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Mathematical models for stream depletion with stream stage decline or drawdown are developed to overcome the deficiency in existing models that typically use the constant-head (Dirichlet) or general (Robin) boundary condition and source terms at the stream-aquifer interface. Existing approaches assume a fixed stream stage during pumping, implies that the stream is an infinite water source, with depletion defined as a decrease in stream discharge. We refer to this depletion without drawdown as the ``stream depletion paradox.'' It is a glaring model limitation, ignoring the most observable adverse effect of long-term groundwater abstraction near a stream, namely stage declines that eventually lead to dry streambeds. Field data are presented to demonstrate that stream stage responds to pumping near the stream, motivating the development of an alternative theory predicts transient stream drawdown based on the concepts of finite stream storage and mass continuity at the stream-aquifer interface. Based on this alternative theory, models are developed for the cases of a non- and a fully-penetrating stream. The proposed model reduces to the fixed-stage model in the limit as stream storage becomes infinitely large and to the limiting case of confined aquifer flow with a no-flow boundary at the streambed when the stream storage vanishes. The model is applied to field observations of both aquifer and stream drawdown from tests conducted in a confined aquifer over which a shallow stream flows. Model fits and parameter estimates are obtained both aquifer and stream drawdown data. Model predicted and observed transient drawdown behavior indicate that fixed-stage models (a) underestimate late-time aquifer drawdown and (b) overestimate the available recharge from streams to pumping wells. This has significant implications for the sustainable management of water resources in hydraulically connected stream-aquifer systems with heavy groundwater abstraction.

Mathematical models for stream depletion typically use the constant-head Dirichlet boundary condition or the general Robin boundary condition at the stream. Both approaches fix stream stage as cons...

We consider the transient electrokinetic response of an aquifer-aquitard system to groundwater abstraction from the aquifer. The system was instrumented with 18 non-polarizable copper/copper sulpha...

To close the water use budget in irrigated agricultural fields in flood plains with substantial riparian corridors, it is necessary to understand groundwater usage by dominant phreatophyte vegetati...

We present an approach to uncoupling the pair of transient governing equations used in electrokinetics (i.e., streaming potential and electroosmosis). This approach allows for the solution of two u...

We report the results of field and laboratory investigations of stream-aquifer interactions in a watershed along the California coast to assess the impact of groundwater pumping for irrigation on stream flows. The methods used include subsurface sediment sampling using direct-push drilling, laboratory permeability and particle size analyses of sediment, piezometer installation and instrumentation, stream discharge and stage monitoring, pumping tests for aquifer characterization, resistivity surveys, and long-term passive monitoring of stream stage and groundwater levels. Spectral analysis of long-term water level data was used to assess correlation between stream and groundwater level time series data. The investigations revealed the presence of a thin low permeability silt-clay aquitard unit between the main aquifer and the stream. This suggested a three layer conceptual model of the subsurface comprising unconfined and confined aquifers separated by an aquitard layer. This was broadly confirmed by resistivity surveys and pumping tests, the latter of which indicated the occurrence of leakage across the aquitard. The aquitard was determined to be 2–3 orders of magnitude less permeable than the aquifer, which is indicative of weak stream-aquifer connectivity and was confirmed by spectral analysis of stream-aquifer water level time series. The results illustrate the importance of site-specific investigations and suggest that even in systems where the stream is not in direct hydraulic contact with the producing aquifer, long-term stream depletion can occur due to leakage across low permeability units. This has implications for management of stream flows, groundwater abstraction, and water resources management during prolonged periods of drought.

We present preliminary results from an electrokinetic laboratory rock characterization approach, which uses electroosmosis and streaming potential to estimate permeability. The device has two modes...

A multiporosity extension of classical double and triple porosity fractured rock flow models for slightly compressible fluids is presented. The multiporosity model is an adaptation of the multirate solute transport model of Haggerty and Gorelick (1995) to viscous flow in fractured rock reservoirs. It is a generalization of both pseudo-steady-state and transient interporosity flow double porosity models. The model includes a fracture continuum and an overlapping distribution of multiple rock matrix continua, whose fracture-matrix exchange coefficients are specified through a discrete probability mass function. Semi-analytical cylindrically symmetric solutions to the multiporosity mathematical model are developed using the Laplace transform to illustrate its behavior. The multiporosity model presented here is conceptually simple, yet flexible enough to simulate common conceptualizations of double and triple porosity flow. This combination of generality and simplicity makes the multiporosity model a good choice for flow in low-permeability fractured rocks., 5 figures, 3 tables

A semianalytical solution is presented for transient streaming potentials associated with flow to a pumping well in an unconfined aquifer, taking into account the effect of flow in the unsaturated zone above the water table. Flow in the unsaturated zone is modeled with a linearized form of Richards' equation using an exponential model for soil moisture retention and unsaturated hydraulic conductivity. Archie's law is invoked for unsaturated electrical conductivity. The unsaturated electrokinetic coupling coefficient is modeled with a decaying exponential, where the maximum value is at and below the water table. The coupled flow and electrokinetic problem is solved using Laplace and Hankel transforms. The results of the model predicted behavior are presented and compared to that observed in laboratory simulations of pump­ ing tests. The early time polarity reversal predicted the model is observable in the experiments. Other non- monotonic streaming potential behaviors predicted by the model are also evident in experimental measurements. The model is used to estimate hydraulic parameters from SP data and these compare well to those obtained from drawdown data. For example, a hydraulic conductivity of 3.6 3 10 24 m/s is obtained from SP data compared to 3.4 3 10 24 m/s from drawdown data.

We present transient streaming potential data collected during falling-head permeameter tests performed on samples of two sands with different physical and chemical properties. The objective of the work is to estimate hydraulic conductivity (K) and the electrokinetic coupling coefficient (Cl) of the sand samples. A semi-empirical model based on the falling-head permeameter flow model and electrokinetic coupling is used to analyze the streaming potential data and to estimate K and Cl. The values of K estimated from head data are used to validate the streaming potential method. Estimates of K from streaming potential data closely match those obtained from the associated head data, with less than 10% deviation. The electrokinetic coupling coefficient was estimated from streaming potential vs. (1) time and (2) head data for both sands. The results indicate that, within limits of experimental error, the values of Cl estimated by the two methods are essentially the same. The results of this work demonstrate that a temporal record of the streaming potential response in falling-head permeameter tests can be used to estimate both K and Cl. They further indicate the potential for using transient streaming potential data as a proxy for hydraulic head in hydrogeology applications.

Model applicability to core-scale solute transport is evaluated using breakthrough data from column experiments conducted with conservative tracers tritium (H-3) and sodium-22, and the retarding solute uranium-232. The three models considered are single-porosity, double-porosity with single-rate mobile-immobile mass-exchange, and the multirate model, which is a deterministic model that admits the statistics of a random mobile-immobile mass-exchange rate coefficient. The experiments were conducted on intact Culebra Dolomite core samples. Previously, data were analyzed using single- and double-porosity models although the Culebra Dolomite is known to possess multiple types and scales of porosity, and to exhibit multirate mobile-immobile-domain mass transfer characteristics at field scale. The data are reanalyzed here and null-space Monte Carlo analysis is used to facilitate objective model selection. Prediction (or residual) bias is adopted as a measure of the model structural error. The analysis clearly shows single- and double-porosity models are structurally deficient, yielding late-time residual bias that grows with time. On the other hand, the multirate model yields unbiased predictions consistent with the late-time -5/2 slope diagnostic of multirate mass transfer. The analysis indicates the multirate model is better suited to describing core-scale solute breakthrough in the Culebra Dolomite than the other two models.

[1] Riparian zones in semiarid regions often exhibit high rates of evapotranspiration (ET) in spite of low-soil moisture content due to the presence of phreatophytic vegetation that is able to withdraw water from shallow aquifers. This work seeks to better define the relationship between ET, the saturated zone and the river boundary by comparing observed water table drawdown records to analytically modeled drawdown in fully penetrating wells of an unconfined aquifer in response to daily ET flux. ET at the Boise Hydrogeophysical Research Site (BHRS), a riparian zone in a temperate, semiarid environment, is calculated using a radiation-based method to provide ET values at four different wells with different vegetation densities. Analytically modeled drawdown response to ET forcing shows that drawdown magnitude increases with increasing distance from the river edge even as the surficial ET forcing remains constant. This behavior is also observed in well hydrographs and shows the buffering effect that flow from the river has on drawdown in fully penetrating riparian wells in highly permeable, unconfined aquifers. Relative contributions of river water to aquifer storage are calculated for ET-induced diurnal fluctuations of the water table at increasing distances from the river boundary. Failure to account for these spatial differences in drawdown related to the river source may explain some errors associated with estimating ET from well hydrographs alone.

Two models for slug tests conducted in unconfined aquifers are developed by (a) extending the unconfined KGS solution to oscillatory responses, yielding a model referred to herein as the unified model, and (b) replacing the constant head condition with the linearized kinematic condition at the water table. The models can be used to analyze the full range of responses from highly oscillatory to overdamped. The second model, refered to as the moving water table (MWT) model, is only applicable when effects of well bore skin are negligible. The models are validated by comparison with published solutions, and by application to a published case study of field tests conducted in wells without skin in an unconfined aquifer at the MSEA site in Nebraska. In this regard (a) the MWT model essentially yields the same results as the confined KGS model, except very close to the water table, and (b) the unified model yields slightly smaller aquifer K-values relative to the MWT model at all positions in the well. All model solutions yield comparable results when fitted to published field data obtained in an unconfined fluvial aquifer at the MSEA site in Nebraska. The unified model is fitted to field data collected in wells known to exhibit positive skin effects at the Boise Hydrogeophysical Research Site (BHRS) in Boise, Idaho. It is shown to yield hydraulic conductivity estimates of comparable magnitude to those obtained with the KGS model for overdamped responses, and the Springer–Gelhar model for oscillatory responses. Sensitivity of the MWT model to specific yield, S y , and hydraulic anisotropy, j is evaluated and the results, when plotted in log–log space and with consideration of log-scale time derivatives of the response, indicate that these two parameters should be estimable from slug test data, though challenges still remain.

Summary A recently developed unified model for partially-penetrating slug tests in unconfined aquifers ( Malama et al., in press ) provides a semi-analytical solution for aquifer response at the wellbore in the presence of inertial effects and wellbore skin, and is able to model the full range of responses from overdamped/monotonic to underdamped/oscillatory. While the model provides a unifying framework for realistically analyzing slug tests in aquifers (with the ultimate goal of determining aquifer properties such as hydraulic conductivity K and specific storage S s ), it is currently unclear whether parameters of this model can be well-identified without significant prior information and, thus, what degree of information content can be expected from such slug tests. In this paper, we examine the information content of slug tests in realistic field scenarios with respect to estimating aquifer properties, through analysis of both numerical experiments and field datasets. First, through numerical experiments using Markov Chain Monte Carlo methods for gauging parameter uncertainty and identifiability, we find that: (1) as noted by previous researchers, estimation of aquifer storage parameters using slug test data is highly unreliable and subject to significant uncertainty; (2) joint estimation of aquifer and skin parameters contributes to significant uncertainty in both unless prior knowledge is available; and (3) similarly, without prior information joint estimation of both aquifer radial and vertical conductivity may be unreliable. These results have significant implications for the types of information that must be collected prior to slug test analysis in order to obtain reliable aquifer parameter estimates. For example, plausible estimates of aquifer anisotropy ratios and bounds on wellbore skin K should be obtained, if possible, a priori. Secondly, through analysis of field data – consisting of over 2500 records from partially-penetrating slug tests in a heterogeneous, highly conductive aquifer, we present some general findings that have applicability to slug testing. In particular, we find that aquifer hydraulic conductivity estimates obtained from larger slug heights tend to be lower on average (presumably due to non-linear wellbore losses) and tend to be less variable (presumably due to averaging over larger support volumes), supporting the notion that using the smallest slug heights possible to produce measurable water level changes is an important strategy when mapping aquifer heterogeneity. Finally, we present results specific to characterization of the aquifer at the Boise Hydrogeophysical Research Site. Specifically, we note that (1) K estimates obtained using a range of different slug heights give similar results, generally within ±20%; (2) correlations between estimated K profiles with depth at closely-spaced wells suggest that K values obtained from slug tests are representative of actual aquifer heterogeneity and not overly affected by near-well media disturbance (i.e., “skin”); (3) geostatistical analysis of K values obtained indicates reasonable correlation lengths for sediments of this type; and (4) overall, K values obtained do not appear to correlate well with porosity data from previous studies.

Summary An alternative linearization of the nonlinear kinematic condition at the water table used in unconfined aquifer flow theory is proposed. It simulates the downward propagation of the water table, during water extraction via a pumping well, as a diffuse process controlled by a dimensionless linearization parameter, β D . The limiting value of β D = 0 corresponds to the solution of Neuman (1972) whereas that of β D → ∞ corresponds to the early-time Theis solution. Using the solution obtained with this linearization, data collected during a pumping test conducted at the Boise Hydrogeophysical Research Site in Idaho, US, were analyzed. The estimates of hydraulic conductivity and specific storage obtained in this study compare well with those obtained with the other models. The most significant improvement is in the estimated value of specific yield, with the proposed model yielding values that are close to those expected from known porosity values ( n ∼ 0.25) at the site. The results show that meaningful estimates of specific yield can be obtained by treating the water table as a diffuse moving material boundary, without recourse to more complex models for water table decline or inclusion of unsaturated zone flow.

Summary We investigate the response of the saturated zone (unconfined aquifer) to evapotranspiration (ET) flux at ground surface. We neglect fluid flow and storage in the unsaturated zone and treat ET as a sinusoidal forcing function at the watertable. The linearized kinematic condition is imposed at the watertable. Analytical solutions are developed for the case of flow in a domain of (a) semi-infinite extent to simulate response in a domain bounded by a river and (b) infinite lateral extent to simulate the response in a domain with no river boundaries. These solutions are fitted to observed groundwater head fluctuations recorded in observation wells at the Boise Hydrogeophysical Research Site in Idaho and the Larned Research Site in Kansas. Estimates of the amplitude of the ET flux, aquifer hydraulic conductivity, specific storage and specific yield are obtained and these compare well to published results from pumping tests conducted at the site. The field exercise is used to explore the potential for using groundwater head fluctuations to estimate ET and hydraulic parameters of unconfined aquifers.

Summary An analytical solution for flow in the vicinity of an observation well is developed. The observation is emplaced in a homogeneous aquifer of infinite radial extent that is pumped at a constant rate, and satisfies the Theis solution. We attempt to account for the effect of an observation well on the drawdown response in a neighborhood of finite radial extent centered around the well. The model of Black and Kipp [Black, J.H., Kipp Jr., K.L., 1977. Observation well response time and its effect upon aquifer tests. Journal of Hydrology 34, 297–306] only makes a correction to the drawdown response at the well location and does not modify the flow pattern in the neighborhood of the well. This may be sufficient for isolated observation wells but, for well-fields or sites with relatively closely spaced wells, the flow patterns in the neighborhoods of the wells may significantly impact drawdown response. The model we develop is applied to field data and is shown to yield an aquifer hydraulic diffusivity that is comparable to that estimated with the model of Black and Kipp [Black, J.H., Kipp Jr., K.L., 1977. Observation well response time and its effect upon aquifer tests. Journal of Hydrology 34, 297–306]. In addition to providing estimates of formation conductivity and specific storage, the solution yield estimates of the hydraulic conductivity and specific storage of the zone of influence and has the ability to predict the effect of the observation well on drawdown response in a finite region of influence in the vicinity of the well.

Summary A semi-analytical solution is presented for the problem of flow in a system consisting of unconfined and confined aquifers, separated by an aquitard. The unconfined aquifer is pumped continuously at a constant rate from a well of infinitesimal radius that partially penetrates its saturated thickness. The solution is termed semi-analytical because the exact solution obtained in double Laplace‐Hankel transform space is inverted numerically. The solution presented here is more general than similar solutions obtained for confined aquifer flow as we do not adopt the assumption of unidirectional flow in the confined aquifer (typically assumed to be horizontal) and the aquitard (typically assumed to be vertical). Model predicted results show significant departure from the solution that does not take into account the effect of leakage even for cases where aquitard hydraulic conductivities are two orders of magnitude smaller than those of the aquifers. The results show low sensitivity to changes in radial hydraulic conductivities for aquitards that are two or more orders of magnitude smaller than those of the aquifers, in conformity to findings of earlier workers that radial flow in aquitards may be neglected under such conditions. Hence, for cases were aquitard hydraulic conductivities are two or more orders of magnitude smaller than aquifer conductivities, the simpler models that restrict flow to the radial direction in aquifers and to the vertical direction in aquitards may be sufficient. However, the model developed here can be used to model flow in aquifer‐aquitard systems where radial flow is significant in aquitards. a 2008 Elsevier B.V. All rights reserved.

This study presents a semi-analytical solution for the problem of leakage in an unconfined aquifer bounded below by an aquitard of finite or semi-infinite extent. The homogeneous anisotropic unconfined aquifer of infinite radial extent is pumped continuously at a constant rate from a well of infinitesimal radius. The aquitard is also homogeneous, anisotropic and of infinite radial extent. Flow in both the aquifer and the aquitard is allowed to occur both vertically and horizontally. Exact solutions to the governing equations given in this work are developed in the double Laplace-Hankel transform space for drawdown response in the unconfined aquifer and the underlying aquitard. The inverse transforms of the solutions are obtained numerically. The theoretical results show that leakage can cause significant departure, at both early and late times, from the solution with no leakage. The solution presented here can be used in least-squares routines for estimation of hydraulic parameters for two-layered unconfined aquifer-aquitard systems.

To simulate brittle rocks, a mixture of glastone, sand and water was used as a model material. Thin galvanized sheets of thickness 0.254 mm were used to create joints in blocks made out of the model material. To investigate the failure modes and strength, both the intact material blocks as well as jointed model material blocks of size 35.6 × 17.8 × 2.5 cm having different joint geometry configurations were subjected to uniaxial and biaxial compressive loadings. A new intact rock failure criterion is proposed at the 3-D level. This criterion is validated for biaxial loading through laboratory experimental results obtained on intact model material blocks. Results obtained from both the intact and jointed model material blocks are used to develop a strongly non-linear new rock mass failure criterion for biaxial loading. In this failure criterion, the fracture tensor component is used to incorporate the directional effect of fracture geometry system on jointed block strength. The failure criterion shows the important role, the intermediate principal stress plays on rock mass strength.

A new semi-empirical model that can be used to predict fracture deformation behavior under normal compressive loading is presented. The development of a simple exponential model is presented first after which a modified and more general exponential model, with an additional degree of freedom in the model parameters, is obtained. The simple and the modified exponential models are then compared to available fracture closure models, namely the empirical Barton–Bandis hyperbolic model, and a power-law model based on Hertzian contact theory, to determine how good they fit the results of fracture closure experiments under monotonically increasing normal compressive loading. A new parameter called the half-closure stress, σ 1/2 , is introduced and is used, in addition to the maximum fracture closure, Δ v m , in the model fitting procedures for the Barton–Bandis and the simple exponential model. The half-closure stress is shown to be related to the initial normal stiffness, K ni , used in the original Barton–Bandis model. An additional parameter, n, is used in fitting the modified exponential model to the experimental data. Of the models presented herein, the modified exponential model was found to provide the best fit to the experimental data, for the same values of σ 1/2 and Δ v m , over the entire range of compressive stresses. The power-law model based on Hertzian contact theory was found to be unsuitable for predicting normal fracture deformation behavior.

Laboratory experiments and numerical simulations, using Particle Flow Code (PFC3D ), were performed to study the behavior of jointed blocks of model material under uniaxial loading. The effect of joint geometry parameters on the uniaxial compressive strength of jointed blocks was investigated and this paper presents the results of the experiments and numerical simulations. The fracture tensor component in a given direction is used to quantify the combined directional effect of joint geometry parameters including joint density, orientation and size distributions, and the number of joint sets. The variation of the uniaxial compressive strength of the jointed blocks of the model material with the fracture tensor component was investigated. Both the laboratory experiments and the numerical simulations showed that the uniaxial block strength decreases in a nonlinear manner with increasing values of the fracture tensor component. It was observed that joint geometry configuration controls the mode of failure of the jointed blocks and three modes of failure were identified, namely (a) tensile splitting through the intact material, (b) failure by sliding along the joint plane and/or by displacement normal to the joint plane and, (c) mixed mode failure involving both the failure mechanisms in (a) and (b). It has also been shown that with careful parameter calibration procedures, PFC3D could be used to model the strength behavior of jointed blocks of rock.

We present transient streaming potential data collected during falling-head permeameter tests performed on samples of two sands with different physical and chemical properties. The objective of the work is to estimate hydraulic conductivity (K) and the electrokinetic coupling coefficient (Cl ) of the sand samples. A semi-empirical model based on the falling-head permeameter flow model and electrokinetic coupling is used to analyze the streaming potential data and to estimate K and Cl . The values of K estimated from head data are used to validate the streaming potential method. Estimates of K from streaming potential data closely match those obtained from the associated head data, with less than 10% deviation. The electrokinetic coupling coefficient was estimated from streaming potential vs. (1) time and (2) head data for both sands. The results indicate that, within limits of experimental error, the values of Cl estimated by the two methods are essentially the same. The results of this work demonstrate that a temporal record of the streaming potential response in falling-head permeameter tests can be used to estimate both K and Cl . They further indicate the potential for using transient streaming potential data as a proxy for hydraulic head in hydrogeology applications.

This report is a summary of the physical processes, primary governing equations, solution approaches, and historic testing related to brine migration in geologic salt. Although most information presented in this report is not new, we synthesize a large amount of material scattered across dozens of laboratory reports, journal papers, conference proceedings, and textbooks. We present a mathematical description of the governing brine flow mechanisms in geologic salt. We outline the general coupled thermal, multi-phase hydrologic, and mechanical processes. We derive these processes' governing equations, which can be used to predict brine flow. These equations are valid under a wide variety of conditions applicable to radioactive waste disposal in rooms and boreholes excavated into geologic salt.