Kristopher L. Kuhlman

Review of inverse Laplace transform algorithms for Laplace-space numerical approaches

A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, considering general requirements of Laplace-space numerical approaches. The two-dimensional BEM solution is used to solve the Laplace-transformed diffusion equation, producing a time-domain solution after a numerical Laplace transform inversion. Motivated by the needs of numerical methods posed in Laplace-transformed space, we compare five inverse Laplace transform algorithms and discuss implementation techniques to minimize the number of Laplace-space function evaluations. We investigate the ability to calculate a sequence of time domain values using the fewest Laplace-space model evaluations. We find Fourier-series based inversion algorithms work for common time behaviors, are the most robust with respect to free parameters, and allow for straightforward image function evaluation re-use across at least a log cycle of time.

Basin-scale transmissivity and storativity estimation using hydraulic tomography

While tomographic inversion has been successfully applied to laboratory- and field-scale tests, here we address the new issue of scale that arises when extending the method to a basin. Specifically, we apply the hydraulic tomography (HT) concept to jointly interpret four multiwell aquifer tests in a synthetic basin to illustrate the superiority of this approach to a more traditional Theis analysis of the same tests. Transmissivity and storativity are estimated for each element of a regional numerical model using the geostatistically based sequential successive linear estimator (SSLE) inverse solution method. We find that HT inversion is an effective strategy for incorporating data from potentially disparate aquifer tests into a basin-wide aquifer property estimate. The robustness of the SSLE algorithm is investigated by considering the effects of noisy observations, changing the variance of the true aquifer parameters, and supplying incorrect initial and boundary conditions to the inverse model. Ground water flow velocities and total confined storage are used as metrics to compare true and estimated parameter fields; they quantify the effectiveness of HT and SSLE compared to a Theis solution methodology. We discuss alternative software that can be used for implementing tomography inversion.

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

Krypton-81 in groundwater of the Culebra Dolomite near the Waste Isolation Pilot Plant, New Mexico

The Waste Isolation Pilot Plant (WIPP) in New Mexico is the first geologic repository for disposal of transuranic nuclear waste from defense-related programs of the US Department of Energy. It is constructed within halite beds of the Permian-age Salado Formation. The Culebra Dolomite, confined within Rustler Formation evaporites overlying the Salado Formation, is a potential pathway for radionuclide transport from the repository to the accessible environment in the human-disturbed repository scenario. Although extensive subsurface characterization and numerical flow modeling of groundwater has been done in the vicinity of the WIPP, few studies have used natural isotopic tracers to validate the flow models and to better understand solute transport at this site. The advent of Atom-Trap Trace Analysis (ATTA) has enabled routine measurement of cosmogenic (81)Kr (half-life 229,000 yr), a near-ideal tracer for long-term groundwater transport. We measured (81)Kr in saline groundwater sampled from two Culebra Dolomite monitoring wells near the WIPP site, and compared (81)Kr model ages with reverse particle-tracking results of well-calibrated flow models. The (81)Kr model ages are ~130,000 and ~330,000 yr for high-transmissivity and low-transmissivity portions of the formation, respectively. Compared with flow model results which indicate a relatively young mean hydraulic age (~32,000 yr), the (81)Kr model ages imply substantial physical attenuation of conservative solutes in the Culebra Dolomite and provide limits on the effective diffusivity of contaminants into the confining aquitards.

Saturated-unsaturated flow in a compressible leaky-unconfined aquifer

An analytical solution is developed for three-dimensional flow towards a partially penetrating largediameter well in an unconfined aquifer bounded below by a leaky aquitard of finite or semi-infinite extent. The analytical solution is derived using Laplace and Hankel transforms, then inverted numerically. Existing solutions for flow in leaky unconfined aquifers neglect the unsaturated zone following an assumption of instantaneous drainage due to Neuman. We extend the theory of leakage in unconfined aquifers by (1) including water flow and storage in the unsaturated zone above the water table, and (2) allowing the finite-diameter pumping well to partially penetrate the aquifer. The investigation of model-predicted results shows that aquitard leakage leads to significant departure from the unconfined solution without leakage. The investigation of dimensionless time-drawdown relationships shows that the aquitard drawdown also depends on unsaturated zone properties and the pumping-well wellbore storage effects.

Advances in hydrogeology

Recent Advances in Statistical and Scaling Analyses of Earth and Environmental Variables Environmental Variables.- A new P-K-S Characteristic-Based Multiple Phase Flow Model for Simulation Compressible Subsurface Flows.- Fluid Pressure Redistribution Events within a Fault: Impact of Material Property Correlation.- Sparsity-Promoting Solution of Subsurface Flow Model Calibration Inverse Problems.- Analytic Modelling of Transient Multi-Layer Flow.- Tortuosity and Archies Law.- Measurement of Streaming Potentials Generated during Laboratory Simulations of Unconfined Aquifer Tests.- Description, Analysis and Interpretation of an Infiltration Experiment in a Semi-Arid Deep Vadose Zone.- Unconfined Aquifer Flow Theory - From Dupuit to Present.- Index.

Influence of Pressure Change During Hydraulic Tests on Fracture Aperture

In a series of field experiments, we evaluate the influence of a small water pressure change on fracture aperture during a hydraulic test. An experimental borehole is instrumented at the Korea Atomic Energy Research Institute (KAERI) Underground Research Tunnel (KURT). The target fracture for testing was found from the analyses of borehole logging and hydraulic tests. A double packer system was developed and installed in the test borehole to directly observe the aperture change due to water pressure change. Using this packer system, both aperture and flow rate are directly observed under various water pressures. Results indicate a slight change in fracture hydraulic head leads to an observable change in aperture. This suggests that aperture change should be considered when analyzing hydraulic test data from a sparsely fractured rock aquifer.

Unconfined Aquifer Flow Theory: From Dupuit to Present

Analytic and semi-analytic solution are often used by researchers and practitioners to estimate aquifer parameters from unconfined aquifer pumping tests. The nonlinearities associated with unconfined (i.e., water table) aquifer tests make their analysis more complex than confined tests. Although analytical solutions for unconfined flow began in the mid-1800s with Dupuit, Thiem was possibly the first to use them to estimate aquifer parameters from pumping tests in the early 1900s. In the 1950s, Boulton developed the first transient well test solution specialized to unconfined flow. By the 1970s, Neuman had developed solutions considering both primary transient storage mechanisms (confined storage and delayed yield) without nonphysical fitting parameters. In the last decade, research into developing unconfined aquifer test solutions has mostly focused on explicitly coupling the aquifer with the linearized vadose zone. Despite the many advanced solution methods available, there still exists a need for realism to accurately simulate real-world aquifer tests.

Nonlinear dynamics and instability of aqueous dissolution of silicate glasses and minerals

Aqueous dissolution of silicate glasses and minerals plays a critical role in global biogeochemical cycles and climate evolution. The reactivity of these materials is also important to numerous engineering applications including nuclear waste disposal. The dissolution process has long been considered to be controlled by a leached surface layer in which cations in the silicate framework are gradually leached out and replaced by protons from the solution. This view has recently been challenged by observations of extremely sharp corrosion fronts and oscillatory zonings in altered rims of the materials, suggesting that corrosion of these materials may proceed directly through congruent dissolution followed by secondary mineral precipitation. Here we show that complex silicate material dissolution behaviors can emerge from a simple positive feedback between dissolution-induced cation release and cation-enhanced dissolution kinetics. This self-accelerating mechanism enables a systematic prediction of the occurrence of sharp dissolution fronts (vs. leached surface layers), oscillatory dissolution behaviors and multiple stages of glass dissolution (in particular the alteration resumption at a late stage of a corrosion process). Our work provides a new perspective for predicting long-term silicate weathering rates in actual geochemical systems and developing durable silicate materials for various engineering applications.

Modeling Dynamic Helium Release as a Tracer of Rock Deformation.

We use helium released during mechanical deformation of shales as a signal to explore the effects of deformation and failure on material transport properties. A dynamic dual-permeability model with evolving pore and fracture networks is used to simulate gases released from shale during deformation and failure. Changes in material properties required to reproduce experimentally observed gas signals are explored. We model two different experiments of 4He flow rate measured from shale undergoing mechanical deformation, a core parallel to bedding and a core perpendicular to bedding. We find that the helium signal is sensitive to fracture development and evolution as well as changes in the matrix transport properties. We constrain the timing and effective fracture aperture, as well as the increase in matrix porosity and permeability. Increases in matrix permeability are required to explain gas flow prior to macroscopic failure, and the short-term gas flow post failure. Increased matrix porosity, is required to match the long-term, post-failure gas flow. Our model provides the first quantitative interpretation of helium release as a result of mechanical deformation. The sensitivity of this model to changes in the fracture network, as well as to matrix properties during deformation, indicates that helium release can be used as a quantitative tool to evaluate the state of stress and strain in earth materials.