Evaluating the quality of hydraulic conductivity estimates from piezometer slug tests in peat

Although widely used in wetland hydrological studies, hydraulic conductivity (K) estimates from piezometer slug tests are often of questionable validity. Frequently, this is because insufficient attention is paid to the details of the test procedure. Further, in a potentially heterogeneous and anisotropic medium such as peat, the use of slug tests is prone to error. In this paper we address some of the methodological issues surrounding piezometer slug tests in peat. We compare slug test data with laboratory determinations of vertical and horizontal K obtained using a new method. Piezometers were installed at three depths in a floodplain fen peat in Norfolk, UK. Slug tests were initiated by both slug insertion and slug withdrawal, and repeat tests were conducted to examine the robustness of our K estimates. Most of the tests displayed departures from the log‐linear model of Hvorslev, the form of departure being consistent with compressible soil behaviour. The results suggest that insertion tests gave similar results to those initiated by withdrawal. Repeat testing showed that withdrawal data, in particular, gave highly reproducible normalized responses that were independent of the initial head. Values for K estimated using the slug tests were in the range 1 × 10⁻⁴ to 1·6 × 10⁻³ cm s⁻¹, which is towards the upper end of the range reported for peats generally. Laboratory tests yielded similar values of K to those obtained from the slug tests. Although the laboratory tests showed that the peat was anisotropic, the K values generated by slug testing proved relatively good estimates of both vertical and horizontal K. Copyright © 2005 John Wiley & Sons, Ltd.     

Analysis of depth-dependent pressure head of slug tests in highly permeable aquifers

A curve-matching method is developed for the analysis of depth-dependent pressure head responding to a slug test in a highly permeable aquifer. The depth dependency is due to the fact that the pressure transducer is placed at depth relatively far from the initial water level. The Springer and Gelhar solution and a depth correction relation are used to generate theoretical curves of pressure head vs. time. A trial-and-error procedure is established to find the theoretical curve best fitting the field data by adjusting the two unknown parameters, the horizontal hydraulic conductivity, and the effective length of the water column. Analytic relations for some oscillation characteristics of the converted pressure head are derived. A field example indicates that the theoretical relations and the curve-matching method developed herein are suitable to deal with the oscillatory head data dependent on depth of measurement. Nevertheless, it is recognized that placing the pressure transducer close to the initial water level and using a small initial water displacement can effectively avoid complicating the data analysis, such that previous, simpler data analysis methods can be used.     

Using high hydraulic conductivity nodes to simulate seepage lakes

In a typical ground water flow model, lakes are represented by specified head nodes requiring that lake levels be known a priori. To remove this limitation, previous researchers assigned high hydraulic conductivity (K) values to nodes that represent a lake, under the assumption that the simulated head at the nodes in the high-K zone accurately reflects lake level. The solution should also produce a constant water level across the lake. We developed a model of a simple hypothetical ground water/lake system to test whether solutions using high-K lake nodes are sensitive to the value of K selected to represent the lake. Results show that the larger the contrast between the K of the aquifer and the K of the lake nodes, the smaller the error tolerance required for the solution to converge. For our test problem, a contrast of three orders of magnitude produced a head difference across the lake of 0.005 m under a regional gradient of the order of 10(-3) m/m, while a contrast of four orders of magnitude produced a head difference of 0.001 m. The high-K method was then used to simulate lake levels in Pretty Lake, Wisconsin. Results for both the hypothetical system and the application to Pretty Lake compared favorably with results using a lake package developed for MODFLOW (Merritt and Konikow 2000). While our results demonstrate that the high-K method accurately simulates lake levels, this method has more cumbersome postprocessing and longer run times than the same problem simulated using the lake package.     

Practical issues in imaging hydraulic conductivity through hydraulic tomography

Hydraulic tomography has been developed as an alternative to traditional geostatistical methods to delineate heterogeneity patterns in parameters such as hydraulic conductivity (K) and specific storage (S(s)). During hydraulic tomography surveys, a large number of hydraulic head data are collected from a series of cross-hole tests in the subsurface. These head data are then used to interpret the spatial distribution of K and S(s) using inverse modeling. Here, we use the Sequential Successive Linear Estimator (SSLE) of Yeh and Liu (2000) to interpret synthetic pumping test data created through numerical simulations and real data generated in a laboratory sandbox aquifer to obtain the K tomograms. Here, we define "K tomogram" as an image of K distribution of the subsurface (or the inverse results) obtained via hydraulic tomography. We examine the influence of signal-to-noise ratio and biases on results using inverse modeling of synthetic and real cross-hole pumping test data. To accomplish this, we first show that the pumping rate, which affects the signal-to-noise ratio, and the order of data included into the SSLE algorithm both have large impacts on the quality of the K tomograms. We then examine the role of conditioning on the K tomogram and find that conditioning can improve the quality of the K tomogram, but can also impair it, if the data are of poor quality and conditioning data have a larger support volume than the numerical grid used to conduct the inversion. Overall, these results show that the quality of the K tomogram depends on the design of pumping tests, their conduct, the order in which they are included in the inverse code, and the quality as well as the support volume of additional data that are used in its computation.     

Methods of modeling hydraulic heterogeneity of sedimentary formations

The approaches and methods now in use for simulating the hydraulic heterogeneity of sedimentary rocks are reviewed, classified, and described. Special attention is paid to the statistical (geostatistical) models, including the most promising hydrofacies simulation methods.     

A simple correction for slug tests in small-diameter wells

A simple procedure is presented for correcting hydraulic conductivity (K) estimates obtained from slug tests performed in small-diameter installations screened in highly permeable aquifers. Previously reported discrepancies between results from slug tests in small-diameter installations and those from tests in nearby larger-diameter wells are primarily a product of frictional losses within the small-diameter pipe. These frictional losses are readily incorporated into existing models for slug tests in high-K aquifers, which then serve as the basis of a straightforward procedure for correcting previously obtained K estimates. A demonstration of the proposed procedure using data from a series of slug tests performed in a controlled field setting confirms the validity of the approach. The results of this demonstration also reveal the detailed view of spatial variations in K that can be obtained using slug tests in small-diameter installations.     

A rapid method for hydraulic profiling in unconsolidated formations

Information on vertical variations in hydraulic conductivity ( K ) can often shed much light on how a contaminant will move in the subsurface. The direct-push injection logger has been developed to rapidly obtain such information in shallow unconsolidated settings. This small-diameter tool consists of a short screen located just behind a drive point. The tool is advanced into the subsurface while water is injected through the screen to keep it clear. Upon reaching a depth at which information about K is desired, advancement ceases and the injection rate and pressure are measured on the land surface. The rate and pressure values are used in a ratio that serves as a proxy for K . A vertical profile of this ratio can be transformed into a K profile through regressions with K estimates determined using other techniques. The viability of the approach was assessed at an extensively studied field site in eastern Germany. The assessment demonstrated that this tool can rapidly identify zones that may serve as conduits for or barriers to contaminant movement.     

Factors affecting the measurement of the vertical hydraulic conductivity of a streambed sediment using standpipe tests

The vertical hydraulic conductivity (K_v) of a stream or lake sediment is often determined in the field using standpipe tests. Calculation of K_v is based on the assumption that the hydraulic head in the pipe is equal to that of the stream or lake stage. In this work, a modified equation for K_v is developed for the standpipe test which is applicable when this assumption is not valid. The equation involves not only the hydraulic head at different times but also the difference in the hydraulic head (a) between the groundwater level and river stage. The effects of certain factors on K_v, such as the ratio of the hydraulic head at different times (h₁/h₂), the difference a, and the initial water table height (h₀), are also discussed. The results show that when h₁/h₂ is constant, the relative error (E_r) in K_v increases with the ratio a/h₂. Furthermore, if a/h₂ < 0.05, then for any value of h₁/h₂, E_r is less than 5% using the modified equation. Also, if a/h₂ is large, hydraulic head readings with larger h₁/h₂ ratios must be used to avoid large E_r values. The results of a field test also indicate that the error in K_v decreases as the value of h₀ increases. Copyright © 2013 John Wiley & Sons, Ltd.     

Effective hydraulic conductivity of nonstationary aquifers

Assuming that the ln hydraulic conductivity in an aquifer is mathematically approximated by a spatial deterministic surface, or trend, plus a stationary random noise, we treat the problem of finding what the effective hydraulic conductivity of that aquifer is. This problem is tackled by spectral methods applied to a type of diffusion equation of groundwater flow, together with suitable coordinate transformations. Analytical (exact) solutions in terms of elementary functions are presented for one- and three-dimensional finite and infinite domains. Stability criteria are obtained for the solutions, in terms of a critical parameter, that turns out to involve the product of correlation scale and trend gradient. For the case of finite and symmetrical domains, additional provisions to insure the stability of numerical calculations of effective hydraulic conductivity are provided. Effective hydraulic conductivity is an important property, with potential applications in the calibrations of groundwater and transport numerical models.     

Effective hydraulic conductivity of nonstationary aquifers

Assuming that the ln hydraulic conductivity in an aquifer is mathematically approximated by a spatial deterministic surface, or trend, plus a stationary random noise, we treat the problem of finding what the effective hydraulic conductivity of that aquifer is. This problem is tackled by spectral methods applied to a type of diffusion equation of groundwater flow, together with suitable coordinate transformations. Analytical (exact) solutions in terms of elementary functions are presented for one- and three-dimensional finite and infinite domains. Stability criteria are obtained for the solutions, in terms of a critical parameter, that turns out to involve the product of correlation scale and trend gradient. For the case of finite and symmetrical domains, additional provisions to insure the stability of numerical calculations of effective hydraulic conductivity are provided. Effective hydraulic conductivity is an important property, with potential applications in the calibrations of groundwater and transport numerical models.     

An analytic data analysis method for oscillatory slug tests

An analytical data analysis method is developed for slug tests in partially penetrating wells in confined or unconfined aquifers of high hydraulic conductivity. As adapted from the van der Kamp method, the determination of the hydraulic conductivity is based on the occurrence times and the displacements of the extreme points measured from the oscillatory data and their theoretical counterparts available in the literature. This method is applied to two sets of slug test response data presented by Butler et al.: one set shows slow damping with seven discernable extremities, and the other shows rapid damping with three extreme points. The estimates of the hydraulic conductivity obtained by the analytic method are in good agreement with those determined by an available curve-matching technique.     

Diagrammatic theory of effective hydraulic conductivity

This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media. A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained. The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous limit.     

Diagrammatic theory of effective hydraulic conductivity

This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media. A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained. The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous limit.     

Influence of coarse soils with high hydraulic conductivity on the applicability of the SCS-CN method

The impact of the existence of coarse soils with high hydraulic conductivity on the applicability of the Soil Conservation Service curve number (SCS-CN) method is investigated in a heterogeneous catchment in the Zagros mountain region, southwest Iran. The findings indicate that curve numbers (CN) decline steadily as rainfall depths increase, showing no evidence of reaching stable CN values. This is attributed to a small low permeability area in the catchment, although most parts of the region are covered by high to very high permeability soils. Although this behaviour has been attributed mainly to forested areas by some researchers, it is shown here that it can be observed in mountain regions with coarse soils. The results also reveal that a linear rainfall–runoff formula of the form Q = CP provides more accurate results than the SCS-CN method, and the runoff coefficient (C) can be taken as equal to the low-permeability area fraction, meaning that these parts can be considered to be the main runoff-producing areas.     

Multiple parameterization for hydraulic conductivity identification

Hydraulic conductivity identification remains a challenging inverse problem in ground water modeling because of the inherent nonuniqueness and lack of flexibility in parameterization methods. This study introduces maximum weighted log-likelihood estimation (MWLLE) along with multiple generalized parameterization (GP) methods to identify hydraulic conductivity and to address nonuniqueness and inflexibility problems in parameterization. A scaling factor for information criteria is suggested to obtain reasonable weights of parameterization methods for the MWLLE and model averaging method. The scaling factor is a statistical parameter relating to a desired significance level in Occam's window and the variance of the chi-squares distribution of the fitting error. Through model averaging with multiple GP methods, the conditional estimate of hydraulic conductivity and its total conditional covariances are calculated. A numerical example illustrates the issue arising from Occam's window in estimating model weights and shows the usefulness of the scaling factor to obtain reasonable model weights. Moreover, the numerical example demonstrates the advantage of using multiple GP methods over the zonation and interpolation methods because GP provides better models in the model averaging method. The methodology is applied to the Alamitos Gap area, California, to identify the hydraulic conductivity field. The results show that the use of the scaling factor is necessary in order to incorporate good parameterization methods and to avoid a dominant parameterization method.     

Evaluation of vertical variations in hydraulic conductivity in unconsolidated sediments

Detailed information on vertical variations in hydraulic conductivity (K) is essential to describe the dynamics of groundwater movement at contaminated sites or as input data used for modeling. K values in high vertical resolution should be determined because K tends to be more continuous in the horizontal than in the vertical direction. To determine K in shallow unconsolidated sediments and in the vertical direction, the recently developed direct-push injection logger can be used. The information obtained by this method serves as a proxy for K and has to be calibrated to obtain quantitative K values of measured vertical profiles. In this study, we performed direct-push soil sampling, sieve analyses and direct-push slug tests to obtain K values in vertical high resolution. Using the results of direct-push slug tests, quantitative K values obtained by the direct-push injection logger could be determined successfully. The results of sieve analyses provided lower accordance with the logs due to the inherent limitations of the sieving method.     

Characterizing hydraulic conductivity with the direct-push permeameter

The direct-push permeameter (DPP) is a promising approach for obtaining high-resolution information about vertical variations in hydraulic conductivity (K) in shallow unconsolidated settings. This small-diameter tool, which consists of a short screened section with a pair of transducers inset in the tool near the screen, is pushed into the subsurface to a depth at which a K estimate is desired. A short hydraulic test is then performed by injecting water through the screen at a constant rate (less than 4 L/min) while pressure changes are monitored at the transducer locations. Hydraulic conductivity is calculated using the injection rate and the pressure changes in simple expressions based on Darcy's Law. In units of moderate or higher hydraulic conductivity (more than 1 m/d), testing at a single level can be completed within 10 to 15 min. Two major advantages of the method are its speed and the insensitivity of the K estimates to the zone of compaction created by tool advancement. The potential of the approach has been assessed at two extensively studied sites in the United States and Germany over a K range commonly faced in practical field investigations (0.02 to 500 m/d). The results of this assessment demonstrate that the DPP can provide high-resolution K estimates that are in good agreement with estimates obtained through other means.