Search

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 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...

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.

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.

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.

International audience; The importance of estimating spatially variable aquifer parameters such as transmissivity is widely recognized for studies in resource evaluation and contaminant transport. A useful approach for mapping such parameters is inverse modeling of data from series of pumping tests, that is, via hydraulic tomography. This inversion of field hydraulic tomographic data requires development of numerical forward models that can accurately represent test conditions while maintaining computational efficiency. One issue this presents is specification of boundary and initial conditions, whose location, type, and value may be poorly constrained. To circumvent this issue when modeling unconfined steady-state pumping tests, we present a strategy that analyzes field data using a potential difference method and that uses dipole pumping tests as the aquifer stimulation. By using our potential difference approach, which is similar to modeling drawdown in confined settings, we remove the need for specifying poorly known boundary condition values and natural source/sink terms within the problem domain. Dipole pumping tests are complementary to this strategy in that they can be more realistically modeled than single-well tests due to their conservative nature, quick achievement of steady state, and the insensitivity of near-field response to far-field boundary conditions. After developing the mathematical theory, our approach is first validated through a synthetic example. We then apply our method to the inversion of data from a field campaign at the Boise Hydrogeophysical Research Site. Results from inversion of nine pumping tests show expected geologic features, and uncertainty bounds indicate that hydraulic conductivity is well constrained within the central site area.

International audience; Ground water flow associated with pumping and injection tests generates self-potential signals that can be measured at the ground surface and used to estimate the pattern of ground water flow at depth. We propose an inversion of the self-potential signals that accounts for the heterogeneous nature of the aquifer and a relationship between the electrical resistivity and the streaming current coupling coefficient. We recast the inversion of the self-potential data into a Bayesian framework. Synthetic tests are performed showing the advantage in using self-potential signals in addition to in situ measurements of the potentiometric levels to reconstruct the shape of the water table. This methodology is applied to a new data set from a series of coordinated hydraulic tomography, self-potential, and electrical resistivity tomography experiments performed at the Boise Hydrogeophysical Research Site, Idaho. In particular, we examine one of the dipole hydraulic tests and its reciprocal to show the sensitivity of the self-potential signals to variations of the potentiometric levels under steady-state conditions. However, because of the high pumping rate, the response was also influenced by the Reynolds number, especially near the pumping well for a given test. Ground water flow in the inertial laminar flow regime is responsible for nonlinearity that is not yet accounted for in self-potential tomography. Numerical modeling addresses the sensitivity of the self-potential response to this problem.

International audience; We present a semi-analytical solution for the transient streaming potential response of an unconfined aquifer to continuous constant rate pumping. We assume that flow occurs without leakage from the unit below a transverse anisotropic aquifer and neglect flow in the unsaturated zone by treating the water-table as a moving material boundary. In the development of the solution to the streaming potential problem, we impose insulating boundary conditions at land surface and the lower boundary of the lower confining unit. We solve the problem exactly in the double Laplace–Hankel transform space and obtain the inverse transforms numerically. The solution is used to analyse transient streaming potential data collected during dipole hydraulic tests conducted at the Boise Hydrogeophysical Research Site in 2007 June. This analysis yields estimates of aquifer hydraulic parameters. The estimated hydraulic parameters, namely, hydraulic conductivity, transverse hydraulic anisotropy, specific storage and specific yield, compare well to published estimates obtained by inverting drawdown data collected at the field site.