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USGS1991

An exact solution of solute transport by one-dimensional random velocity fields

The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity. ?? 1991 Springer-Verlag.

Stochastic Hydrology and Hydraulics↗

USGS2010

Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst and Fractured-Rock Aquifers of Minnesota

Assessment of groundwater-flow conditions in the vicinity of production wells in karst and fractured-rock settings commonly is difficult due in part to the lack of detailed hydrogeologic information and the resources needed to collect it. To address this concern and to better understand the hydrogeology and aquifer properties of karst and fractured-rock aquifers in Minnesota, the U.S. Geological Survey, in cooperation with the Minnesota Department of Health, conducted a study to evaluate methods for delineating zones of transport for 24 production wells in karst and fractured-rock aquifers in Minnesota. Two empirical methods for delineating zones of transport around wells were applied to the 24 production wells that extract groundwater from karst and fractured-rock aquifers in nine Minnesota communities. These methods were the truncated-parabola and modified-ellipse methods, and both methods assume porous-media flow conditions. The 24 wells extracted water from a karst aquifer (Prairie du Chien-Jordan aquifer), porous aquifers interspersed with solution-enhanced fractures (Jordan and Hinckley aquifers), or fractured-bedrock aquifers (Biwabik Iron-Formation and Sioux Quartzite aquifers). Zones of transport delineated using these two empirical methods were compared with zones of transport previously delineated by Minnesota Department of Health hydrologists for the wells using the calculated-fixed-radius method and groundwater-flow models. Large differences were seen in the size and shapes of most zones of transport delineated using the truncated-parabola and modified-ellipse methods compared with the zones of transport delineated by the Minnesota Department of Health. In general, the zones of transport delineated using the truncated-parabola and modified-ellipse methods were smaller in area than those delineated by the Minnesota Department of Health and included only small parts of the Minnesota Department of Health zones of transport. About two-thirds(67 percent) of the individual or composite truncated parabolas and modified ellipses covered less than 50 percent of the area included in zones of transport delineated by the Minnesota Department of Health. The shapes of some of the truncated parabola and modified ellipses did not closely match the zones of transport delineated by the Minnesota Department of Health using the calculated-fixed-radius method and groundwater-flow models. Differences between the zones of transport delineated by the truncated-parabola and modified-ellipse methods and those delineated by the Minnesota Department of Health can be explained by variations inherent to the methods and by the amount of complexity taken into account by different groundwater-flow models. Additional field hydrogeologic studies would be needed at specific sites to support the use of these zone-of-transport delineation methods. Application of the truncated-parabola and modified-ellipse methods to sites for which existing hydrogeologic information is limited can produce questionable results in karst and fractured-rock settings, particularly in areas where many high-capacity wells or active mining operations are nearby.

Scientific Investigations Report↗

USGS2002

User's guide to SEAWAT; a computer program for simulation of three-dimensional variable-density ground-water flow

The SEAWAT program was developed to simulate three-dimensional, variable-density, transient ground-water flow in porous media. The source code for SEAWAT was developed by combining MODFLOW and MT3DMS into a single program that solves the coupled flow and solute-transport equations. The SEAWAT code follows a modular structure, and thus, new capabilities can be added with only minor modifications to the main program. SEAWAT reads and writes standard MODFLOW and MT3DMS data sets, although some extra input may be required for some SEAWAT simulations. This means that many of the existing pre- and post-processors can be used to create input data sets and analyze simulation results. Users familiar with MODFLOW and MT3DMS should have little difficulty applying SEAWAT to problems of variable-density ground-water flow. MODFLOW was modified to solve the variable-density flow equation by reformulating the matrix equations in terms of fluid mass rather than fluid volume and by including the appropriate density terms. Fluid density is assumed to be solely a function of the concentration of dissolved constituents; the effects of temperature on fluid density are not considered. Temporally and spatially varying salt concentrations are simulated in SEAWAT using routines from the MT3DMS program. SEAWAT uses either an explicit or implicit procedure to couple the ground-water flow equation with the solute-transport equation. With the explicit procedure, the flow equation is solved first for each timestep, and the resulting advective velocity field is then used in the solution to the solute-transport equation. This procedure for alternately solving the flow and transport equations is repeated until the stress periods and simulation are complete. With the implicit procedure for coupling, the flow and transport equations are solved multiple times for the same timestep until the maximum difference in fluid density between consecutive iterations is less than a user-specified tolerance. The SEAWAT code was tested by simulating five benchmark problems involving variable-density ground-water flow. These problems include two box problems, the Henry problem, Elder problem, and HYDROCOIN problem. The purpose of the box problems is to verify that fluid velocities are properly calculated by SEAWAT. For each of the box problems, SEAWAT calculates the appropriate velocity distribution. SEAWAT also accurately simulates the Henry problem, and SEAWAT results compare well with those of SUTRA. The Elder problem is a complex flow system in which fluid flow is driven solely by density variations. Results from SEAWAT, for six different times, compare well with results from Elder's original solution and results from SUTRA. The HYDROCOIN problem consists of fresh ground water flowing over a salt dome. Simulated contours of salinity compare well for SEAWAT and MOCDENSE.

Techniques of Water-Resources Investigations↗

USGS1987

Solute transport with equilibrium aqueous complexation and either sorption or ion exchange: Simulation methodology and applications

Methodologies that account for specific types of chemical reactions in the simulation of solute transport can be developed so they are compatible with solution algorithms employed in existing transport codes. This enables the simulation of reactive transport in complex multidimensional flow regimes, and provides a means for existing codes to account for some of the fundamental chemical processes that occur among transported solutes. Two equilibrium-controlled reaction systems demonstrate a methodology for accommodating chemical interaction into models of solute transport. One system involves the sorption of a given chemical species, as well as two aqueous complexations in which the sorbing species is a participant. The other reaction set involves binary ion exchange coupled with aqueous complexation involving one of the exchanging species. The methodology accommodates these reaction systems through the addition of nonlinear terms to the transport equations for the sorbing species. Example simulation results show (1) the effect equilibrium chemical parameters have on the spatial distributions of concentration for complexing solutes; (2) that an interrelationship exists between mechanical dispersion and the various reaction processes; (3) that dispersive parameters of the porous media cannot be determined from reactive concentration distributions unless the reaction is accounted for or the influence of the reaction is negligible; (4) how the concentration of a chemical species may be significantly affected by its participation in an aqueous complex with a second species which also sorbs; and (5) that these coupled chemical processes influencing reactive transport can be demonstrated in two-dimensional flow regimes.

Journal of Hydrology↗

USGS1999

Age, double porosity, and simple reaction modifications for the MOC3D ground-water transport model

This report documents modifications for the MOC3D ground-water transport model to simulate (a) ground-water age transport; (b) double-porosity exchange; and (c) simple but flexible retardation, decay, and zero-order growth reactions. These modifications are incorporated in MOC3D version 3.0. MOC3D simulates the transport of a single solute using the method-of-characteristics numerical procedure. The age of ground water, that is the time since recharge to the saturated zone, can be simulated using the transport model with an additional source term of unit strength, corresponding to the rate of aging. The output concentrations of the model are in this case the ages at all locations in the model. Double porosity generally refers to a separate immobile-water phase within the aquifer that does not contribute to ground-water flow but can affect solute transport through diffusive exchange. The solute mass exchange rate between the flowing water in the aquifer and the immobile-water phase is the product of the concentration difference between the two phases and a linear exchange coefficient. Conceptually, double porosity can approximate the effects of dead-end pores in a granular porous media, or matrix diffusion in a fractured-rock aquifer. Options are provided for decay and zero-order growth reactions within the immobile-water phase. The simple reaction terms here extend the original model, which included decay and retardation. With these extensions, (a) the retardation factor can vary spatially within each model layer, (b) the decay rate coefficient can vary spatially within each model layer and can be different for the dissolved and sorbed phases, and (c) a zero-order growth reaction is added that can vary spatially and can be different in the dissolved and sorbed phases. The decay and growth reaction terms also can change in time to account for changing geochemical conditions during transport. The report includes a description of the theoretical basis of the model, a detailed description of input requirements and output options, and the results of model testing and evaluation. The model tests illustrate use of these modifications and demonstrate that accurate solutions can be obtained for these simple cases. Two test cases have no dispersion, illustrating the suitability of this method-of-characteristics model for simulation of advection-dominated transport in ground water.

Water-Resources Investigations Report↗

USGS1974

Storage of low-level radioactive wastes in the ground; hydrogeologic and hydrochemical factors

The status of mathematical simulation techniques, as they apply to radioactive waste burial sites, is briefly reviewed, and hydrogeologic and hydrochemical data needs are listed in order of increasing difficulty and cost of acquisition. Predictive modeling, monitoring, and management of radionuclides dissolved and transported by ground water can best be done for sites in relatively simple hydrogeologic settings; namely, in unfaulted relatively flat-lying strata of intermediate permeability such as silt, siltstone and silty sandstone. In contrast, dense fractured or soluble media, and poorly permeable porous media (aquitards) are not suitable for use as burial sites, first because of media heterogeneity and difficulties of sampling, and consequently of predictive modeling, and second, because in humid zones burial trenches in aquitards may overflow. A buffer zone several thousands of feet to perhaps several miles around existing or proposed sites is a mandatory consequence of the site selection criteria. As a specific example, the Maxey Flats, Kentucky low-level waste disposal site is examined. (Woodard-USGS)

Open-File Report↗

USGS2004

Testing density-dependent groundwater models: Two-dimensional steady state unstable convection in infinite, finite and inclined porous layers

This study proposes the use of several problems of unstable steady state convection with variable fluid density in a porous layer of infinite horizontal extent as two-dimensional (2-D) test cases for density-dependent groundwater flow and solute transport simulators. Unlike existing density-dependent model benchmarks, these problems have well-defined stability criteria that are determined analytically. These analytical stability indicators can be compared with numerical model results to test the ability of a code to accurately simulate buoyancy driven flow and diffusion. The basic analytical solution is for a horizontally infinite fluid-filled porous layer in which fluid density decreases with depth. The proposed test problems include unstable convection in an infinite horizontal box, in a finite horizontal box, and in an infinite inclined box. A dimensionless Rayleigh number incorporating properties of the fluid and the porous media determines the stability of the layer in each case. Testing the ability of numerical codes to match both the critical Rayleigh number at which convection occurs and the wavelength of convection cells is an addition to the benchmark problems currently in use. The proposed test problems are modelled in 2-D using the SUTRA [SUTRA––A model for saturated–unsaturated variable-density ground-water flow with solute or energy transport. US Geological Survey Water-Resources Investigations Report, 02-4231, 2002. 250 p] density-dependent groundwater flow and solute transport code. For the case of an infinite horizontal box, SUTRA results show a distinct change from stable to unstable behaviour around the theoretical critical Rayleigh number of 4 π 2 and the simulated wavelength of unstable convection agrees with that predicted by the analytical solution. The effects of finite layer aspect ratio and inclination on stability indicators are also tested and numerical results are in excellent agreement with theoretical stability criteria and with numerical results previously reported in traditional fluid mechanics literature.

Advances in Water Resources↗

USGS1993

Diffusional limits to the consumption of atmospheric methane by soils

Net transport of atmospheric gases into and out of soil systems is primarily controlled by diffusion along gas partial pressure gradients. Gas fluxes between soil and the atmosphere can therefore be estimated by a generalization of the equation for ordinary gaseous diffusion in porous unsaturated media. Consumption of CH4 by methylotrophic bacteria in the top several centimeters of soil causes the uptake of atmospheric CH4 by aerated soils. The capacity of the methylotrophs to consume CH4 commonly exceeds the potential of CH4 to diffuse from the atmosphere to the consumers. The maximum rate of uptake of atmospheric CH4 by soil is, therefore, limited by diffusion and can be calculated from soil physical properties and the CH4 concentration gradient. The CH4 concentration versus depth profile is theoretically described by the equation for gaseous diffusion with homogeneous chemical reaction in porous unsaturated media. This allows for calculation of the in situ rate of CH4 consumption within specified depth intervals.

Conference Paper↗

USGS2002

SUTRA: A model for 2D or 3D saturated-unsaturated, variable-density ground-water flow with solute or energy transport

SUTRA (Saturated-Unsaturated Transport) is a computer program that simulates fluid movement and the transport of either energy or dissolved substances in a subsurface environment. This upgraded version of SUTRA adds the capability for three-dimensional simulation to the former code (Voss, 1984), which allowed only two-dimensional simulation. The code employs a two- or three-dimensional finite-element and finite-difference method to approximate the governing equations that describe the two interdependent processes that are simulated: 1) fluid density-dependent saturated or unsaturated ground-water flow; and 2) either (a) transport of a solute in the ground water, in which the solute may be subject to: equilibrium adsorption on the porous matrix, and both first-order and zero-order production or decay; or (b) transport of thermal energy in the ground water and solid matrix of the aquifer. SUTRA may also be used to simulate simpler subsets of the above processes. A flow-direction-dependent dispersion process for anisotropic media is also provided by the code and is introduced in this report. As the primary calculated result, SUTRA provides fluid pressures and either solute concentrations or temperatures, as they vary with time, everywhere in the simulated subsurface system. SUTRA flow simulation may be employed for two-dimensional (2D) areal, cross sectional and three-dimensional (3D) modeling of saturated ground-water flow systems, and for cross sectional and 3D modeling of unsaturated zone flow. Solute-transport simulation using SUTRA may be employed to model natural or man-induced chemical-species transport including processes of solute sorption, production, and decay. For example, it may be applied to analyze ground-water contaminant transport problems and aquifer restoration designs. In addition, solute-transport simulation with SUTRA may be used for modeling of variable-density leachate movement, and for cross sectional modeling of saltwater intrusion in aquifers at near-well or regional scales, with either dispersed or relatively sharp transition zones between freshwater and saltwater. SUTRA energy-transport simulation may be employed to model thermal regimes in aquifers, subsurface heat conduction, aquifer thermal-energy storage systems, geothermal reservoirs, thermal pollution of aquifers, and natural hydrogeologic convection systems. Mesh construction, which is quite flexible for arbitrary geometries, employs quadrilateral finite elements in 2D Cartesian or radial-cylindrical coordinate systems, and hexahedral finite elements in 3D systems. 3D meshes are currently restricted to be logically rectangular; in other words, they are similar to deformable finite-difference-style grids. Permeabilities may be anisotropic and may vary in both direction and magnitude throughout the system, as may most other aquifer and fluid properties. Boundary conditions, sources and sinks may be time dependent. A number of input data checks are made to verify the input data set. An option is available for storing intermediate results and restarting a simulation at the intermediate time. Output options include fluid velocities, fluid mass and solute mass or energy budgets, and time-varying observations at points in the system. Both the mathematical basis for SUTRA and the program structure are highly general, and are modularized to allow for straightforward addition of new methods or processes to the simulation. The FORTRAN-90 coding stresses clarity and modularity rather than efficiency, providing easy access for later modifications.

Water-Resources Investigations Report↗

USGS2017

Bioremediation in fractured rock: 1. Modeling to inform design, monitoring, and expectations

Field characterization of a trichloroethene (TCE) source area in fractured mudstones produced a detailed understanding of the geology, contaminant distribution in fractures and the rock matrix, and hydraulic and transport properties. Groundwater flow and chemical transport modeling that synthesized the field characterization information proved critical for designing bioremediation of the source area. The planned bioremediation involved injecting emulsified vegetable oil and bacteria to enhance the naturally occurring biodegradation of TCE. The flow and transport modeling showed that injection will spread amendments widely over a zone of lower‐permeability fractures, with long residence times expected because of small velocities after injection and sorption of emulsified vegetable oil onto solids. Amendments transported out of this zone will be diluted by groundwater flux from other areas, limiting bioremediation effectiveness downgradient. At nearby pumping wells, further dilution is expected to make bioremediation effects undetectable in the pumped water. The results emphasize that in fracture‐dominated flow regimes, the extent of injected amendments cannot be conceptualized using simple homogeneous models of groundwater flow commonly adopted to design injections in unconsolidated porous media (e.g., radial diverging or dipole flow regimes). Instead, it is important to synthesize site characterization information using a groundwater flow model that includes discrete features representing high‐ and low‐permeability fractures. This type of model accounts for the highly heterogeneous hydraulic conductivity and groundwater fluxes in fractured‐rock aquifers, and facilitates designing injection strategies that target specific volumes of the aquifer and maximize the distribution of amendments over these volumes.

Groundwater↗

USGS2012

Surface heat flow and CO2 emissions within the Ohaaki hydrothermal field, Taupo Volcanic Zone, New Zealand

Carbon dioxide emissions and heat flow have been determined from the Ohaaki hydrothermal field, Taupo Volcanic Zone (TVZ), New Zealand following 20 a of production (116 MW e ). Soil CO 2 degassing was quantified with 2663 CO 2 flux measurements using the accumulation chamber method, and 2563 soil temperatures were measured and converted to equivalent heat flow (W m −2 ) using published soil temperature heat flow functions. Both CO 2 flux and heat flow were analysed statistically and then modelled using 500 sequential Gaussian simulations. Forty subsoil CO 2 gas samples were also analysed for stable C isotopes. Following 20 a of production, current CO 2 emissions equated to 111 ± 6.7 T/d. Observed heat flow was 70 ± 6.4 MW, compared with a pre-production value of 122 MW. This 52 MW reduction in surface heat flow is due to production-induced drying up of all alkali–Cl outflows (61.5 MW) and steam-heated pools (8.6 MW) within the Ohaaki West thermal area (OHW). The drying up of all alkali–Cl outflows at Ohaaki means that the soil zone is now the major natural pathway of heat release from the high-temperature reservoir. On the other hand, a net gain in thermal ground heat flow of 18 MW (from 25 MW to 43.3 ± 5 MW) at OHW is associated with permeability increases resulting from surface unit fracturing by production-induced ground subsidence. The Ohaaki East (OHE) thermal area showed no change in distribution of shallow and deep soil temperature contours despite 20 a of production, with an observed heat flow of 26.7 ± 3 MW and a CO 2 emission rate of 39 ± 3 T/d. The negligible change in the thermal status of the OHE thermal area is attributed to the low permeability of the reservoir beneath this area, which has limited production (mass extraction) and sheltered the area from the pressure decline within the main reservoir. Chemistry suggests that although alkali–Cl outflows once contributed significantly to the natural surface heat flow (∼50%) they contributed little (<1%) to pre-production CO 2 emissions due to the loss of >99% of the original CO 2 content due to depressurisation and boiling as the fluids ascended to the surface. Consequently, the soil has persisted as the major (99%) pathway of CO 2 release to the atmosphere from the high temperature reservoir at Ohaaki. The CO 2 flux and heat flow surveys indicate that despite 20 a of production the variability in location, spatial extent and magnitude of CO 2 flux remains consistent with established geochemical and geophysical models of the Ohaaki Field. At both OHW and OHE carbon isotopic analyses of soil gas indicate a two-stage fractionation process for moderate-flux (>60 g m −2 d −1 ) sites; boiling during fluid ascent within the underlying reservoir and isotopic enrichment as CO 2 diffuses through porous media of the soil zone. For high-flux sites (>300 g m −2 d −1 ), the δ 13 CO 2 signature (−7.4 ± 0.3‰ OHW and −6.5 ± 0.6‰ OHE) is unaffected by near-surface (soil zone) fractionation processes and reflects the composition of the boiled magmatic CO 2 source for each respective upflow. Flux thresholds of <30 g m −2 d −1 for purely diffusive gas transport, between 30 and 300 g m −2 d −1 for combined diffusive–advective transport, and ⩾300 g m −2 d −1 for purely advective gas transport at Ohaaki were assigned. δ 13 CO 2 values and cumulative probability plots of CO 2 flux data both identified a threshold of ∼15 g m −2 d −1 by which background (atmospheric and soil respired) CO 2 may be differentiated from hydrothermal CO 2 .

Taupo Volcanic Zone↗

USGS1990

Movement and fate of atrazine and bromide in central Kansas croplands

Two flooding experiments were conducted at two sites with different soils to study the transport and fate of the commonly used herbicide atrazine and inorganic chemicals in the Great Bend Prairie croplands of south-central Kansas. The instantaneous profile method supplemented by the use of an organic (atrazine) and an inorganic (bromide) tracer chemical was used to characterize in situ the hydraulic and chemical properties of the appropriately instrumented field sites. Atrazine readily degraded to hydroxyatrazine and biodegradation by-products and was not detected deeper in the soil profile and underlying shallow aquifer. The classical processes of chemical movement based on porous media-equilibrium-diffuse flow did not fit the data well at either site. Incompletely mixed, slug flow appeared to predominate at one of the sites and preferential flow at the other. The slug movement caused 'piston-type' displacement of more saline solutions in the soil profile to the shallow water table. Recommendations for conducting related field studies based on our sampling experience are given.

Kansas↗

USGS2018

Time-dependent pore filling

Capillarity traps fluids in porous media during immiscible fluid displacement. Most field situations involve relatively long time scales, such as hydrocarbon migration into reservoirs, resource recovery, nonaqueous phase liquid remediation, geological CO 2 storage, and sediment‐atmosphere interactions. Yet laboratory studies and numerical simulations of capillary phenomena rarely consider the impact of time on these processes. We use time‐lapse microphotography to record the evolution of saturation in air‐ or hydrocarbon‐filled capillary tubes submerged in water to investigate long‐term pore filling phenomena beyond imbibition. Microphotographic sequences capture a lively pore filling history where various concurrent physical phenomena coexist. Dissolution and diffusion play a central role. Observations indicate preferential transport of the wetting liquid along corners, vapor condensation, capillary flow induced by asymmetrical interfaces, and interface pinning that defines the diffusion length. Other processes include internal snap‐offs, fluid redistribution, and changes in wettability as fluids dissolve into each other. Overall, the rate of pore filling is diffusion‐controlled for a given interfacial configuration; diffusive transport takes place at a constant rate for pinned interfaces and is proportional to the square root of time for free interfaces where the diffusion length increases with time.

Water Resources Research↗

USGS1982

Field, model, and computer simulation study of some aspects of the origin and distribution of Colorado Plateau-type uranium deposits

Numerous hypotheses have been proposed to account for the nature and distribution of tabular uranium and vanadium-uranium deposits of the Colorado Plateau. In one of these hypotheses it is suggested that the deposits resulted from geochemical reactions at the interface between a relatively stagnant groundwater solution and a dynamic, ore-carrying groundwater solution which permeated the host sandstones (Shawe, 1956; Granger, et al., 1961; Granger, 1968, 1976; and Granger and Warren, 1979). The study described here was designed to investigate some aspects of this hypothesis, particularly the nature of fluid flow in sands and sandstones, the nature and distribution of deposits, and the relations between the deposits and the host sandstones. The investigation, which was divided into three phases, involved physical model, field, and computer simulation studies. During the initial phase of the investigation, physical model studies were conducted in porous-media flumes. These studies verified the fact that humic acid precipitates could form at the interface between a humic acid solution and a potassium aluminum sulfate solution and that the nature and distribution of these precipitates were related to flow phenomena and to the nature and distribution of the host porous-media. During the second phase of the investigation field studies of permeability and porosity patterns in Holocene stream deposits were investigated and the data obtained were used to design more realistic porous media models. These model studies, which simulated actual stream deposits, demonstrated that precipitates possess many characteristics, in terms of their nature and relation to host sandstones, that are similar to ore deposits of the Colorado Plateau. The final phase of the investigation involved field studies of actual deposits, additional model studies in a large indoor flume, and computer simulation studies. The field investigations provided an up-to-date interpretation of the depositional environments of the host sandstones in the Slick Rock District and data on the nature and distribution of the ore deposits which are found to be directly related to the architecture of the host sandstones which acted as conduits for the transport of mineralized groundwaters. Large-scale model studies, designed to simulate Grants Mineral Belt deposits, demonstrated that precipitates had characteristics similar to those of actual uranium deposits and data obtained from these studies strongly supported the hypothesis that the ores formed soon after deposition of the host sandstones and that their distribution was largely controlled by permeability and porosity patterns established at the time of deposition of the host sandstones. A numerical model was developed during the second and third stages of the investigation that can predict favorable locations for mineralization given sufficient data on porosity, hydraulic conductivity, the distribution and thickness of sandstone hosts, and an estimate of the initial hydrologic conditions. The model was successfully tested using data from the Slick Rock District.

Open-File Report↗

USGS1996

Analysis of tests of subsurface injection, storage, and recovery of freshwater in the lower Floridan aquifer, Okeechobee County, Florida

A series of freshwater subsurface injection, storage, and recovery tests were conducted at an injection-well site near Lake Okeechobee in Okeechobee County, Florida, to assess the recoverability of injected canal water from the Lower Floridan aquifer. At the study site, the Lower Floridan aquifer is characterized as having four local, relatively independent, high-permeability flow zones (389 to 398 meters, 419 to 424 meters, 456 to 462 meters, and 472 to 476 meters below sea level). Four subsurface injection, storage, and recovery cycles were performed at the Lake Okeechobee injection-well site in which volumes of water injected ranged from about 387,275 to 1,343,675 cubic meters for all the cycles, and volumes of water recovered ranged from about 106,200 to 484,400 cubic meters for cycles 1, 2, and 3. The recovery efficiency for successive cycles 2 and 3 increased from 22 to 36 percent and is expected to continue increasing with additional cycles. A comparison of chloride concentration breakthrough curves at the deep monitor well (located about 171 meters from the injection well) for cycles 1, 4, and test no. 4 (from a previous study) revealed unexpected finings. One significant result was that the concentration asymptote, expected to be reached at concentration levels equivalent or close to the injected water concentration, was instead reached at higher concentration levels. The injection to recovery rate ratio might affect the chloride concentration breakthrough curve at the deep monitor well, which could explain this unexpected behavior. Because there are four high-permeability zones, if the rate of injection is smaller than the rate of recovery (natural artesian flow), the head differential might not be transmitted through the entire open wellbore, and injected water would probably flow only through the upper high- permeability zones. Therefore, observed chloride concentration values at the deep monitor well would be higher than the concentration of the injected water and would represent a mix of water from the different high-permeability zones. A generalized digital model was constructed to simulate the subsurface injection, storage, and recovery of freshwater in the Lower Floridan aquifer at the Lake Okeechobee injection-well site. The model was constructed using a modified version of the Saturated-Unsaturated TRAnsport code (SUTRA), which simulates variable-density advective-dispersive solute transport and variable-density ground-water flow. Satisfactory comparisons of simulated to observed dimensionless chloride concentrations for the deep monitor well were obtained when using the model during the injection and recovery phases of cycle 1, but not for the injection well during the recovery phase of cycle 1 even after several attempts. This precluded the determination of the recovery efficiency values by using the model. The unsatisfactory comparisons of simulated to observed dimensionless chloride concentrations for the injection well and failure of the model to represent the field data at this well could be due to the characteristics of the Lower Floridan aquifer (at the local scale), which is cavernous or conduit in nature. To test this possibility, Reynolds numbers were estimated at varying distances from the injection well, taking into consideration two aquifer types or conceptual systems, porous media and cavernous. For the porous media conceptual system, the Reynolds numbers were greater than 10 at distances less than 1.42 meters from the injection well. Thus, application of Darcy's law to ground-water flow might not be valid at this distance. However, at the deep monitor well (171 meters from the injection well), the Reynolds number was 0.08 which is indicative of laminar porous media flow. For the cavernous conceptual system, the Reynolds numbers were greater than 2,000 at distances less than 1,000 meters from the well. This number represents the upper limit of laminar flow, which is the fundamental assumption

Florida↗

USGS2016

Experimental studies and model analysis of noble gas fractionation in porous media

The noble gases, which are chemically inert under normal terrestrial conditions but vary systematically across a wide range of atomic mass and diffusivity, offer a multicomponent approach to investigating gas dynamics in unsaturated soil horizons, including transfer of gas between saturated zones, unsaturated zones, and the atmosphere. To evaluate the degree to which fractionation of noble gases in the presence of an advective–diffusive flux agrees with existing theory, a simple laboratory sand column experiment was conducted. Pure CO2 was injected at the base of the column, providing a series of constant CO2 fluxes through the column. At five fixed sampling depths within the system, samples were collected for CO2 and noble gas analyses, and ambient pressures were measured. Both the advection–diffusion and dusty gas models were used to simulate the behavior of CO2 and noble gases under the experimental conditions, and the simulations were compared with the measured depth-dependent concentration profiles of the gases. Given the relatively high permeability of the sand column (5 ´ 10−11 m2), Knudsen diffusion terms were small, and both the dusty gas model and the advection–diffusion model accurately predicted the concentration profiles of the CO2 and atmospheric noble gases across a range of CO2 flux from ?700 to 10,000 g m−2 d−1. The agreement between predicted and measured gas concentrations demonstrated that, when applied to natural systems, the multi-component capability provided by the noble gases can be exploited to constrain component and total gas fluxes of non-conserved (CO2) and conserved (noble gas) species or attributes of the soil column relevant to gas transport, such as porosity, tortuosity, and gas saturation.

Vadose Zone Journal↗

USGS2016

Simulating groundwater flow in karst aquifers with distributed parameter models—Comparison of porous-equivalent media and hybrid flow approaches

Understanding karst aquifers, for purposes of their management and protection, poses unique challenges. Karst aquifers are characterized by groundwater flow through conduits (tertiary porosity), and (or) layers with interconnected pores (secondary porosity) and through intergranular porosity (primary or matrix porosity). Since the late 1960s, advances have been made in the development of numerical computer codes and the use of mathematical model applications towards the understanding of dual (primary [matrix] and secondary [fractures and conduits]) porosity groundwater flow processes, as well as characterization and management of karst aquifers. The Floridan aquifer system (FAS) in Florida and parts of Alabama, Georgia, and South Carolina is composed of a thick sequence of predominantly carbonate rocks. Karst features are present over much of its area, especially in Florida where more than 30 first-magnitude springs occur, numerous sinkholes and submerged conduits have been mapped, and numerous circular lakes within sinkhole depressions are present. Different types of mathematical models have been applied for simulation of the FAS. Most of these models are distributed parameter models based on the assumption that, like a sponge, water flows through connected pores within the aquifer system and can be simulated with the same mathematical methods applied to flow through sand and gravel aquifers; these models are usually referred to as porous-equivalent media models. The partial differential equation solved for groundwater flow is the potential flow equation of fluid mechanics, which is used when flow is dominated by potential energy and has been applied for many fluid problems in which kinetic energy terms are dropped from the differential equation solved. In many groundwater model codes (basic MODFLOW), it is assumed that the water has a constant temperature and density and that flow is laminar, such that kinetic energy has minimal impact on flow. Some models have been developed that incorporate the submerged conduits as a one-dimensional pipe network within the aquifer rather than as discrete, extremely transmissive features in a porous-equivalent medium; these submerged conduit models are usually referred to as hybrid models and may include the capability to simulate both laminar and turbulent flow in the one-dimensional pipe network. Comparisons of the application of a porous-equivalent media model with and without turbulence (MODFLOW-Conduit Flow Process mode 2 and basic MODFLOW, respectively) and a hybrid (MODFLOW-Conduit Flow Process mode 1) model to the Woodville Karst Plain near Tallahassee, Florida, indicated that for annual, monthly, or seasonal average hydrologic conditions, all methods met calibration criteria (matched observed groundwater levels and average flows). Thus, the increased effort required, such as the collection of data on conduit location, to develop a hybrid model and its increased computational burden, is not necessary for simulation of average hydrologic conditions (non-laminar flow effects on simulated head and spring discharge were minimal). However, simulation of a large storm event in the Woodville Karst Plain with daily stress periods indicated that turbulence is important for matching daily springflow hydrographs. Thus, if matching streamflow hydrographs over a storm event is required, the simulation of non-laminar flow and the location of conduits are required. The main challenge in application of the methods and approaches for developing hybrid models relates to the difficulty of mapping conduit networks or having high-quality datasets to calibrate these models. Additionally, hybrid models have long simulation times, which can preclude the use of parameter estimation for calibration. Simulation of contaminant transport that does not account for preferential flow through conduits or extremely permeable zones in any approach is ill-advised. Simulation results in other karst aquifers or other parts of the FAS may differ from the comparison demonstrated herein.

Florida↗

USGS2020

Formation criteria for hyporheic anoxic microzones: Assessing interactions of hydraulics, nutrients and biofilms

Recent experimental studies have detected the presence of anoxic microzones in hyporheic sediments. These microzones are small‐scale anoxic pores, embedded within oxygen‐rich porous media and can act as anaerobic reaction sites producing reduction compounds such as nitrous oxide, a potent greenhouse gas. Microbes are a key control on nutrient transformation in hyporheic sediment, but their associated biomass growth is also capable of altering hydraulic flux, leading to potential bioclogging. Here, we developed one of the first computational modeling approaches that combined hydraulics and microbial conditions to explore the continuous evolution of microzones in stream sediments. The model assessed stream and sediment conditions with different hydraulic flux (0.1–1.0 m/day Darcy flux), nutrient concentrations (O 2 = 8 mg/L, OrgC = 20 mg/L, NO − 3 = 1.5–3 mg/L, and NH 3 = 0.5–1 mg/L), and biomass scenarios (with and without). The model domain is a pore network model with random sized pore‐throat radii creating heterogeneous and anisotropic flow that is representative of a natural streambed composed of medium sand with a hydraulic conductivity of 0.8 m/day. Results from 30 day simulations indicate that hyporheic microzone formation will occur and microzone distributions are not simply controlled by residence time alone, rather by the complex interactions of hydraulic flux, nutrient concentrations, and biomass, with bioclogging having strong feedbacks on both hydraulics and nutrients. Under all conditions with biomass growth, anoxic microzones were unstable, perishing a few days after formation, because bioclogging primarily occurs near the influent (downwelling) area of the hyporheic zone. In turn, this bioclogging shifts transport conditions from advection‐dominated to diffusion‐dominated transport, removing all oxic regions in the hyporheic zone. Overall, results from the modeling show that anoxic microzones are likely to form under many hyporheic zone conditions, and be dynamic through space and time as they are dependent on both hydraulic flux and nutrient transport.

Water Resources Research↗