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.     

Transient analysis of a step-drawdown test using a time-varying well-loss equation

Hydrogeology Journal - A step-drawdown test is one of the most widely used aquifer tests to estimate the groundwater well yield and the well performance. A method is proposed for analyzing...     

地下含水层水资源赋存条件及其水化学特征—以贵州省安龙县幅为例

以贵州省安龙县1∶50 000水文地质图幅为例,采用含水层探采井的水质、水量监测数据,分析不同含水层水资源赋存特征及其与水化学的相关性。研究结果表明:（1）研究区含水层可分为纯碳酸盐岩管道含水层、非纯碳酸盐岩裂隙含水层、碎屑岩裂隙含水层、松散岩类孔隙含水层4种类型,各含水层中地下水水化学类型均以HCO-Ca?Mg型为主;（2）除非纯碳酸盐岩含水层探采井的降深与水体中Mg2+、HCO-3浓度呈现出显著的负相关性（R2=-0.77/-0.74）外,其余离子浓度与钻井单位涌水量、降深的相关性均不显著,相关系数(R2)均小于0.3;（3）非纯碳酸盐岩含水层和松散岩类含水层的总矿化度（TDS）、总硬度（TH）含量均比纯碳酸盐岩含水层低5 mg?L-1以上,TDS、TH的高值区均集中于纯碳酸盐岩含水层中,而低值区则分布于松散岩类含水层。      

Automatic interpretation of pumping tests data using metaheuristics

Pumping tests data interpretation is of major importance in groundwater engineering. It is traditionally performed in a subjective manner by means of standard type curves. In this paper, an automatic interpretation of time-drawdown data has been proposed based on two algorithms, the real-coded genetic algorithm and differential evolution. The proposed approaches combine metaheuristic algorithms with an appropriate analytical drawdown solution depending upon the nature of the considered aquifer system, leaky or naturally fractured rock aquifers. The standard error of estimate (SEE) was used as a performance criterion to evaluate the discrepancies between predicted and observed drawdown data in different pumping time periods. Both of the proposed metaheuristic algorithms provide accurate aquifer parameters. For all analyzed pumping tests data, the differential evolution yielded the most accurate results with an improvement in SEE values ranged from 0.2 to 50% compared to previously published results, and exhibits speed and robustness. Furthermore, a new full range numerical evaluation of the Hantush well function based on a tanh-sinh quadrature scheme has been proposed. Our results indicate that our method is accurate, since the maximum relative error was found to be equal to 0.00036%, and practical, since it is free from special functions and could be easily incorporated within an optimization technique to analyze transient time-drawdown data.     

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     

Vertical movement of water in a High Plains Aquifer induced by a pumping well

Field observation and numerical simulations were carried out to evaluate the hydraulic relationship between the shallow and deep aquifer of a High Plains Aquifer system, in which shallow and deep aquifers are separated by an aquitard. Pumping from the lower aquifer resulted in a small drawdown in the upper aquifer and a larger drawdown in the aquitard; pumping from the shallow aquifer caused a small drawdown in the aquitard and the deep aquifer. Analysis of pumping test data gives the values of the hydraulic conductivity of the aquitard and the deep aquifer. Long-term observation of groundwater levels in the shallow and deep aquifers showed that a strong downward hydraulic gradient was maintained during an irrigation season. Numerical simulations were used to calculate the induced leakage of water from the shallow to the deep aquifer. Water budget analyses suggested that after pumping continues for a couple of days, the leakage from the overlying layers begins to supply the majority of the withdrawal from the deep aquifer. However, the induced leakage from the upper shallow aquifer can travel only a few meters into the aquitard, and it can not reach the lower aquifer during a 90 day pumping period. The major portion of the induced leakage occurred during the pumping period, but a small leakage can continue as a residual effect after the pumping period. The vertical hydraulic conductivity of the aquitard plays a major role in partitioning the ratio of the induced leakage for the pumping and after-pumping periods.     

用水位恢复数据反演越流承压含水层参数

水文地质勘测中,由于水位恢复阶段没有人力和机械因素干扰,由测量数据可以画出平滑的曲线,更适宜于分析水文地质参数,但经典非稳定流Theis公式和Theis水位恢复法所依据的若干假设条件在实际中难以满足。针对越流承压含水层具有补给条件而很快稳定以及非稳定抽水阶段流量常“抖动”的特点,论证了利用稳定流量和Hantush-Jacob越流模型计算的可行性,并用扩展的卡尔曼滤波器反演水文地质参数,经文献中历史数据和实地抽水试验检验结果表明,由该方法反演的预测值和实测值吻合良好。     

基于广义径向流模型的非均质孔隙含水层井流试验分析

Theis模型、Dupuit模型等经典井流模型分析非均质含水层井流试验数据有一定的局限性,获取的参数不适合表征非均质含水层特性。而GRF模型可以获取含水层流动特性的数据。相比于Theis模型、Dupuit模型,GRF模型更能表征非均质含水层特性。以黄石东湖新村棋盘洲长江大桥的抽水试验数据为例,采用Theis模型和GRF模型计算含水层渗透系数,结合实际水文地质条件,对比分析不同方法计算的水文地质参数,并计算含水层水流维数和表观压力传导系数（K_f /S_sf）。结果表明:研究区含水层为细砂夹条带状黏土透镜体的非均质含水层,采用GRF模型计算结果更符合实际情况,渗透系数为 4.09×10?3cm/s;含水层水流维数为1.61,地下水为双线性流动状态,含水层对抽水试验的响应主要受黏土条带控制;观测井和抽水主井的K_f /S_sf呈非线性相关,进一步验证了含水层的非均质性。在非均质孔隙含水层中,应用多孔联合非稳定GRF井流试验方法不仅能确定水文地质参数,并且能丰富对含水层特性的认知。     

Parameters affecting the occurrence of quicksand and the drying up of large diameter wells that gain water from the bottom: a case study from Iran

Large diameter fully cased wells that gain water from the bottom are often dug in sandy and collapsible aquifers. They have cylindrical vertical walls lined with brick or concrete. The well bottom is partially filled with aquifer material through which the flow is vertically upward. When the vertical hydraulic gradient reaches a critical value, quicksand occurs and the well structure can be destroyed. Another difficulty encountered is drawdown in the wellbore and the drying up of the well. To overcome these problems, the flow around and beneath these wells is numerically simulated. The simulation results are used to investigate the effect of well and aquifer parameters on quicksand and drawdown. For practical purposes, the dimensionless drawdown-time and dimensionless vertical gradient-time curves are developed. It was found that the ratio of filling material thickness to well radius affects the shape of these type curves. The type curves may be used to predict the time after pumping commences when quicksand occurs and the well dries up. They are also useful to design the safe pumping rate and duration as well as the optimum well radius. These are demonstrated by analyzing the pumping test data from a case study in the arid Chah Kutah region, southern Iran.     

A numerical investigation to illustrate the consequences of hydraulic connections between granular and fractured-rock aquifers

Natural or artificial hydraulic connections between a granular aquifer in contact with a fractured-rock aquifer can have significant physical and chemical impacts at both a local and a regional scale. In this study, numerical simulations are conducted in order to illustrate the hydrogeological consequences of such hydraulic relationships. The numerical investigation, based on a conceptual model, focuses on the effects of the hydraulic connections when conducting a pumping test in a well that is set into a granular confined aquifer overlying a fractured-rock aquifer which presents a few fractures directly connected to the granular aquifer. It is illustrated that when interpreting the pumping test with the conventional methods consisting of plotting the drawdown versus time, a bias is introduced on the estimation of the transmissivity of the granular aquifer due to groundwater flowing from the fractured-rock aquifer via connecting fractures. However, it is underlined that plotting drawdown log-derivative versus time helps to diagnose the existence of these hydraulic relationships and therefore avoids committing a bias on the transmissivity estimation of the granular aquifer. Numerical simulation results also illustrate that hydraulic connections between the two aquifers can have significant impacts on the hydrogeochemical signature of the granular aquifer under investigation.     

基于数值模拟的含水层参数识别

利用地下水流数值模拟软件Modflow耦合大型抽水试验和长观孔水位两个模型的方法,对含水层参数进行了识别与校验,该方法求得的含水层参数避免了只利用抽水试验模型校验所带来的不确定性。同时利用抽水实验数据进行抽水与恢复的全过程曲线拟合,水位降深模拟相对误差小于6％,并且对均衡水量、泉水的溢出量以及末流场拟合程度进行了分析,均衡水量模拟相对误差最大为2．6％,泉水溢出量模拟相对误差最大为8．14％,末流场拟合程度也较好,从而提高了含水层参数的准确性。实例研究表明,这种求参方法精度高、切实可行,可以推广到其他的含水层参数确定中。     

分析隔水边界附近抽水-恢复试验数据的新方法

为能同时分析含水层具有直线隔水边界条件下,抽水试验中抽水―恢复阶段降深数据,提出了一种新的数据分析方法。在建立这种方法时,将表示抽水和恢复阶段水头降深表达式中Theis井函数的级数表达式的前3项作为其近似表达式,经过推导,分别得到抽水和恢复2个阶段的直线方程。2个直线方程的因变量和自变量均为观测数据的函数,而直线常数为待求参数的函数,在进行数据分析时,只要将试验观测数据分别转化为直线方程的因变量和自变量数据,就能够利用一元线性回归法分别计算2个直线方程的常数,而利用直线常数的表达式,能够推导得到计算含水层参数和映射井到观测孔间距离的公式。通过算例说明了方法的具体应用步骤。      

Modeling the Neuman’s well function by an artificial neural network for the determination of unconfined aquifer parameters

An artificial neural network is designed as an improved alternative approach to the conventional type-curve matching technique for the determination of unconfined aquifer parameters. The network is implemented in a six-step protocol consisted of input selection, data splitting, design of network architecture, determination of network structure, network training, and network validation. The network is trained for the well function of unconfined aquifers by the back-propagation technique, adopting the Levenberg-Marquardt optimization algorithm. By applying a principal component analysis (PCA) on the training input data and through a trial-and-error procedure, the structure of the network is optimized with the topology of (3 × 6 × 3). The replicative, predictive, and structural validity of the developed network are evaluated with synthetic and real field data. The network eliminates graphical error inherent in the type-curve matching technique and provides an automatic and fast procedure for aquifer parameter estimation, particularly when analyzing many alternative pumping tests routinely obtained from continuous data loggers/data collection systems.     

抽水试验和长观水位联合模拟确定含水层参数

为了更加准确地确定含水层参数,提出了利用地下水流数值模拟软件Modflow耦合大型抽水试验和长观孔水位两个模型的方法,对含水层参数进行了识别与校验。该方法求得的含水层参数避免了只利用抽水试验模型校验所带来的不确定性,同时利用抽水实验数据进行抽水与恢复的全过程曲线拟合,水位降深模拟相对误差小于6%,提高了含水层参数的准确性。     

双重介质含水层求参方法探讨

双重介质模型能较好地刻画天然裂隙含水层的非均质性及液体流动和溶质迁移特征。在石油开采、核废物处置安全评价和环境水文地质等方面受到广泛重视。但是,双重介质模型的实际应用远远落后于其理论发展。其原因除了双重介质模型复杂、计算工作量大以外,模型参数确定的理论和测试方法很不完善,难以取得两套较客观的模型参数是另一重要原因。本文就双重介质含水层参数的确定问题,从其介质特征和水流运动特征入手,探讨了双重介质含水层中抽水和注水条件下的井流动力学方程及其求解方法,并讨论了其适用条件及存在的问题,最后,用实际资料说明了求参过程,检验了公式。     

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.     

水力联系系数法定量评价含水层之间水力联系

为了定量研究与评价含水层之间地下水水力联系程度,首次提出了水力联系系数C（hydraulic connection coefficient）的概念。将水力联系系数C定义为观测孔目的含水层水位降深与该观测孔位置抽水含水层水位降深的比值。通过水力联系系数,可定量评价某含水层水平上同层之间和垂向上不同含水层之间的水力联系程度。依据鄂尔多斯盆地白垩系洛河组各含水层段的水力联系系数C值,将含水层之间水力联系分为5个等级。其中,0.000 0 ≤ C<0.062 5,0.062 5 ≤ C<0.125 0,0.125 0 ≤ C<0.250 0,0.250 0 ≤ C<0.500 0,C ≥ 0.500 0,分别代表水力联系等级为极弱、弱、中等、强、极强。以高家堡井田钻孔抽（放）水试验数据为例,采用水力联系系数和观测孔水位响应时间两个指标定量评价了区内巨厚层状非均质洛河组含水层内部水力联系。结果表明：洛河组中上段水平同层之间的水力联系系数分别为0.373 0、0.413 8,观测孔水位响应时间较短（约为5 min）,水力联系强;洛河组下段水平同层之间水力联系系数分别为0.440 1、0.491 1,观测孔水位响应时间较短（为9~20 min）,水力联系强;洛河组中上段与下段垂向水力联系系数分别为0.000 2、0.007 2、0.089 7,观测孔水位响应时间较长（大于60 min）,水力联系极弱至弱。     

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。     

Pumping-induced Well Hydraulics and Groundwater Budget in a Leaky Aquifer System with Vertical Heterogeneity in Aquitard Hydraulic Properties

In groundwater hydrology, aquitard heterogeneity is often less considered compared to aquifers, despite its significant impact on groundwater hydraulics and groundwater resources evaluation. A semi-analytical solution is derived for pumping-induced well hydraulics and groundwater budget with consideration of vertical heterogeneity in aquitard hydraulic conductivity (K) and specific storage (Ss). The proposed new solution is innovative in its partitioning of the aquitard into multiple homogeneous sub-layers to enable consideration of various forms of vertically heterogeneous K or Ss. Two scenarios of analytical investigations are explored: one is the presence of aquitard interlayers with distinct K or Ss values, a common field-scale occurrence; another is an exponentially depth-decaying aquitard Ss, a regional-scale phenomenon supported by statistical analysis. Analytical investigations reveal that a low-K interlayer can significantly increase aquifer drawdown and enhance aquifer/aquitard depletion; a high-Ss interlayer can noticeably reduce aquifer drawdown and increase aquitard depletion. Locations of low-K or high-Ss interlayers also significantly impact well hydraulics and groundwater budget. In the context of an exponentially depth-decaying aquitard Ss, a larger decay exponent can enhance aquifer drawdown. When using current models with a vertically homogeneous aquitard, half the sum of the geometric and harmonic means of exponentially depth-decaying aquitard Ss should be used to calculate aquitard depletion and unconfined aquifer leakage.     

改进的Theis井流模型及其解析解——考虑含水层顶板的挠曲作用

传统承压含水层井流理论都假定承压水层顶面总应力不变，其隐含的意义是忽略含水层顶板的刚度，从而忽略了顶板弯曲对含水层释水的影响。指出考虑顶板弯曲时，抽水井周围承压含水层顶部的总应力将减小，从而产生比传统理论估计更大的地下水降深，并结合弹性板理论对Theis井流模型作出了改进，新模型的解析解证明Theis模型计算的地下水龙头降深偏低。