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.     

Steady critical discharge rates from vertical and horizontal wells in fresh–saline aquifers with sharp interfaces

In this study, the critical (or maximum) discharge rates before saline water enters a well were determined for vertical and horizontal wells in a freshwater aquifer which is separated from a static saline aquifer by a sharp interface. Flow around the well was solved by integration of a point sink solution along the well axis, and both the critical discharge rate and critical interface rise were determined through a comparison of the heads and vertical gradients at the saline–fresh water interface. The rates were determined for vertical and horizontal wells with various lengths and depths for different aquifer salinities. Results were generalized by drawing dimensionless type curves. The results showed that the dimensionless total critical discharge rates are higher for the longer horizontal wells and longer vertical wells with a certain bottom depth, and they almost linearly decrease with well depth at rates of 0.7–0.9. For the dimensionless well length of 0.2, the dimensionless total discharge rate of a horizontal well is about 0.1 more than that of a vertical well with the same length and well-top depth. Also, the critical discharge rates per unit length of well are inversely proportional to well length and remarkably higher for shallower wells. Additionally, the critical pumping rate is proportional to the salinity difference of the aquifers. These results were confirmed by comparison to existing solutions for vertical wells with dimensionless lengths of 0.2, 0.5 and 0.6, and for critical interface rises in the range of 0.75–0.9.     

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。     

非承压含水层底部单孔疏放水渗流特征

由含水层底部向上施工疏放水孔（井）进行疏水降压是保证煤矿安全开采的重要措施之一,该类疏放水孔与地面抽水井的渗流特征具有显著差别。为了研究井下疏放水孔的渗流特征,以非承压含水层底部单井疏放水孔为例,采用数值模拟的方法对其渗流特征进行研究。研究结果表明,当疏放水井的井长l_w小于临界长度l_c时,即l_wc,疏放水井上部含水层孔隙水压力大于0,且由下而上呈先增加后减小的分布规律,渗流量与井长呈指数函数关系增加;当l_w ≥ l_c时,疏放水非完整井的渗流特征及渗流量与完整井相同;渗流量随井半径增加呈指数关系增加,且指数小于1;将s+l_w代替水位降深s对裘布依（Dupuit）潜水完整井计算公式进行修正,当l_wc时,采用修正的Dupuit潜水完整井计算公式计算疏放水非完整井渗流量更精确。该研究结果对认识井下疏放水井上部孔隙水压力分布特征及合理布置疏放水井具有重要的借鉴意义。      

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     

Analysis of Steady-State Flow To Multiscreened Wells Under Natural Vertical Flow Conditions

Water levels measured at multiscreened wells in unconfined aquifers may not coincide, in general, with the elevation of the water table. The presence of vertical gradients (as often is the case in recharge areas) or the existence of confining layers may cause the water levels to differ from local hydraulic heads in the aquifer. In these cases, a misinterpretation of water levels may lead to the erroneous conclusion that observed drawdowns are provoked by overpumping. In this paper, we analyze the effect that a natural vertical gradient has on water levels in wells screened over their entire saturated thickness. As one would expect, it is observed that, even without pumping, the water level in the wells lies below the water table. Type curves relating the steady-state drawdown to the vertical gradient and to the hydraulic conductivity anisotropy are presented. These curves were obtained using a groundwater flow numerical model (FREESURF: Neuman and Witherspoon, 1970). The theoretical results are checked with field data from deep wells in the detrital Madrid aquifer. In this particular aquifer, it is observed that the effect of vertical gradients is important both in terms of drawdowns and flow rates.

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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。     

Physical model test of transparent soil on coupling effect of cut-off wall and pumping wells during foundation pit dewatering

Water level is decreased during foundation pit excavation to avoid water inrush under confined water pressure. Cut-off wall is often used as waterproof curtain to partially cut off the dewatered aquifer. When a foundation pit is located in a built-up area and the underlying confined aquifer is not cut off, the drawdown must be minimized outside the pit to avoid land subsidence in buildings and pipelines. The coupling effect of the cut-off wall and pumping well is used to control the drawdown outside the foundation pit. However, the coupling mechanism is not intuitively well understood because of the limitations of existing experimental methods. In this study, transparent soil was introduced to model the coupling mechanism in the physical model test. High-purity fused silica and mixed paraffin oil were used as skeleton and fluid to simulate the confined aquifer and groundwater. Industrial solid dye and paraffin oil were used as tracers. A camera was used to collect flow information. Tests were performed for the combinations of cut-off wall and partially penetrating pumping wells. The insertion depth ratio of the cut-off wall most effectively influenced the drawdown. The layout of the pumping wells in horizontal direction influenced water level distribution and flow rate. The optimal depth of the pumping wells was 1–5 m above the bottom of the cut-off wall, and the optimal horizontal distance between the cut-off wall and the pumping wells was 25% of the pit width. Non-Darcy flow was observed within the range of 0–10 m around the bottom of the cut-off wall. These results were significant in understanding the cut-off wall and pumping well coupling effect on foundation pit dewatering.

     

侧向有限越流承压含水层中非完整井非稳定流模型及解析解

工程建设中当距离抽水井r=rb处水位基本没有变化或不受抽水影响时,或当此处存在止水帷幕时,含水层系统视为侧向有限延伸,rb为有限半径。为此,构建更加符合工程实际的侧向有限延伸的典型弱透水层-承压水层系统中非完整井非稳定流计算模型,同时考虑井径和井储效应的影响,应用Laplace变换和分离变量法得到了水位降深在拉氏空间下的解析解,并应用拉氏数值逆变换Stehfest法得到真实空间下的水位降深。新建立的解析解可以进一步退化为诸多已有解,并进一步将其与已知解和有限元数值解进行对比,验证了所得解的正确性和可靠性。基于新建解重点分析了侧向边界和井的完整性对承压水层水位降深的影响。结果表明:含水层系统的侧向有限边界仅对抽水后期的水位降深影响明显,含水层系统侧向无限延伸情况下的水位降深要大于情形1(在r=rb处为定水头边界)且明显小于情形2(在r=rb处为不透水边界)下的水位降深,rb越小,两者之间的误差越大;抽水井的完整性对整个抽水期间不同情形下的水位降深均有明显的影响,承压含水层顶板处的水位降深随着抽水井滤管的长度和埋深的增加而减小。     

The dependence of stream depletion by seasonal pumping on various hydraulic characteristics and engineering factors

Compensation pumping is used to alleviate deficiencies in streamflow discharge during dry seasons. Short-term groundwater pumping can use aquifer storage instead of catchment-zone water until the drawdown reaches the edge of the stream. The capacitance is a complex, dimensionless parameter of an aquifer system that defines the delayed effect on streamflow when there is groundwater pumping. This parameter is a function of aquifer hydraulic characteristics, pumping time, and distance between the well and stream edge; the latter can involve stream leakance and vertical leakance of an associated aquitard. Three typical hydraulic cases of combined water systems (major catchment-zone wells close to the stream and compensation pumping wells) were classified depending on their capacitance structure (i.e. the relationship between surface water and groundwater): (1) perfect hydraulic connection between the stream and aquifer; (2) imperfect hydraulic connection between the stream and aquifer; and (3) essentially imperfect hydraulic connection between the stream and the underlying confined aquifer. The impact of various hydraulic characteristics and engineering factors on stream depletion was examined by conceptual and numerical modeling. To predict the suitability and efficiency of a combined water system application, regression tests were undertaken on unit stream depletion and capacitance, and power dependencies were defined.     

垃圾填埋场抽水试验及降水方案设计

垃圾填埋场中的渗滤液水位过高会引发一系列环境和稳定问题,工程上可用竖井抽水降低渗滤液水位。通过在填埋场现场进行抽水试验,确定垃圾土的渗透系数和抽水影响半径,在此基础上对填埋场降水的瞬态流问题进行有限元模拟,分析了抽水井口径和间距对填埋场降水的影响,提出了降水方案的设计步骤和方法。抽水试验表明,现场垃圾的渗透系数约为3.6×10-4cm/s,抽水影响半径约为20m。数值分析表明,井径的变化对于降水效果影响不大,而合理选择抽水井间距对降水十分关键。进行抽水方案设计时,应首先根据工期和降水幅度要求计算井间距,按井的出水速度选择水泵,再根据水泵确定井径,最后根据井径和过滤层形式确定钻孔尺寸并选择钻机。     

A case history of field pumping tests in a deep gravel formation in the Taipei Basin,Taiwan

33 large-diameter wells embedded in 2-m thick, 63-m deep diaphragm walls were constructed to reduce both the uplift pressures and the groundwater inflow during the excavations. As the actual thickness of the pumped aquifer is unknown, the installed wells are regarded as partial penetration wells. Single-well and multi-well pumping tests were conducted in the deep gravel formation of Taipei Basin to derive the hydraulic parameters and to investigate the drawdown characteristics at both the construction and remote sites. However, the tidal effect on the drawdown of both the pumping well and nearby observation wells was found significant. Additionally, wellbore storage, skin, and leakage need to be taken into account for deriving the hydraulic parameters. Hence, a method to remove these five factors influencing the drawdown curve is developed, which takes advantage from the late-time characteristics of drawdown data and the early-time behavior of drawdown. Some currently available semi-log graphic techniques are therefore proven applicable for parameter determination. Validity of the proposed method is verified by the good agreement between the calculated and the measured drawdown of both the pumping well and observation well.     

The extreme well-loss component of drawdown in two deep artesian wells in Israel

Hydrogeology Journal - The water-level drawdown in pumping wells is the sum of two components: aquifer loss and well loss. The latter results from mostly turbulent and nonlaminar flow in and around...     

Steady flow rate to a partially penetrating well with seepage face in an unconfined aquifer

The flow rate to fully screened, partially penetrating wells in an unconfined aquifer is numerically simulated using MODFLOW 2000, taking into account the flow from the seepage face and decrease in saturated thickness of the aquifer towards the well. A simple three-step method is developed to find the top of the seepage face and hence the seepage-face length. The method is verified by comparing it with the results of previous predictive methods. The results show that the component of flow through the seepage face can supply a major portion of the total pumping rate. Variations in flow rate as a function of the penetration degree, elevation of the water level in the well and the distance to the far constant head boundary are investigated and expressed in terms of dimensionless curves and equations. These curves and equations can be used to design the degree of penetration for which the allowable steady pumping rate is attained for a given elevation of water level in the well. The designed degree of penetration or flow rate will assure the sustainability of the aquifer storage, and can be used as a management criterion for issuing drilling well permits by groundwater protection authorities.     

Analytical solutions for constant-rate test in bounded confined aquifers with non-Darcian effect

This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries. The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle, of which the non-Darcian effect is characterized by Izbash’s equation. The solutions are derived by Boltzmann and dimensionless transformations. Then, the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution. The results show that the aquifer boundaries have non-negligible effects on pumping, and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping. The higher the degree of non-Darcian, the smaller the drawdown.     

Development of a simple method for determining the influence radius of a pumping well in steady-state condition

Influence radius of a pumping well is a crucial parameter for hydrogeologists and engineers. Knowing the radius of influence for a designed drawdown enables one to calculate the pumping rate required to layout a project foundation that may need lowering of groundwater level to a certain depth due to dewatering operation. In addition, this is important for hydrogeologists to determine ground water contamination flow paths and contributing recharge area for domestic water supply and aquifer management purposes. Empirical formulas that usually neglect vital parameters to determine the influence radius accurately have been traditionally utilized due to lack of adequate methods. In this study, a physically based method, which incorporates aquifer hydraulic gradient for determining the influence radius of a pumping well in steady-state flow condition, was developed. It utilizes Darcy and Dupuit laws to calculate the influence radius, where Darcy's law and Dupuit equation, in steady-state condition, represent the inflow and the outflow of the pumping well, respectively. In an untraditional manner, this method can be also used to determine aquifer hydraulic conductivity as an alternative to other pumping test methods with high degree of accuracy. The developed method is easy to use; where a simple mathematical calculator may be used to calculate the influence radius and the pumping rate or hydraulic conductivity. By comparing the results from this method with the MODFLOW numerical model outputs with different simulated scenarios, it is realized that this method is much superior and more advantageous than other commonly used empirical methods.     

炭质灰岩地区抽水致塌控制因素和影响因素

为研究炭质灰岩地区抽水致塌控制因素和影响因素,通过电法物探、地质钻探及抽水致塌试验相结合的综合手段,对兴安县石炭系下统岩关组（C₁y）炭质灰岩地区的岩溶塌陷进行关联分析,建立降深水位与时间、恢复水位与时间的关系对比曲线。研究结果表明:在炭质灰岩地区进行抽水活动时,其主要补给源为小溶洞内储存水,运输通道为岩溶裂隙;该炭质灰岩地区岩溶裂隙具有不规则性,因此,在同类地层中测得的渗透系数k及影响半径R有较大差异;研究区域内抽水致塌的位置受地质构造的影响较为明显;钻井人为抽水致塌受多种因素共同作用影响,而地下水位升降为主要影响因素。     

Field experiments and numerical simulations of whirlpool foundation pit dewatering

A whirlpool foundation pit is a small-diameter, deep circular pit. Because of its depth and small diameter, a large drawdown is required, and a limited number of wells can be installed inside the pit. During excavation, partially penetrating wells inside and outside the foundation pit have to be installed to lower the water level when the aquifer is too thick. However, partially penetrating wells near partially penetrating curtains cannot be treated by analytical methods. Therefore, it is necessary to use numerical methods to predict dewatering during excavation. Field experiments were performed on whirlpool foundation pit 1880 of Baosteel Group, Shanghai, China, to obtain pumping rates and drawdown, pumping with a single well and two wells in the confined aquifer. The results indicate that the drawdown inside the pit induced by pumping wells outside the foundation pit was small, whereas it was large for pumping wells inside the pit. The pumping wells inside and outside the pit had to be combined to lower the water level. A three-dimensional numerical model was developed to simulate the dewatering process. The hydraulic conductivities of the confined aquifers were inversed by using the pumping tests. Operation schedules were simulated with the corrected model for different combinations of wells inside and outside the pit. The results suggest that different schedules and operation conditions affect drawdown. The monitored results during dewatering indicate that the simulation and field measurements were in agreement. The results can be applied to similar situations.     

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.      

水资源和环境工程中水平井研究简介

简单介绍了水平井在水资源和环境工程中的近期研究进展, 重点介绍了在不同含水层(如承压含水层、潜水含水层、越流含水层及河下含水层) 中, 水平井抽水条件下降深的半解析解, 同时分析了降深随抽水时间变化的标准曲线和微分标准曲线.这些半解析解可用于分析小流量水平井在中长时段的降深特性.分析了用于排水和供水的大流量水平井的水力学特征, 并介绍了求解渗流-管流耦合井流系统的一种新方法.同时介绍了在非饱和含水层中水平井抽取气体的动力学特征, 并分析了地面覆盖和未覆盖2种情况下的气体清除效率, 报告了在不同饱和含水层条件下水平井的捕获区和捕获时间的计算.