Near‐Well Nonlinear Flow Identified by Various Displacement Well Response Testing

The impact of nonlinear flow phenomena on well response tests is still not completely understood today. With the present paper, a set of 10 well response tests is investigated. The tests were conducted in a fractured Devonian limestone formation close to the western national border of Germany. The test design incorporates a packer as well as different solid cylinders to initiate a series of slug‐injection and slug‐withdrawal tests by various initial displacements. Nonlinear response characteristics were observed in the course of the tests, which cannot be explained by tubing‐controlled flow inside the cased well. The analysis shows that the nonlinear response characteristics are likely to be either formation controlled according to non‐Darcian flow developing in a high‐conductivity fracture compartment of the tested limestone formation or a consequence of a severe well inefficiency caused by some sort of screen clogging. This inference is obtained from analyzing the data by a nonlinear well response test model, which differentiates between wellbore internal hydraulic head losses and a generalized rate‐dependent skin effect accounting for nonlinear flow processes in the vicinity of the well. The potential of identifying near‐well nonlinear flow by various displacement well response testing may indicate this methodology to be a valuable complement to modern high‐resolution borehole imaging techniques used when characterizing fractured reservoirs and the tightness of fractured reservoir cap rocks.     

Static and dynamic conceptual model of a complexly fractured crystalline rock aquifer

A conceptual model of anisotropic and dynamic permeability is developed from hydrogeologic and hydromechanical characterization of a foliated, complexly fractured, crystalline rock aquifer at Gates Pond, Berlin, Massachusetts. Methods of investigation include aquifer‐pumping tests, long‐term hydrologic monitoring, fracture characterization, downhole heat‐pulse flow meter measurements, in situ extensometer testing, and earth tide analysis. A static conceptual model is developed from observations of depth‐dependent and anisotropic permeability that effectively compartmentalizes the aquifer as a function of foliation intensity. Superimposed on the static model is dynamic permeability as a function of hydraulic head in which transient bulk aquifer transmissivity is proportional to changes in hydraulic head due to hydromechanical coupling. The dynamic permeability concept is built on observations that fracture aperture changes as a function of hydraulic head, as measured during in situ extensometer testing of individual fractures, and observed changes in bulk aquifer transmissivity as determined from earth tides during seasonal changes in hydraulic head, with higher transmissivity during periods of high hydraulic head, and lower transmissivity during periods of relatively lower hydraulic head. A final conceptual model is presented that captures both the static and dynamic properties of the aquifer. The workflow presented here demonstrates development of a conceptual framework for building numerical models of complexly fractured, foliated, crystalline rock aquifers that includes both a static model to describe the spatial distribution of permeability as a function of fracture type and foliation intensity and a dynamic model that describes how hydromechanical coupling impacts permeability magnitude as a function of hydraulic head fluctuation. This model captures important geologic controls on permeability magnitude, anisotropy, and transience and therefor offers potentially more reliable history matching and forecasts of different water management strategies, such as resource evaluation, well placement, permeability prediction, and evaluating remediation strategies.     

An Analytical Model for Hydraulic Fracturing in Shallow Bedrock Formations

A theoretical method is proposed to estimate post‐fracturing fracture size and transmissivity, and as a test of the methodology, data collected from two wells were used for verification. This method can be employed before hydrofracturing in order to obtain estimates of the potential hydraulic benefits of hydraulic fracturing. Five different pumping test analysis methods were used to evaluate the well hydraulic data. The most effective methods were the Papadopulos‐Cooper model (1967), which includes wellbore storage effects, and the Gringarten‐Ramey model (1974), known as the single horizontal fracture model. The hydraulic parameters resulting from fitting these models to the field data revealed that as a result of hydraulic fracturing, the transmissivity increased more than 46 times in one well and increased 285 times in the other well. The model developed by dos Santos (2008) , which considers horizontal radial fracture propagation from the hydraulically fractured well, was used to estimate potential fracture geometry after hydrofracturing. For the two studied wells, their fractures could have propagated to distances of almost 175 m or more and developed maximum apertures of about 2.20 mm and hydraulic apertures close to 0.30 mm. Fracturing at this site appears to have expanded and propagated existing fractures and not created new fractures. Hydraulic apertures calculated from pumping test analyses closely matched the results obtained from the hydraulic fracturing model. As a result of this model, post‐fracturing geometry and resulting post‐fracturing well yield can be estimated before the actual hydrofracturing.     

Asymptotic analysis of cross-hole hydraulic tests in fractured granite

Illman and Tartakovsky (2005a, 2005b) developed a new approach for the interpretation of three-dimensional pneumatic well tests conducted in porous or fractured geologic media, which is based on a straight-line analysis of late-time data. We modify this approach to interpret three-dimensional well tests in the saturated zone and use it to analyze the cross-hole hydraulic test data collected in the Full-Scale Engineered Barrier Experiment gallery at the Grimsel Test Site in Switzerland. The equivalent hydraulic conductivity and specific storage obtained from our analysis increase with the radial distance between the centroids of the pumping and monitoring intervals. Since this scale effect is observed from a single test type (cross-hole tests), it is less ambiguous than scale effects typically inferred from laboratory and multiple types of hydraulic tests (e.g., slug, single- and cross-hole tests). The statistical analysis of the estimated hydraulic parameters shows a strong correlation between equivalent hydraulic conductivity and specific storage.     

Three-dimensional geostatistical inversion of synthetic tomographic pumping and heat-tracer tests in a nested-cell setup

A main purpose of groundwater inverse modeling lies in estimating the hydraulic conductivity field of an aquifer. Traditionally, hydraulic head measurements, possibly obtained in tomographic setups, are used as data. Because the groundwater flow equation is diffusive, many pumping and observation wells would be necessary to obtain a high resolution of hydraulic conductivity, which is typically not possible. We suggest performing heat tracer tests using the same already installed pumping wells and thermometers in observation planes to amend the hydraulic head data set by the arrival times of the heat signals. For each tomographic combinations of wells, we recommend installing an outer pair of pumping wells, generating artificial ambient flow, and an inner well pair in which the tests are performed. We jointly invert heads and thermal arrival times in 3-D by the quasi-linear geostatistical approach using an efficiently parallelized code running on a mid-range cluster. In the present study, we evaluate the value of heat tracer versus head data in a synthetic test case, where the estimated fields can be compared to the synthetic truth. Because the sensitivity patterns of the thermal arrival times differ from those of head measurements, the resolved variance in the estimated field is 6 to 10 times higher in the joint inversion in comparison to inverting head data only. Also, in contrast to head measurements, reversing the flow field and repeating the heat-tracer test improves the estimate in terms of reducing the estimation variance of the estimate. Based on the synthetic test case, we recommend performing the tests in four principal directions, requiring in total eight pumping wells and four intersecting observation planes for heads and temperature in each direction.     

ANALYSIS OF AQUIFER TESTS CONDUCTED IN FRACTURED ROCK: A REVIEW OF THE PHYSICAL BACKGROUND AND THE DESIGN OF A COMPUTER PROGRAM FOR GENERATING TYPE CURVES

Abstract. Assessing the hydrogeological character of fractured bedrock between two or more wells is usually accomplished through an analysis of the results of traditional pumping tests. Because these tests are subject to field boundary conditions that may be different from those conducted in porous media, alternative testing techniques or analytical methods are required. To provide an adaptable interpretive package for analyzing interwell hydraulic tests in fractured rock, a FORTRAN program was developed to generate type curves for pumping tests and pulse interference tests. A review of the physical conditions which most influence the results of these tests is conducted to provide the background for the development and use of the program. The analytical solutions included in the program consider inner boundary conditions such as wellbore storage, infinitesimally thin skin and finite-thickness skin. In addition, a solution is included to analyze results influenced by wellbore storage and infinitesimally thin skin at both the pumping and observation wells. The solutions are given in the Laplace domain and are numerically inverted to generate data for the type curves. The curves can be plotted using any standard plotting program, or they can be plotted manually. The program is menu driven, easily adaptable to include additional solutions, and can be executed on a personal computer.     

The influence of geologic structures on deformation due to ground water withdrawal

A 62 day controlled aquifer test was conducted in thick alluvial deposits at Mesquite, Nevada, for the purpose of monitoring horizontal and vertical surface deformations using a high-precision global positioning system (GPS) network. Initial analysis of the data indicated an anisotropic aquifer system on the basis of the observed radial and tangential deformations. However, new InSAR data seem to indicate that the site may be bounded by an oblique normal fault as the subsidence bowl is both truncated to the northwest and offset from the pumping well to the south. A finite-element numerical model was developed using ABAQUS to evaluate the potential location and hydromechanical properties of the fault based on the observed horizontal deformations. Simulation results indicate that for the magnitude and direction of motion at the pumping well and at other GPS stations, which is toward the southeast (away from the inferred fault), the fault zone (5 m wide) must possess a very high permeability and storage coefficient and cross the study area in a northeast-southwest direction. Simulated horizontal and vertical displacements that include the fault zone closely match observed displacements and indicate the likelihood of the presence of the inferred fault. This analysis shows how monitoring horizontal displacements can provide valuable information about faults, and boundary conditions in general, in evaluating aquifer systems during an aquifer test.     

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.     

Flow depletion in a small stream caused by ground water abstraction from wells

The interaction between a gaining stream and a water-table aquifer is studied at an outwash plain. The aquifer is hydraulically well connected to the stream. Pumping tests were carried out in 1997 and 1998 in two wells 60 m from the stream, screening different depths of the aquifer. Drawdown was measured on both sides of the stream. Hydraulic head, drawdown, and stream depletion data were analyzed using numerical flow models. Similar models were fitted to each of two different data sets: Model A was fitted to steady-state hydraulic head and streamflow gain data not influenced by pumping; and model B was fitted to drawdown data measured during the 1998 pumping test. Each calibrated model closely fits its calibration data; however, predictions were biased if model A was used to predict the calibration data of model B, and vice versa. To further test the models, they were used to predict streamflow depletion during the two pumping tests as well as the drawdown during the 1997 test. Neither of these data were used for calibration. Model A predicted the measured depletions fairly accurately during both tests, whereas the predicted drawdowns in 1997 were significantly larger than actually measured. Contrary to this, the 1997 drawdowns predicted by model B were nearly unbiased; the predicted depletions deviate significantly from the measured depletions in 1997, but they compare well with the observations in 1998. Thus, although field work and analyses were extensive and done carefully to develop a ground water flow model that could predict both drawdown and streamflow depletion, the model predictions are biased. Analyses indicate that the deviations between model and data may be because of error in the models' representations of either the release of water from storage or of the hydrology in the riparian zone.     

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.     

Redundant and Nonredundant Information for Model Calibration or Hydraulic Tomography

Drawdown data from independent pumping tests have widely been used to validate the estimated hydraulic parameters from inverse modeling or hydraulic tomography (HT). Yet, the independent pumping test has not been clearly defined. Therefore, the goal of this paper is to define this independent pumping test concept, based on the redundant or nonredundant information about aquifer heterogeneity embedded in the observed heads during cross-hole pumping tests. The definition of complete, moderate redundancy and high nonredundancy of information are stipulated using cross-correlation analysis of the relationship between the head and heterogeneity. Afterward, data from numerical experiments and field sequential pumping test campaigns reinforce the concept and the definition.     

Site characterization in densely fractured dolomite: comparison of methods

One of the challenges in characterizing fractured-rock aquifers is determining whether the equivalent porous medium approximation is valid at the problem scale. Detailed hydrogeologic characterization completed at a small study site in a densely fractured dolomite has yielded an extensive data set that was used to evaluate the utility of the continuum and discrete-fracture approaches to aquifer characterization. There are two near-vertical sets of fractures at the site; near-horizontal bedding-plane partings constitute a third fracture set. Eighteen boreholes, including five coreholes, were drilled to a depth of approximately 10.6 m. Borehole geophysical logs revealed several laterally extensive horizontal fractures and dissolution zones. Flowmeter and short-interval packer testing identified which of these features were hydraulically important. A monitoring system, consisting of short-interval piezometers and multilevel samplers, was designed to monitor four horizontal fractures and two dissolution zones. The resulting network consisted of >70 sampling points and allowed detailed monitoring of head distributions in three dimensions. Comparison of distributions of hydraulic head and hydraulic conductivity determined by these two approaches suggests that even in a densely fractured-carbonate aquifer, a characterization approach using traditional long-interval monitoring wells is inadequate to characterize ground water movement for the purposes of regulatory monitoring or site remediation. In addition, traditional multiwell pumping tests yield an average or bulk hydraulic conductivity that is not adequate for predicting rapid ground water travel times through the fracture network, and the pumping test response does not appear to be an adequate tool for assessing whether the porous medium approximation is valid.     

Influence of Pressure Change During Hydraulic Tests on Fracture Aperture

In a series of field experiments, we evaluate the influence of a small water pressure change on fracture aperture during a hydraulic test. An experimental borehole is instrumented at the Korea Atomic Energy Research Institute (KAERI) Underground Research Tunnel (KURT). The target fracture for testing was found from the analyses of borehole logging and hydraulic tests. A double packer system was developed and installed in the test borehole to directly observe the aperture change due to water pressure change. Using this packer system, both aperture and flow rate are directly observed under various water pressures. Results indicate a slight change in fracture hydraulic head leads to an observable change in aperture. This suggests that aperture change should be considered when analyzing hydraulic test data from a sparsely fractured rock aquifer.     

Cross-borehole flowmeter tests for transient heads in heterogeneous aquifers

Cross-borehole flowmeter tests have been proposed as an efficient method to investigate preferential flowpaths in heterogeneous aquifers, which is a major task in the characterization of fractured aquifers. Cross-borehole flowmeter tests are based on the idea that changing the pumping conditions in a given aquifer will modify the hydraulic head distribution in large-scale flowpaths, producing measurable changes in the vertical flow profiles in observation boreholes. However, inversion of flow measurements to derive flowpath geometry and connectivity and to characterize their hydraulic properties is still a subject of research. In this study, we propose a framework for cross-borehole flowmeter test interpretation that is based on a two-scale conceptual model: discrete fractures at the borehole scale and zones of interconnected fractures at the aquifer scale. We propose that the two problems may be solved independently. The first inverse problem consists of estimating the hydraulic head variations that drive the transient borehole flow observed in the cross-borehole flowmeter experiments. The second inverse problem is related to estimating the geometry and hydraulic properties of large-scale flowpaths in the region between pumping and observation wells that are compatible with the head variations deduced from the first problem. To solve the borehole-scale problem, we treat the transient flow data as a series of quasi-steady flow conditions and solve for the hydraulic head changes in individual fractures required to produce these data. The consistency of the method is verified using field experiments performed in a fractured-rock aquifer.     

High-resolution slug testing

The hydraulic conductivity (K) variation has important ramifications for ground water flow and the transport of contaminants in ground water. The delineation of the nature of that variation can be critical to complete characterization of a site and the planning of effective and efficient remedial measures. Site-specific features (such as high-conductivity zones) need to be quantified. Our alluvial field site in the Kansas River valley exhibits spatial variability, very high conductivities, and nonlinear behavior for slug tests in the sand and gravel aquifer. High-resolution, multilevel slug tests have been performed in a number of wells that are fully screened. A general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the wellbore, and a Hvorslev model for the aquifer has been used to analyze the data, employing an automated processing system that runs within the Excel spreadsheet program. It is concluded that slug tests can provide the necessary data to identify the nature of both horizontal and vertical K variation in an aquifer and that improved delineation or higher resolution of K structure is possible with shorter test intervals. The gradation into zones of higher conductivity is sharper than seen previously, and the maximum conductivity observed is greater than previously measured. However, data from this project indicate that well development, the presence of fines, and the antecedent history of the well are important interrelated factors in regard to slug-test response and can prevent obtaining consistent results in some cases.     

SUPRPUMP: An Interactive Program for Well Test Analysis and Design

Abstract. We have developed a program which aids in the design and analysis of pumping tests and slug tests. In design mode, the program emphasizes calculation and plotting of the sensitivities of drawdown (or head) to well function parameters. In analysis mode, the program can analyze a given set of experimental data. For pumping tests, the program allows multiple observation wells and multiple variable-rate pumping wells. The program is written in a modular fashion, allowing easy addition of well functions to the currently existing library. An example based on a hypothetical pumping test illustrates the utility of sensitivity analysis for well test design.     

Measuring the hydraulic conductivity of shallow submerged sediments

The hydraulic conductivity of submerged sediments influences the interaction between ground water and surface water, but few techniques for measuring K have been described with the conditions of the submerged setting in mind. Two simple, physical methods for measuring the hydraulic conductivity of submerged sediments have been developed, and one of them uses a well and piezometers similar to well tests performed in terrestrial aquifers. This test is based on a theoretical analysis that uses a constant-head boundary condition for the upper surface of the aquifer to represent the effects of the overlying water body. Existing analyses of tests used to measure the hydraulic conductivity of submerged sediments may contain errors from using the same upper boundary conditions applied to simulate terrestrial aquifers. Field implementation of the technique requires detecting minute drawdowns in the vicinity of the pumping well. Low-density oil was used in an inverted U-tube manometer to amplify the head differential so that it could be resolved in the field. Another technique was developed to measure the vertical hydraulic conductivity of sediments at the interface with overlying surface water. This technique uses the pan from a seepage meter with a piezometer fixed along its axis (a piezo-seep meter). Water is pumped from the pan and the head gradient is measured using the axial piezometer. Results from a sandy streambed indicate that both methods provide consistent and reasonable estimates of K. The pumping test allows skin effects to be considered, and the field data show that omitting the skin effect (e.g., by using a single well test) can produce results that underestimate the hydraulic conductivity of streambeds.     

Field study of hydrogeologic characterization methods in a heterogeneous aquifer

Hydraulic conductivity (K) and specific storage (S(s)) are required parameters when designing transient groundwater flow models. The purpose of this study was to evaluate the ability of commonly used hydrogeologic characterization approaches to accurately delineate the distribution of hydraulic properties in a highly heterogeneous glaciofluvial deposit. The metric used to compare the various approaches was the prediction of drawdown responses from three separate pumping tests. The study was conducted at a field site, where a 15 m × 15 m area was instrumented with four 18-m deep Continuous Multichannel Tubing (CMT) wells. Each CMT well contained seven 17 cm × 1.9 cm monitoring ports equally spaced every 2 m down each CMT system. An 18-m deep pumping well with eight separate 1-m long screens spaced every 2 m was also placed in the center of the square pattern. In each of these boreholes, cores were collected and characterized using the Unified Soil Classification System, grain size analysis, and permeameter tests. To date, 471 K estimates have been obtained through permeameter analyses and 270 K estimates from empirical relationships. Geostatistical analysis of the small-scale K data yielded strongly heterogeneous K fields in three-dimensions. Additional K estimates were obtained through slug tests in 28 ports of the four CMT wells. Several pumping tests were conducted using the multiscreen and CMT wells to obtain larger scale estimates of both K and S(s). The various K and S(s) estimates were then quantitatively evaluated by simulating transient drawdown data from three pumping tests using a 3D forward numerical model constructed using HydroGeoSphere (Therrien et al. 2005). Results showed that, while drawdown predictions generally improved as more complexity was introduced into the model, the ability to make accurate drawdown predictions at all CMT ports was inconsistent.     

Derivative‐Assisted Classification of Fractured Zones Crossing a Deep Borehole

In this study, the derivative analysis using the derivative of drawdown with respect to log‐time was utilized to determine candidates for hydraulic conductor domains (HCDs). At a 500‐m deep borehole in the study site, the fractured rocks crossing the borehole were first classified in fractured and nonfractured zones by core logging and geophysical loggings, such as acoustic televiewing, density, and flow loggings. After conducting the hydraulic tests such as constant head withdrawal and recovery tests at the fractured zones and the nonfractured zones, the derivative analyses were carried out, of which the results were evaluated to determine the candidates for HCDs. For the nonfractured zones, the diagnostic plot has only a big hump indicating poor connection of the background fractures to the permeable geologic media, while those of the candidates for HCDs show various flow regimes. On the basis of these results, the candidates for HCDs among the fractured zones were determined. From discussion on the results, the combination of the spacing analysis and derivative analysis following a hydraulic test is recommended for determining the candidates for HCDs rather than other geophysical loggings.     

Application of a nonlinear slug test model

Knowledge of the hydraulic conductivity distribution is of utmost importance in understanding the dynamics of an aquifer and in planning the consequences of any action taken upon that aquifer. Slug tests have been used extensively to measure hydraulic conductivity in the last 50 years since Hvorslev's (1951) work. A general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the wellbore, and a Hvorslev model for the aquifer has been implemented in this work. The nonlinear model has three parameters: beta, which is related primarily to radius changes in the water column; A, which is related to the nonlinear head losses; and K, the hydraulic conductivity. An additional parameter has been added representing the initial velocity of the water column at slug initiation and is incorporated into an analytical solution to generate the first time step before a sequential numerical solution generates the remainder of the time solution. Corrections are made to the model output for acceleration before it is compared to the experimental data. Sensitivity analysis and least squares fitting are used to estimate the aquifer parameters and produce some diagnostic results, which indicate the accuracy of the fit. Finally, an example of field data has been presented to illustrate the application of the model to data sets that exhibit nonlinear behavior. Multiple slug tests should be taken at a given location to test for nonlinear effects and to determine repeatability.