A new method for the interpretation of pumping tests in leaky aquifers

A novel methodology for the interpretation of pumping tests in leaky aquifer systems, referred to as the double inflection point (DIP) method, is presented. The method is based on the analysis of the first and second derivatives of the drawdown with respect to log time for the estimation of the flow parameters. Like commonly used analysis procedures, such as the type-curve approach developed by Walton (1962) and the inflection point method developed by Hantush (1956), the mathematical development of the DIP method is based on the assumption of homogeneity of the leaky aquifer layers. However, contrary to the two methods developed by Hantush and Walton, the new method does not need any fitting process. In homogeneous media, the two classic methods and the one proposed here provide exact results for transmissivity, storativity, and leakage factor when aquifer storage is neglected and the recharging aquifer is unperturbed. The real advantage of the DIP method comes when applying all methods independently to a test in a heterogeneous aquifer, where each method yields parameter values that are weighted differently, and thus each method provides different information about the heterogeneity distribution. Therefore, the methods are complementary and not competitive. In particular, the combination of the DIP method and Hantush method is shown to lead to the identification of contrasts between the local transmissivity in the vicinity of the well and the equivalent transmissivity of the perturbed aquifer volume.     

Microbiological response to well pumping

To better constrain sampling strategies for observing biologically sensitive parameters in ground water, we vigorously pumped for 120 h a lightly pumped well completed in a confined glacial aquifer while observing how various physical and chemical parameters evolve in the water produced. The parameters commonly monitored when sampling a well stabilized within about an hour, after 5 wellbore volumes were produced; these parameters include temperature, pH, dissolved oxygen, oxidation-reduction potential (Eh), and electrical conductivity. The concentrations of ferrous iron, sulfide, and sulfate and various biological or biologically sensitive parameters, including the concentrations of dissolved hydrogen and methane, direct cell counts, and the microbial community profile, in contrast, required more than 8 h or 36 well volumes to stabilize. We interpret this result to mean that the zone of influence of the wellbore on biologic processes in the aquifer extends beyond the commonly recognized zone where physical properties are affected. A second period of adjustment of these biologically sensitive parameters began after about 50 h of pumping, following displacement of 230 wellbore volumes, and continued to the end of the experiment. During this period, the cell density and the composition of the microbial community suspended in the water samples changed. This finding indicates that the microbial community in and near the wellbore changed in response to pumping and the changes affected aspects of the composition of water produced from the well. The study demonstrates the importance of allowing adequate pumping time when sampling ground water for the analysis of biologically sensitive parameters.     

A procedure for automated analysis of brief pumping tests of domestic wells

A new computer program has been developed to automate analysis of brief single-well pumping tests. Adapted from a procedure developed by Picking (1994) that does not require measurement of the pumping rate, this new program is menu-driven and eliminates one significant source of imprecision in Picking's original method, namely, selection of "well function of u" values by interpolation in a lookup table. This new program has been applied to tests of 25 domestic wells penetrating bedrock, each pumped for <2 min.     

Stable pumping rates for horizontal wells in bank filtration systems

We consider common bank filtration systems and develop an explicit analytic solution representing steady, two-dimensional, groundwater flow to a horizontal well near a river in an unconfined aquifer. For the boundary-value problem investigated, we find that a unique solution exists for all negative well discharges. For positive discharges, a maximum value exists which corresponds to the formation of a cusp on the free surface. For positive discharges less than the maximum, the solution is not unique, consisting of two alternate configurations of the free surface. One solution includes a stable free surface on a single-valued physical plane, while the alternate solution includes a looped free surface lying on two sheets of a Riemann surface. Imposing a stability condition on the free surface results in a unique solution to the problem. We use the solution to investigate the behavior of the free surface under varying well discharges to identify stable pumping rates and predict well yield. In particular, we examine the well yield and the stability of the free surface when the head in the horizontal well is maintained at the top of the well screen. This condition is shown to produce a stable free surface for a wide range of well radii; the stability is independent of the hydraulic conductivity of the aquifer, the location of the well, or the presence of a skin resistance at the well.     

评估空间—发生率—震级地震预测的基于似然的检验

区域地震似然模型(RELM)工作组的5年实验是设计用来比较预测加州及附近各纬度-经度-震级单元地震发生率的若干有希望的方法。这种预测模式被作为世界范围内其他地震可预测性试验的蓝本,因此考虑如何评估这种预测的性能是很重要的。最近采用的两个试验都基于给定预测情况下观测到的地震分布的概率,一个测试比较了空间-发生率-震级单元的观测值和预测值,另一个测试仅仅比较了预测的发生率和观测地震的数目。在本文中,我们讨论了目前关于发生率预测的微小的缺陷,我们建议采用另外两个测试分别进行空间-发生率-震级预测的空间和震级分量的预测。为了更好地说明问题,我们考虑了区域地震似然模型预测和进行区域地震似然模型实验的前半期观测到的地震分布。我们得出空间—发生率—震级预测好像是和观测地震的分布相一致,尽管空间预测和观测地震的空间分布是不一致的,我们建议这些新的测试应该被用于提供更详细的地震预测评估。我们也讨论了每个基于似然测试的统计学功效以及基于似然测试的结果的稳定性(相对于地震目录的不确定性)。     

A new solution and data analysis for gas flow to a barometric pumping well

When an open well is installed in an unsaturated zone, gas will flow to/from the well depending on the pressure difference between the well and the surrounding media. This process is called barometric pumping and the well is called a barometric pumping well (BPW). Understanding subsurface gas pressure distribution and gas flow rate to/from a BPW is indispensable to optimize passive soil vapor extraction. This study presents a 2-D semi-analytical solution to calculate the subsurface gas pressure and gas flow rate to/from a BPW with and without a check valve. The problem is conceptualized as a mixed-type boundary value problem. The solution for pumping without a check valve is used to analyze the behavior of the radius of influence (ROI). Results show that ROI is time-dependent. It increases with radial gas permeability and decreases with vertical gas permeability. Field application of the solution without a check valve demonstrates the high accuracy of the developed solution.     

Analytical model for computing residence times near a pumping well

An analytical solution for calculating the residence time of fluid flowing toward a pumping well in an unconfined aquifer has been developed. The analytical solution was derived based on a radial, steady-state, Dupuit-Forchheimer flow model. The resulting integral expression involved computing the imaginary error function, for which a simple series expansion is proposed. The validity of the analytical expression is demonstrated by testing its results against numerical results for an example problem. The analytical solution compared favorably with the numerical approximation.     

Stream-stage response tests and their joint interpretation with pumping tests

Hydraulic head response to stream-stage variations can be used to explore the hydraulic properties of stream-aquifer systems at a relatively large scale. These stream-stage response tests, also called flooding tests, are typically interpreted using one- or two-dimensional models that assume flow perpendicular to the river. Therefore, they cannot be applied to systems that are both horizontally and vertically heterogeneous. In this work, we use the geostatistical inverse problem to jointly interpret data from stream-stage response and pumping tests. The latter tests provide flow data (which are needed to resolve aquifer diffusivity into transmissivity and storage coefficient) and may supply supplementary small-scale information. Here, we summarize the methodology for the design, execution, and joint numerical interpretation of these tests. Application to the Aznalcóllar case study allows us to demonstrate that the proposed methodology may help in responding to questions such as the continuity of aquitards, the role and continuity of highly permeable paleochannels, or the time evolution of stream-aquifer interaction. These results expand the applicability and scope of stream-stage response tests.     

测井岩性识别新方法研究

为了更好地解决测井岩性识别问题,引入了一种基于粒子群优化的支持向量机算法.通过实际测井资料和岩性剖面资料进行学习训练支持向量机,并利用粒子群优化算法对支持向量机参数进行优化,建立了测井岩性识别的支持向量机模型,应用该方法对准噶尔盆地某井的测井岩性进行识别,并将该方法的识别结果与BP神经网络方法的识别结果进行了比较,结果表明该方法优于BP神经网络方法,具有识别正确率高、收敛速度快、推广能力强等优点.     

Predicting horizontal velocities from well data

The Imperial College borehole test site consists of four boreholes with depths lying between 260 and 280 m. The boreholes intersect several cyclical sequences of sandstones, mudstones and limestones. The formations are highly laminated and ultrasonic measurements on preserved core have shown that the mudstones are intrinsically anisotropic. Little or no anisotropy is associated with the sandstones and limestones. A scheme is proposed to predict synthetic vertical and horizontal P- and S-wave logs. Combining (an)isotropic effective medium theories, the Gassmann equation and Backus averaging, the scheme extends previous sand-shale models to transversely isotropic rock formations. The model assumes that the anisotropy is due to layering and due to the preferred horizontal orientation of the clay minerals, pores and cracks within the mudstones. The pores and cracks within the sandstones and limestones are randomly orientated. After fitting the model to the ultrasonic data to obtain the unknown parameters, the model successfully predicts the sonic log and the direct arrival times from a cross-hole survey.     

城市防震减灾能力的定义及评估方法

城市防震减灾能力本身是一个涉及因素众多的复杂体系,对它的评估也是涉及到地震科学、社会科学和经济科学的交叉学科问题。本文首先提出了城市防震减灾能力的概念,把人员伤亡、经济损失和震后恢复时间3方面作为衡量城市防震减灾能力的准则;围绕这三个准则,从影响城市防震减灾能力的众多复杂因素中归纳出6大因素,并用一些简单、可测量的指标来代表这6大因素,建立起城市防震减灾能力指标体系;然后再分别建立这些指标体系中的各种因素或其子因素与评价三准则中的人员伤亡、经济损失和恢复时间的联系;最后,用灰色关联分析方法将3个评价准则综合成一个防震减灾能力指数。从而为城市防震减灾能力评估提供了一个较系统、完整的理论体系框架。城市防震减灾能力评价体系的建立能够对城市的防震减灾能力进行定量的评价,从而指导城市进行防震减灾努力的决策。     

Unconfined linear flow to a horizontal well

The validity of a previously proposed but untested modification to equations for flow to a horizontal well is assessed using a specially developed finite-difference model. This modification extends confined flow equations to allow the head in the well and the saturated depth at the well to be estimated in unconfined conditions. The study is limited to the case of two-dimensional flow with no flow in the direction parallel to the line of the well. The results show that the modified equations for both a finite unconfined aquifer and, by inference, an infinite unconfined aquifer are adequately accurate for practical application.     

Optimal design of pumping tests in leaky aquifers for stream depletion analysis

We analyze the optimal design of a pumping test for estimating hydrogeologic parameters that are subsequently used to predict stream depletion caused by groundwater pumping in a leaky aquifer. A global optimization method is used to identify the test’s optimal duration and the number and locations of observation wells. The objective is to minimize predictive uncertainty (variance) of the estimated stream depletion, which depends on the sensitivities of depletion and drawdown to relevant hydrogeologic parameters. The sensitivities are computed analytically from the solutions of Zlotnik and Tartakovsky [Zlotnik, V.A., Tartakovsky, D.M., 2008. Stream depletion by groundwater pumping in leaky aquifers. ASCE Journal of Hydrologic Engineering 13, 43–50] and the results are presented in a dimensionless form, facilitating their use for planning of pumping test at a variety of sites with similar hydrogeological settings. We show that stream depletion is generally very sensitive to aquitard’s leakage coefficient and stream-bed’s conductance. The optimal number of observation wells is two, their optimal locations are one close to the stream and the other close to the pumping well. We also provide guidelines on the test’s optimal duration and demonstrate that under certain conditions estimation of aquitard’s leakage coefficient and stream-bed’s conductance requires unrealistic test duration and/or signal-to-noise ratio.     

A general analytical solution for flow to a single horizontal well by Fourier and Laplace transforms

The objective of this paper is to present an analytical solution for describing the head distribution in an unconfined aquifer with a single pumping horizontal well parallel to a fully penetrating stream. The Laplace-domain solution is developed by applying Fourier sine, Fourier and Laplace transforms to the governing equation as well as the associated initial and boundary conditions. The time-domain solution is obtained after taking the inverse Laplace transform along with the Bromwich integral method and inverse Fourier and Fourier sine transforms. The upper boundary condition of the aquifer is represented by the free surface equation in which the second-order slope terms are neglected. Based on the solution and Darcy’s law, the equation representing the stream depletion rate is then derived. The solution can simulate head distributions in an aquifer infinitely extending in horizontal direction if the well is located far away from the stream. In addition, the solution can also simulate head distributions in confined aquifers if specific yield is set zero. It is shown that the solution can be applied practically to evaluate flow to a horizontal well.     

Interpretation of transmissivity estimates from single-well pumping aquifer tests

Interpretation of single-well tests with the Cooper-Jacob method remains more reasonable than most alternatives. Drawdowns from 628 simulated single-well tests where transmissivity was specified were interpreted with the Cooper-Jacob straight-line method to estimate transmissivity. Error and bias as a function of vertical anisotropy, partial penetration, specific yield, and interpretive technique were investigated for transmissivities that ranged from 10 to 10,000 m(2)/d. Cooper-Jacob transmissivity estimates in confined aquifers were affected minimally by partial penetration, vertical anisotropy, or analyst. Cooper-Jacob transmissivity estimates of simulated unconfined aquifers averaged twice the known values. Transmissivity estimates of unconfined aquifers were not improved by interpreting results with an unconfined aquifer solution. Judicious interpretation of late-time data consistently improved estimates where transmissivity exceeded 250 m(2)/d in unconfined aquifers.     

Comparison of continuous and cyclic pumping from a well.

Two practically applicable pumping patterns for wells are: (1) continuous pumping at a sustainable constant rate; and (2) pumping at a sustainable constant rate for a fixed period every day (cyclic pumping). Theoretical analysis shows that with the cyclic pumping pattern the pump can be run at a higher rate than with continuous pumping. However continuous pumping at the maximum continuously sustainable constant rate produces considerably more water. If the objective is to produce as much water as possible, it is important to use a pump designed for running at the maximum continuously sustainable rate.     

一种评估地震前兆可信度的方法

本文提出了一种可以对地震前兆的可信度进行评估的方法. 通过对前兆信息的抽取、各类非地震干扰的识别、前兆与地震事件在时间和空间的相关性分析以及前兆的随机检验等一系列手段来评估前兆信息的真伪,提高地震前兆信息的显著性和可信度. 该方法及思路也可为其他非地震前兆的可信度评估所借鉴. 作为一个具体的例子,本文利用日本气象厅的地震目录以及能定量描述地震活动的时、空、强信息演化特征的RTL(Region_Time_Length)方法对2000年10月6日在日本鸟取县西部发生的7.3级地震前周围地区近26年的地震活动进行了系统的研究,得到了可能的地震活动前兆信息,并采用本文提出的方法对该前兆进行了评估,证实了上述前兆的显著性和可信性.     

测井约束地震波形反演的同伦摄动法

测井数据和地震数据是地震勘探中两种最重要的资料. 测井约束地震波形反演是在非线性波形反演的基础上,利用已知测井资料详细的垂直分辨能力和地震资料均匀密集的水平采样特点, 通过迭代反演来求取一个具有较高分辨率的速度参数.本文建立了测井约束反演模型,研究了测井约束下地震波形反演的同伦摄动求解方法.同伦摄动法作为一种新的、求解数学物理中各种非线性问题的有效方法,具有计算速度快、计算精度高的优点.这对于提高反演的精度和效率是十分有益的. 为了表征该方法的有效性和稳定性,分别对水平层状介质模型和逆冲断层带模型进行了数值模拟,并与Landweber迭代法相对比,结果表明该算法具有更好的收敛性,能够取得更为满意的反演效果.     

A new method for the interpretation of the constant-head well permeameter

A novel semi-analytical solution for the interpretation of the constant-head permeameter test is introduced, which accounts for the correct mixed-type boundary condition at the wellbore, unlike all published analytical solutions. Capillarity can also be accounted for. The simplifications are that flow from the bottom of the borehole is neglected (therefore the solution is applicable to slender boreholes, where the ponding depth is at least 10 times the radius) and capillarity can be modeled with a quasi-linear approach. The Green's function approach leads to an integral equation, the solution of which does not show significant ill-posedness. Two sub-cases are presented: the first neglects capillary effects (the all-saturated approximation) and the second (general solution) takes them into account. The all-saturated solution is successfully tested against finite element simulations. The corresponding values of the borehole shape factor C are slightly larger than the ones obtained with approximate analytical solutions from the literature. When capillarity is accounted for, C changes of a factor of 10 when the dimensionless sorptive number A goes from typical values for fine soils to typical values for coarse soils (about two orders of magnitude of variation for A). This range shifts to lower values of A as the dimensionless borehole depth increases. Consequently, the all-saturated solution is a good approximation of the soil behavior for boreholes with large ponding depth, and coarse soils. The proposed semi-analytical solution is fast to compute and thus it is possible to use it in an automated optimization technique to fit field data and estimate the field-saturated hydraulic conductivity and the sorptive number; this would not be feasible using a numerical solution.