Russell L. Detwiler

Solute Transport in Variable Aperture Fractures: An Investigation of the Relative Importance of Taylor Dispersion and Macrodispersion

Dispersion of solutes in a variable aperture fracture results from a combination of molecular diffusion and velocity variations in both the plane of the fracture (macrodispersion) and across the fracture aperture (Taylor dispersion). We use a combination of physical experiments and computational simulations to test a theoretical model in which the effective longitudinal dispersion coefficient DL is expressed as a sum of the contributions of these three dispersive mechanisms. The combined influence of Taylor dispersion and macrodispersion results in a nonlinear dependence of DL on the Peclet number (Pe 5 V^b&/Dm, where V is the mean solute velocity, ^b& is the mean aperture, and Dm is the molecular diffusion coefficient). Three distinct dispersion regimes become evident: For small Pe (Pe , , 1), molecular diffusion dominates resulting in D L } Pe 0 ; for intermediate Pe, macrodispersion dominates (DL } Pe); and for large Pe, Taylor dispersion dominates (D L } Pe 2 ). The Pe range corresponding to these different regimes is controlled by the statistics of the aperture field. In particular, the upper limit of Pe corresponding to the macrodispersion regime increases as the macrodispersivity increases. Physical experiments in an analog, rough-walled fracture confirm the nonlinear Pe dependence of DL predicted by the theoretical model. However, the theoretical model underestimates the magnitude of DL. Computational simulations, using a particle-tracking algorithm that incorporates all three dispersive mechanisms, agree very closely with the theoretical model predictions. The close agreement between the theoretical model and computational simulations is largely because, in both cases, the Reynolds equation describes the flow field in the fracture. The discrepancy between theoretical model predictions and DL estimated from the physical experiments appears to be largely due to deviations from the local cubic law assumed by the Reynolds equation.

Saturated flow in a single fracture: evaluation of the Reynolds Equation in measured aperture fields

Fracture transmissivity and detailed aperture fields are measured in analog fractures specially designed to evaluate the utility of the Reynolds equation. The authors employ a light transmission technique with well-defined accuracy ({approximately}1% error) to measure aperture fields at high spatial resolution ({approximately}0.015 cm). A Hele-Shaw cell is used to confirm the approach by demonstrating agreement between experimental transmissivity, simulated transmissivity on the measured aperture field, and the parallel plate law. In the two rough-walled analog fractures considered, the discrepancy between the experimental and numerical estimates of fracture transmissivity was sufficiently large ({approximately} 22--47%) to exclude numerical and experimental errors (< 2%)as a source. They conclude that the three-dimensional character of the flow field is important for fully describing fluid flow in the two rough-walled fractures considered, and that the approach of depth averaging inherent in the formulation of the Reynolds equation is inadequate. They also explore the effects of spatial resolution, aperture measurement technique, and alternative definitions for link transmissivities in the finite-difference formulation, including some that contain corrections for tortuosity perpendicular to the mean fracture plane and Stokes flow. Various formulations for link transmissivity are shown to converge at high resolution ({approximately} 1/5 the spatial correlation length) in the smoothly varying fracture. At coarser resolutions, the solution becomes increasingly sensitive to definition of link transmissivity and measurement technique. Aperture measurements that integrate over individual grid blocks were less sensitive to measurement scale and definition of link transmissivity than point sampling techniques.

Measurement of fracture aperture fields using transmitted light: An evaluation of measurement errors and their influence on simulations of flow and transport through a single fracture

Understanding of single-phase and multiphase flow and transport in fractures can be greatly enhanced through experimentation in transparent systems (analogs or replicas) where light transmission techniques yield quantitative measurements of aperture, solute concentration, and phase saturation fields. Here we quantify aperture field measurement error and demonstrate the influence of this error on the results of flow and transport simulations (hypothesized experimental results) through saturated and partially saturated fractures. We find that precision and accuracy can be balanced to greatly improve the technique and present a measurement protocol to obtain a minimum error field. Simulation results show an increased sensitivity to error as we move from flow to transport and from saturated to partially saturated conditions. Significant sensitivity under partially saturated conditions results in differences in channeling and multiple-peaked breakthrough curves. These results emphasize the critical importance of defining and minimizing error for studies of flow and transport in single fractures.

Experimental observations of fracture dissolution: The role of Peclet number on evolving aperture variability

[1] Dissolution of the surfaces of rock fractures can cause significant alteration of the fracture void space (aperture) and fracture permeability (k). Both surface reaction rates and transport of reactants within the fracture can limit local dissolution. We investigated the role of Peclet number (Pe), a measure of the relative importance of advective and diffusive transport of reactants, on fracture dissolution in two identical transparent analog fractures with different initial values of Pe (Peo). High-resolution light-transmission techniques provided direct measurements of the evolving aperture field during each experiment. For Peo = 54 distinct dissolution channels formed, while for Peo = 216 we measured minimal channeling and a reduction in short wavelength aperture variability. The nature of the dissolution patterns strongly influenced the relative increase in k. A 110% increase in the mean aperture due to dissolution resulted in estimated permeability increases of 440% and 640% for the Peo =5 4 and Peo = 216 experiments, respectively. INDEX TERMS: 5104 Physical Properties of Rocks: Fracture and flow; 5114 Physical Properties of Rocks: Permeability and porosity; 1829 Hydrology: Groundwater hydrology; 1832 Hydrology: Groundwater transport. Citation: Detwiler, R. L., R. J. Glass, and W. L. Bourcier, Experimental observations of fracture dissolution: The role of Peclet number on evolving aperture variability, Geophys. Res. Lett., 30(12), 1648, doi:10.1029/ 2003GL017396, 2003.

Environmental Fate and Transport Modeling for Perfluorooctanoic Acid Emitted from the Washington Works Facility in West Virginia

Perfluorooctanoic acid (PFOA) has been detected in environmental samples in Ohio and West Virginia near the Washington Works Plant in Parkersburg, West Virginia. This paper describes retrospective fate and transport modeling of PFOA concentrations in local air, surface water, groundwater, and six municipal water systems based on estimates of historic emission rates from the facility, physicochemical properties of PFOA, and local geologic and meteorological data beginning in 1951. We linked several environmental fate and transport modeling systems to model PFOA air dispersion, transit through the vadose zone, surface water transport, and groundwater flow and transport. These include AERMOD, PRZM-3, BreZo, MODFLOW, and MT3DMS. Several thousand PFOA measurements in municipal well water have been collected in this region since 1998. Our linked modeling system performs better than expected, predicting water concentrations within a factor of 2.1 of the average observed water concentration for each of the six municipal water districts after adjusting the organic carbon partition coefficient to fit the observed data. After model calibration, the Spearmans rank correlation coefficient for predicted versus observed water concentrations is 0.87. These models may be useful for estimating past and future public well water PFOA concentrations in this region.

Nonaqueous‐phase‐liquid dissolution in variable‐aperture fractures: Development of a depth‐averaged computational model with comparison to a physical experiment

Dissolution of nonaqueous-phase liquids (NAPLs) from variable-aperture fractures couples fluid flow, transport of the dissolved NAPL, interphase mass transfer, and the corresponding NAPL-water-interface movement. Each of these fundamental processes is controlled by fracture-aperture variability and entrapped-NAPL geometry. We develop a depth-averaged computational model of dissolution that incorporates the fundamental processes that control dissolution at spatial resolutions that include all scales of variability within the flow field. Thus this model does not require empirical descriptions of local mass transfer rates. Furthermore, the depth-averaged approach allows us to simulate dissolution at scales that are larger than the scale of the largest entrapped NAPL blobs. We compare simulation results with an experiment in which we dissolved residual entrapped trichloroethylene (TCE) from a 15.4×30.3 cm, analog, variable-aperture fracture. We measured both fracture aperture and the TCE distribution within the fracture at high spatial resolution using light transmission techniques. Digital images acquired over the duration of the experiment recorded the evolution of the TCE distribution within the fracture and are directly compared with the results of a computational simulation. The evolution with time of the distribution of the entrapped TCE and the total TCE saturation are both predicted well by the dissolution model. These results suggest that detailed parametric studies, employing the depth-averaged dissolution model, can be used to develop a comprehensive understanding of NAPL dissolution in terms of parameters characterizing aperture variability, phase structure, and hydrodynamic conditions.

The interaction of two fluid phases in fractured media

In fractured porous media, interactions between immiscible fluid phases within the fractures place a critical control on system behavior. A key component of the interactions is the geometry, or structure, of the respective phases. Over the past 10 years, process-based experiments have greatly increased our understanding of phase structure development within individual fractures. In the past 2 years, new calculational models that incorporate some of this understanding have further demonstrated the influence of phase structure on flow and transport within the phases, and inter-phase mass transport. These computational models can now be applied to consider the efficacy and parameterization of constitutive relations for a subset of two-phase situations. Full understanding of the morphology, connectivity, and temporal dynamics of phase structure in rough-walled fractures is yet to be developed, and is a promising area for further research.

Simulation of flow and transport in a single fracture: Macroscopic effects of underestimating local head loss

Fluid flow in a single fracture is commonly simulated using the Reynolds equation. Recent work suggests that this depth-averaged approach underestimates head loss in regions of changing aperture. Implementing an ad hoc correction in the numerical formulation of the Reynolds equation allows us to modify local head loss, and calibrate simulation results to existing experimental data. Calibrated flow fields provide an improved estimate of longitudinal dispersivity, demonstrating the importance of adequately describing local head loss.

Fracture Permeability Alteration due to Chemical and Mechanical Processes: A Coupled High-Resolution Model

Reactive fluid-flow experiments in fractures subjected to normal stress suggest the potential for either increased or decreased permeability resulting from fracture-surface dissolution. We present a computational model that couples mechanical deformation and chemical alteration of fractures subjected to constant normal stress and reactive fluid flow. The model explicitly represents micro-scale roughness of the fracture surfaces and calculates elastic deformation of the rough surfaces using a semi-analytical approach that ensures the surfaces remain in static equilibrium. A depth-averaged reactive transport model calculates chemical alteration of the surfaces, which leads to alteration of the contacting fracture surfaces. The mechanical deformation and chemical alteration calculations are explicitly coupled, which is justified by the disparate timescales required for equilibration of mechanical stresses and reactive transport processes. An idealized analytical representation of dissolution from a single contacting asperity shows that under reaction-limited conditions, contacting asperities can dissolve faster than the open regions of the fracture. Computational simulations in fractures with hundreds of contacting asperities show that the transition from transport-limited conditions (low flow rates) to reaction-rate-limited conditions (high flow rates) causes a shift from monotonically increasing permeability to a more complicated process in which permeability initially decreases and then increases as contacting asperities begin to dissolve. These results are qualitatively consistent with a number of experimental observations reported in the literature and suggest the potential importance of the relative magnitude of mass transport and reaction kinetics on the evolution of fracture permeability in fractures subjected to combined normal stress and reactive fluid flow.

Ambient groundwater flow diminishes nitrate processing in the hyporheic zone of streams

Modeling and experimental studies demonstrate that ambient groundwater reduces hyporheic exchange, but the implications of this observation for stream N-cycling is not yet clear. Here we utilize a simple process-based model (the Pumping and Streamline Segregation or PASS model) to evaluate N-cycling over two scales of hyporheic exchange (fluvial ripples and riffle-pool sequences), ten ambient groundwater and stream flow scenarios (five gaining and losing conditions and two stream discharges), and three biogeochemical settings (identified based on a principal component analysis of previously published measurements in streams throughout the United States). Model-data comparisons indicate that our model provides realistic estimates for direct denitrification of stream nitrate, but overpredicts nitrification and coupled nitrification-denitrification. Riffle-pool sequences are responsible for most of the N-processing, despite the fact that fluvial ripples generate 3–11 times more hyporheic exchange flux. Across all scenarios, hyporheic exchange flux and the Damkohler Number emerge as primary controls on stream N-cycling; the former regulates trafficking of nutrients and oxygen across the sediment-water interface, while the latter quantifies the relative rates of organic carbon mineralization and advective transport in streambed sediments. Vertical groundwater flux modulates both of these master variables in ways that tend to diminish stream N-cycling. Thus, anthropogenic perturbations of ambient groundwater flows (e.g., by urbanization, agricultural activities, groundwater mining, and/or climate change) may compromise some of the key ecosystem services provided by streams.