Non-Darcian flow toward a larger-diameter partially penetrating well in a confined aquifer

In this study, non-Darcian flow to a larger-diameter partially penetrating well in a confined aquifer was investigated. The flow in the horizontal direction was assumed to be non-Darcian and described by the Izbash equation, and the flow in the vertical direction was assumed to be Darcian. A linearization procedure was used to approximate the nonlinear governing equation. The Laplace transform associated with the finite cosine Fourier transform was used to solve such non-Darcian flow model. Both the drawdowns inside the well and in the aquifer were analyzed under different conditions. The results indicated that the drawdowns inside the well were generally the same at early times under different conditions, and the features of the drawdowns inside the well at late times were similar to those of the drawdowns in the aquifer. The drawdown in the aquifer for the non-Darcian flow case was larger at early times and smaller at late times than their counterparts of Darcian flow case. The drawdowns for a partially penetrating well were the same as those of a fully penetrating well at early times, and were larger than those for a fully penetrating well at late times. A longer well screen resulted in a smaller drawdown in the aquifer at late times. A larger power index n in the Izbash equation resulted in a larger drawdown in the aquifer at early times and led to a smaller drawdown in the aquifer at late times. A larger well radius led to a smaller drawdown at early times, but it had little impact on the drawdown at late times. The wellbore storage effect disappears earlier when n is larger.     

非承压完整或不完整井稳定流

本文根据现有的实验资料说明裘布依假定适用于虚构流网,故所得出的自由水面方程和流量方程也应适用于虚构流网。根据虚构流网概念,获得了完整井或非完整井抽水时流量方程。另一方面,用分析方法获得不完整井抽降不大时的流量方程;利用室内实验资料对方程中的参变数值编成曲线图,并说明此方程的精度亦较一些经验公式为高。     

How appropriate is the Thiem equation for describing groundwater flow to actual wells?

The Thiem equation of radial groundwater flow to a well is more than 100 years old and is still commonly used. Here, deviations caused by some of its simplifications are quantified by comparing the analytical to a numerical model that allows the implementation of more complex geometries. The assumption of horizontal flow in the Thiem equation, which necessitates uniform inflow over the entire screen length of the fully penetrating well, was found to cause deviations from actual pumping wells where the pump is placed above the screen, resulting in non-uniform inflow and additional drawdown. The same applies to partially penetrating wells, where inflow peaks and additional drawdown occur, especially when the well is screened in the lower part of the aquifer. The use of the Thiem equation in the near-field of a well should thus be restricted to situations where the screen inflow is relatively uniformly distributed, e.g. when it covers large portions of the aquifer thickness. The presence of a gravel pack and a background gradient, on the other hand, are of limited importance.     

宝鸡市高速公路客运中心主楼基坑降水补充设计

宝鸡市高速公路客运中心主楼基坑降水采用管井方案,原设计6个降水井,后又增加了2个降水井,但降水效果不甚理想,达不到降水设计要求,随进行了补充设计。根据场地地层情况及地下水条件,结合基坑开挖、降水现状和降水要求,依据现场抽水试验获得的水文地质参数,进行水文地质计算,确定出合适的集水井数量,并合理布置集水井和排水沟。通过集水明排与管井相结合的方法,节省了费用,取得了良好的降水效果。     

井周流场,水跃值与井内水位降深的关系

本文以单井稳定流抽水为例，从井固流场与地下水向集水井幅射流的涌水量方程入手，阐明井结构，井周泥浆堵塞和井内水位降深的关系。证明了水跃值是井周泥浆堵塞降深与井周三维流域或紊流引起的二次项降深（简称“井损“）之代数和，并得出了水跃值不同组成部分随井内降深变化而变化的规律。从而提出了消除水跃值，利用裘布依涌水量方程进行水文地质参数计算。     

Multi-aquifer pumping test to determine cutoff wall length for groundwater flow control during site excavation in Tokyo, Japan

Multi-aquifer pumping tests, using a multi-screen pumping well and multi-level piezometers, were carried out for groundwater flow control in a large-scale excavation site in Tokyo, Japan. The site was underlain by multi-layered confined aquifers. In the tests, pumping was carried out using a multi-aquifer pumping well in which a screen depth was chosen arbitrarily. Changes in groundwater pressure heads in each aquifer were measured at each screen position of the multi-aquifer pumping well. Hydraulic conductivity (K) and specific storage (S _s) of not only aquifers, but also for low permeability layers between the aquifers, were estimated using the Cooper-Jacob method, and calibrated by a finite element method (FEM) groundwater model. Four different cutoff wall lengths were assumed for final excavation depth, and correlations among wall length, pumping discharge and drawdown at the back of the cutoff wall were obtained from simulations using the K and S _s parameters in the FEM model. Then, the most suitable wall length was selected based on the simulated correlations considering environmental condition, construction period and cost of the cutoff wall.     

Non-Darcian flow to a well in a leaky aquifer using the Forchheimer equation

Non-Darcian flow to a well in a leaky aquifer was investigated using a finite difference method. Flow in the leaky aquifer is assumed to be non-Darcian and horizontal, while flow in the aquitard is assumed to be Darcian and vertical. The Forchheimer equation was employed to describe the non-Darcian flow in the aquifer. The finite difference solution was compared with the solution of Birpinar and Sen (2004). The latter overestimates the drawdown at early times and underestimates the drawdown at late times; also, the impact of β _D on the drawdown depends on the value of B _D, where β _D is a dimensionless turbulent factor in the Forchheimer equation and B _D is the dimensionless leakage parameter. The impact of leakage on drawdown is similar to that of Darcian flow. A sensitivity analysis indicated that the drawdown is very sensitive to the change in the dimensionless well radius r _cD when B _D is relatively large, while it is sensitive to the change in B _D when B _D is relatively small. The numerical solution has been applied to analyze the pumping test data in Chaj-Doab area of Pakistan. Birpinar ME, Sen Z (2004) Forchheimer groundwater flow law type curves for leaky aquifers. J Hydrol Eng 9(1):51??9     

承压含水层中非完整井附近“非达西-达西”两区渗流模型近似解析解

抽水井附近由于流速过快往往发生非达西流,而远离抽水井随着流速下降又变为达西流.为了描述这些特征,建立了承压含水层中非完整井附近“非达西-达西”两区渗流模型,即距离抽水井较近的区域由于流速较快假设发生非达西渗流,并利用Izbash公式刻画,而距离抽水井较远由于流速较慢假设仍然满足达西定律,含水层中垂向流速较小也利用达西定律描述.通过线性化近似方法结合Laplace变换和有限Fourier余弦变换对模型进行了求解,分析探讨了该两区模型下水位降深曲线特征.结果表明:抽水初期,非达西渗流区域水位降深与全非达西渗流模型结果吻合,而抽水后期两区模型非达西渗流区域的水位降深与全达西模型水位降深基本一致,但大于全非达西渗流模型的水位降深;抽水初期,两区模型中达西渗流区域的水位降深比全达西渗流模型结果大,但比全非达西渗流模型结果小;对不同时间的水位降深随井距变化曲线分析发现非达西渗流区域水位降深随Izbash公式中的幂指数n增大而减小,而在达西渗流区域水位降深基本不受n值的影响.研究成果对非完整井抽水试验参数反演具有重要理论意义.      

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin

Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin was investigated. The Izbash equation is used to describe the non-Darcian flow in the horizontal direction, and the vertical flow is described as Darcian. The solution for the newly developed non-Darcian flow model can be obtained by applying the linearization procedure in conjunction with the Laplace transform and the finite Fourier cosine transform. The flow model combines the effects of the non-Darcian flow, partial penetration of the well, and the finite thickness of the well skin. The results show that the depression cone spread is larger for the Darcian flow than for the non-Darcian flow. The drawdowns within the skin zone for a fully penetrating well are smaller than those for the partially penetrating well. The skin type and skin thickness have great impact on the drawdown in the skin zone, while they have little influence on drawdown in the formation zone. The sensitivity analysis indicates that the drawdown in the formation zone is sensitive to the power index (n), the length of well screen (w), the apparent radial hydraulic conductivity of the formation zone (K _r2), and the specific storage of the formation zone (S _s2) at early times, and it is very sensitive to the parameters n, w and K _r2 at late times, especially to n, while it is not sensitive to the skin thickness (r _s).     

Effects of parameter error on Cooper-Jacob drawdown estimates

Parameters employed in the Cooper-Jacob equation to describe drawdown are transmissivity, storativity, radial distance, time and pumping rate. An approach is described for quantifying how error or uncertainty in any one of the parameters used causes error in estimated drawdown. Dimensionless fractional error in estimated drawdown is expressed quantitatively as a function of (1) dimensionless fractional error of a given parameter, and (2) dimensionless argument of the well function, u. Fractional error in estimated drawdown is a linear function of fractional error in pumping rate and, for any given value of u, a nonlinear function of fractional error in transmissivity, storativity, radial distance or time. Fractional error in estimated drawdown for a given fractional parameter error varies considerably between parameters. The greatest sensitivity is for transmissivity and flow rate. Sensitivity is less for radial distance and time, and even less for storativity. The magnitude of the fractional error in drawdown may be affected by the sign of the fractional parameter error.     

New Insight Into The Step-Drawdown Test In Fractured-Rock Aquifers

Review of the historical development of the step-drawdown pumping test and interpretations of well test data using the step-drawdown method indicates considerable differences in the importance attributed to head losses in the artificial environment (e.g., the gravel pack and screen) in the immediate vicinity of the wellbore and the losses resulting from non-laminar flow in the aquifer itself. These differences appear to be greatest when attempts have been made to apply the step-drawdown analysis to data from wells in fractured rock aquifers. The empirical flow-head loss relationship for a single, hydraulically-rough, open fracture have been incorporated into a mathematical expression for two-regime, radial, convergent flow. The resulting equation estimates the laminar and non-laminar head losses resulting from flow to a well over a range of flow rates. Combining these head loss components yields a non-linear relationship between production, Q, and drawdown, s, that is similar to those observed for actual step-drawdown tests in fractured rock aquifers. These test data are well approximated by: s = BQ + CQⁿ where both B and C are assumed to be constants and n is typically in the range of 2.0 to 3.0.     

Estimation of transmissivity and storage coefficient by means of a derivative method using the early-time drawdown

A novel methodology is proposed to calculate transmissivity (T) and storage coefficient (S) in a confined aquifer, based on the Theis (1935) solution and using only the first derivative of the drawdown with respect to time. By analyzing the behavior of the third derivative of the drawdown with respect to the logarithm of time, it is apparent that the third derivative vanishes when the first derivative attains its peak value. Since the third log-derivative is zero if, and only if, the argument, u, of the Theis well function is equal to unity, this condition can be used to estimate T and S, knowing the time at which the first derivative reaches its peak, and so overcoming the problem of actually computing the third log-derivative, which is very unstable. The main characteristic of the proposed method is that it does not require long pumping tests, since T and S are calculated using only the early-time drawdown. The proposed method was verified with a synthetic, an experimental and a field pumping test showing its validity when applied to homogeneous media. Theis CV (1935) The relation between lowering the piezometric surface and the rate and duration of discharge of a well using groundwater storage. Trans Am Geophys Union 16(2):519–524     

Approximate analytical and numerical solutions for radial non‐Darcian flow to a well in a leaky aquifer with wellbore storage and skin effect

This study investigated non‐Darcian flow to a well in a leaky aquifer considering wellbore storage and a finite‐thickness skin. The non‐Darcian flow is described by the Izbash equation. We have used a linearization procedure associated with the Laplace transform to solve such a non‐Darcian flow model. Besides, the Stehfest method has been used to invert the Laplace domain solutions for the drawdowns. We further analyzed the drawdowns inside the well for different cases. The results indicated that a smaller B_D results in a smaller drawdown at late times and the leakage has little effect on the drawdown inside the well at early times, where B_D is a dimensionless parameter reflecting the leakage. We have also found that the flow for the negative skin case approaches the steady‐state earlier than that for the positive skin. In addition, the drawdown inside the well with a positive skin is larger than that without skin effect at late times, and a larger thickness of the skin results in a greater drawdown inside the well at late times for the positive skin case. A reverse result has been found for the negative skin case. Finally, we have developed a finite‐difference solution for such a non‐Darcian flow model and compared the numerical solution with the approximate analytical solution. It has been shown that the linearization procedure works very well for such a non‐Darcian flow model at late times, and it underestimates the drawdowns at early times. Copyright © 2012 John Wiley & Sons, Ltd.     

渗流井合理竖井降深确定

通过采用单位面积河流在单位水头差作用下的渗漏量来表征河流渗漏能力,建立渗流井取水理想模型,分别计算了在不同河流渗漏能力和含水层渗透性能条件下,竖井降深对渗流井出水量的影响。建立渗流井取水非稳定流模型,计算了在前期稳定竖井降深不同条件下,河流断流后渗流井出水量衰减过程及竖井降深发展过程。提出渗流井合理竖井降深应根据河流与地下水是否脱节以及含水层渗透性能,在岸边渗流井中部及一侧各布设一个观测孔,根据观测孔水位进行确定。对于含水层渗透性能较强地区,渗流井竖井降深应使得渗流井范围内地下水位与河流脱节,但高于辐射孔顶面;对于含水层渗透性能较差地区,渗流井竖井降深应使得侧部观测孔水位接近河床底面或刚出现脱节。     

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.      

一种新的凝析气藏无因次产能评价方程

凝析气藏在衰竭开发过程中存在复杂的相态变化,凝析油的析出使得地层呈现出油气两相混合渗流状态.针对目前凝析气藏无因次产能评价方程的研究较少的现状,在凝析气藏拟稳态流入动态方程的基础上,利用泰勒级数展开、多项式回归等一系列解析方法建立了一种新的凝析气藏无因次产能评价方程.首先对拟稳态流入动态方程中的拟压力函数定积分进行泰勒级数展开,然后利用稳态定理和多项式回归方法求解出泰勒展开式的各项系数,最后通过解析方法得到了凝析气藏的无因次产能评价方程.应用实例表明,该无因次产能方程与实际系统试井数据基本吻合,能够较好地描述凝析气藏的油气两相流入动态;无因次产能评价法所得到无阻流量比常规干气法低,且考虑高速效应的无因次产能评价法所得到的无阻流量要大于忽略高速流动的无因次产能评价法所得到的结果.      

沈阳市阳光港湾建筑群基坑降水施工研究

沈阳市阳光港湾建筑群高层建筑采用筏板基础,多层建筑采用人工挖孔灌注桩基础,在基础施工时,均需进行相应的降水工作。采用了分期降水的施工方法,首期降水施工是在分析场地水文地质条件的基础上,利用稳定流"大井法"预算基坑的涌水量,布置了9口井,使基坑周边的1#、2#、3#、4#观测孔水位均下降至5.11m,基本上达到了首期的降水的目的;第二期降水是利用首期降水观测的水位资料,采用稳定流干扰井群计算公式对场区地下水位进行了预报,重新设计了3口井。12口井全部投放使用后,测得稳定排水量为43 000m3/d,并形成了以基坑为中心的地下水降落漏斗,降水效果明显。此经验值得同类工程借鉴。     

深厚强透水含水层超大基坑降水群井效应研究

基坑减压降水的幅度与群井效应密切相关。某超大面积基坑,含水层组厚40m,中下部透水性强,采用非完整井降水。对水文地质条件概化,建立了地下水三维非稳定流数值模型,对均匀布置群井、不均匀布置群井、分块开挖降水、不同的井结构、布设回灌井等工况,进行了渗流场模拟。研究表明,强透水性含水层超大面积基坑降水的群井效应极为明显;井位角密中疏布置,可实现降深调平,避免降深不足和超降;基坑分块降水,可减少坑外降深;短滤管井结构可减少基坑总涌水量和坑外降深;强透水性含水层可灌性强,回灌对减少坑外水位下降有较明显的效果。模拟结果与现场监测较为一致。研究成果可为类似工程地下水控制设计提供参考。     

非承压和非稳定抽水试验资料的有限单元分析

在抽水条件下水位随空间和时间变化的预测,依赖于潜水层的透水率和给水度的准确测定。如何利用抽水试验资料求这两种参数也是一个关键。这种相辅相成的关系是有效地开发利用地下水资源的前提。     

The extrapolation of elastic moduli to high pressure and temperature

The elastic constants of a crystal under stress, defined as the second derivative of the crystal free energy with respect to strain, require a correction related to the static pressure at non-zero pressures. The corrections required for the elastic constants calculated by the free energy minimisation code PARAPOCS are described and tested by comparison with the elastic constants calculated numerically by applying small stresses in the appropriate orientations to simulated crystals of fluorite, forsterite, α-quartz and albite. The corrected elastic constants are then used to investigate the extrapolation of the bulk and shear moduli (and hence also the seismic wave velocities V _p and V _s) of β-spinel and forsterite to upper mantle pressures. A Murnaghan equation, thirdorder Eulerian finite strain equation, second order polynomial equation and a logistic equation were all fitted to the simulated bulk and shear moduli between 0 and 3 GPa pressure. The parameters derived for these equations are used to extrapolate the bulk and shear moduli to 14 GPa and the results are compared to the simulated high pressure moduli. Over this pressure range, the second order polynomial provides the best extrapolation of the bulk modulus, but the use of the logistic equation results in the best extrapolation of the shear modulus.