Tide-induced head fluctuations in a coastal aquifer: effects of the elastic storage and leakage of the submarine outlet-capping

This paper considers the tidal head fluctuations in a single coastal confined aquifer which extends under the sea for a certain distance. Its submarine outlet is covered by a silt-layer with properties dissimilar to the aquifer. Recently, Li et al. (2007) gave an analytical solution for such a system which neglected the effect of the elastic storage (specific storage) of the outlet-capping. This article presents an analytical solution which generalizes their work by incorporating the elastic storage of the outlet-capping. It is found that if the outlet-capping is thick enough in the horizontal direction, its elastic storage has a significant enhancing effect on the tidal head fluctuation. Ignoring this elastic storage will lead to significant errors in predicting the relationship of the head fluctuation and the aquifer hydrogeological properties. Quantitative analysis shows the effect of the elastic storage of the outlet-capping on the groundwater head fluctuation. Quantitative conditions are given under which the effect of this elastic storage on the aquifer’s tide-induced head fluctuation is negligible. Li, H.L., Li, G.Y., Chen, J.M., Boufadel, M.C. (2007) Tide-induced head fluctuations in a confined aquifer with sediment covering its outlet at the sea floor. [Fluctuations du niveau piézométrique induites par la marée dans un aquifère captif à décharge sous-marine.] Water Resour. Res 43, doi:10.1029/2005WR004724     

海底泉对在海底有限延伸的越流含水层系统中地下水潮汐效应的增强作用

海底泉在滨海地下水排泄过程中起着重要的作用。本文给出了含有一个海底泉的在海底延伸的越流承压含水层系统中地下水水头在海潮作用下波动的近似解析解。该含水层顶底板隔水且向海底延伸有限距离。假设含水层的海底露头被一层隔水层覆盖,海底泉由一个渗透性很好的完全穿透海底含水层硕板的圆柱体渗漏天窗（海底泉孔）来表示。近似解析解中包含了6个参数：承压含水层的海潮传播参数,海底泉孔中心到海岸线的距离,表示泉的圆柱体的等效半径,海底泉孔中心到含水层海底露头处的距离,承压含水层的海潮载荷效率和弱透水层的越流。分析表明,如果海底泉孔中心到海岸线的距离远大于泉孔的等效半径,且海底泉孔中心到含水层海底露头处的距离远大于泉孔的等效半径时,解析解的近似误差可以忽略。然后本文讨论了解析解的两个基本性质,分析了海底泉对海底地下水水头波动的影响。     

滨海多层含水层系统中海潮引起的地下水位波动

通过对一个滨海多层含水层系统的考察,该含水层系统由上、下弱透水层和介于中间的承压含水层组成,海底露头处被淤泥层覆盖.建立了描述该系统中地下水水头随潮汐波动的数学模型,并得到其解析解.该解析解与六个基本参数有关,分别是承压含水层的海潮传播参数,淤泥层的无量纲透水系数,上下弱透层与承压含水层贮水率的比率 (无量纲)和上下弱透层的无量纲越流.当这些参数取某些特殊值时,我们的解便化简为前人考虑的几种简单情形对应的解.分析表明,承压含水层中地下水水头波幅是上、下弱透水层贮水率和越流系数的减函数,是淤泥层相对透水系数的增函数;波动相位(时滞)是上、下弱透水层贮水率和越流系数的增函数,是淤泥层相对透水系数的减函数.     

利用岸边水头动态确定含水层在临海方向上的边界

本文建立了潮汐效率与越流共同作用条件下承压水头动态的数学模型.利用复变函数的基本原理,考虑到地下水流动的连续性,推导出了相应的承压水头动态公式.以此动态公式为基础,提出了直接利用承压水头的潮汐动态来确定延伸到海底的含水层长度(边界条件)的计算方法.最后结合广西北海市的地下水头长观资料,对上述方法进行了应用和分析研究.     

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.      

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。     

考虑淤泥层弹性储水的滨海承压含水层中海潮引起的地下水头波动

综合考虑了海底淤泥层的弹性储水系数、海潮荷载效应和渗透性,对海底露头处具有淤泥层的滨海承压含水层系统中海潮引起的水头波动进行分析,给出了相应的数学模型,并推导出其解析解,讨论了淤泥层弹性储水对于水头波动的影响.分析表明,当淤泥层的厚度或弹性储水系数较小时,或者其渗透性较好时,可以忽略其弹性储水效应,从而把整个淤泥层简化为第三类边界条件来处理.文章还考虑了承压含水层和淤泥层中可能存在的垂向流动,对垂向剖面二维地下水流动方程进行了数值模拟,将二维数值解与忽略垂向流动的一维解析解进行了比较,结果表明该含水层系统的垂向流动是可以被忽略的.     

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.     

承压含水层井流-盖层弯曲效应的解析理论

指出承压含水层盖层的弯曲变形与开采井周围的径向地下水运动存在相互作用, 而这一效应在传统的井流理论中没有被认识到.通过引入弹性薄板理论, 建立了无越流的承压含水层井流-顶板弯曲效应的解析模型, 同时考虑了含水层和水的压缩性, 结果表明Theis井流方程给出的抽水降深偏小.在此基础上推导了有越流承压含水层井流-盖层弯曲效应的偏微分方程, 求出了解析解, 并与传统理论的结果进行了对比, 表明Hantush-Jacob公式计算的降深也是偏小的.在抽水井附近和抽水初期, 传统理论可能导致显著的相对误差.      

海潮引起有越流的滨海承压含水层地下水头变化的数值模拟

海潮波动可以引起海岸带有越流的承压含水层地下水头发生波动。建立了基于有限差分法的滨海地区一维承压含水层地下水运动数值模型。通过将潮汐波动概化为正弦波,分别对初始水头水平及线性倾斜的承压含水层模拟了滨海地区有越流的承压含水层地下水头随潮汐波动的变化。通过对两种情形下的变化比较,结果表明,受海潮影响的滨海承压含水层地下水头与海潮有相似的波动特征,但变幅减小,受海潮的影响程度与离海岸的距离有关,随着离海岸距离的增加,地下水头的变幅及潮汐效率呈负指数函数衰减,水头倾斜情形下变幅更小,潮汐效率更小,滞后时间更短,地下水头对海潮的滞后时间随距离呈线性增加。     

用地下水潮汐效应确定潜水含水层水文地质参数

目前对潜水含水层地下水潮汐效应和水文地质参数求解方法的研究相对较少.通过对福建古雷半岛滨海潜水含水层地下水潮汐效应和海水潮汐动态的观测, 运用Fourier频谱分析方法确定了研究区海水潮汐波动方程(波动特征参数), 并以此作为地下水的边界条件, 推导了潜水含水层地下水潮汐效应的波动方程, 利用最小二乘法以地下水水位波动观测值为目标函数对潜水含水层的渗透系数与重力给水度的比值进行了反演识别, 为类似地区水文地质参数的确定提供了借鉴, 也为该区后续地下水中溶质迁移规律的研究奠定了基础.      

Groundwater response to dual tidal fluctuations in a peninsula or an elongated island

Groundwater flow in a peninsula or an elongated island is influenced by tidal fluctuations on both sides of the peninsula or island, which is named as dual tidal fluctuations. In this study, semianalytical solutions of transient groundwater flow in response to dual tidal fluctuations in an aquifer–aquitard system were presented for cases with and without the aquitard storage. These solutions were first derived using the Laplace transform and subsequently computed by the Fourier series numerical inverse Laplace transform. The derived solutions were found to agree very well with the results of numerical simulations by MODFLOW. The solution ignoring the aquitard storage approached the quasi‐steady state solution quickly when the mean sea level initial condition was used. The solutions with and without the aquitard storage were nearly the same at the early time and were separated from each other during the intermediate time, and the difference of solutions became constant at late time for small aquifer/aquitard storativity ratio and large tidal frequency. The propagation bias, which is the departure from the theoretical ratio of tidal attenuation to tidal lag, was enhanced not only with increase of the dimensionless specific leakage (aquitard/aquifer hydraulic conductance ratio) but also with decrease of the aquifer/aquitard storativity ratio and with the increase of the dimensionless tidal frequency. The solution with the aquitard storage was more sensitive to these three parameters. The newly developed solutions were capable of handling realistic initial conditions that might be approximated by piecewise linear functions. Copyright © 2012 John Wiley & Sons, Ltd.     

A data-driven approach for analyzing dynamics of tide–aquifer interaction in coastal aquifer systems

Analysis of tidal effects on aquifer systems plays an important role in coastal aquifer management owing to various hydrological, engineering and environmental problems in coastal areas. Using the real-world data of unconfined and confined aquifers, a data-driven approach is presented in this study for the analysis of tide–aquifer interaction in coastal aquifers. Six analytical tide–aquifer interaction models were selected which take into account the effects of vertical beach, sloping beach, tidal loading, aquifer leakage, outlet capping, and combined leakage and outlet capping on tide-induced groundwater fluctuations. The tide–aquifer interaction datasets were obtained from the Konan groundwater basin (unconfined aquifer) of Japan and the Dridrate groundwater basin (confined aquifer) of Morocco. The analysis of the results obtained by the sloping beach model revealed that for a given beach slope, the amplitude of groundwater level increases with an increase in aquifer diffusivity and a decrease in aquifer thickness. However, no significant effect of beach slope was observed in this study at unconfined sites for all the datasets. The influence of tidal loading was found to be considerably less for all the three confined sites. Further, the analysis of the results of the leakage model indicated that with an increase in leakage into the aquifer, the amplitude of groundwater level as well as the phase shift (time lag) decreases. Of all the confined and unconfined datasets, only two confined sites were found to be affected by outlet capping. Overall, it is concluded that the coastal beach bordering the Konan basin is not significantly sloping, the contribution of tidal loading to tide-induced groundwater fluctuations in the Dridrate aquifer is not appreciable, and that the aquifer leakage and outlet capping do not exist at the unconfined sites under investigation.     

具有越流补给的含水煤层渗流模型求解与典型曲线

为了分析水层越流补给对煤层气井早期排水的影响,根据不稳定渗流理论,引入越流系数,建立了考虑层间越流现象的煤层中水的渗流数学模型。通过Laplace变换对模型求解,并利用Stehfest反演得到实空间的解,采用新的参数组合,分别绘制了压力和压力导数双对数曲线图版。从物理渗流机理上分析了层间越流对曲线形态的影响,随着越流系数的增大,径向流结束的时间越早;同时提出了利用典型图版拟合确定储层渗透率、表皮系数以及越流系数的方法。典型图版有助于定量评价越流的强弱,对煤层气井后续排采制度的调整具有指导意义。      

Estimating aquifer hydraulic properties using sinusoidal pumping at the Savannah River site,South Carolina,USA

A framework for estimating aquifer hydraulic properties using sinusoidal pumping is presented that (1) derives analytical solutions for confined, leaky, and partially penetrating conditions; (2) compares the analytical solutions with a finite element model; (3) establishes a field protocol for conducting sinusoidal aquifer tests; and (4) estimates aquifer parameters using the analytical solutions. The procedure is demonstrated in one surficial and two confined aquifers containing potentially contaminated water in coastal plain sediments at the Savannah River site, a federal nuclear facility. The analytical solutions compare favorably with finite-element solutions, except immediately adjacent to the pumping well where the assumption of zero borehole radius is not valid. Estimated aquifer properties are consistent with previous studies for the two confined aquifers, but are inconsistent for the surficial aquifer; conventional tests yielded estimates of the specific yield—consistent with an unconfined response—while the shorter-duration sinusoidal perturbations yielded estimates of the storativity—consistent with a confined, elastic response. The approach minimizes investigation-derived wastes, a significant concern where contaminated fluids must be disposed of in an environmentally acceptable manner. An additional advantage is the ability to introduce a signal different from background perturbations, thus easing detection.     

运用地下水对潮汐的响应识别压力传导系数

在地下水扩散方程中,压力传导系数是描述地下水运动的重要参数。传统的方法是通过抽水或注水给地下水系统一个扰动,监测地下水水位的响应,由此计算含水层的压力传导系数。文章提出用潮汐衰减率方法识别含水层压力传导系数,其适用于滨海区承压含水层的参数识别。在推导出解析解的基础上,通过数值拟合、最小二乘法、牛顿迭代法求得含水层的压力传导系数,提出潮汐衰减率的概念,建立余切函数与潮汐衰减率的线性关系,用线性关系中的斜率和截距识别压力传导系数。用潮汐衰减率方法识别出的压力传导系数与其实际值相等,说明该方法是正确有效的。潮汐信号衰减率与海水振荡的余切函数线性相关。数值仿真表明,该方法可以准确地估算出含水层的压力传导系数。潮汐衰减率方法具有少打井,经济高效等优点。潮汐衰减率方法为实际工程应用提供了可靠的理论基础,它可以用于部分实际工程中。该方法的局限性在于需要提供含水层的部分参数,如含水层的长度、海水波动振幅、频率等。     

MT3D-通用的三维地下水污染物运移数值模型

定量研究污染物在地下水中的运移过程通常采用数值模拟方法。MT3D是一套基于有限差分方法的污染物运移模拟软件，近年来在国外水文地质和水环境模拟等领域的研究中已经得到较为广泛的认可。MT3D比较全面地考虑了污染物在地下水中的对流、弥散和化学反应等过程，可以灵活处理各种复杂的源汇项和边界条件，能够准确模拟承压、无压和越流含水层中的污染物运移过程。MT3D具有模块化的程序结构、灵活的求解方法以及全面的模拟功能，非常适合实际问题的研究，值得在国内推广使用。     

A novel analytical solution for constant‐head test in a patchy aquifer

A mathematical model describing the hydraulic head distribution for a constant‐head test performed in a well situated at the centre of a patchy aquifer is presented. The analytical solution for the mathematical model is derived by the Laplace transforms and the Bromwich integral method. The solution for the hydraulic head has been shown to satisfy the governing equations, related boundary conditions, and continuity requirements for the hydraulic head and flow rate at the interface of the patch and outer regions. An efficient numerical approach is proposed to evaluate the solution, which has an integral covering an integration range from zero to infinity and an integrand consisting the product and square of the Bessel functions. This solution can be used to produce the curves of dimensionless hydraulic head against dimensionless time for investigating the effect of the contrast of formation properties on the dimensionless hydraulic head distribution. Define the ratio of outer‐region transmissivity to patch‐region transmissivity as α. The dimensionless hydraulic head for α=0.1 case is about 2.72 times to that for α=10 case at dimensionless large time (e.g. τ?10⁶) when the dimensionless distance (ρ) equals 10. The results indicate that the hydraulic head distribution highly depends on the hydraulic properties of two‐zone formations. Copyright © 2006 John Wiley & Sons, Ltd.     

利用滨海地下水潮汐效应估计含水层参数:以北海半岛为例

通过分析滨海含水层中观测孔的水位动态资料,确定含水层的水力性质和某些参数,或推测含水层在海底的延伸长度和露头处是否存在覆盖层,是水文地质学家一直很感兴趣的问题之一。文中充分分析了广西北海半岛滨海地区水文地质条件,将研究区第一个承压含水层系统概化为具有上覆弱透水层越流和含水层海底露头覆盖层的垂向三层结构的不稳定流模型。应用该模型的解析解对广西北海半岛滨海含水层系统的观测数据进行了分析,拟合效果很好,并利用最小平方罚函数法估算了研究区含水层的参数。     

运用三维变密度潮汐效应模型确定滨海含水系统的海底等效边界——山东烟台夹河中下游地区为例

确定咸淡水界面的位置是滨海地区海水入侵研究的主要任务之一。对于天然条件承压含水层而言，含水层顶板向海底延伸的距离直接影响了咸淡水界面的位置，它可以通过承压含水层中地下水的潮汐效应信息来确定。考虑到咸淡水之间密度的差异，建立了山东省夹河中下游地区滨海含水系统地下水三维变密度潮汐效应模型。通过反复对比潮汐效应观测中的地下水水头波动与模型计算出的水头波动，确定了滨海承压含水系统的海底边界。同时，也初步估计出海区与近海陆区含水层的水文地质参数。