated by nuclear waste, and that shale formations are generally anisotropic.     

Probabilistic analysis of groundwater and radionuclide transport model from near surface disposal facilities

As per the regulatory requirements controlling the disposal of radioactive waste, the performance of waste disposal facilities needs to be assessed quantitatively using predictive models. This estimates the potential impact of disposal on the environment and public health. Near Surface Disposal Facilities (NSDFs), constructed to contain the low level radioactive waste are considered to model the radionuclide migration from the system to the geo-sphere. The radiation dose experienced by an individual through drinking water pathway is the endpoint of assessment of the model. A three dimensional groundwater contaminant transport model with a decaying source is modelled numerically to determine the radiation dose for short-lived and long-lived radionuclides. The consideration of uncertainties constitutes an intrinsic part of modelling. The uncertain input parameters include porosity, longitudinal dispersivity, transverse dispersivity, diffusion coefficient and distribution coefficient. The uncertainty propagation and quantification is carried out using collocation based stochastic response surface method (CSRSM). To run the simulations for the huge set of input, a code is developed using built-in python interface in the numerical model. The results are processed further to obtain the sensitive parameters affecting the output concentrations. Further, the probability of radiation dose exceeding permissible value is estimated by subset simulation.     

Flow and transport through clay membrane barriers

Flux equations for liquid and solute migration through clay barriers that behave as semi-permeable membranes used in waste containment and remediation applications, known as clay membrane barriers (CMBs), are discussed. The results of a simplified analysis of flow through a geosynthetic clay liner (GCL) using measured values for the chemico-osmotic efficiency coefficient (ω) of the GCL indicate a total liquid flux that counters the outward Darcy (hydraulic) flux due to chemico-osmosis associated with clay membrane behavior of the GCL. Also, the solute (contaminant) flux through the GCL is reduced relative to the solute flux that would occur in the absence of membrane behavior due to chemico-osmotic counter advection and solute restriction. Since diffusion commonly controls solute transport through GCLs and other low-permeability clay barriers, the implicit (empirical) correlation between ω and the effective salt-diffusion coefficient of the migrating contaminant is an important consideration with respect to contaminant restriction in CMBs.