Variable-density groundwater flow and solute transport in heterogeneous porous media: approaches, resolutions and future challenges

In certain hydrogeological situations, fluid density variations occur because of changes in the solute or colloidal concentration, temperature, and pressure of the groundwater. These include seawater intrusion, high-level radioactive waste disposal, groundwater contamination, and geothermal energy production. When the density of the invading fluid is greater than that of the ambient one, density-driven free convection can lead to transport of heat and solutes over larger spatial scales and significantly shorter time scales than compared with diffusion alone. Beginning with the work of Lord Rayleigh in 1916, thermal and solute instabilities in homogeneous media have been studied in detail for almost a century. Recently, these theoretical and experimental studies have been applied in the study of groundwater phenomena, where the assumptions of homogeneity and isotropy rarely, if ever, apply. The critical role that heterogeneity plays in the onset as well as the growth and/or decay of convective motion is discussed by way of a review of pertinent literature and numerical simulations performed using a variable-density flow and solute transport numerical code. Different styles of heterogeneity are considered and range from continuously "trending" heterogeneity (sinusoidal and stochastic permeability distributions) to discretely fractured geologic media. Results indicate that both the onset of instabilities and their subsequent growth and decay are intimately related to the structure and variance of the permeability field. While disordered heterogeneity tends to dissipate convection through dispersive mixing, an ordered heterogeneity (e.g., sets of vertical fractures) allows instabilities to propagate at modest combinations of fracture aperture and separation distances. Despite a clearer understanding of the processes that control the onset and propagation of instabilities, resultant plume patterns and their migration rates and pathways do not appear amenable to prediction at present. The classical Rayleigh number used to predict the occurrence of instabilities fails, in most cases, when heterogeneous conditions prevail. The incorporation of key characteristics of the heterogeneous permeability field into relevant stability criteria and numerical models remains a challenge for future research.     

Entrapment and dissolution of DNAPLs in heterogeneous porous media

Two-dimensional multiphase flow and transport simulators were refined and used to numerically investigate the entrapment and dissolution behavior of tetrachloroethylene (PCE) in heterogeneous porous media containing spatial variations in wettability. Measured hydraulic properties, residual saturations, and dissolution parameters were employed in these simulations. Entrapment was quantified using experimentally verified hydraulic property and residual saturation models that account for hysteresis and wettability variations. The nonequilibrium dissolution of PCE was modeled using independent estimates of the film mass transfer coefficient and interfacial area for entrapped and continuous (PCE pools or films) saturations. Flow simulations demonstrate that the spatial distribution of PCE is highly dependent on subsurface wettability characteristics that create differences in PCE retention mechanisms and the presence of subsurface capillary barriers. For a given soil texture, the maximum and minimum PCE infiltration depth was obtained when the sand had intermediate (an organic-wet mass fraction of 25%) and strong (water- or organic-wet) wettability conditions, respectively. In heterogeneous systems, subsurface wettability variations were also found to enhance or diminish the performance of soil texture-induced capillary barriers. The dissolution behavior of PCE was found to depend on the soil wettability and the spatial PCE distribution. Shorter dissolution times tended to occur when PCE was distributed over large regions due to an increased access of flowing water to the PCE. In heterogeneous systems, capillary barriers that produced high PCE saturations tended to exhibit longer dissolution times.     

Multispecies transport of metal–EDTA complexes and chromate through undisturbed columns of weathered fractured saprolite

Laboratory-scale tracer experiments were conducted to investigate the geochemical and hydrological processes that govern the fate and transport of organically chelated radionuclides and toxic metals in undisturbed saturated columns of weathered, fractured shale saprolite. Three long-term, reactive contaminant injections were pulsed onto three separate soil columns, with the following influent mixtures: (1) ¹⁰⁹CdEDTA²⁻, (2) ¹⁰⁹CdEDTA²⁻ and ^57,58Co(II)EDTA²⁻, and (3) ¹⁰⁹CdEDTA²⁻, ⁵⁷Co(III)EDTA⁻, and H⁵¹CrO₄⁻. Both single and multiple species experiments were conducted to determine the importance of interaction between the contaminants and competition for surface sites. Flow interruption was used to identify physical and chemical non-equilibrium (PNE and CNE) which were caused by multiple pore-region flow and rate-limited chemical reactions, respectively. Reactive contaminant transport through the fractured, weathered shale was affected by sorption, redox, and dissociation reactions, which were mediated by soil organic matter and surficial oxides of Fe, Mn, and Al. The transport of CdEDTA²⁻ was significantly influenced by ligand-promoted dissolution of subsurface Fe and Al sources, resulting in the liberation of Cd²⁺, Al(III)EDTA⁻ and Fe(III)EDTA⁻. Flow interruption confirmed that the surface-mediated dissociation reaction was time-dependent, with the stability of the CdEDTA²⁻ complex dependent on its residence time within the soil. The migration of Co(II)EDTA²⁻ was dominated by oxidization to the highly stable Co(III)EDTA⁻ species, and elevated effluent Mn²⁺ suggested that surficial Mn(IV) oxides likely catalyzed the redox reaction, though Fe-oxides may have also contributed to the reaction. Dissociation (12%) of the Co(II)EDTA²⁻ complex was first observed during flow interruption, indicating that rate-limited dissociation of the complex by Fe-oxides may be significant under equilibrium conditions. The transport of HCrO₄⁻ was significantly altered by the reduction of mobile Cr(VI) to irreversibly bound Cr(III). The reduction reaction was catalyzed by surface-bound natural organic matter and flow interruption confirmed that the reaction was time-dependent. There was little evidence of competitive effects between the various contaminants in the multispecies experiments, since each was influenced by a different geochemical process during transport through the soil. The results of this study further support research findings that suggest anionic toxic metals and radionuclide–organic complexes can be significantly influenced by soil geochemical processes that can both enhance and impede the subsurface migration of these contaminants.     

Field-scale effective matrix diffusion coefficient for fractured rock: results from literature survey

Matrix diffusion is an important mechanism for solute transport in fractured rock. We recently conducted a literature survey on the effective matrix diffusion coefficient, D_m^e, a key parameter for describing matrix diffusion processes at the field scale. Forty field tracer tests at 15 fractured geologic sites were surveyed and selected for the study, based on data availability and quality. Field-scale D_m^e values were calculated, either directly using data reported in the literature, or by reanalyzing the corresponding field tracer tests. The reanalysis was conducted for the selected tracer tests using analytic or semi-analytic solutions for tracer transport in linear, radial, or interwell flow fields. Surveyed data show that the scale factor of the effective matrix diffusion coefficient (defined as the ratio of D_m^e to the lab-scale matrix diffusion coefficient, D_m, of the same tracer) is generally larger than one, indicating that the effective matrix diffusion coefficient in the field is comparatively larger than the matrix diffusion coefficient at the rock-core scale. This larger value can be attributed to the many mass-transfer processes at different scales in naturally heterogeneous, fractured rock systems.Furthermore, we observed a moderate, on average trend toward systematic increase in the scale factor with observation scale. This trend suggests that the effective matrix diffusion coefficient is likely to be statistically scale-dependent. The scale-factor value ranges from 0.5 to 884 for observation scales from 5 to 2000 m. At a given scale, the scale factor varies by two orders of magnitude, reflecting the influence of differing degrees of fractured rock heterogeneity at different geologic sites. In addition, the surveyed data indicate that field-scale longitudinal dispersivity generally increases with observation scale, which is consistent with previous studies. The scale-dependent field-scale matrix diffusion coefficient (and dispersivity) may have significant implications for assessing long-term, large-scale radionuclide and contaminant transport events in fractured rock, both for nuclear waste disposal and contaminant remediation.     

A serendipitous, long-term infiltration experiment: Water and tritium circulation beneath the CAMBRIC trench at the Nevada Test Site

Underground nuclear weapons testing at the Nevada Test Site introduced numerous radionuclides that may be used subsequently to characterize subsurface hydrologic transport processes in arid climates. In 1965, a unique, 16-year pumping experiment designed to examine radionuclide migration away from the CAMBRIC nuclear test, conducted in the saturated zone beneath Frenchman Flat, Nevada, USA, gave rise to an unintended second experiment involving radionuclide infiltration through the vadose zone, as induced by seepage of pumping effluents beneath an unlined discharge trench. The combined experiments have been reanalyzed using a detailed, three-dimensional numerical model of transient, variably saturated flow and mass transport in a heterogeneous subsurface, tailored specifically for large-scale and efficient calculations. Simulations have been used to estimate tritium travel and residence times in various parts of the system for comparison with observations in wells. Model predictions of mass transport were able to clearly demonstrate radionuclide recycling behavior between the trench and pumping well previously suggested by isotopic age dating information; match travel time estimates for radionuclides moving between the trench, the water table, and monitoring and pumping wells; and provide more realistic ways in which to interpret the pumping well elution curves. Collectively, the results illustrate the utility of integrating detailed numerical modeling with diverse observational data in developing more accurate interpretations of contaminant migration processes.     

Investigation of surfactant-enhanced mass removal and flux reduction in 3D correlated permeability fields using magnetic resonance imaging

Magnetic resonance imaging (MRI) was used to visualize the NAPL source zone architecture before and after surfactant-enhanced NAPL dissolution in three-dimensional (3D) heterogeneously packed flowcells characterized by different longitudinal correlation lengths: 2.1 cm (aquifer 1) and 1.1 cm (aquifer 2). Surfactant flowpaths were determined by imaging the breakthrough of a paramagnetic tracer (MnCl(2)) analyzed by the method of moments. In both experimental aquifers, preferential flow occurred in high permeability materials with low NAPL saturations, and NAPL was preferentially removed from the top of the aquifers with low saturation. Alternate flushing with water and two surfactant pulses (5-6 pore volumes each) resulted in approximately 63% of NAPL mass removal from both aquifers. However, overall reduction in mass flux (Mass Flux 1) exiting the flowcell was lower in aquifer 2 (68%) than in aquifer 1 (81%), and local effluent concentrations were found to increase by as high as 120 times at local sampling ports from aquifer 2 after surfactant flushing. 3D MRI images of NAPL revealed that NAPL migrated downward and created additional NAPL source zones in previously uncontaminated areas at the bottom of the aquifers. The additional NAPL source zones were created in the direction transverse to flow in aquifer 2, which explains the higher mass flux relative to aquifer 1. Analysis using a total trapping number indicates that mobilization of NAPL trapped in the two coarsest sand fractions is possible when saturation is below 0.5 and 0.4, respectively. Results from this study highlight the potential impacts of porous media heterogeneity and NAPL source zone architecture on advanced in-situ flushing technologies.     

Characterization of binding site heterogeneity for copper within dissolved organic matter fractions using two-dimensional correlation fluorescence spectroscopy

The heterogeneity of copper binding characteristics for dissolved organic matter (DOM) fractions was investigated based on the fluorescence quenching of the synchronous fluorescence spectra upon the addition of copper and two-dimensional correlation spectroscopy (2D-COS). Hydrophobic acid (HoA) and hydrophilic (Hi) fractions of two different DOM (algal and leaf litter DOM) were used for this study. For both DOM, fluorescence quenching occurred at a wider range of wavelengths for the HoA fractions compared to the Hi fractions. The combined information of the synchronous and asynchronous maps derived from 2D-COS provided a clear picture of the heterogeneous distribution of the copper binding sites within each DOM fraction, which was not readily recognized by a simple comparison of the changes in the synchronous fluorescence spectra upon the addition of copper. For the algal DOM, higher stability constants were exhibited for the HoA versus the Hi fractions. The logarithms of the stability constants ranged from 4.8 to 6.1 and from 4.5 to 5.0 for the HoA and the Hi fractions of the algal DOM, respectively, depending on the associated wavelength and the fitted models. In contrast, no distinctive difference in the binding characteristics was found between the two fractions of the leaf litter DOM. This suggests that influences of the structural and chemical properties of DOM on copper binding may differ for DOM from different sources. The relative difference of the calculated stability constants within the DOM fractions were consistent with the sequential orders interpreted from the asynchronous 2D-COS. It is expected that 2D-COS will be widely applied to other DOM studies requiring detailed information on the heterogeneous nature and subsequent effects under a range of environmental conditions.     

Bacteriophage transport through a fining-upwards sedimentary sequence: laboratory experiments and simulation

A column containing four concentric layers of progressively finer-grained glass beads (graded column) was used to study the transport of the bacteriophage T7 in water flowing parallel to layering through a fining-upwards (FU) sedimentary structure. By passing a pulse of T7, and a conservative solute tracer upwards through a column packed with a single bead size (uniform column), the capacity of each bead type to attenuate the bacteriophage was determined. Solute and bacteriophage responses were modelled using an analytical solution to the advection-dispersion equation, with first-order kinetic deposition simulating bacteriophage attenuation. Resulting deposition constants for different flow velocities indicated that filtration theory-determined values differed from experimentally determined values by less than 10%. In contrast, the responses of solute and bacteriophage tracers passing upwards through graded columns could not be reproduced with a single analytical solution. However, a flux-weighted summation of four one-dimensional advective-dispersive analytical terms approximated solute breakthrough curves. The prolonged tailing observed in the resulting curve resembled that typically generated from field-based tracer test data, reflecting the potential importance of textural heterogeneity in the transport of dissolved substances in groundwater. Moreover, bacteriophage deposition terms, determined from filtration theory, reproduced the T7 breakthrough curve once desorption and inactivation on grain surfaces were incorporated. To evaluate the effect of FU sequences on mass transport processes in more detail, bacteriophage passage through sequences resembling those sampled from a FU bed in a fluvioglacial gravel pit were carried out using an analogous approach to that employed in the laboratory. Both solute and bacteriophage breakthrough responses resembled those generated from field-based test data and in the graded column experiments. Comparisons with the results of simulations using averaged hydraulic conductivities show that simulations employing averaged parameters overestimate bacteriophage travel times and underestimate masses recovered and peak concentrations.     

Evaluation of uncertainties originating from the different modeling approaches applied to analyze regional groundwater flow in the Tono area of Japan

Qualitative evaluation of the effects of uncertainties originating from scenario development, modeling approaches, and parameter values is an important subject in the area of safety assessment for high-level nuclear waste disposal sites. In this study, regional-scale groundwater flow analyses for the Tono area, Japan were conducted using three continuous models designed to handle heterogeneous porous media. We evaluated the simulation results to quantitatively analyze uncertainties originating from modeling approaches. We found that porous media heterogeneity is the main factor which causes uncertainties. We also found that uncertainties originating from modeling approaches greatly depend on the types of hydrological structures and heterogeneity of hydraulic conductivity values in the domain assigned by modelers. Uncertainties originating from modeling approaches decrease as the amount of labor and time spent increase, and iterations between investigation and analyses increases.     

Evaluation of groundwater flow patterns around a dual-screened groundwater circulation well

Dual-screened groundwater circulation wells (GCWs) can be used to remove contaminant mass and to mix reagents in situ. GCWs are so named because they force water in a circular pattern between injection and extraction screens. The radial extent, flux and direction of the effective flow of this circulation cell are difficult to measure or predict. The objective of this study is to develop a robust protocol for assessing GCW performance. To accomplish this, groundwater flow patterns surrounding a GCW are assessed using a suite of tools and data, including: hydraulic head, in situ flow velocity, measured hydraulic conductivity data from core samples, chemical tracer tests, contaminant distribution data, and numerical flow and transport models. The hydraulic head data show patterns that are consistent with pumping on a dual-screened well, however, many of the observed changes are smaller than expected. In situ thermal perturbation flow sensors successfully measured horizontal flow, but vertical flow could not be determined with sufficient accuracy to be useful in mapping flow patterns. Two types of chemical tracer tests were utilized at the site and showed that much of the flow occurs within a few meters of the GCW. Flow patterns were also assessed based on changes in contaminant (trichloroethylene, TCE) concentrations over time. The TCE data clearly showed treated water moving away from the GCW at shallow and intermediate depths, but the circulation of that water back to the well, except very close to the well, was less clear. Detailed vertical and horizontal hydraulic conductivities were measured on 0.3 m-long sections from a continuous core from the GCW installation borehole. The measured vertical and horizontal hydraulic conductivity data were used to construct numerical flow and transport models, the results of which were compared to the head, velocity and concentration data. Taken together, the field data and modeling present a fairly consistent picture of flow and transport around the GCW. However, the time and expense associated with conducting all of those tests would be prohibitive for most sites. As a consequence, a sequential protocol for GCW characterization is presented here in which the number of tools used can be adjusted to meet the needs of individual sites. While not perfect, we believe that this approach represents the most efficient means for evaluating GCW performance.