Carl D. McElwee

Slug tests in partially penetrating wells

A semianalytical solution is presented to a mathematical model describing the flow of groundwater in response to a slug test in a confined or unconfined porous formation. The model incorporates the effects of partial penetration, anisotropy, finiteradius well skins, and upper and lower boundaries of either a constant-head or an impermeable form. This model is employed to investigate the error that is introduced into hydraulic conductivity estimates through use of currently accepted practices (i.e., Hvorslev, 1951; Cooper et al., 1967) for the analysis of slug-test response data. The magnitude of the error arising in a variety of commonly faced field configurations is the basis for practical guidelines for the analysis of slug-test data that can be utilized by field practitioners.

Pumping tests in networks of multilevel sampling wells: Motivation and methodology

The identification of spatial variations in hydraulic conductivity (K) on a scale of relevance for transport investigations has proven to be a considerable challenge. Recently, a new field method for the estimation of interwell variations in K has been proposed. This method, hydraulic tomography, essentially consists of a series of short-term pumping tests performed in a tomographic-like arrangement. In order to fully realize the potential of this approach, information about lateral and vertical variations in pumping-induced head changes (drawdown) is required with detail that has previously been unobtainable in the field. Pumping tests performed in networks of multilevel sampling (MLS) wells can provide data of the needed density if drawdown can accurately and rapidly be measured in the small-diameter tubing used in such wells. Field and laboratory experiments show that accurate transient drawdown data can be obtained in the small-diameter MLS tubing either directly with miniature fiber-optic pressure sensors or indirectly using air-pressure transducers. As with data from many types of hydraulic tests, the quality of drawdown measurements from MLS tubing is quite dependent on the effectiveness of well development activities. Since MLS ports of the standard design are prone to clogging and are difficult to develop, alternate designs are necessary to ensure accurate drawdown measurements. Initial field experiments indicate that drawdown measurements obtained from pumping tests performed in MLS networks have considerable potential for providing valuable information about spatial variations in hydraulic conductivity.

A nonlinear model for analysis of slug‐test data

While doing slug tests in high-permeability aquifers, we have consistently seen deviations from the expected response of linear theoretical models. Normalized curves do not coincide for various initial heads, as would be predicted by linear theories, and are shifted to larger times for higher initial heads. We have developed a general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the well bore, and a Hvorslev model for the aquifer, which explains these data features. The model produces a very good fit for both oscillatory and nonoscillatory field data, using a single set of physical parameters to predict the field data for various initial displacements at a given well. This is in contrast to linear models which have a systematic lack of fit and indicate that hydraulic conductivity varies with the initial displacement. We recommend multiple slug tests with a considerable variation in initial head displacement to evaluate the possible presence of nonlinear effects. Our conclusion is that the nonlinear model presented here is an excellent tool to analyze slug tests, covering the range from the underdamped region to the overdamped region.

The use of slug tests to describe vertical variations in hydraulic conductivity

Abstract Multilevel slug tests provide one means of obtaining estimates of hydraulic conductivity on a scale of relevance for contaminant transport investigations. A numerical model is employed here to assess the potential of multilevel slug tests to provide information about vertical variations in hydraulic conductivity under conditions commonly faced in field settings. The results of the numerical simulations raise several important issues concerning the effectiveness of this technique. If the length of the test interval is of the order of the average layer thickness, considerable error may be introduced into the conductivity estimates owing to the effects of adjoining layers. The influence of adjoining layers is dependent on the aspect ratio (length of test interval/well radius) of the tesy interval and the flow properties of the individual layers. If a low-permeability skin is present at the well, the measured vertical variations will be much less than the actual variations, owing to the influence of the skin conductivity on the parameter estimates. A high-permeability skin can also produce apparent vertical variations that are much less than the actual, owing to water flowing vertically along the conductive skin. In cases where the test interval spans a number of layers, a slug test will yield an approximate thickness-weighted average of the hydraulic conductivities of the intersected layers. In most cases, packer circumvention should not be a major concern when packers of 0.75 m or longer are employed. Results of this study are substantiated by recently reported field tests that demonstrate the importance of well emplacement and development activities for obtaining meaningful estimates from a program of multilevel slug tests.

Sensitivity analysis of slug tests. Part 1. The slugged well

Abstract In this paper, we apply the techniques of sensitivity analysis to the Cooper et al. model for slug tests in confined aquifers. A sensitivity analysis of slug-test responses can provide valuable information concerning optimal test design (within the limitations of the chosen model). The sensitivity analysis enables a family of generic sensitivity coefficients for transmissivity (T) and storage coefficient (S) to be defined by two parameters a (related to S) and β (related to time and T). Two facts stand out from this family of curves. First, the sensitivity to S is much lower than that to T; second, the sensitivity curves for T and S are very similar in shape (i.e. the correlation is high) making it difficult to reliably estimate both T and S. Sensitivity analysis shows that the estimated standard errors of the parameters are inversely proportional to the initial head (H0), so large initial heads should be used when possible. Generally, an increased number of measurements improves parameter estimation, if properly placed in time. Early time measurements are important for defining H0 accurately. The best estimates for T and S are obtained by minimizing the correlation between the sensitivity coefficients for T and S and sampling at points of maximum sensitivity.

Improving the analysis of slug tests

Abstract This paper examines several techniques that have the potential to improve the quality of slug test analysis. These techniques are applicable in the range from low hydraulic conductivities with overdamped responses to high hydraulic conductivities with nonlinear oscillatory responses. Four techniques for improving slug test analysis will be discussed: use of an extended capability nonlinear model, sensitivity analysis, correction for acceleration and velocity effects, and use of multiple slug tests. The four-parameter nonlinear slug test model used in this work is shown to allow accurate analysis of slug tests with widely differing character. The parameter β represents a correction to the water column length caused primarily by radius variations in the wellbore and is most useful in matching the oscillation frequency and amplitude. The water column velocity at slug initiation ( V o ) is an additional model parameter, which would ideally be zero but may not be due to the initiation mechanism. The remaining two model parameters are A (parameter for nonlinear effects) and K (hydraulic conductivity). Sensitivity analysis shows that in general β and V o have the lowest sensitivity and K usually has the highest. However, for very high K values the sensitivity to A may surpass the sensitivity to K . Oscillatory slug tests involve higher accelerations and velocities of the water column; thus, the pressure transducer responses are affected by these factors and the model response must be corrected to allow maximum accuracy for the analysis. The performance of multiple slug tests will allow some statistical measure of the experimental accuracy and of the reliability of the resulting aquifer parameters.

Sensitivity analysis of slug tests Part 2. Observation wells

Abstract An earlier paper (Part 1, this issue) dealt with the use of sensitivity analysis for the design of a slug test that would give reasonably accurate estimates of the aquifer parameters by an informed choice of the number and times of measurements. An investigation of the radial dependence of the Cooper et al. analytical solution for a slug test in a confined aquifer shows that the use of one or more observation wells can vastly improve the parameter estimates, particularly the estimate of the storage parameter. Generally, the observation well must be fairly close (about 10 m or less) to the slugged well to be effective. The storage coefficient must be small in order to see the effect of the slug at greater distances from the stressed well. Since the temporal and spatial dependence of the sensitivities for transmissivity and storage are considerably different, the addition of one or more observation wells will substantially reduce the correlation between these two parameters, which will result in much better estimates than are usually obtained in slug tests. These ideas are illustrated using typical data representative of our research sites.

Sensitivity Analysis of Ground-Water Models

One of the most difficult tasks in ground-water modeling is the estimation of aquifer parameters from field measurements of hydraulic head. This paper examines model sensitivity through the use of sensitivity analysis. For each model parameter one can define a sensitivity coefficient. These sensitivity coefficients depend on the choice of model, the spatial coordinates, the time variable, the number and type of model parameters, and the boundary conditions. For good sensitivity to the parameters, all sensitivity coefficients should be independent and as large as possible at the locations and times of interest. Methods for determining sensitivity coefficients are discussed and some typical examples showing certain important characteristics are presented. The sensitivity coefficients can be used to estimate variances and confidence intervals for the aquifer parameters. The model sensitivity can be increased for parameter estimation by applying some general principles from sensitivity analysis. Several examples of improved sensitivity are presented.

Theory and application of an approximate model of saltwater upconing in aquifers.

Abstract Motion and mixing of salt water and fresh water are vitally important for water-resource development throughout the world. An approximate model of saltwater upconing in aquifers is developed, which results in three non-linear coupled equations for the freshwater zone, the saltwater zone, and the transition zone. The description of the transition zone uses the concept of a boundary layer. This model invokes some assumptions to give a reasonably tractable model, considerably better than the sharp interface approximation but considerably simpler than a fully three-dimensional model with variable density. We assume the validity of the Dupuit-Forchheimer approximation of horizontal flow in each layer. Vertical hydrodynamic dispersion into the base of the transition zone is assumed and concentration of the saltwater zone is assumed constant. Solute in the transition zone is assumed to be moved by advection only. Velocity and concentration are allowed to vary vertically in the transition zone by using shape functions. Several numerical techniques can be used to solve the model equations, and simple analytical solutions can be useful in validating the numerical solution procedures. We find that the model equations can be solved with adequate accuracy using the procedures presented. The approximate model is applied to the Smoky Hill River valley in central Kansas. This model can reproduce earlier sharp interface results as well as evaluate the importance of hydrodynamic dispersion for feeding salt water to the river. We use a wide range of dispersivity values and find that unstable upconing always occurs. Therefore, in this case, hydrodynamic dispersion is not the only mechanism feeding salt water to the river. Calculations imply that unstable upconing and hydrodynamic dispersion could be equally important in transporting salt water. For example, if groundwater flux to the Smoky Hill River were only about 40% of its expected value, stable upconing could exist where hydrodynamic dispersion into a transition zone is the primary mechanism for moving salt water to the river. The current model could be useful in situations involving dense saltwater layers.