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Minipermeameters are rapidly becoming a popular tool for collecting localized measurements of permeability in both laboratory and field studies. While one of the main advantages of minipermeameters is their ability to collect data on various support volumes, there have been only limited attempts to analyze their size and geometry. We define the support volume of minipermeameter measurements as a region containing 90% of the total gas flow, i.e., a region bounded by the 10% streamline. Using our new semianalytical solutions for the Stokes' stream function, we demonstrate that the support volume has a shape of the semitoroid adjacent to the sample surface. Hence there is a blind spot directly below the minipermeameter, which is not probed by the measurement. We demonstrate that the support volume of the minipermeameter measurements decreases with the tip-seal's ratio (a ratio of the inner tip-seal radius to the outer tip-seal radius), while the size of the corresponding blind spot increases.

A mathematical model of average nonuniform flow in heterogeneous stratified media is developed. The averaged Darcy's law is obtained by deriving the analytical expression of the effective conductivity tensor for media with small heterogeneities. The fundamental solution of the average flow equation (mean Green function) corresponding to the flow toward a single point source of deterministic discharge is derived. The mean head distribution is calculated for a fully penetrating well, for a finite length well in an infinite domain, and for a dipole well. The concept of equivalent conductivity is defined for use in identifying the formation conductivity properties. The procedure for identifying the mean conductivity, log conductivity variance, and vertical integral scale is suggested for the case of dipole flow. 1. Introduction Natural aquifers reveal a wide spatial variability of their properties, which affects their flow and transport parameters. The effect of formation structure on the process characteristics has been recognized for a long time, and numerous approaches that account for the formation heterogeneities have been sug- gested. The objective of these approaches is to develop theo- ries applicable to both identifying aquifer parameters and fore- casting flow and transport processes. Early theories modeled formation heterogeneity by regard- ing hydraulic conductivities in the "horizontal" and "vertical"

A theory of dipole flow is developed to model flow induced by a vertical circulation well consisting of injection and extraction chambers in a single borehole. Included in the theory are an analytical description of the kinematic flow structure around a vertical circulation well and the drawdown in the well chambers. Using Stokes' stream function, simple criteria are derived to determine the region of intensive recirculation. This region extends (from the dipole center) approximately five distances between chamber centers in the radial direction and two distances between chamber centers in both vertical directions. The vertical scale does not depend on anisotropy of hydraulic conductivity, and the radial scale is corrected for anisotropic aquifers. Based on these estimates, criteria are given for the selection of the appropriate aquifer model to employ in five settings, including infinite, semi-infinite confined, semi-infinite unconfined, finite confined, and finite unconfined aquifers. Applications of dipole flow theory are given for analytical estimation of the capture zone for recirculation wells and for simultaneous measurement of horizontal and vertical hydraulic conductivity in uniform anisotropic aquifers using steady state measurements of drawdown in the well chambers.

Three-dimensional solutions for the hydraulic head and velocity components for transient groundwater flow in an unconfined compressible aquifer of finite thickness with a rectangular areal recharge source are analyzed using a linearized mathematical model. The solution generalizes Dagan's (1967) results, which were obtained for an idealized aquifer of infinite thickness, and Hantush's (1967) results, which were derived using the Dupuit assumptions. Hydraulic head and velocity components are estimated by asymptotic methods for large times, which are most appropriate for contaminant transport problems. Numerical analysis of the solution demonstrates spatial features of the velocity components in general and a transient effect of upward flow in particular, similar to that found for circular sources (Zlotnik and Ledder, 1992). Obtained formulas show that applicability of the Dupuit assumption for computation of velocity components in an unconfined aquifer is limited to a far-field zone given approximately by |x| > 1.5X, |y| > 1.5Y, where X and Y are the half width and half-length, respectively, of the contaminant source.

The distributions of the hydraulic head and velocity components of the transient groundwater flow in an unconfined compressible aquifer of finite thickness under constant uniform circular recharge are obtained from the linearized mathematical model by the use of integral transforms. The result generalizes Dagan's (1967) solution which was derived by neglecting the compressibility. By treating the compressibility parameter as a small value, the formula for the hydraulic head is analyzed by asymptotic methods, resulting in approximations to the exact solutions for the head and velocities on small and large time scales. The hydraulic head and flow velocities can be accurately approximated by Dagan's formula for large times; for small times, neglecting the compressibility gives a large relative error but small absolute error.

] This study was performed as a part of the GrasslandDestabilization Experiment at the University of Nebraska’sBarta Brothers Ranch site (BBRS) in the eastern NSH(Figure 1), which investigates the ecological and geomor-phic stability of the NSH from an interdisciplinary perspec-tive and focuses on atmosphere–land surface–groundwaterinteractions [Wang et al., 2008]. The Nebraska Sand Hills isthe largest native grassland–stabilized sand dune area inthe Western Hemisphere and an important groundwaterrecharge source for the High Plains aquifer [Loope andSwinehart, 2000]. Mean annual temperature at the site is8.1 C and mean annual precipitation is 576 mm. About90% of the landscape at the site is composed by uplanddunes and dry interdunal areas covered by native warm-season grasslands, while the remaining 10% consists of wetmeadows and wetlands. Holocene dune sands overlie Qua-ternary and/or Pliocene alluvial sand and silt with low SOMcontent throughout the NSH.[

[1] Process-based vadose zone models are becoming common tools for evaluating spatial distributions of groundwater recharge (GR), but their applications are restricted by complicated parameterizations, especially because of the need for highly nonlinear and spatially variable soil hydraulic characteristics (SHCs). In an attempt to address the scarcity of field SHC data, pedotransfer functions (PTF) were introduced in earlier attempts to estimate SHCs. However, the accuracy of this method is rarely questioned in spite of significant uncertainties of PTF-estimated SHCs. In this study, we investigated the applicability of coupling vadose zone models and PTFs for evaluating GR in sand and loamy sand soils in a semiarid region and also their sensitivity to lower boundary conditions. First, a data set containing measured SHCs was used in the simulations. A second data set contained correlated SHCs drawn from the covariance matrix of the first data set. The third SHC data set used was derived from a widely used PTF. Although standard deviations for individual parameters were known for this PTF, no covariance matrix was available. Hence, we assumed that the parameters of this PTF were uncorrelated, thereby potentially overestimating the volume of the parameter space. Results were summarized using histograms of GR for various sets of input parameters. Under the unit gradient flow lower boundary condition, the distributions of GR for sand and loamy sand significantly overlap. Values of GR based on mean SHCs (or GR*) generally lie off the mode of the GR distribution. This indicates that the routinely used method of taking GR* as a regional representation may not be viable. More importantly, the computed GR largely depends in a nonlinear fashion on the shape factor n in the van Genuchten model. Under the same meteorological conditions, a coarser soil with a larger n generally produces a higher GR. Therefore, the uncertainty in computed GR is largely determined by the uncertainty in estimated n by PTFs (e.g., mean and standard deviation). Under the constant head lower boundary condition, upward soil moisture flux may exist from the lower boundary. Especially for regions with shallow water tables where upward flux exists, choosing an appropriate lower boundary condition is more important than selecting SHC values for calculating GR. The results show that the distribution of GR is less scattered and GR is more intense if the constant head lower boundary is located at deeper depths.

[1] Advection through hyporheic zones (HZ) consisting of heterogeneous channel bend streambed deposits and their equivalent homogenous medium was investigated using finite difference groundwater flow and transport simulations and forward particle tracking. The top prescribed head boundary was varied in order to mimic various stream channel head distributions resulting from the presence of bed forms and channel curvature. Flux calculations show that heterogeneity causes significant additional HZ flux compared to an equivalent homogenous medium. However, the major cause of HZ flux is a spatially periodic (sinusoidal) head distribution along the boundary, representing the effect of bed forms. The additional influence of heterogeneity on the total channel-bed exchange and the overall HZ geometry are increased when boundary head sinusoidal fluctuation is more subdued. We present dimensionless numbers that summarize these relationships. Heterogeneity's influence is further magnified by considering the effect of channel curvature on boundary heads. The simulations illustrate the dynamic influence of heterogeneity on the hyporheic zone since the various head boundaries employed in our modeling efforts are a proxy for different surface water conditions and bed form states that may occur during a single flood. Furthermore, we show that residence times (total tracking times) of particles originating from the streambed follow a lognormal distribution. In the presence of heterogeneity, residence times can decrease or they can increase compared to residence times for homogeneous conditions depending on the relative positions of the heterogeneities and the bed forms. Hence streambed heterogeneity and stream curvature, factors often neglected in previous modeling efforts, combine with bed form configuration to dynamically determine HZ geometry, fluxes, and residence time distributions.

[1] Existing analytical models for evaluating stream depletion by wells in alluvial aquifers are based on the assumption that stream depletion supplies 100% of groundwater withdrawals. Analysis of specific hydrostratigraphic conditions in leaky aquifers indicates that stream depletion may range from 0 to 100%. A new concept of maximum stream depletion rate (MSDR) is introduced and defined as a maximum fraction of the pumping rate contributed by the stream depletion. Several new analytical solutions indicate that the MSDR is determined by aquifer hydrostratigraphic conditions, geometry of recharge and discharge zones, and locations of pumping wells.

[1] This field study compares three techniques for estimating the vertical distribution of horizontal hydraulic conductivity Kr in a heterogeneous aquifer and evaluates possible support volume effects. The dipole flow test (DFT), multilevel slug test (MLST), and borehole flowmeter test (BFT) are based on different kinematic flow structures and the shape and the size of the support volumes. The experiment design employed an identical characteristic linear scale for all tests. Vertical profiles of Kr ranging up to 260 m/day from tested wells in an alluvial aquifer exhibit a strong correlation in spite of the differences between test hydraulics. Results suggest that tested screen length is an important indicator of the averaging mechanism for hydraulic tests. Correlation between the DFT and MLST is especially strong. Correlation between data from the BFT and other tests is not as strong due to the absence of a distinct physical vertical scale, among other factors. The differences between the tests are discussed using the concept of a weighting function associated with the magnitude of instantaneous local velocity.

[1] New semianalytical solutions for evaluation of the drawdown near horizontal and slanted wells with finite length screens in unconfined aquifers are presented. These fully three-dimensional solutions consider instantaneous drainage or delayed yield and aquifer anisotropy. As a basis, solution for the drawdown created by a point source in a uniform anisotropic unconfined aquifer is derived in Laplace domain. Using superposition, the point source solution is extended to the cases of the horizontal and slanted wells. The previous solutions for vertical wells can be described as a special case of the new solutions. Numerical Laplace inversion allows effective evaluation of the drawdown in real time. Examples illustrate the effects of well geometry and the aquifer parameters on drawdown. Results can be used to generate type curves from observations in piezometers and partially or fully penetrating observation wells. The proposed solutions and software are useful for the parameter identification, design of remediation systems, drainage, and mine dewatering.

[1] Considerable progress has been made in developing a theoretical framework for modeling slug test responses in formations with high hydraulic conductivity K. However, several questions of practical significance remain unresolved. Given the rapid and often oscillatory nature of test responses, the traditional hydrostatic relationship between the water level and the transducer-measured head in the water column may not be appropriate. A general dynamic interpretation is proposed that describes the relationship between water level response and transducer-measured head. This theory is utilized to develop a procedure for transforming model-generated water level responses to transducer readings. The magnitude of the difference between the actual water level position and the apparent position based on the transducer measurement is a function of the acceleration and velocity of the water column, test geometry, and depth of the transducer. The dynamic approach explains the entire slug test response, including the often-noted discrepancy between the actual initial water level displacement and that measured by a transducer in the water column. Failure to use this approach can lead to a significant underestimation of K when the transducer is a considerable distance below the static water level. Previous investigators have noted a dependence of test responses on the magnitude of the initial water level displacement and have developed various approximate methods for analyzing such data. These methods are re-examined and their limitations clarified. Practical field guidelines are proposed on the basis of findings of this work. The soundness of the dynamic approach is demonstrated through a comparison of K profiles from a series of multilevel slug tests with those from dipole-flow tests performed in the same wells.