Probability of plume interception using conditional simulation of hydraulic head and inverse modeling

A procedure to estimate the probability of intercepting a contaminant groundwater plume for monitoring network design has been developed and demonstrated. The objective of the procedure is to use all available information in a method that accounts for the heterogeneity of the aquifer and the paucity of data. The major components of the procedure are geostatistical conditional simulation and parameter estimation that are used sequentially to generate flow paths from a suspected contaminant source location to a designated monitoring transect. From the flow paths, a histogram is constructed that represents the spatial probability distribution of plume centerlines. With an independent estimate of the plume width, a relationship between the total cost and the probability of detecting a plume can be made. The method uses geostatistical information from hydraulic head measurements and is conditioned by the data and the physics of groundwater flow. This procedure was developed specifically for the design of monitoring systems at sites where very few, if any, hydraulic conductivity data are available.     

A Simple Approach to Account for Radial Flow and Boundary Conditions When Kriging Hydraulic Head Fields for Confined Aquifers

The estimation and mapping of realistic hydraulic head fields, hence of flow paths, is a major goal of many hydrogeological studies. The most widely used method to obtain reliable head fields is the inverse approach. This approach relies on the numerical approximation of the flow equation and requires specifying boundary conditions and the transmissivity of each grid element. Boundary conditions are often unknown or poorly known, yet they impose a strong signature on the head fields obtained by inverse analysis. A simpler alternative to the inverse approach is the direct kriging of the head field using the measurements obtained at observation wells. The kriging must be modified to incorporate the available information. Use of the dual kriging formalism enables simultaneously estimating the head field, the aquifer mean transmissivity, and the regional hydraulic gradient from head data in steady or transient state conditions. In transient state conditions, an estimate of the storage coefficient can be obtained. We test the approach on simple analytical cases, on synthetic cases with solutions obtained numerically using a finite element flow simulator, and on a real aquifer. For homogeneous aquifers, infinite or bounded, the kriging estimate retrieves the exact solution of the head field, the exact hydrogeological parameters and the flow net. With heterogeneous aquifers, kriging accurately estimates the head field with prediction errors of the same magnitude as typical head measurement errors. The transmissivities are also accurately estimated by kriging. Moreover, if inversion is required, the kriged head along boundaries can be used as realistic boundary conditions for flow simulation.     

初始裂隙对岩溶水紊流形成的影响

岩溶地区地下发育着大量的溶洞和地下河管道,地下水流状态既有层流也有紊流,而紊流是溶洞管道形成的重要条件。紊流的形成受到岩石初始裂隙的影响,初始裂隙的张开度、分布、走向、迹长、密度等因素都影响着裂隙发育过程中水流状态的变化。通过对不同统计特征的初始裂隙网络进行水流和溶蚀的数值模拟发现,以张开度标准差反映的裂隙网络非均匀性越强,模拟紊流出现的时间就越早;主要裂隙的存在使裂隙网络的非均性增强,主要裂隙与水力梯度总方向的角度越小,紊流出现的时间就越早;当裂隙平均迹长过小时会导致裂隙连通性较差,影响裂隙水流和溶蚀作用;裂隙密度,尤其是主要裂隙密度,对岩溶发育的影响较大。相对于次要裂隙,如果主要裂隙密度偏小,紊流形成时间会大大增加,甚至很难形成紊流。当初始裂隙张开度小于0.001 cm,增大水力梯度仍没有紊流发生,岩溶几乎不发育。      

潜水回水初始阶段的定性半定量分析及对水跃成因的解释

文章提出并采用水力坡度分析方法,对潜水回水初始阶段进行了定性-半定量分析,为了解潜水回水过程提供了新的视角。通过分析潜水回水初始时刻的水力坡度,河渠侧的界面被分为2段:河间潜水位之上的铅直段和之下的水平段。水平段上点的水力坡度最大且相等,方向为水平向右;铅直段上点的水力坡度方向趋于铅直向下,越向上水力坡度越小。经过微小时间段Δt后,水力坡度均相应变小,铅直段相邻点间地下水运动发生冲突,水力坡度方向由趋于铅直向下向右偏转。将水力坡度分析方法用于分析潜水井流的过程和特征,水跃的成因可解释为:在相同水力坡度和过水断面面积下,井内大空间水流速度远大于孔隙中的潜水流速度,井内水位急速下降,从而形成水跃;水跃越大,进入井内的流量就越大。     

均质非饱和土一维稳态流水头垂直分布的解析解

渗流场水头分布计算是进行渗流量和渗流水力坡降计算的基础,准确、有效地求取渗流场水头分布是渗流计算的关键环节。对均质非饱和土体一维稳态流的流动方程进行分析,考虑到渗透系数是与基质吸力相关的函数,通过数学变换,给出了稳定渗流场的解析通式,并基于渗透性函数中的Gardner模型,给出了非饱和土一维稳态流水头垂直分布的解析解。该解析通式表明,均质非饱和土一维稳态流水头垂直分布主要受地表水头、深度和流动率3个因素控制。分别计算了一维稳态蒸发条件下粉土和黏土两种典型土类水头沿垂直方向的分布。计算结果表明：稳态蒸发条件下粉土层和黏土层内的水头分布表现出相似的变化规律,即自地表至地下水位处随着土层深度的增加,水头分布呈现出加速递减的趋势;在相同的蒸发条件下,对于相同深度处的黏土和粉土而言,黏土层内水头更高些;对同一种土类而言,在较大的蒸发状态下同一深度处土层内水头更高。反之,则较低。     

A simple solution for drainage through a 2-dimensional hydraulic fill stope

Inadequate drainage has been attributed as the major cause of failure of several hydraulic fill stopes that have claimed lives. Therefore it is necessary to be able to predict the pore water pressure developments and flow rates throughout the filling operation. There are computer programmes that can simulate the hydraulic filling of a mine stope and enable computations of the pore water pressures, flow rates and hydraulic gradients at any time. This paper presents a simple analytical solution for estimating the maximum pore water pressure within the stope, flow rate and the hydraulic gradients at the entry and exit. The proposed solutions are verified against solutions derived from FLAC, a finite difference software, and the agreement is found to be excellent. A simple equation for the hydraulic gradient at the top of the stope, as a function of the height of water within the fill, is also presented.     

离散裂隙渗流方法与裂隙化渗透介质建模

流体渗流模拟的连续介质方法通常适用于多孔地质体，并不一定适用于裂隙岩体，由于裂隙分布及其特征与孔隙差异较大。若流体渗流主要受裂隙的控制，对于一定尺寸的裂隙岩体，多孔介质假设则较难刻划裂隙岩体的渗流特征。离散裂隙渗流方法不但可直接用于模拟裂隙岩体非均质性和各向异性等渗流特征，而且可用其确定所研究的裂隙岩体典型单元体及其水力传导（渗透）张量大小。主要讨论了以下问题：（1）饱和裂隙介质中一般的离散流体渗流模拟；（2）裂隙岩体中的REV（典型单元体）及其水力传导（渗透）张量的确定；（3）利用离散裂隙网络流体渗流模型研究裂隙方向几何参数对水力传导系数和REV的影响；（4）在二维和三维离散裂隙流体渗流模型中对区域大裂隙和局部小裂隙的处理方法。调查结果显示离散裂隙流体渗流数学模型可用来评价不同尺度上的裂隙岩体的水力特征，以及裂隙方向对裂隙化岩体的水力特征有着不可忽视的影响。同时，局部小裂隙、区域大裂隙应当区别对待，以便据其所起的作用及水力特征，建立裂隙化岩体相应的流体渗流模型。     

Influence of geologic layering on heat transport and storage in an aquifer thermal energy storage system

A modeling study was carried out to evaluate the influence of aquifer heterogeneity, as represented by geologic layering, on heat transport and storage in an aquifer thermal energy storage (ATES) system in Agassiz, British Columbia, Canada. Two 3D heat transport models were developed and calibrated using the flow and heat transport code FEFLOW including: a “non-layered” model domain with homogeneous hydraulic and thermal properties; and, a “layered” model domain with variable hydraulic and thermal properties assigned to discrete geological units to represent aquifer heterogeneity. The base model (non-layered) shows limited sensitivity for the ranges of all thermal and hydraulic properties expected at the site; the model is most sensitive to vertical anisotropy and hydraulic gradient. Simulated and observed temperatures within the wells reflect a combination of screen placement and layering, with inconsistencies largely explained by the lateral continuity of high permeability layers represented in the model. Simulation of heat injection, storage and recovery show preferential transport along high permeability layers, resulting in longitudinal plume distortion, and overall higher short-term storage efficiencies.     

渗透系数的空间变异性对污染物运移的影响研究

随机水文地质学方法,较传统的确定性方法而言,是解决非均质含水层中水流和溶质运移问题的一种更为合理的手段。据以往研究,假设渗透系数场遵循对数正态分布,利用直接傅立叶变换方法来生成渗透系数随机场。应用基于随机理论的蒙特卡罗方法,来研究渗透系数的空间变异性对污染物运移结果的影响。实例研究表明,污染物在含水层中运移过程中污染羽的展布范围(二阶矩)随着渗透系数空间变异方差的增大而扩大,而污染羽在空间上的质心位置(一阶矩)基本不受方差的影响,仅取决于渗透系数随机场的均值大小。另外还分析了污染羽在各点的浓度变化方差和变异系数分别随渗透系数变异方差的变化状况。     

等效水力隙宽和水力梯度对岩体裂隙网络非线性渗流特性的影响

等效水力隙宽和水力梯度是影响岩体裂隙网络渗流特性的重要因素。制作裂隙网络试验模型,建立高精度渗流试验系统;求解纳维-斯托克斯方程,模拟流体在裂隙网络内的流动状态,研究等效水力隙宽和水力梯度对非线性渗流特性的影响。结果表明,当水力梯度较小时,等效渗透系数保持恒定的常数,流体流动属于达西流动区域,流量与压力具有线性关系,可采用立方定律计算流体流动;当水力梯度较大时,等效渗透系数随着水力梯度的增加而急剧减少,流体流动进入强惯性效应流动区域,流量与压力具有强烈的非线性关系,可采用Forchheimer方程计算流体流动。随着等效水力隙宽的增加,区别线性和非线性流动区域的临界水力梯度呈幂函数关系递减。当水力梯度小于临界水力梯度时,控制方程可选立方定律;当水力梯度大于临界水力梯度时,控制方程可选Forchheimer方程,其参数A和B可根据经验公式计算得到。其研究结果可为临界水力梯度的确定及流体流动控制方程的选取提供借鉴意义。     

土体渗透稳定性判定准则

土体的渗透稳定性是指在渗流条件下宽级配土体内粗颗粒阻止细颗粒流失的能力,土体的渗透稳定性受几何条件、水力条件和物理条件的影响。从几何条件出发,通过对收集的167种土的室内渗透侵蚀试验结果的分析,基于对土体渗透稳定性控制变量地研究,将土分成良好级配土和间断级配土两大类;基于细粒（小于0.063 mm）含量的不同,将每类土又细分为3类,针对不同细类土提出了不同的渗透稳定性几何判定准则。从水力条件出发,研究了应力状态对土体渗透侵蚀起动及破坏水力梯度的影响。试验结果表明,起动水力梯度和破坏水力梯度都随着围压的增大而增大,是由于增大围压使得颗粒间的摩擦力增大的结果。     

河床地形影响潜流交换作用的数值分析

选取对潜流交换具有重要影响的河床地形作为主要研究内容,采用数值模拟(MODFLOW程序)的方法研究在河床横剖面地形不均匀的条件下,潜流交换量的空间分布以及地下水流场的演变机制。结果表明:在河床地形起伏不均的情况下,潜流交换量更易发生在河道的深水区域;地下水流向受河床地形影响较小;近河床界面处的地下水流速受地形起伏影响剧烈,深水区域的地下水流速远大于浅水区地下水流速;通过与现场试验结果对比分析,得出河床地形起伏是引起潜流带渗透系数非均质现象的重要原因之一。     

基于离散裂隙网络模型的裂隙水渗流计算

离散裂隙网络模型(Discrete Fracture Network（DFN）)是研究裂隙水渗流最为有效的手段之一。文章根据裂隙几何参数和水力参数的统计分布,利用Monte Carlo随机模拟技术生成二维裂隙网络,基于图论无向图的邻接矩阵判断裂隙网络的连通,利用递归算法提取出裂隙网络的主干网或优势流路径。基于立方定律和渗流连续性方程,利用数值解析法建立了二维裂隙网络渗流模型,分析不同边界条件下裂隙网络中的流体流动。结果表明,该方法可以模拟区域宏观水力梯度和边界条件下,裂隙网络水力梯度方向总的流量,以及节点的水位、节点间的流量和流动方向的变化特征,为区域岩溶裂隙水渗流计算提供了一种实用、可行的方法。      

双层结构堤基渗透变形发展过程的数值模拟

通过算例采用分时段稳定流理论模拟了基于临界水力坡降的流砂动态发展过程,建立了双层结构堤基发生流土的完整井流砂和半球形井底流砂物理模型。堤基发生渗透变形而形成的集中渗漏通道,将自涌砂口沿垂直堤轴方向发展,并在平面上自涌砂口到河床不断扩大,在深度上不断加深。通道的规模取决于涌砂口的流量大小和水位高低,尤其在较低水位时通道规模将最大。减压井在降低了井附近水头的同时也加大了水力坡降,从而更易发展渗透变形,因此应特别重视减压井的反滤层设计和施工,以使土体保持在原位而不致发生渗透变形。     

Stability of sandy slopes under seepage conditions

Stability against shallow mass sliding in saturated sandy slopes under seepage depends on the flow direction and hydraulic gradient, particularly near the ground surface. Two modes of instability i.e., Coulomb sliding and liquefaction have been studied and the critical flow directions discussed. The utility of the numerical approach in solving complex flow problems with irregular boundaries and surface topography is demonstrated by means of two slope examples with different internal drainage conditions. The numerical results for the seepage gradients at different points are compared with those predicted by the simple expression derived in this study, and the corresponding effects on the stability are evaluated.     

Impact of liquid waste disposal on potable groundwater resources near Perth,Western Australia

 Drilling of 15 boreholes at a disused liquid waste disposal site near Perth, Western Australia, has indicated that a contamination plume extends about 1000 m in a southerly direction from the site in the direction of groundwater flow. The plume is up to 600 m wide and 5–40 m thick. Chemical and microbiological analyses have indicated that contaminated groundwater contains high concentrations of ammonia, iron, and bacteria at levels that commonly exceed national drinking water guidelines. It is likely that a proposed water supply production well in the path of the contamination plume will have to be abandoned, and additional wells may have to be abandoned if the plume continues to extend in the direction of groundwater flow. There is currently insufficient information to indicate whether the plume is continuing to expand, but studies on similar plumes in the Perth metropolitan area have indicated that contaminated groundwater can move at rates up to 100 m yr^–1. Several other liquid waste disposal sites are now located in residential areas of Perth where wells are used for garden irrigation. Further work is required to ensure that there is no potential impact of groundwater contamination on public health in these areas. Received: 31 July 1995 · Accepted: 18 September 1995     

高水力梯度条件下颗粒堆积型多孔介质渗流规律试验研究

煤矿开采面临的水文地质条件越来越复杂,尤其是遭遇承压含水层的水压力越来越大,突水灾害发生时必然会带来高水力梯度引起的破碎岩体突水通道内高速非线性渗流问题。据此,研制高水力梯度（最大600）条件下堆积型多孔介质中高速非线性渗流试验装置,采用堆积型钢球模拟破碎岩体,对粒径为1、2、3、4、5、6 mm共6种光滑钢球分别开展了一维均质圆柱渗流试验。试验结果表明：对于由1～6 mm钢球堆积而成的孔隙率为0.44～0.45的多孔介质,当水力梯度大于145时,通过分析水力梯度-平均流速（J-v）曲线和水力梯度-雷诺数（J-Re）关系曲线,将流动状态划分为3个模式：线性层流、非线性层流、紊流,并获得了从线性层流过渡到非线性层流的临界流速为0.23～0.78 cm/s、临界水力梯度为3～8;从层流到紊流转捩的临界流速为1.6～4.8 cm/s、临界水力梯度为90～145。从小粒径多孔介质到大粒径多孔介质的渗流过程中,临界流速越来越大,而临界水力梯度逐渐减小。 渗透率与粒径的平方、非达西流影响系数与粒径的倒数均呈线性正相关,非达西流影响系数随着渗透率的增加呈指数减小。该研究对多孔介质非线性渗流的理论研究以及实际工程中高承压含水层突涌水问题有重要借鉴意义。     

多个相关随机参数的空间变异性对溶质运移的影响

根据给定渗透系数、孔隙度以及吸附系数的概率分布,采用顺序高斯模拟生成相关的多参数随机场的实现,作为地下水流和溶质运移模型的输入参数,对污染物浓度进行随机分析。研究结果表明,与仅考虑渗透系数空间变异性相比,考虑相关的多参数空间变异性导致污染羽的扩散程度有显著不同。当孔隙度与渗透系数呈正相关关系时,会减少污染羽的扩散程度,反之,当孔隙度与渗透系数为负相关关系时,会加剧污染羽的扩散程度。吸附系数也是如此。在考虑吸附系数的空间变异性之后,污染羽的分布表现出拖尾现象。同时考虑渗透系数、孔隙度以及吸附系数空间变异性时,孔隙度非均质性对溶质运移的影响较吸附系数非均质性的影响更大。     

Application of mass-balance and flow simulation calculations to interpretation of mixing at Äspö, Sweden

The hydrogeology of a vertical fracture zone at 70 m depth at the access tunnel to the Äspö Hard Rock Laboratory was monitored over 3 a for hydrochemical changes that could be effected by construction of a deep repository for high-level nuclear waste. Tunnel construction dramatically disturbed the hydrogeological system, but this provided an opportunity to integrate hydrogeochemical and hydrological evaluation of the zone. The objective of this study was to evaluate hydrogeochemical evolution, groundwater flow and surface water intrusion during the experiment using an integrated approach of geochemical mass-balance calculations and numerical flow simulations.The dilution of major ions was the dominant hydrochemical trend. However, HCO₃ and SO₄ showed significant enrichment. Increasing activity of ¹⁴C suggested that oxidation of organic C was the likely source of HCO₃. Any mineral source dissolving during the experiment seemed insufficient to account for changes in SO₄ and current intrusion of sea water was excluded according to the data. Cation exchange as well as minor calcite reactions in fractures were assumed probable in such temporary chemical conditions. Conservative two end-member mixing models with shallow groundwater in the zone and initial groundwater at tunnel level also assumed remarkable mass transfer (several mmol/l). Therefore a third SO₄-rich end-member, a regional shallow groundwater type which may mix by lateral flow in the system, was tested. This was also expected from hydraulic measurements and preliminary flow simulations assuming homogeneity.Three end-member mixing calculations using Cl and SO₄ as conservative tracers give a constant proportion of lateral water in all boreholes after 300 days, which is consistent with the steady state character of the flow field in the late part of the experiment. To predict reactions on plausible levels needs significant adjustments of initial and final waters, indicating uncertainties in the hydrochemical information of the fracture zone. In the flow simulations the transmissivities were selected so that the chemical mixing proportions would match simulated portions of flow as closely as possible. The simulated total recoveries (drawdowns) differ from the measurements mainly due to overly simple parametrisation of the transmissivity in the fracture zone. However, integrating hydrochemistry in flow modelling is considered encouraging in producing additional information of the heterogeneity of a flow structure.     

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。