A new solution for a partially penetrating constant‐rate pumping well with a finite‐thickness skin

A mathematical model describing the constant pumping is developed for a partially penetrating well in a heterogeneous aquifer system. The Laplace‐domain solution for the model is derived by applying the Laplace transforms with respect to time and the finite Fourier cosine transforms with respect to vertical co‐ordinates. This solution is used to produce the curves of dimensionless drawdown versus dimensionless time to investigate the influences of the patch zone and well partial penetration on the drawdown distributions. The results show that the dimensionless drawdown depends on the hydraulic properties of the patch and formation zones. The effect of a partially penetrating well on the drawdown with a negative patch zone is larger than that with a positive patch zone. For a single‐zone aquifer case, neglecting the effect of a well radius will give significant error in estimating dimensionless drawdown, especially when dimensionless distance is small. The dimensionless drawdown curves for cases with and without considering the well radius approach the Hantush equation (Advances in Hydroscience. Academic Press: New York, 1964) at large time and/or large distance away from a test well. Copyright © 2007 John Wiley & Sons, Ltd.     

基于现场双管试验确定弱透水层水力参数的方法

弱透水层水力参数对基础工程设计、建设和地下水资源评价、地下水污染预测具有重要意义。现提出一种现场确定含水层系统中弱透水层水力参数的钻孔双管试验方法。利用麻花钻钻孔,到达地下水位线以下揭露到目的层位后布设外管,以起到护壁防止土层塌孔的作用。在外管内通过锤击的方式将内管嵌入到目的层中,使其下部管中有一定厚度的土样作为现场固定试验土柱。待内外管中地下水位稳定后迅速加高内管水头,并通过马里奥特瓶装置保持定水头。建立钻孔双管试验土柱的数学模型,推导了土柱顶底面单位面积流量随时间变化的解析解,将其无量纲化后作出标准曲线。作为该方法应用的实例,在长江下游三角洲苏锡常冲积平原的常州天宁区德安医院附近的空旷场地进行了专门的钻孔试验。确定了该地区的细砂质粉土和粉质黏土的渗透系数和贮水率分别为：K=1.66×10?6 m/s,?s =8.21×10?3 m?1;K=6.06×10?7 m/s,?s =2.26×10?3 m?1。结果表明,该方法对于现场确定弱透水层的水力参数有较好的适用性。     

Hydraulic conductivity distribution in crystalline rocks, derived from inflows to tunnels and galleries in the Central Alps, Switzerland

Inflow data from 23 tunnels and galleries, 136 km in length and located in the Aar and Gotthard massifs of the Swiss Alps, have been analyzed with the objective (1) to understand the 3-dimensional spatial distribution of groundwater flow in crystalline basement rocks, (2) to assess the dependency of tunnel inflow rate on depth, tectonic overprint, and lithology, and (3) to derive the distribution of fracture transmissivity and effective hydraulic conductivity at the 100-m scale. Brittle tectonic overprint is shown to be the principal parameter regulating inflow rate and dominates over depth and lithology. The highest early time inflow rate is 1,300 l/s and has been reported from a shallow hydropower gallery intersecting a 200-m wide cataclastic fault zone. The derived lognormal transmissivity distribution is based on 1,361 tunnel intervals with a length of 100 m. Such interval transmissivities range between 10^?9 and 10^?1 m²/s within the first 200–400 m of depth and between 10^?9 and 10^?4 m²/s in the depth interval of 400–1,500 m below ground surface. Outside brittle fault zones, a trend of decreasing transmissivity/hydraulic conductivity with increasing depth is observed for some schistous and gneissic geological units, whereas no trend is identified for the granitic units.     

Compartmented flow at the Bátaapáti site in Hungary

Integration of hydrogeological and geological data into a conceptual model is critical for site investigation programs, since this model is the basis for hydrogeological modeling and for engineering. In the Hungarian Radioactive Waste Disposal Investigation Program, several methods have been used to characterize the potential host rock (granite) at the Bátaapáti site for a repository for low and intermediate level radioactive waste. Hydrogeological data acquisition revealed some characteristic aspects of the site. One of the most important is the presence of extensive rock deformation zones (faults) with low hydraulic conductivity, which strongly reduce the direct hydraulic communication between adjacent blocks of rock (compartmentalization). This characteristic of the rock mass results in a mosaic-like distribution of rock compartments, each with an almost constant hydraulic head. Within the compartments, hydraulic tests have shown that transmissivity is strongly scale dependent: the larger the scale, the higher the measured transmissivity. The extensive highly transmissive zones cause very low hydraulic gradients within each block, thus the transport processes are strongly influenced by the low or average transmissivity zones and the rock matrix.     

The 2D Steady Hydraulic Head Field Surrounding a Pumping Well in a Finite Heterogeneous Confined Aquifer

We present a second-order analytic solution [in terms of a heterogeneous log-transmissivity Y(r) = ln T(r)] for the hydraulic head field in a finite 2D confined heterogeneous aquifer under steady radial flow conditions assuming fixed head boundary conditions at the well and at a circular exterior boundary. The solution may be used to obtain the gradient used in calculation of solute transport to a well in a heterogeneous transmissivity field. The solution, obtained using perturbation methods coupled with Green's function techniques, leads us to postulate a more general form of the head for arbitrarily large-variance fields and may be used to obtain moment relations between the log-transmissivity and head under convergent flow conditions when Y(r) is expressed as a random space function. We present expressions for the mean head field when the log-transmissivity is Gaussian and conditioned on the transmissivity value at the well for an arbitrary ln T covariance. Finally, we look at the effect of parameter variations on the mean head behavior and present numerical simulations verifying the second-order mean head expressions.     

Hydrogeological studies on the Nubian sandstone aquifer in El-Bahariya Oasis, Western Desert, Egypt

The current study aimed to evaluate hydrogeologically the Nubian sandstone aquifer in El-Bahariya Oasis. It represents the main water-bearing horizon in the study area and consists of continental elastic sediments, mainly sandstone alternating with shale and clays. The general flow lines are directed from SW to NE direction, as detected from the constructed potentiometric head contour map. The piezometric surface reaches 149 m in El-Heiz area at the southern part, while it reaches 90 m at the northern, reflecting higher pressure head of the aquifer in the southern part. The map also illustrates that the southern part is considered as the most promising location for development. The structural elements play an important role in the deposition and distribution of the sedimentary succession of the Nubian sandstone sediments. Consequently, this sedimentary pattern affects the occurrences and movements of the groundwater within the aquifer system. Along the structurally high areas, in the study area, the piezometric head increases, while the reverse is recorded along the structurally low areas. The step-drawdown tests data were carried out by calculating the aquifer loss coefficient (B) and the well loss constant (C). The B values are smaller compared with C values, indicating that the aquifer under pressure has a behavior of leaky aquifer; therefore, it shows hydraulic connection with surrounding formation. The values of well efficiency range from 78.50% to 87.76%. Analysis of 12 pumping test data (constant discharge tests) was carried out in order to calculate the Nubian aquifer hydraulic parameters (transmissivity, hydraulic conductivity, and storage coefficient). The transmissivity values decrease from 3,045 m²/day in the southern part (El-Heiz area) to 236 m²/day in the northeastern part (El-Harra area). Accordingly, the aquifer classified as a high to moderate potentiality. Transmissivity contour map observes gradual increase of transmissivity values from the southern to northeastern direction. This may be due to the increase of shale or clay content in the concerned aquifer in that direction. The storage coefficient values range between 1.04 × 10^?4 and 5.22 × 10^?3, as obtained from the results of pumping test analysis, which ensure that the Nubian sandstone aquifer is classified as semi-confined to confined aquifer type. The S values show a decrease from southwest to northeast direction as detected from S-map. The hydraulic conductivity values vary from to 0.46 m/day in the northern part to 10.88 m/day in the southern part with an average of 5.67 m/day. According to the classification based on K values, the aquifer is mainly composed of coarse sand.     

振荡试验确定倾斜承压含水层水文地质参数

为评价振荡试验在获取倾斜承压含水层水文地质参数过程中含水层倾角对计算结果的影响,基于Kipp模型推导了考虑承压含水层倾角的振荡试验解析解模型。倾斜承压含水层量纲一贮水系数和量纲一导水系数不变条件下,测试井-含水层系统的量纲一阻尼系数随着倾角的增加而增加。修正模型计算的量纲一阻尼系数与Kipp模型计算的量纲一阻尼系数偏差10%以上时,必须考虑倾角的影响并且承压含水层倾角对水头响应曲线造成影响临界角度约为34°。修正模型和Kipp模型对现场振荡试验水头响应曲线分析结果的差异表明,忽略含水层倾角会对倾斜承压含水层导水系数和贮水系数的计算结果产生较大误差。     

含水岩组概化的累积导水系数法

地下水流系统理论和数值模拟技术分别是水文地质学的基本理论和技术方法,含水岩组的概化是地下水流系统分析和地下水数值模拟的重要基础,直接影响着数值模拟和水流系统分析的精度和可信度.为提高含水岩组概化的精度和可信度,提出一种含水岩组概化的新方法,即累积导水系数法.依据岩层厚度与渗透系数乘积累积值随深度的变化,以及水文地质剖面岩性分布的整体特征,概化含水介质结构.以玛纳斯河流域为例,应用该方法概化流域内的岩性剖面,结合GMS软件中TINS模块构建水文地质结构模型.结果表明,应用该方法概化后的含水层结构具有较好的合理性和仿真性,建立的三维模型很好地显示了研究区含水介质的空间展布特征,为建立地下水流模型奠定了良好的基础.      

A practical approach for the interpretation of flowing well tests

Flowing well test is one of the tools employed to identify transmissivity and storage coefficient of a confined aquifer where the potentiometric surface is located above the ground surface, so that the groundwater flows naturally from the well without pumping. During a flowing well test, constant hydraulic head is preserved at the well while the discharge from the well decreases with time and the temporal variation of discharge provides significant information about aquifer characteristics. In this study, a simple and straightforward approach is presented as an alternative to a number of graphical or error minimization-based techniques available in the literature for analyzing data from flowing well tests. The proposed method employs a polynomial regression equation to establish a link between observed discharge and the theoretical dimensionless discharge that is introduced in the analytical solution, so as to retrieve the aquifer parameters. The method is tested with a vast number of synthetically generated data sets as well as a real data set reported in the literature. Besides its simplicity, the present method is seen to produce highly accurate and reliable estimations.     

Analytical solution for transient groundwater flow during slug test in vertical cutoff walls

An analysis method for transient groundwater flow during slug tests performed in vertical cutoff walls is presented. The analytical solution for evaluating hydraulic conductivity of vertical cutoff walls is derived by applying the method of images to the previously developed analytical solution that is exclusively applicable to an infinite aquifer. Two distinct boundary conditions are considered to account for the configuration of the vertical cutoff wall: the wall‐soil formation interfaces with or without the existence of filter cakes, that is, constant‐head boundary and no‐flux boundary conditions. A series of type curves is constructed from the analytical solution and compared with those of a partially penetrated well within an aquifer. The constant‐head boundary condition provides faster hydraulic head recovery than the aquifer case. On the other hand, the no‐flux boundary condition leads to a delayed hydraulic head recovery. The greater the shape factor and well offset from the center of the cutoff wall, and the smaller the width of the cutoff wall, the greater the effect of the boundary condition observed in the type curves. This result shows the significance of considering proper boundary conditions at the vertical cutoff wall in analyzing slug tests. Copyright © 2014 John Wiley & Sons, Ltd.     

Regional evaluation of hydraulic properties in variably fractured rock using a hydrostructural domain approach

A hydrostructural domain approach was tested and validated in fractured bedrock aquifers of the Gulf Islands, British Columbia (BC), Canada. Relative potential hydraulic properties for three hydrostructural domains in folded and faulted sedimentary rocks were derived using stochastically generated fracture data and hybrid discrete fracture network-equivalent porous media (DFN-EPM) modelling. Model-derived relative potential transmissivity values show good spatial agreement with transmissivity values obtained from pumping tests at selected sites. A spatial pattern of increasing transmissivity towards the southeast along the island chain is consistent between both datasets. Cluster analysis on relative potential permeability values obtained from a larger dataset for the region identified four clusters with geometric means of 9?×?10^?13, 4?×?10^?13, 2?×?10^–13, and 3?×?10^–14 m². The general trend is an increase in relative potential permeability toward the southeast, emulating the trends identified in the site-specific analyses. Relative potential permeability values increase with proximity to the hinge line of a regional northwest-trending asymmetric fault propagation fold structure, and with proximity to superimposed high-angle north- and northeast-trending brittle faults. The results are consistent with documented patterns of structurally controlled fluid flow and show promise for use in regional characterization of fractured bedrock aquifers.     

Heat extraction from aquifer geothermal systems

This study aims to model temperature distributions in an aquifer thermal extraction (ATE) system that contains a single extraction well in a thin confined aquifer. The aquifer is bounded by hot dry rocks with different thermomechanical properties and thicknesses. Based on the heat convection–conduction equation, a mathematical model is developed to describe the spatial and temporal temperature distributions of the ATE systems. The mechanisms of heat transfer in the model involve horizontal convection and thermal conduction in the aquifer, and vertical thermal conduction in both rocks. A semi‐analytical solution in dimensionless form is developed using the Laplace transform technique and its corresponding time‐domain result is computed by the modified Crump method. In addition, the steady‐state solution is obtained by applying the final value theorem. The simulation results from the semi‐analytical solution indicate that the aquifer temperature distributions are affected by aquifer thickness, the thermomechanical properties of the aquifer and rocks, geothermal gradient, outer boundary temperatures of the rocks, extraction rate, and operating time. The present solution can be used as a preliminary tool for assessing heat extraction efficiency in ATE systems. Copyright © 2010 John Wiley & Sons, Ltd.     

Erratum: Properties of a pair of fracture networks produced by triaxial deformation experiments: insights on fluid flow using discrete fracture network models

Results of a series of deformation experiments conducted on gabbro samples and numerical models for computation of flow are presented. Rocks were subjected to triaxial tests (σ1 > σ2 = σ3) under σ3 = 150 MPa confining pressure at room temperature, to generate fracture network patterns. These patterns were either produced by keeping a constant confining pressure and loading the sample up to failure (conventional test: CT), or by building up a high differential stress and suddenly releasing the confining pressure (confining pressure release test: CPR). The networks are similar in overall density but differ primarily in the orientation of smaller fractures. In the case of CT tests, a conjugate fracture set is observed with one dominant fracture zone running at about 20° from σ1. CPR tests do not show such a conjugate pattern and the mean fracture orientation is at around 35° from σ1. Discrete fracture network (DFN) methodology was used to determine the distribution of flow and hydraulic head for both fracture sets under simple boundary conditions and uniform transmissivity values. The fracture network generated by CT and CPR tests exhibit different patterns of flow field and hydraulic head configurations, but convey approximately the same amount of flow at all scales for which DFN models were simulated. The numerical modelling results help to develop understanding of qualitative differences in flow distribution that may arise in rocks of the same mineralogical composition and mechanical properties, but under the influence of different stress conditions, albeit at similar overall stress magnitude.

     

露头处具有淤泥层的滨海含水层系统中海潮引起的水头波动

滨海地区社会与经济的发展引发了各种各样的水文地质问题, 因此对滨海地区的水文地质条件, 尤其是地下水与海水之间的水力联系的研究尤为重要.本文考察了海底露头处具有淤泥层的滨海含水层系统中由海潮引起的水头波动.该系统由潜水含水层、承压含水层和介于其间的弱透水层构成.建立了该系统的数学模型, 得到了该模型的解析解.该解析解包含2个无量纲参数: 弱透水层的相对越流系数和淤泥层的相对透水系数.解析解表明, 淤泥层使各处的水头波幅被缩小了一个常数倍(波幅缩减因子), 并使各处的波动相位产生了一个不超过45°的正位移常数(时滞).该时滞对半日潮不超过1.5h, 对全日潮不超过3h.波幅缩减因子和正位移常数只与弱透水层的相对越流系数和淤泥层的相对透水系数有关.当这两个无量纲参数取某些特殊值时, 本次研究的解和前人考虑的几种较简单情形所对应的解一致.承压含水层中水头波幅随着淤泥层的相对透水系数的递增而严格递增, 随弱透水层的相对越流系数的递增而严格递减; 波动相位随着这2个无量纲参数的递增均严格递减.分析表明弱透水层的越流和淤泥层的存在均对承压含水层水头波动有显著影响.      

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.     

Interpolation of Horizontal Transmissivity Anisotropy from Head and Flowpath Observations

Rocks are rarely equally permeable in all directions. Ground water does not flow directly downgradient through anisotropic aquifers, but deviates at an angle determined by the direction and magnitude of the major and minor transmissivities. We show a mathematical model whereby the orientation and ratio of major to minor transmissivities can be estimated by an analysis of the deviation of ground-water flow from the hydraulic gradient. The solution is derived from the construction of transmissivity ellipse where the hydraulic gradient and flow direction are known. An example is given using an ethylene dibromide contaminant plume at Nemo, South Dakota, where the plume has been deflected because of bedrock foliation.     

基于水力层析法的某煤矿承压含水层叠加放水试验分析

水文地质参数是衡量含水层富水性的重要指标,其空间分布特征的准确推算,对于矿井突水灾害预报与防治具有积极意义。传统放水试验分析方法得到的是等效水文地质参数,不能准确刻画含水层的空间异质性。基于随时间变化的水头数据与水文地质参数的互相关分析,将水力层析法应用在陕西榆林柠条塔煤矿井下承压含水层叠加放水试验数据分析中,获得了研究区水文地质参数的空间分布特征。结果表明,工作面南北富水性差异大,涌水区位于强导水带上;从涌水区往北,导水系数和储水系数整体上逐渐减小;南部导水系数和储水系数均较大,属于富水异常区。研究表明,水力层析法是一种有效的非均质含水层参数识别的新技术,将井下放水视为针对含水层的刺激源,结合水头与水文地质参数的互相关分析,联合多个观测孔的水头响应数据,反演刻画研究区域的主要地质结构特征。在矿井水文地质条件分析中,预先采用水力层析法识别富水异常区域,可以有效降低突水事故风险。     

A generalized solution for groundwater head fluctuation in a tidal leaky aquifer system

A new analytical solution is developed for describing groundwater level fluctuations in a coupled leaky confined aquifer system which consists of an unconfined aquifer, confined aquifer, and an aquitard in between. The aquifer system has a tidal boundary at the seashore, a no flow boundary at remote inland side, and a confined aquifer extending under the sea and terminated with an outlet-capping. This new solution has shown to be a generalisation of most existing analytical solutions for a tidal aquifer system which includes single confined and leaky confined aquifers. In addition, the solution is used to explore the influences of the dimensionless leakance of the outlet-capping, the dimensionless hydraulic diffusivities, and the leakages of the inland and offshore aquitards on the head responses in the leaky confined aquifer.     

A cost-effective device and methodology to compute aquifer transmissivity and piezometry from free-flowing artesian wells

Artesian aquifers offer interesting opportunities for water supply by providing a low-vulnerability groundwater resource that is easily abstracted without any installation of pumps or power supply costs. However, hydraulic tests are challenging to perform, notably where the piezometric head is above ground level with free-flowing wells not equipped with valves and open for years. This paper describes a low-cost, easy to reproduce and adaptable device, the free-flowing artesian well device (FFAWD), which is mainly designed with a set of PVC tubes equipped with a pressure probe and a valve. This device is used to perform hydraulic tests on free-flowing artesian wells, to measure the piezometric head of the aquifer and to compute its transmissivity. The practical use of the FFAWD is described and a method is proposed to compute the piezometric head and the transmissivity of the aquifer from this data set (free-flowing well discharge and pressure increase measurements) with any adapted analytical solution, using the Houpeurt-Pouchan method. Artefacts such as post-production effects, surge effects, and the impact of a leaky well are identified to avoid any misinterpretation. The FFAWD was applied to the volcano-sedimentary artesian plain of Pasuruan (Indonesia). The advantages and limitations of using the device, along with the interpretation methodology, are also discussed.

     

Steady infiltration from buried point source into heterogeneous cross‐anisotropic unsaturated soil

The paper presents the analytical solution for the steady‐state infiltration from a buried point source into two types of heterogeneous cross‐anisotropic unsaturated half‐spaces. In the first case, the heterogeneity of the soil is modelled by an exponential relationship between the hydraulic conductivity and the soil depth. In the second case, the heterogeneous soil is represented by a multilayered half‐space where each layer is homogeneous. The hydraulic conductivity varies exponentially with moisture potential and this leads to the linearization of the Richards equation governing unsaturated flow. The analytical solution is obtained by using the Hankel integral transform. For the multilayered case, the combination of a special forward and backward transfer matrix techniques makes the numerical evaluation of the solution very accurate and efficient. The correctness of both formulations is validated by comparison with alternative solutions for two different cases. The results from typical cases are presented to illustrate the influence on the flow field of the cross‐anisotropic hydraulic conductivity, the soil heterogeneity and the depth of the source. Copyright © 2004 John Wiley & Sons, Ltd.