Andrew F. B. Tompson

Random‐Walk Simulation of Transport in Heterogeneous Porous Media: Local Mass‐Conservation Problem and Implementation Methods

The random-walk method for simulating solute transport in porous media is typically based on the assumption that the velocity and velocity-dependent dispersion tensor vary smoothly in space. However, in cases where sharp interfaces separate materials with contrasting hydraulic properties, these quantities may be discontinuous. Normally, velocities are interpolated to arbitrary particle locations when finite difference or finite element methods are used to solve the flow equation. The use of interpolation schemes that preserve discontinuities in velocity at material contacts can result in a random-walk model that does not locally conserve mass unless a correction is applied at these contacts. Test simulations of random-walk particle tracking with and without special treatment of material contacts demonstrate the problem. Techniques for resolving the problem, including interpolation schemes and a reflection principle, are reviewed and tested. Results from simulations of transport in porous media with discontinuities in the dispersion tensor show which methods satisfy continuity. Simulations of transport in two-dimensional heterogeneous porous media demonstrate the potentially significant effect of using a nonconservative model to compute spatial moments and breakthrough of a solute plume.

Numerical simulation of chemical migration in physically and chemically heterogeneous porous media

A series of chemical transport simulations in saturated porous media are conducted to examine the coupled impacts on chemical mobility induced by nonuniform sorption reactions and heterogeneous flow fields. The simulations involve the calculation of fluid flow and chemical migration within highly resolved, three-dimensional cubic regions with synthetically derived material properties. Nonuniformities in subsurface materials are represented as randomly correlated hydraulic conductivity and sorption partition coefficient fields. Transport computations are based upon a random walk particle model, appropriately modified to treat equilibrium sorption reactions. Current experiments focus on four hypothetical constituents, one being inert, and the other three independently obeying linear, Freundlich, and Langmuir partitioning relationships. Results show distinct effects of the nonuniform flow and sorption processes on the overall displacement, dispersion, and partitioning/retardation and the breakthrough behavior of the constituent plumes, as well as on the sharpening fronts and skewed concentration profiles associated with nonlinear partitioning models. 37 refs., 9 figs., 4 tabs.

Application of particle methods to reliable identification of groundwater pollution sources

An alternative strategy for identifying sources of contamination in groundwater systems is presented. Under the assumption that the remediation cost is affected by the level of contamination, the proposed scheme provides probabilistic estimates of source locations and spill-time histories. Moreover, the method successfully assesses the relative importance of each potential source.

On the development of a new methodology for groundwater-Driven health risk assessment

A methodology and hypothetical case study are presented for incorporation of uncertainty and variability into calculations of human health risk appropriate for regional, or basin-scale, groundwater management problems. Uncertainty in well water concentration is introduced through complex contaminant migration patterns in the subsurface. Variability is considered in parameters related to individual behavior patterns and biological effects and to groundwater extraction and distribution networks. A joint uncertainty and variability (JUV) analysis is used to generate a two-dimensional distribution or risk surface that spans both transport uncertainty as well as individual variability. Cuts in this distributional surface (fractiles of variability and percentiles of uncertainty) are presented and discussed. Comparisons with alternative approaches based upon deterministic transport models are also made. In addition, important distinctions are made between the case where household water is derived from the nearest well and the case where household water is mixed from many wells in a distribution system.

Experimental analysis of pore-scale flow and transport in porous media

Abstract A novel, non-intrusive fluorescence imaging technique has been used to quantitatively measure the pore geometry, fluid velocity, and solute concentration within a saturated, three-dimensional porous medium. Discrete numerical averages of these quantities have been made over a representative volume of the medium and used to estimate macroscopic quantities that appear in conventional continuum models of flow and transport. The approach is meant to illustrate how microscopic information can be measured, averaged, and used to characterize medium-scale processes that are typically approximated constitutively. The experimental system consisted of a clear, cylindrical column packed with clear spherical beads and a refractive index-matched fluid seeded with fluorescent tracer particles and solute dye. By illuminating the fluid within the column with a scanning planar laser beam, details of flow and concentration within the pore spaces can be quantitatively observed, allowing for three-dimensional, dimensional, time dependent information to be obtained at good resolution. In time dependent information to be obtained at good resolution. In the current experiment, volumetrically averaged velocities and void-to-volume ratios are first compared with bulk measurements of fluid flux and medium porosity. Microscopic measurements of concentration are then used to construct cross-sectionally averaged profiles, mean breakthrough curves, and direct measurements of the dispersive flux, velocity variance, and concentration variance. In turn, the dispersive flux measurements are compared with mean concentration gradients to provide a basis for confirming the Fickian dispersion model and estimating dispersion coefficients for the medium. Coefficients determined in this manner are compared with others based upon traditional length-scale arguments, mean breakthrough analyses, and curve fits with numerical simulations.

Development of a Coupled Groundwater–Atmosphere Model

Abstract Complete models of the hydrologic cycle have gained recent attention as research has shown interdependence between the coupled land and energy balance of the subsurface, land surface, and lower atmosphere. PF.WRF is a new model that is a combination of the Weather Research and Forecasting (WRF) atmospheric model and a parallel hydrology model (ParFlow) that fully integrates three-dimensional, variably saturated subsurface flow with overland flow. These models are coupled in an explicit, operator-splitting manner via the Noah land surface model (LSM). Here, the coupled model formulation and equations are presented and a balance of water between the subsurface, land surface, and atmosphere is verified. The improvement in important physical processes afforded by the coupled model using a number of semi-idealized simulations over the Little Washita watershed in the southern Great Plains is demonstrated. These simulations are initialized with a set of offline spinups to achieve a balanced state of ini...

Analysis of groundwater migration from artificial recharge in a large urban aquifer: A simulation perspective

The increased use of reclaimed water for artificial groundwater recharge purposes has led to concerns about future groundwater quality, particularly as it relates to the introduction of new organic and inorganic contaminants into the subsurface. Here we review the development and initial application of a detailed numerical model of groundwater flow and migration in a region encompassing a large groundwater recharge operation in Orange County, California. The model is based upon a novel representation of geologic heterogeneity, which has long been known to influence local flow and transport behavior in the subsurface. The model and complementary series of isotopic analyses provide an improved scientific basis to understand flow paths, migration rates, and residence times of recharged groundwater, as well as to identify the source composition of water produced in wells near the recharge operation. From a management perspective these issues need to be confronted in order to respond to proposed regulatory constraints that would govern the operation of recharge facilities and nearby production wells. While model calibration is greatly aided by isotopic source and residence time analyses, the model also provides unique insights on the interpretation of isotopic data themselves. Isotopic estimates of groundwater age help discriminate between several equally acceptable simulations calibrated to head data only. However, the results also suggest that groundwater reaching a well spans a wide-ranging distribution of age, demonstrating the importance of geologic heterogeneity in affecting flow paths, mixing, and residence times in the vicinity of recharge basins and wells.

Impacts of Physical and Chemical Heterogeneity on Cocontaminant Transport in a Sandy Porous Medium

A simplified numerical study of the transport of a uranyl-citric acid mixture through a nonuniform and reactive sandy porous medium is presented. The study seeks to identify the more important impacts of medium heterogeneity, as embodied in spatially variable physical and chemical properties, on the migration and dilution rates of a model cocontaminant mixture, as well as on the overall partitioning among the aqueous and solid species formed from complexation and sorption reactions. Solid phase reactions are considered to occur on hydrous-ferric oxide (goethite) coatings on the sand and are controlled by the abundance of the oxide as a function of the specific sand surface area and larger-scale patterns of oxide deposition. The simulations involve calculation of fluid flow and chemical migration within highly resolved, two- and three-dimensional regions with synthetic material properties that approximate observed conditions in a sandy coastal aquifer. Model simulations in this system indicate that (1) the impact of correlation between reactive surface area and hydraulic conductivity, although evident, seems much less significant than the overall abundance and distribution of the reactive area, such as the kind of banded goethite patterns observed in a coastal sand body; (2) strong multicomponent interactions clearly reinforce the need to treat the mixture as a coupled system, as opposed to a series of independently reactive compounds; (3) simplifications can be made in extremely dilute problems that allow retardation effects to become concentration independent; and (4) for nonlinear reaction problems, three-dimensional models will be more appropriate than two-dimensional models to the extent that dispersion in the added dimension accelerates chemical dilution rates.

Analysis of subsurface contaminant migration and remediation using high performance computing

Abstract Highly resolved simulations of groundwater flow, chemical migration and contaminant recovery processes are used to test the applicability of stochastic models of flow and transport in a typical field setting. A simulation domain encompassing a portion of the upper saturated aquifer materials beneath the Lawrence Livermore National Laboratory was developed to hierarchically represent known hydrostratigraphic units and more detailed stochastic representations of geologic heterogeneity within them. Within each unit, Gaussian random field models were used to represent hydraulic conductivity variation, as parameterized from well test data and geologic interpretation of spatial variability. Groundwater flow, transport and remedial extraction of two hypothetical contaminants were made in six different statistical realizations of the system. The effective flow and transport behavior observed in the simulations compared reasonably with the predictions of stochastic theories based upon the Gaussian models, even though more exacting comparisons were prevented by inherent nonidealities of the geologic model and flow system. More importantly, however, biases and limitations in the hydraulic data appear to have reduced the applicability of the Gaussian representations and clouded the utility of the simulations and effective behavior based upon them. This suggests a need for better and unbiased methods for delineating the spatial distribution and structure of geologic materials and hydraulic properties in field systems. High performance computing can be of critical importance in these endeavors, especially with respect to resolving transport processes within highly variable media.©1998 Elsevier Science Limited. All rights reserved

Reactive transport modeling of plug-flow reactor experiments: quartz and tuff dissolution at 240°C

Abstract Extension of reactive transport modeling to predict the coupled thermal, hydrological, and chemical evolution of complex geological systems is predicated on successful application of the approach to simulate well-constrained physical experiments. In this study, steady-state effluent concentrations and dissolution/precipitation features associated with crushed quartz and tuff dissolution at 240°C have been determined experimentally using a plug-flow reactor (PFR) and scanning electron microscopy (SEM) techniques, then modeled with the reactive transport simulator GIMRT ( Steefel and Yabusaki, 1996 ) using a linear rate law from transition state theory (TST) . For quartz dissolution, interdependence of the specific surface area (Am) and reaction rate constant (km) predicted from the modeling agrees closely with that obtained from an analytical solution to the reaction–transport equation without diffusion/dispersion, verifying the advection-dominant nature of the PFR experiments. Independently-determined Aqtz and kqtz from the literature are shown to be internally consistent with respect to the model and analytical interdependence, implying appropriateness of the linear TST rate law and adequacy of BET-determined Am for use in modeling PFR experiments. Applications of this integrated approach for monomineralic dissolution include assessment of internal consistency among independent Am and km data, estimation of km from BET-determined Am, and rapid evaluation of alternative rate laws. For tuff dissolution, accurate simulation of the experimental steady-state effluent concentrations (to within 3% for Na, Al and K; to within 15% for Si and Ca) and dearth of alteration phases (