Effect of wellbore storage and finite thickness skin on flow to a partially penetrating well in a phreatic aquifer

An analytical model is presented for the analysis of constant flux tests conducted in a phreatic aquifer having a partially penetrating well with a finite thickness skin. The solution is derived in the Laplace transform domain for the drawdown in the pumping well, skin and formation regions. The time-domain solution in terms of the aquifer drawdown is then obtained from the numerical inversion of the Laplace transform and presented as dimensionless drawdown–time curves. The derived solution is used to investigate the effects of the hydraulic conductivity contrast between the skin and formation, in addition to wellbore storage, skin thickness, delayed yield, partial penetration and distance to the observation well. The results of the developed solution were compared with those from an existing solution for the case of an infinitesimally thin skin. The latter solution can never approximate that for the developed finite skin. Dimensionless drawdown–time curves were compared with the other published results for a confined aquifer. Positive skin effects are reflected in the early time and disappear in the intermediate and late time aquifer responses. But in the case of negative skin this is reversed and the negative skin also tends to disguise the wellbore storage effect. A thick negative skin lowers the overall drawdown in the aquifer and leads to more persistent delayed drainage. Partial penetration increases the drawdown in the case of a positive skin; however its effect is masked by the negative skin. The influence of a negative skin is pronounced over a broad range of radial distances. At distant observation points the influence of a positive skin is too small to be reflected in early and intermediate time pumping test data and consequently the type curve takes its asymptotic form.     

A novel analytical solution for a slug test conducted in a well with a finite-thickness skin

An aquifer containing a skin zone is considered as a two-zone system. A mathematical model describing the head distribution is presented for a slug test performed in a two-zone confined aquifer system. A closed-form solution for the model is derived by Laplace transforms and Bromwich integral. This new solution is used to investigate the effects of skin type, skin thickness, and the contrast of skin transmissivity to formation transmissivity on the distributions of dimensionless hydraulic head. The results indicate that the effect of skin type is marked if the slug-test data is obtained from a radial two-zone aquifer system. The dimensionless well water level increases with the dimensionless positive skin thickness and decreases as the dimensionless negative skin thickness increases. In addition, the distribution of dimensionless well water level due to the slug test depends on the hydraulic properties of both the wellbore skin and formation zones.     

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.     

A review of thermal response test analysis using pumping test concepts

The design of ground-coupled heat pump systems requires knowledge of the thermal properties of the subsurface and boreholes. These properties can be measured with in situ thermal response tests (TRT), where a heat transfer fluid flowing in a ground heat exchanger is heated with an electric element and the resulting temperature perturbation is monitored. These tests are analogous to standard pumping tests conducted in hydrogeology, because a system that is initially assumed at equilibrium is perturbed and the response is monitored in time, to assess the system's properties with inverse modeling. Although pumping test analysis is a mature topic in hydrogeology, the current analysis of temperature measurements in the context of TRTs is comparatively a new topic and it could benefit from the application of concepts related to pumping tests. The purpose of this work is to review the methodology of TRTs and improve their analysis using pumping test concepts, such as the well function, the superposition principle, and the radius of influence. The improvements are demonstrated with three TRTs. The first test was conducted in unsaturated waste rock at an active mine and the other two tests aimed at evaluating the performance of thermally enhanced pipe installed in a fully saturated sedimentary rock formation. The concepts borrowed from pumping tests allowed the planning of the duration of the TRTs and the analysis of variable heat injection rate tests accounting for external heat transfer and temperature recovery, which reduces the uncertainty in the estimation of thermal properties.     

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.     

Sensitivity analysis of a no-crossflow model for the transient flowmeter test

 Logarithmic sensitivities and plausible relative errors are studied in a simple no-crossflow model of a transient flowmeter test (TFMT). This model is identical to the model of a constant-rate pumping test conducted on a fully penetrating well with wellbore storage, surrounded by a thick skin zone, and situated in a homogeneous confined aquifer. The sensitivities of wellbore drawdown and wellface flowrate to aquifer and skin parameters are independent of the pumping rate. However, the plausible relative errors in the aquifer and skin parameters estimated from drawdown and wellface flowrate data can be proportionally decreased by increasing the pumping rate. The plausible relative errors vary by many orders of magnitude from the beginning of the TFMT. The practically important flowrate and drawdown measurements in this test, for which the plausible relative errors vary by less than one order of magnitude from the minimum plausible relative errors, can begin approximately when the dimensionless wellface flowrate exceeds q _D =q/Q≈0.4. During most of this stage of the test, the plausible relative errors in aquifer hydraulic conductivity (K _a ) are generally an order of magnitude smaller than those in aquifer specific storativity. The plausible relative errors in the skin hydraulic conductivity (K _s ) are generally larger than the plausible relative errors in the aquifer specific storativity when the thick skin is normal (K _s >K _a ) and smaller when the thick skin is damaged (K _s <K _a ). The specific storativity of the skin zone would be so biased that one should not even attempt to estimate it from the TFMT. We acknowledge Wiebe H. van der Molen for recommending the De Hoog algorithm and sharing his code. This research was partially supported by the US Geological Survey, USGS Agreement #1434-HQ-96-GR-02689 and North Carolina Water Resources Research Institute, WRRI Project #70165.     

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.     

Analysis of the water content in an unconfined aquifer with a partially penetrated pumping well

Most methods developed to represent water flow phenomena in an unconfined aquifer with a fully penetrated pumping well are either numerical, such as the well‐known FEMWTER model, or experimental; analytical models of a partially penetrated pumping well are rare. This study employs the linearized Richards equation as the governing equation, with the aid of Fourier Integral Transformation, to obtain an analytical solution of the water content distribution in an unconfined aquifer with a partially penetrated pumping well. The results from this study could serve to substantiate in some sense results from numerical models. In addition, the theory developed herein can be modified to simulate a vacuum‐pressured pumping well since it is derived by considering, among others, the location and length of a well screen with fluxes. Copyright © 2008 John Wiley & Sons, Ltd.     

Travel time to a well pumping an unconfined aquifer without recharge

A solution is given for the travel time to a well pumping an ideal, horizontal unconfined aquifer, under steady-state conditions, when recharge from infiltration is negligible. Three forms of the solution are provided: a closed-form solution, an integral to be calculated in a worksheet, and a simple equation. The three forms of the solution give travel times nearly identical to those obtained using a finite-element code for saturated and unsaturated flow and particle tracking.     

Hydraulics of a partially penetrating well with skin zone in a confined aquifer

A steady/quasi-steady model is developed for predicting flow into a partially penetrating well with skin zone in a confined aquifer overlying an impervious layer. The model takes into account flow through the bottom of the wellbore, finite skin thickness and finite horizontal and vertical extent of the aquifer. Moreover, the solution can be easily extended to include the mixed-type boundary condition at the well face, where a Dirichlet in the form of a specified hydraulic head and a Neumann in the form of zero flux coexist at the same time at different portions of the well face. The validity of the proposed solution is tested by comparing a few results obtained from the developed model with corresponding results obtained by analytical and numerical means. The study shows that, among other factors remaining constant, both the horizontal and vertical extent of an artesian aquifer, thickness of the skin zone, bottom flow and conductivity contrast of the skin and formation zones, play an important part in deciding flow to a well dug in the aquifer, and hence these factors must be considered while analyzing the problem. The model proposed here can be used to estimate skin thickness as well as hydraulic conductivities of the skin and formation zones of a well with skin zone in an artesian aquifer underlain by an impervious layer by utilizing pumping test data falling in the steady or quasi-steady state of a typical pumping test. As the proposed solution is of a general nature in the sense that it can handle, apart from partial penetration and bottom flow, the finite size skin zone and finite horizontal and vertical extent of an artesian aquifer together with the mixed-type boundary condition at the well face, it is hoped that the predictions coming out of the model will be more realistic than those obtained using solutions developed with more stringent assumptions.     

Empirical relationships for estimating stream depletion by a well pumping near a gaining stream

Siting wells near streams requires an accurate estimate of the quantity of water derived from the river due to pumping. A number of hydrogeological and hydraulic parameters influence this value. This study estimates stream depletion under steady-state conditions for a variety of hydrogeological systems. A finite differences model was used to analyze several hydrogeological situations, and for each of these the stream depletion was estimated using an advective transport method. An empirical equation for stream depletion was obtained for the case of a stream that partially penetrates the aquifer and a pumping well that is screened over a portion of the aquifer. The derived equation, which is valid for both isotropic and anisotropic conditions, expresses stream depletion as a function of the unit inflow to the river, the discharge of the pumping well, the well screen length, the distance between the river and pumping well, the wetted perimeter, and a new parameter called "overlap," which is defined to be the distance between the riverbed and the top of well screen. The overlap parameter makes it possible to consider indirectly the vertical component of flow, which is accentuated when the well is screened below the streambed. The formula proposed here should be useful in deciding where to locate a pumping well and to decide the appropriate length of its screen.     

Improved characterization of small "u" for Jacob pumping test analysis methods

Numerous refinements have been proposed to traditional pumping test analyses, yet many hydrogeologists continue to use the Jacob method due to its simplicity. Recent research favors hydraulic tomography and inverse numerical modeling of pumping test data. However, at sites with few wells, or relatively short screens, the data requirements of these methods may be impractical within physical and fiscal constraints. Alternatively, an improved understanding of the assumptions and limitations of Theis and, due to their widespread usage, Jacob analyses, leads to improved interpretations in data-poor environments. A fundamental requirement of Jacob is a "small" value of u = f(r(2)/t), with radial distance, r, and pumping time, t. However, selection of a too stringent (i.e., too low) maximum permissible u-value, u(max), results in rejection of usable data from wells beyond a maximum radius, r(max). Conversely, data from small radii, less than r(min), where turbulent- and vertical-flow components arise, can result in acceptance of inappropriate data. Usage of drawdown data from wells too close to the pumping well, and exclusion of data from wells deemed too far, can cause unrealistic aquifer transmissivity, permeability, and storativity determinations. Here, data from an extensive well field in a glacial-outwash aquifer in north-central Minnesota, USA, are used to develop a new estimate for u(max). Traditionally quoted values for u(max) range from 0.01 to 0.05. Our proposed value for Jacob distance-drawdown analyses is significantly higher with u(max) up to 0.2, resulting in larger allowable r(max)-values and a higher likelihood of inclusion of additional wells in such pumping test analyses.     

Three-dimensional geostatistical inversion of flowmeter and pumping test data

We jointly invert field data of flowmeter and multiple pumping tests in fully screened wells to estimate hydraulic conductivity using a geostatistical method. We use the steady-state drawdowns of pumping tests and the discharge profiles of flowmeter tests as our data in the inference. The discharge profiles need not be converted to absolute hydraulic conductivities. Consequently, we do not need measurements of depth-averaged hydraulic conductivity at well locations. The flowmeter profiles contain information about relative vertical distributions of hydraulic conductivity, while drawdown measurements of pumping tests provide information about horizontal fluctuation of the depth-averaged hydraulic conductivity. We apply the method to data obtained at the Krauthausen test site of the Forschungszentrum Jülich, Germany. The resulting estimate of our joint three-dimensional (3D) geostatistical inversion shows an improved 3D structure in comparison to the inversion of pumping test data only.     

Measurement and analysis of depression storage on a hillslope

A precise photogrammetric technique was used to determine the microtopography of seven 2.6 m × 1.2 m experimental units located on a hillslope. Surface elevations were determined with an accuracy of better than 1 mm, from which contours at 2mm intervals were interpolated. These contour plots were then manually interpreted to define depressions and associated storage volumes. Analysis of the results highlighted the complex variability of depression storage over the hillslope, for example there being little relation between depression storage volumes and unit slope. This study also highlights the sampling problem for the measurement of depression storage on natural surfaces, which appears not to have been formally recognized previously, and also emphasizes the practical difficulty of achieving depression storage estimates with coefficients of variation less than ten per cent to 50 per cent, much of this variability being due to problems of interpretation rather than measurement of the surface.     

Influence of aquifer heterogeneity and return flow on pumping test data interpretation

Analytical solutions of drawdown in unconfined aquifers are widely applied for determining the specific yield, S_y, and the horizontal and the vertical hydraulic conductivity K_r and K_z, respectively. In many previous studies, estimates of S_y and K_z were observed to be highly variable and physically unrealistic. This has been attributed to the conceptualization of flow above the declining water table and aquifer heterogeneity in the applied models. We present the analysis of time-drawdown data from a pumping test instrumented with depth-differentiated observation piezometers arranged in clusters. Applying homogeneous anisotropic aquifer models in combination with nonlinear least squares parameter identification techniques, the data were analyzed in different groups: analysis of data from individual piezometer clusters and simultaneous analysis of the entire data set from all piezometer clusters (global analysis). From the cluster analyses, estimates of S_y and K_z exhibit large variances and depart from a priori estimates inferred from the hydrostratigraphy. Parameter estimates from the global analysis do not fall within the parameter bounds (minimum and maximum values) defined by the cluster analyses. While heterogeneity appears to be the important reason for large parameter variances, we discuss the influence of rarely considered aquifer return flow on drawdown and the inconsistent results from the cluster and global analyses. We corroborate our findings with data on hydraulic gradients, slug test data, and results from the application of a more realistic numerical flow model.     

地热深井生产过程的井筒传热数值模拟

从地热储层中提取热流体的过程中,在井筒流体与周围地层之间存在着热量交换,使得热流温度发生着变化,为探究流体在生产井中的热量损失过程,本文的目的 是开发一种可靠的数值模型用以说明地热井在生产过程中的流动与换热问题,在此选取COMSOL Multiphysics建立了仿真模型,并对模拟结果进行了解析验证.井筒热量损失的表征要素除了温度以外,热损失功率也起着至关重要的作用,为了全面评价地热生产井的热能损失,故对井口水温及热损失功率两项评价指标进行研究,分析得出水的操作参数及环空热导率变化对井筒热损失的影响.研究结果表明:(1)数值模拟中应用TD代数表达式的连续形式与解析模型中应用Ramey定义的f(t)不连续函数表达式进行热流温度的求解时,对于较长的生产时间,数值解与解析解吻合良好.(2)井底水温的线性变化也将带来井口水温和井筒热损失功率的线性变化,井口水温和井筒热损失功率随井底水温的变化直线斜率随时间的增加略有减小,纵截距也略有减小,说明时间越长,井口温度升高的越慢,井筒热损失功率增大的越小,系统越趋于稳定状态.(3)增量为10 kg/s的采出流量与增量为10℃的井底水温相比,对井口水温的升高及热损失功率的减小影响程度均相应减弱,最终也将趋于稳定状态.(4)环空热导率对井口水温和井筒热损失功率的影响呈现相反的效应,即环空热导率增大井口水温降低,井筒热损失功率增大.结论 认为,综合考虑热流温度及井筒热损失功率两项指标对于高效地热能开采,提高热能利用率等方面具有重要意义,并可全面评价井筒的热量损失大小,为地热能开发提供可靠理论依据.     

Sensitivity analysis of conservative and reactive stream transient storage models applied to field data from multiple-reach experiments

The transient storage model (TSM) has been widely used in studies of stream solute transport and fate, with an increasing emphasis on reactive solute transport. In this study we perform sensitivity analyses of a conservative TSM and two different reactive solute transport models (RSTM), one that includes first-order decay in the stream and the storage zone, and a second that considers sorption of a reactive solute on streambed sediments. Two previously analyzed data sets are examined with a focus on the reliability of these RSTMs in characterizing stream and storage zone solute reactions. Sensitivities of simulations to parameters within and among reaches, parameter coefficients of variation, and correlation coefficients are computed and analyzed. Our results indicate that (1) simulated values have the greatest sensitivity to parameters within the same reach, (2) simulated values are also sensitive to parameters in reaches immediately upstream and downstream (inter-reach sensitivity), (3) simulated values have decreasing sensitivity to parameters in reaches farther downstream, and (4) in-stream reactive solute data provide adequate data to resolve effective storage zone reaction parameters, given the model formulations. Simulations of reactive solutes are shown to be equally sensitive to transport parameters and effective reaction parameters of the model, evidence of the control of physical transport on reactive solute dynamics. Similar to conservative transport analysis, reactive solute simulations appear to be most sensitive to data collected during the rising and falling limb of the concentration breakthrough curve.     

Mixing at the interface between fresh and salt waters in 3D steady flow with application to a pumping well in a coastal aquifer

We consider 3D steady flow of fresh water over a salt water body in a confined aquifer of constant thickness D, with application to a pumping well in a coastal aquifer. With neglect of mixing, a sharp interface separates the two fluid bodies and an existing analytical solution, based on the Dupuit assumption, is adopted. The aim is to solve for the mixing between the fresh and salt waters for α_T/D  1 (α_T transverse dispersivity), as field studies indicate that α_T = O(10⁻³ − 10⁻² m). The mixing zone around the interface is narrow and solutions by existing codes experience numerical difficulties. The problem is solved by the boundary layer (BL) approximation, extending a method, applied previously to two-dimensional flows. The BL equations of variable-density flow are solved by using the Von Karman integral method, to determine the BL thickness and the rate of entrainment of salt water along the interface. Application to the pumping well problem yields the salinity of the pumped water, as function of the parameters of the problem (well discharge, seaward discharge, well distance from the coast and density difference).     

基于振动台试验的移动通信节点机房蓄电池组地震易损性分析

关键移动通信设备的地震易损性是城市移动通信系统地震灾害预测的基础。本文以移动通信系统节点机房中常用的蓄电池组作为研究对象,通过振动台试验来研究蓄电池组的抗震性能,并获得其地震易损性。试验过程中,首先采用FEMA P695建议的方法从美国PEER强震数据库中遴选出对蓄电池组较为危险的地震动记录作为试验激励,随后逐步增大各条地震动记录的幅值,基于振动台进行增量动力分析。试验后根据蓄电池组的地震损伤特征,定义了其损伤指标和损伤水平,并基于振动台试验数据分析获得了典型蓄电池组的地震易损性曲线。