Bwalya Malama

A Potential‐Based Inversion of Unconfined Steady‐State Hydraulic Tomography

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.

Tomography of the Darcy velocity from self-potential measurements

[1] An algorithm is developed to interpret self-potential (SP) data in terms of distribution of Darcy velocity of the ground water. The model is based on the proportionality existing between the streaming current density and the Darcy velocity. Because the inverse problem of current density determination from SP data is underdetermined, we use Tikhonov regularization with a smoothness constraint based on the differential Laplacian operator and a prior model. The regularization parameter is determined by the L-shape method. The distribution of the Darcy velocity depends on the localization and number of non-polarizing electrodes and information relative to the distribution of the electrical resistivity of the ground. A priori hydraulic information can be introduced in the inverse problem. This approach is tested on two synthetic cases and on real SP data resulting from infiltration of water from a ditch.

Physical and particle flow modeling of jointed rock block behavior under uniaxial loading

Abstract 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.

Reconstruction of the Water Table from Self-Potential Data: A Bayesian Approach

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.

Models for normal fracture deformation under compressive loading

Abstract 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.

Multiporosity flow in fractured low‐permeability rocks

A multiporosity extension of classical double and triple porosity fractured rock ow models for slightly compressible uids is presented. The multiporosity model is an adaptation of the multirate solute transport model of Haggerty and Gorelick (1995) to viscous ow in fractured rock reservoirs. It is a generalization of both pseudo-steady

Modeling Transient Streaming Potentials in Falling‐Head Permeameter Tests

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.

Measurement of Streaming Potentials Generated During Laboratory Simulations of Unconfined Aquifer Pumping Tests

The streaming potential method has emerged as a promising hydrogeophysical technique for indirect acquisition of spatially dense measurements of the hydraulic response of aquifers to pumping or other system forcings. The method relies on measurements of electric potentials generated by groundwater flow. They arise due to the existence of the electric double layer at the rock–water interface. Mathematical solutions describing the transient electric potentials associated with pumping tests conducted in confined and unconfined aquifers have been recently developed and demonstrated to yield reasonable estimates of hydraulic parameters when applied to tests conducted at the field-scale. We present results of laboratory experiments conducted to investigate the applicability of the unconfined aquifer model under controlled conditions in a sand tank instrumented with pressure transducers for direct measurement of the hydraulic system state, and nonpolarizable electrodes for measurement of the associated electric field. Measurements show unambiguous transient streaming potential responses to groundwater flow in a bounded cylindrical system. Parameters estimated from streaming potential data are compared to those from drawdown data.

DRSPALL: Impact of the Modification of the Numerical Spallings Model on Waste Isolation Pilot Plant Performance Assessment.

The numerical code DRSPALL (from direct release spallings) is written to calculate the volume of Waste Isolation Pilot Plant (WIPP) solid waste subject to material failure and transport to the surface as a result of a hypothetical future inadvertent drilling intrusion. An error in the implementation of the DRSPALL finite difference equations was discovered as documented in Software Problem Report (SPR) 13-001. The modifications to DRSPALL to correct the finite difference equations are detailed, and verification and validation testing has been completed for the modified DRSPALL code. The complementary cumulative distribution function (CCDF) of spallings releases obtained using the modified DRSPALL is higher compared to that found in previous WIPP performance assessment (PA) calculations. Compared to previous PAs, there was an increase in the number of vectors that result in a nonzero spallings volume, which generally translates to an increase in spallings releases. The overall mean CCDFs for total releases using the modified DRSPALL are virtually unchanged, thus the modification to DRSPALL did not impact WIPP PA calculation results. 1 Stoller Newport News Nuclear, Inc. (SN3), a wholly owned subsidiary of Huntington Ingalls Industries, Inc., Carlsbad, New Mexico 88220, Sandia Contract No. 1018118. 2 Sandia National Laboratories, Carlsbad, New Mexico 88220. 3 Presently with Natural Resources Management & Environmental Sciences Department, California Polytechnic State University, San Luis Obispo, California 93407. The work described in this report was performed while employed by Sandia National Laboratories. 4 GRAM, Inc., Albuquerque, New Mexico 87112, Sandia Contract No. 1557789.

Assessment of Contaminated Brine Fate and Transport in MB139 at WIPP

Following the radionuclide release event of February 14, 2014 at the Waste Isolation Pilot Plant (WIPP), actinide contamination has been found on the walls and floor in Panel 7 as a result of a release in Room 7 of Panel 7. It has been proposed to decontaminate Panel 7 at the WIPP by washing contaminated surfaces in the underground with fresh water (Nelson, 2014a). A costeffective cleanup of this contamination would allow for a timely return to waste disposal operations at WIPP. It is expected that the fresh water used to decontaminate Panel 7 will flow as contaminated brine down into the porosity of the materials under the floor – the run-of-mine (ROM) salt above Marker Bed 139 (MB139) and MB139 itself – where its fate will be controlled by the hydraulic and transport properties of MB139. Due to the structural dip of MB139, it is unlikely that this brine would migrate northward towards the Waste-Handling Shaft sump. A few strategically placed shallow small-diameter observation boreholes straddling MB139 would allow for monitoring the flow and fate of this brine after decontamination. Additionally, given that flow through the compacted ROM salt floor and in MB139 would occur under unsaturated (or twophase) conditions, there is a need to measure the unsaturated flow properties of crushed WIPP salt and salt from the disturbed rock zone (DRZ).