A Model to Simulate Pumping Tests in Wells with High Loss and Backflow

Traditional methods of analyzing pumping tests in single wells fail when the well loss is very high due to a low transmissivity skin. Because of the restricted rate at which water can enter a high loss well from the aquifer, well casing storage becomes a significant factor. Additionally, if a slug of water enters the well from the pump column immediately after the pump is switched off, it has a long‐lasting significant effect on the recovering water level in the well because it cannot be absorbed rapidly by the aquifer. A theoretical model is derived here that simulates the water level in a well in these circumstances. In the model, the continuously changing rate of water inflow from the aquifer to the well is approximated by a step function with a finite difference time step. It is demonstrated by a real example that the model can be applied easily to analyze pumping tests, including tests with a varying pumping rate. The analysis confirms suspected high well loss, calculates the unknown rate of backflow, and determines the aquifer's transmissivity.     

Some analytical solutions for sensitivity of well tests to variations in storativity and transmissivity

The theory of a pumping test or a slug test to measure aquifer transmissivity or storativity assumes that the aquifer properties are uniform around the well. The response of the drawdown to small spatial variations in aquifer properties in the volume of influence is determined by spatial weighting functions or Fréchet kernels, which in general are functions of space and time. The Fréchet kernels determine the effective “volume of influence” of the measurements at any time. Under the assumption that the well is a line sink we derive explicit analytical expressions for the Fréchet kernels for storativity and for transmissivity for both pumping and slug tests. We also derive the total sensitivity functions for uniform variations in storativity and transmissivity and show that they are the spatial integrals of the Fréchet kernels. We consider both the case of separate pumping and observation wells and also the radially symmetric case of observations made at the pumped or slugged well. The “volume of influence” is symmetric with respect to the pumping or slugged well and the observation well, and far from the well the contours of equal spatial sensitivity approach the shapes of ellipses with a well at each focus, rather than circles centered on the pumping well. We use the analytical solutions to investigate the nature of the singularities in the spatial sensitivity functions around the wells, which govern the importance of inhomogeneities close to the well or observation point.     

A method for evaluating horizontal well pumping tests

Predicting the future performance of horizontal wells under varying pumping conditions requires estimates of basic aquifer parameters, notably transmissivity and storativity. For vertical wells, there are well-established methods for estimating these parameters, typically based on either the recovery from induced head changes in a well or from the head response in observation wells to pumping in a test well. Comparable aquifer parameter estimation methods for horizontal wells have not been presented in the ground water literature. Formation parameter estimation methods based on measurements of pressure in horizontal wells have been presented in the petroleum industry literature, but these methods have limited applicability for ground water evaluation and are based on pressure measurements in only the horizontal well borehole, rather than in observation wells. This paper presents a simple and versatile method by which pumping test procedures developed for vertical wells can be applied to horizontal well pumping tests. The method presented here uses the principle of superposition to represent the horizontal well as a series of partially penetrating vertical wells. This concept is used to estimate a distance from an observation well at which a vertical well that has the same total pumping rate as the horizontal well will produce the same drawdown as the horizontal well. This equivalent distance may then be associated with an observation well for use in pumping test algorithms and type curves developed for vertical wells. The method is shown to produce good results for confined aquifers and unconfined aquifers in the absence of delayed yield response. For unconfined aquifers, the presence of delayed yield response increases the method error.     

Water Well Hydrographs: An Underutilized Resource for Characterizing Subsurface Conditions

Many of the world's major aquifers are under severe stress as a result of intensive pumping to support irrigated agriculture and provide drinking water supplies for millions. The question of what the future holds for these aquifers is one of global importance. Without better information about subsurface conditions, it will be difficult to reliably assess an aquifer's response to management actions and climatic stresses. One important but underutilized source of information is the data from monitoring well networks that provide near-continuous records of water levels through time. Most organizations running these networks are, by necessity, primarily focused on network maintenance. The result is that relatively little attention is given to interpretation of the acquired hydrographs. However, embedded in those hydrographs is valuable information about subsurface conditions and aquifer responses to natural and anthropogenic stresses. We demonstrate the range of insights that can be gleaned from such hydrographs using data from the High Plains aquifer index well network of the Kansas Geological Survey. We show how information about an aquifer's hydraulic state and lateral extent, the nature of recharge, the hydraulic connection to the aquifer and nearby pumping wells, and the expected response to conservation-based pumping reductions can be extracted from these hydrographs. The value of this information is dependent on accurate water-level measurements; errors in those measurements can make it difficult to fully exploit the insights that water-well hydrographs can provide. We therefore conclude by presenting measures that can help reduce the potential for such errors.     

Assessing radial transmissivity variation in heterogeneous aquifers using analytical techniques

Pumping tests are one of the most commonly used in situ testing techniques for assessing aquifer hydraulic properties. Numerous researches have been conducted to predict the effects of aquifer heterogeneity on the groundwater levels during pumping tests. The objectives of the present work were as follows: (1) to predict drawdown conditions and to estimate aquifer properties during pumping tests undertaken in radially symmetric heterogeneous aquifers, and (2) to identify a method for assessing the transmissivity field along the radial coordinate in radially symmetric and fully heterogeneous transmissivity fields. The first objective was achieved by expanding an existing analytical drawdown formulation that was valid for a radially symmetric confined aquifer with two concentric zones around the pumping well to an N concentric zone confined aquifer having a constant transmissivity value within each zone. The formulation was evaluated for aquifers with three and four concentric zones to assess the effects of the transmissivity field on the drawdown conditions. The specific conditions under which aquifer properties could be identified using traditional methods of analysis were also evaluated. The second objective was achieved by implementing the inverse solution algorithm (ISA), which was developed for petroleum reservoirs to groundwater aquifer settings. The results showed that the drawdown values are influenced by a volumetric integral of a weighting function and the transmissivity field within the cone of depression. The weighting function migrates in tandem with the expanding cone of depression. The ability of the ISA to predict radially symmetric and log‐normally distributed transmissivity fields was assessed against analytical and numerical benchmarks. The results of this investigation indicated that the ISA method is a viable technique for evaluating the radial transmissivity variations of heterogeneous aquifer settings. Copyright © 2013 John Wiley & Sons, Ltd.     

Interaction of Aquifer and River‐Canal Network near Well Field

The article presents semi‐analytical mathematical models to asses (1) enhancements of seepage from a canal and (2) induced flow from a partially penetrating river in an unconfined aquifer consequent to groundwater withdrawal in a well field in the vicinity of the river and canal. The nonlinear exponential relation between seepage from a canal reach and hydraulic head in the aquifer beneath the canal reach is used for quantifying seepage from the canal reach. Hantush's (1967) basic solution for water table rise due to recharge from a rectangular spreading basin in absence of pumping well is used for generating unit pulse response function coefficients for water table rise in the aquifer. Duhamel's convolution theory and method of superposition are applied to obtain water table position due to pumping and recharge from different canal reaches. Hunt's (1999) basic solution for river depletion due to constant pumping from a well in the vicinity of a partially penetrating river is used to generate unit pulse response function coefficients. Applying convolution technique and superposition, treating the recharge from canal reaches as recharge through conceptual injection wells, river depletion consequent to variable pumping and recharge is quantified. The integrated model is applied to a case study in Haridwar (India). The well field consists of 22 pumping wells located in the vicinity of a perennial river and a canal network. The river bank filtrate portion consequent to pumping is quantified.     

Interpretation of Pumping Tests in Heterogeneous Aquifers with Constant Head Boundary

This paper investigates the impact of heterogeneity of the transmissivity field on the interpretation of steady-state pumping test data from aquifer systems delimited by constant head boundaries such as aquifers adjacent to lakes or rivers. Spatially variable transmissivity fields are randomly generated and used to simulate the drawdown due to a pumping well located at different distances from a constant head boundary. The steady-state drawdown simulated at different observation wells are then interpreted using the Hantush method (Hantush 1959). The numerical simulations show that, in contrast to the case of infinite aquifer domains, the interpreted transmissivity varies depending on well locations and the separation distance between pumping well and boundary relative to the correlation length. The ensemble-averaged estimated transmissivity varies between the geometric mean and the arithmetic mean, and can even exceed the arithmetic mean in a narrow domain adjacent to the boundary. It approaches the geometric mean of the underlying transmissivity field only if the distance between the pumping well is more than 20 times the characteristic length of the transmissivity field.     

Reverse Water‐Level Fluctuations Associated with Fracture Connectivity

Reverse water‐level fluctuations (RWFs), a phenomenon in which water levels rise briefly in response to pumping, were detected in monitoring wells in a fractured siliciclastic aquifer system near a deep public supply well. The magnitude and timing of RWFs provide important information that can help interpret aquifer hydraulics near pumping wells. A RWF in a well is normally attributed to poroelastic coupling between the solid and fluid components in an aquifer system. In addition to revealing classical pumping‐induced poroelastic RWFs, data from pressure transducers located at varying depths and distances from the public supply well suggest that the RWFs propagate rapidly through fractures to influence wells hundreds of meters from the pumping well. The rate and cycling frequency of pumping is an important factor in the magnitude of RWFs. The pattern of RWF propagation can be used to better define fracture connectivity in an aquifer system. Rapid, cyclic head changes due to RWFs may also serve as a mechanism for contaminant transport.     

Interpretation of Water Level Changes in the High Plains Aquifer in Western Kansas

Water level changes in wells provide a direct measure of the impact of groundwater development at a scale of relevance for management activities. Important information about aquifer dynamics and an aquifer's future is thus often embedded in hydrographs from continuously monitored wells. Interpretation of those hydrographs using methods developed for pumping‐test analyses can provide insights that are difficult to obtain via other means. These insights are demonstrated at two sites in the High Plains aquifer in western Kansas. One site has thin unconfined and confined intervals separated by a thick aquitard. Pumping‐induced responses in the unconfined interval indicate a closed (surrounded by units of relatively low permeability) system that is vulnerable to rapid depletion with continued development. Responses in the confined interval indicate that withdrawals are largely supported by leakage. Given the potential for rapid depletion of the unconfined interval, the probable source of that leakage, it is likely that large‐scale irrigation withdrawals will not be sustainable in the confined interval beyond a decade. A second site has a relatively thick unconfined aquifer with responses that again indicate a closed system. However, unlike the first site, previously unrecognized vertical inflow can be discerned in data from the recovery periods. In years of relatively low withdrawals, this inflow can produce year‐on‐year increases in water levels, an unexpected occurrence in western Kansas. The prevalence of bounded‐aquifer responses at both sites has important ramifications for modeling studies; transmissivity values from pumping tests, for example, must be used cautiously in regional models of such systems.     

A Simplified Solution Using Izbash's Equation for Non-Darcian Flow in a Constant Rate Pumping Test

This paper derives an equivalent of Darcian Theis solution for non-Darcian flow induced by constant rate pumping of a well in a confined aquifer. The derivation, which is valid at later times only, is original. It utilizes Izbash's equation. This introduces an additional parameter to Darcian condition, namely, empirical exponent. The solution is a non-Drcian equivalent of Jacob straight line method for analyzing pumping tests at late times. It can be used to determine aquifer parameters: storativity, analogous hydraulic conductivity, and empirical exponent. However, while the Jacob method requires a minimum of only one pumping test with one observation well, the additional parameter in the present solution means that a minimum of two observation wells in one test or two pumping tests at different rates with one observation well are required. The derived solution is applied to a case study at Plomeur in Brittany, France, and is shown to provide a practical and efficient method for analyzing pumping tests where non-Darcian groundwater flow occurs.     

Conventional and combined pump-and-treat systems under nonuniform background flow

We investigate the performance of vertical hydraulic barriers in combination with extraction wells for the partial hydraulic isolation of contaminated aquifer areas. The potential advantage of such combinations compared to a conventional pump-and-treat system has already been demonstrated in a previous study. Here we extend the scope of the performance analysis to the impact of uncertainty in the regional flow direction as well as to highly heterogeneous aquifer transmissivity distributions. In addition, two new well-barrier scenarios are proposed and analyzed. The hydraulic efficiency of the scenarios is rated based on the expected (mean) reduction of the pumping rate that is required to achieve downgradient contaminant capture. The uncertain spatial distribution of aquifer transmissivity is considered by means of unconditioned Monte Carlo simulations. The significance of uncertain background flow conditions is incorporated by computing minimized pumping rates for deviations of the regional flow direction up to 30 degrees from a normative base case. The results give an answer on how pumping rates have to be changed for each barrier-well combination in order to achieve robust systems. It is exposed that in comparison to installing exclusively wells, the barrier-supported approach generally yields savings in the (average) pumping rate. The particular efficiency is shown to be highly dependent on the interaction of variance and integral scale of transmissivity distribution, well and barrier position, as well as direction of background flow.     

An Analytical Method to Determine Ground Water Supply Well Network Designs

An analytical method is provided where the ground water practitioner can quickly determine the size (number of wells) and spacing of a well network capable of meeting a known ground water demand. In order to apply the method, two new parameters are derived that relate theoretical drawdown to the maximum drawdown that is achievable without mining the aquifer. The size of a well network is shown to be proportional to the ground water demand and inversely proportional to the transmissivity and available head. The spacing between wells in a supply well network is shown to be most sensitive to a derived parameter r _{HA/ 3}, which is related to the available head and the propagation of drawdown away from a theoretical well if the total ground water demand was applied to that well. The method can be used to quickly determine the required spacing between wells in well networks of various sizes that are completed in confined aquifers with no leakance.     

How to Find Aquifer Statistics Utilizing Pumping Tests? Two Field Studies Using welltestpy

We present a workflow to estimate geostatistical aquifer parameters from pumping test data using the Python package welltestpy . The procedure of pumping test analysis is exemplified for two data sets from the Horkheimer Insel site and from the Lauswiesen site, Germany. The analysis is based on a semi-analytical drawdown solution from the upscaling approach Radial Coarse Graining, which enables to infer log-transmissivity variance and horizontal correlation length, beside mean transmissivity, and storativity, from pumping test data. We estimate these parameters of aquifer heterogeneity from type-curve analysis and determine their sensitivity. This procedure, implemented in welltestpy , is a template for analyzing any pumping test. It goes beyond the possibilities of standard methods, for example, based on Theis' equation, which are limited to mean transmissivity and storativity. A sensitivity study showed the impact of observation well positions on the parameter estimation quality. The insights of this study help to optimize future test setups for geostatistical aquifer analysis and provides guidance for investigating pumping tests with regard to aquifer statistics using the open-source software package welltestpy .     

A stream depletion field experiment

A field experiment was carried out to measure drawdowns in observation wells and stream depletion flows that occurred when water was abstracted from a well beside a stream. The field data is analyzed herein to determine the aquifer transmissivity, T, the aquifer storage coefficient, S, and a streambed leakage parameter, lambda, by comparing measurements with a solution obtained by Hunt (1999). The analysis uses early time drawdowns with a match-point method to determine T and S, and stream depletion measurements at later times are used to determine lambda. The final results are reasonably consistent for measurements taken in four observation wells. The advantages and disadvantages of this approach are discussed, and two alternative ways of estimating lambda are also discussed.     

Determining anisotropic transmissivity using a simplified Papadopulos method

The straight-line method presented by Papadopulos requires a minimum of three observation wells for determining the transmissivity tensor of a homogeneous and anisotropic aquifer. A simplification of this method was developed for fractured aquifers where the principal directions of the transmissivity tensor are known prior to implementation, such as when fracture patterns on outcropping portions of the aquifer may be used to infer the principal directions. This new method assumes that observation wells are drilled along the two principal directions from the pumped well, thus reducing the required number of observation wells to two. This method was applied for an aquifer test in the fractured Navajo Sandstone of southwestern Utah and yielded minimum and maximum principal transmissivity values of 70 and 1800 m(2)/d, respectively, indicating an anisotropy ratio of approximately 24 to 1.     

Effects of Improper Characterization of Aquifer Thickness on Estimates of Hydraulic Conductivity from Pumping Tests

Pumping test data for surficial aquifers are commonly analyzed under the assumption that the base of the aquifer corresponds to the bottom of the test wells (i.e., the aquifer is truncated). This practice can lead to inaccurate hydraulic conductivity estimates, resulting from the use of low saturated thickness values with transmissivity estimates, and not accounting for the effects of partially penetrating wells. Theoretical time-drawdown data were generated at an observation well in a hypothetical unconfined aquifer for various values of saturated thickness and were analyzed by standard curve-matching techniques. The base of the aquifer was assumed to be the bottom of the pumping and observation wells. The overestimation of horizontal hydraulic conductivity was found to be directly proportional to the error in assumed saturated thickness, and to the (actual) ratio of vertical to horizontal hydraulic conductivity (K_v/K_h). Inaccurately high estimates of hydraulic conductivity obtained by aquifer truncation can lead to overestimates of ground water velocity and contaminant plume spreading, narrow capture zone configuration estimates, and overestimates of available ground water resources.     

Analytical Modeling of Well Design in Riverbank Filtration Systems

Analytical studies for well design adjacent to river banks are the most significant practical task in cases involving the efficiency of riverbank filtration systems. In times when high pollution of river water is joined with increasing water demand, it is necessary to design pumping wells near the river that provide acceptable amounts of river water with minimum contaminant concentrations. This will guarantee the quality and safety of drinking water supplies. This article develops an analytical solution based on the Green's function approach to solve an inverse problem: based on the required level of contaminant concentration and planned pumping time period, the shortest distance to the riverbank that has the maximum percentage of river water is determined. This model is developed in a confined and homogenous aquifer that is partially penetrated by the stream due to the existence of clogging layers. Initially, the analytical results obtained at different pumping times, rates and with different values of initial concentration are checked numerically using the MODFLOW software. Generally, the distance results obtained from the proposed model are acceptable. Then, the model is validated by data related to two pumping wells located at the first riverbank filtration pilot project conducted in Malaysia.     

Analysis of steady ground water flow toward wells in a confined-unconfined aquifer

A confined aquifer may become unconfined near the pumping wells when the water level falls below the confining unit in the case where the pumping rate is great and the excess hydraulic head over the top of the aquifer is small. Girinskii's potential function is applied to analyze the steady ground water flow induced by pumping wells with a constant-head boundary in a mixed confined-unconfined aquifer. The solution of the single-well problem is derived, and the critical radial distance at which the flow changes from confined to unconfined condition is obtained. Using image wells and the superposition method, an analytic solution is presented to study steady ground water flow induced by a group of pumping wells in an aquifer bounded by a river with constant head. A dimensionless function is introduced to determine whether a water table condition exists or not near the pumping wells. An example with three pumping wells is used to demonstrate the patterns of potentiometric surface and development of water table around the wells.     

Estimation of Salt Water Upconing Using a Steady‐State Solution for Partial Completion of a Pumped Well

A new steady‐state analytical solution to the two‐dimensional radial‐flow equation was developed for drawdown (head) conditions in an aquifer with constant transmissivity, no‐flow conditions at the top and bottom, constant head conditions at a known radial distance, and a partially completed pumping well. The solution was evaluated for accuracy by comparison to numerical simulations using MODFLOW. The solution was then used to estimate the rise of the salt water‐fresh water interface (upconing) that occurs under a pumping well, and to calculate the critical pumping rate at which the interface becomes unstable, allowing salt water to enter the pumping well. The analysis of salt water‐fresh water interface rise assumed no significant effect on upconing by recharge; this assumption was tested and supported using results from a new steady‐state analytical solution developed for recharge under two‐dimensional radial‐flow conditions. The upconing analysis results were evaluated for accuracy by comparison to those from numerical simulations using SEAWAT for salt water‐fresh water interface positions under mild pumping conditions. The results from the equation were also compared with those of a published numerical sharp‐interface model applied to a case on Cape Cod, Massachusetts. This comparison indicates that estimating the interface rise and maximum allowable pumping rate using the analytical method will likely be less conservative than the maximum allowable pumping rate and maximum stable interface rise from a numerical sharp‐interface model.     

Detecting Drawdowns Masked by Environmental Stresses with Water‐Level Models

Detecting and quantifying small drawdown at observation wells distant from the pumping well greatly expands the characterized aquifer volume. However, this detection is often obscured by water level fluctuations such as barometric and tidal effects. A reliable analytical approach for distinguishing drawdown from nonpumping water‐level fluctuations is presented and tested here. Drawdown is distinguished by analytically simulating all pumping and nonpumping water‐level stresses simultaneously during the period of record. Pumping signals are generated with Theis models, where the pumping schedule is translated into water‐level change with the Theis solution. This approach closely matched drawdowns simulated with a complex three‐dimensional, hypothetical model and reasonably estimated drawdowns from an aquifer test conducted in a complex hydrogeologic system. Pumping‐induced changes generated with a numerical model and analytical Theis model agreed (RMS as low as 0.007 m) in cases where pumping signals traveled more than 1 km across confining units and fault structures. Maximum drawdowns of about 0.05 m were analytically estimated from field investigations where environmental fluctuations approached 0.2 m during the analysis period.