Motion of wetting fronts moving into partially pre-wet soil

We study the motion of wetting fronts for vertical infiltration problems as modeled by Richards’ equation. Parlange and others have shown that wetting fronts in infiltration flows can be described by traveling wave solutions. If the soil layer is not initially dry, but has an initial distribution of water content then the motion of the wetting front will change due to the interaction of the infiltrating flow with the pre-existing soil conditions. Using traveling wave profiles, we construct simple approximate solutions of initial-boundary value problems for Richards’ equation that accurately describe the position and moisture distribution of the wetting front. We show that the influences of surface boundary conditions and initial conditions produce shifts to the position of the wetting front. The shifts can be calculated by examining the cumulative infiltration, and are validated numerically for several problems for Richards’ equation and the linear advection–diffusion equation.     

Stochastic analysis of biodegradation fronts in one-dimensional heterogeneous porous media

We consider a one-dimensional model biodegradation system consisting of two reaction–advection equations for nutrient and pollutant concentrations and a rate equation for biomass. The hydrodynamic dispersion is ignored. Under an explicit condition on the decay and growth rates of biomass, the system can be approximated by two component models by setting biomass kinetics to equilibrium. We derive closed form solutions for constant speed traveling fronts for the reduced two component models and compare their profiles in homogeneous media. For a spatially random velocity field, we introduce travel time and study statistics of degradation fronts via representations in terms of the travel time probability density function (pdf) and the traveling front profiles. The travel time pdf does not vary with the nutrient and pollutant concentrations and only depends on the random water velocity. The traveling front profiles are expressed analytically or semi-analytically as functions of the travel time. The problem of nonlinear transport by a random velocity reduces to two subproblems: one being nonlinear transport by a known (unit) velocity, and the other being linear (advective) transport by a random velocity. The approach is illustrated through some examples where the randomness in velocity stems from the spatial variability of porosity.     

Theory and application of equivalent transformation relationships between plane wave and spherical wave

Based on the governing equations and the equivalent models,we propose an equivalent transformation relationships between a plane wave in a one-dimensional medium and a spherical wave in globular geometry with radially inhomogeneous properties.These equivalent relationships can help us to obtain the analytical solutions of the elastodynamic issues in an inhomogeneous medium.The physical essence of the presented equivalent transformations is the equivalent relationships between the geometry and the material properties.It indicates that the spherical wave problem in globular geometry can be transformed into the plane wave problem in the bar with variable property fields,and its inverse transformation is valid as well.Four different examples of wave motion problems in the inhomogeneous media are solved based on the presented equivalent relationships.We obtain two basic analytical solution forms in Examples Ⅰ and Ⅱ,investigate the reflection behavior of inhomogeneous half-space in Example Ⅲ,and exhibit a special inhomogeneity in Example Ⅳ,which can keep the traveling spherical wave in constant amplitude.This study implies that our idea makes solving the associated problem easier.     

Effects of Process Control Changes on Aquifer Oxygenation Rates During In Situ Air Sparging in Homogeneous Aquifers

In situ air sparging is used to remediate petroleum fuels and chlorinated solvents present as submerged contaminant source /ones and dissolved contaminant plumes, or to provide barriers to dissolved contaminant plume migration. Contaminant removal occurs through a combination of volatilization and aerobic biodegradation: thus, the performance at any given site depends on the contaminant and oxygen mass transfer rates induced by the air injection. It has been hypothesized that these rates are sensitive to changes in process flow conditions and site lithology, but no data is available to identify trends or the magnitude of the changes. In this work, oxygenation rates were measured for a range of air injection rates, ground water flow rates, and pulsing frequencies using a laboratory-scale two-dimensional physical model constructed to simulate a homogeneous hydrogeologic setting. Experiments were conducted with water having low chemical and biochemical oxygen demand. Results suggest the following: that there is an optimum air injection rate: advective How of ground water can be a significant factor when ground water velocities are > 0.3 m/d: and pulsing the air injection had little effect on the oxygenation rate relative lo the continuous air injection case.     

Introduction to seismic travel time methods in anisotropic media

Summary Section 1 (and 11) develops the concepts of the front velocity, the front gradient, the travel time in space and on seismometric profiles, the profile velocity and the profile gradient in connection with the propagation of the fronts of elastic waves in solid isotropic and anisotropic media. The sectional velocity and the sectional gradient are defined in terms of the motion of the curve of intersection of a front with a fixed surface. Section 2 (and 12) relates the coefficients of elasticity of the medium, the front types, and their respective rays. In section 12, the theory of fronts of arbitrary shape and of the corresponding rays for any anisotropic, homogeneous or inhomogeneous solid medium is summarized. In section 3 (and 13), the law of reflection and refraction of fronts on surfaces of discontinuity of arbitrary shape is presented. Sections 4 to 6 (and 14 to 16) treat some elementary applications of seismic travel time methods to homogeneous, uniaxially anisotropic media (=transverse isotropy) in greater detail. In section 4 (and 14), the travel time of a direct front generated by a point source is considered and it is shown how the coefficients of elasticity of the medium can be found based on travel time measurements. The seismic prospection of a plane reflector and of a reflecting boundary of arbitrary shape and position are discussed in section 5 (and 15). In section 6 (and 16), the seismic refraction method is used to locate a plane boundary between a homogeneous, uniaxially anisotropic and a homogeneous isotropic medium, where the boundary is perpendicular or at an arbitrary angle to the direction of anisotropy.     

Analytical solution of the solute transport equation for the binary homovalent ion exchange in groundwater

A binary homovalent ion exchange transport model governed by local chemical equilibrium is considered for a one-dimensional, steady flow in a homogeneous soil column. An analytical solution of the aqueous concentration distribution for the convex exchange is obtained by applying nonlinear shock wave theory. The main nonlinear feature is the breaking of fronts into shock waves. The corresponding mathematical theory is the method of characteristics with a special treatment of shock waves. The wave velocity and front thickness are also obtained to illustrate the front propagation and structure. The derivation of the solution presented may offer a wide range of application opportunities and may also provide a good approach for solving the binary heterovalent exchange transport model.     

Effect of Temporal Changes in Air Injection Rate on Air Sparging Performance Groundwater Remediation

Air sparging (AS) is a commonly applied method for treating groundwater contaminated with volatile organic compounds (VOCs). When using a constant injection of air (continuous mode), a decline in remediation efficiency is often observed, resulting from insufficient mixing of contaminants at the pore scale. It is well known that turning the injection on and off (pulsed mode) may lead to a better remediation performance. In this article, we investigate groundwater mixing and contaminant removal efficiency in different injection modes (i.e., continuous and pulsed), and compare them to those achieved in a third mode, which we denote as “rate changing.” In this mode, injection is always on, and its rate is varying with time by abrupt changes. For the purpose of this investigation, we conducted two separate sets of experiments in a laboratory tank. In the first set of experiments, we used dye plume tracing to characterize the mixing induced by AS. In the second set of experiments, we contaminated the tank with a VOC and compared the remediation efficiency between the different injection modes. As expected, we observed that time‐variable injection modes led to enhanced mixing and contaminant removal. The decrease in contaminant concentrations during the experiment was found to be double for the “rate changing” and “pulsed” modes compared to the continuous mode, with a slightly preferable performance for the “rate changing” mode. These results highlight the critical role that mixing plays in AS, and support the need for further investigation of the proposed “rate changing” injection mode.     

Comparison of alternative upscaled model formulations for simulating DNAPL source dissolution and biodecay

This paper compares the performance of analytical and numerical approaches for modeling DNAPL dissolution with biodecay. A solution derived from a 1-D advective transport formulation (“Parker” model) is shown to agree very closely with high resolution numerical solutions. A simple lumped source mass balance solution in which with decay is assumed proportional to DNAPL mass (“Falta1” model) over- or underpredicts aqueous phase biodecay depending on the magnitude of the exponential factor governing the relationship between dissolution rate and DNAPL mass. A modification of the Falta model that assumes decay proportional to the source exit concentration is capable of accurately simulating source behavior with strong aqueous phase biodecay if model parameters are appropriately selected or calibrated (“Falta2” model). However, parameters in the lumped models exhibit complex interdependencies that cannot be quantified without consideration of transport processes within the source zone. Combining the Falta2 solution with relationships derived from the Parker model was found to resolve these limitations and track the numerical model results. A method is presented to generalize the analytical solutions to enable simulation of partial mass removal with changes in source parameters over time due to various remedial actions. The algorithm is verified by comparison with numerical simulation results. An example application is presented that demonstrates the interactions of partial mass removal, enhanced biodecay, enhanced mass transfer and source zone flow reduction applied at various time periods on contaminant flux reduction. Increasing errors that arise in numerical solutions with coarse discretization and high decay rates are shown to be controlled by using an adjusted decay coefficient derived from the Parker analytical solution.     

Bioventing for in situ remediation

Abstract

The availability of oxygen generally controls the rate at which aerobic in situ bioremediation proceeds. Bioventing, which couples soil venting with bioremediation, is often the most effective means of supplying oxygen to unsaturated zone soil. Laboratory treatability studies were conducted which showed that bioventing could be successfully applied to compounds ranging from light hydrocarbons, such as gasoline or diesel, to heavier hydrocarbons, such as fuel oils, as well as other volatile and semivolatile compounds. In many cases, the promotion of biological activity through the addition of nutrients and moisture, and optimization of the bioventing flow rates, may achieve greater contaminant reductions than venting alone.     

Demonstration of a Microbiologically Enhanced Vertical Ground Water Circulation Well Technology at a Superfund Site

A full-scale ground water circulation well (GCW) system was installed and operated to demonstrate in situ remediation of soil and ground water impacted with a mixture of chlorinated and nonchlorinated organic compounds at a Superfund site in upstate New York. System performance and applicability under site-specific conditions were evaluated based on the system's ability to meet the New York State Department of Environmental Conservation (NYSDEC) cleanup goals for target compounds in ground water and soil. Contaminants from the unsaturated zone were mobilized (volatilized) by one-way vacuum extraction, and treated via enhanced biodegradation (bioventing). In the saturated zone, contaminants were mobilized by soil flushing (solubilized) and treated by a combination of air stripping and biodegradation. An in situ aqueous phase bioreactor, and an ex situ gas phase bioreactor, were integrated into the system to enhance treatment via bioremediation. After 15 months of operation, the mass of target contaminants in soil and ground water combined had been reduced by 75%. Removal by biological mechanisms ranged from 35% to 56% of the total observed mass reduction. The in situ and the ex situ bioreactors mineralized 79% and 76%, respectively, of their target biodegradable contaminant loads. Results indicate that some mass reduction in target contaminants may have been from aerobic and aerobic processes within the circulation cell. Nonchlorinated compounds were relatively easy to mobilize (volatilize, solubilize, and/or transport) and treat when compared to chlorinated compounds. The data collected during the 15-month study indicate that remediation could be accomplished at the Sweden-3 Chapman site using the technology tested.     

Dynamic pile-soil-pile interaction. Part I: Analysis of axial vibration

Simple methods of analysis are developed for computing the dynamic steady-state axial response of floating pile groups embedded in homogeneous and non-homogeneous soil deposits. Physically-motivated approximations are introduced to account for the interaction between two individual piles. It is found that such an interaction arises chiefly from the ‘interference’ of wave fields originating along each pile shaft and spreading outward. For homogeneous deposits the wave fronts originating at an individual pile are cylindrical and the interaction is essentially independent of pile flexibility and slenderness. For non-homogeneous deposits the wave fronts are non-cylindrical and ray-theory approximations are invoked to derive pile flexibility-dependent interaction functions. Results are presented for the dynamic stiffness and damping of several pile groups, as well as for distribution of the applied load among individual piles. For deposits with modulus proportional to depth, the agreement with the few rigorous solutions available is encouraging. A comprehensive parameter study focuses on the effects of soil inhomogeneity and pile-group configuration. It is demonstrated that the ‘dynamic group efficiency’ may far exceed unity at certain frequencies. Increasing soil inhomogeneity tends to reduce the respective resonant peaks and lead to smoother interaction functions, in qualitative agreement with field evidence.     

Estimating Reaction Rate Coefficients Within a Travel‐Time Modeling Framework

A generalized, efficient, and practical approach based on the travel‐time modeling framework is developed to estimate in situ reaction rate coefficients for groundwater remediation in heterogeneous aquifers. The required information for this approach can be obtained by conducting tracer tests with injection of a mixture of conservative and reactive tracers and measurements of both breakthrough curves (BTCs). The conservative BTC is used to infer the travel‐time distribution from the injection point to the observation point. For advection‐dominant reactive transport with well‐mixed reactive species and a constant travel‐time distribution, the reactive BTC is obtained by integrating the solutions to advective‐reactive transport over the entire travel‐time distribution, and then is used in optimization to determine the in situ reaction rate coefficients. By directly working on the conservative and reactive BTCs, this approach avoids costly aquifer characterization and improves the estimation for transport in heterogeneous aquifers which may not be sufficiently described by traditional mechanistic transport models with constant transport parameters. Simplified schemes are proposed for reactive transport with zero‐, first‐, nth‐order, and Michaelis‐Menten reactions. The proposed approach is validated by a reactive transport case in a two‐dimensional synthetic heterogeneous aquifer and a field‐scale bioremediation experiment conducted at Oak Ridge, Tennessee. The field application indicates that ethanol degradation for U(VI)‐bioremediation is better approximated by zero‐order reaction kinetics than first‐order reaction kinetics.     

Bacterial Production Stimulated Across the Zone of Influence of a Ground Water Circulation Well in a BTEX-Contaminated Aquifer

Benzene, toluene, ethylbenzene, and xylene (BTEX) hydrocarbons are typically the most abundant carbon source for bacteria in gasoline-contaminated ground water. In situ bioremediation strategies often involve stimulating bacterial heterotrophic production in an attempt to increase carbon demand of the assemblage. This may, in turn, stimulate biodegradation of contaminant hydrocarbons. In this study, ground water circulation wells (GCWs) were used as an in situ treatment for a fuel-contaminated aquifer to stimulate bacterial production, purportedly by increasing oxygen transfer to the subsurface, circulating limiting nutrients, enhancing bioavailability of hydrocarbons, or by removing metabolically inhibitory volatile organics. Bacterial production, as measured by rates of bacterial protein synthesis, was stimulated across the zone of influence (ZOI) of a series of GCWs. Productivity increased from ∼10² to >10⁵ ng C/L hour across the ZOI, suggesting that treatment stimulated overall biodegradation of carbon sources present in the ground water. However, even if BTEX carbon met all bacterial carbon demand, biodegradation would account for <4.3% of the total estimated BTEX removed from the ground water. Although bacterial productivity measurements alone cannot prove the effectiveness of in situ bioremediation, they can estimate the maximum amount of contaminant that may be biodegraded by a treatment system.     

Lateral stirring of large-scale tracer fields by altimetry

Ocean surface fronts and filaments have a strong impact on the global ocean circulation and biogeochemistry. Surface Lagrangian advection with time-evolving altimetric geostrophic velocities can be used to simulate the submesoscale front and filament structures in large-scale tracer fields. We study this technique in the Southern Ocean region south of Tasmania, a domain marked by strong meso- to submesoscale features such as the fronts of the Antarctic Circumpolar Current (ACC). Starting with large-scale surface tracer fields that we stir with altimetric velocities, we determine ‘advected’ fields which compare well with high-resolution in situ or satellite tracer data. We find that fine scales are best represented in a statistical sense after an optimal advection time of ～2 weeks, with enhanced signatures of the ACC fronts and better spectral energy. The technique works best in moderate to high EKE regions where lateral advection dominates. This technique may be used to infer the distribution of unresolved small scales in any physical or biogeochemical surface tracer that is dominated by lateral advection. Submesoscale dynamics also impact the subsurface of the ocean, and the Lagrangian advection at depth shows promising results. Finally, we show that climatological tracer fields computed from the advected large-scale fields display improved fine-scale mean features, such as the ACC fronts, which can be useful in the context of ocean modelling.     

Development of waves under explosive cyclones in the Northwestern Pacific

The development of ocean waves under explosive cyclones (ECs) is investigated in the Northwestern Pacific Ocean using a hindcast wave simulation around Japan during the period 1994 through 2014. A composite analysis of the ocean wave fields under ECs is used to investigate how the spatial patterns of the spectral wave parameters develop over time. Using dual criteria of a drop in sea level pressure below 980 hPa at the center of a cyclone and a decrease of at least 12 hPa over a 12-h period, ECs are identified in atmospheric reanalysis data. Two areas under an EC were identified with narrow directional spectra: the cold side of a warm front and the right-hand side of an EC (relative to the propagating direction). Because ECs are associated with atmospheric fronts, ocean waves develop very differently under ECs than they do under tropical cyclones. Moreover, ECs evolve very rapidly such that the development of the ocean wave field lags behind the peak wind speed by hours. In a case study of an EC that occurred in January 2013, the wave spectrum indicates that a warm front played a critical role in generating distinct ocean wave systems in the warm and cold zones along the warm front. Both the warm and cold zones have narrow directional and frequency spectra. In contrast, the ocean wave field in the third quadrant (rear left area relative to the propagation direction) of the EC is composed of swell and wind sea systems propagating in different directions.     

Push‐Pull Tests for Estimating RDX and TNT Degradation Rates in Groundwater

In situ bioremediation is being considered to optimize an existing pump‐and‐treat remedy for treatment of explosives‐contaminated groundwater at the Umatilla Chemical Depot. Push‐pull tests were conducted using a phased approach to measure in situ hexahydro‐1,3,5‐trinitro‐1,3,5‐triazine (RDX) and 2,4,6‐trinitrotoluene (TNT) degradation rates associated with various carbon substrates. Phase I included short‐duration transport tests conducted in each well to determine dilution rates and retardation factors for RDX and TNT. Phase II included aquifer “feedings” conducted by injecting 150 gallons of treated site groundwater amended with ethanol, corn syrup, lactose or emulsified oil (concentrations 10, 25 and 27 mM, respectively; 12% by volume for emulsified oil). Wells received up to 6 substrate “feedings” over the course of 3 months followed by monitoring dissolved oxygen, nitrate, Fe(II), and sulfate to gauge in situ redox conditions as indicators of anaerobic microbial activity. Phase III included push‐pull tests conducted by injecting 150 gallons of site groundwater amended with approximately 1000 µg/L RDX, 350 µg/L TNT, carbon substrate and a conservative tracer, followed by sampling over 8 d. Corn syrup resulted in the best RDX removal (82% on average) and the largest RDX degradation rate coefficient (1.4 ± 1.1 d^?1). Emulsified oil resulted in the best TNT removal (99%) and largest TNT degradation rate coefficient (5.7 × 10^?2 d^?1). These results will be used to simulate full‐scale in situ bioremediation scenarios at Umatilla and will support a go/no‐go decision to initiate full‐scale bioremediation remedy optimization.     

Effects of three-dimensionality on seismic response of Gaussian-shaped hills for simple incident pulses

In this paper the boundary element algorithm which uses the time-convoluted traction kernels is applied to a numerical parametric study on the seismic behavior of three-dimensional Gaussian-shaped hills subjected to vertically propagating incident waves. All calculations were executed in the time-domain and the medium was assumed to have a linear elastic constitutive behavior. Results are discussed in both time and frequency domain with respect to the dimensionless parameters. It was shown that wave length and site geometry, including shape and dimension ratios and, to some extent, wave type are the key independent parameters governing hill amplification behavior. Comparing two- and three-dimensional hills with similar shape ratios, two-dimensional hill had greater characteristic periods, where the three-dimensional hill had greater maximum amplification potential. Three-dimensionality has a strong effect on the seismic responses of the hill; however the rate of seismic response variation with the three-dimensionality factor depends on the shape ratio. It was shown that two-dimensional behavior was dominant in low height three-dimensional hills, however, as the shape ratio increased, three-dimensionality effects appeared and the seismic response of the hill tends toward the axisymmetric three-dimensional hill.     

Numerical Analysis of Thermal Remediation in 3D Field‐Scale Fractured Geologic Media

Thermal methods are promising for remediating fractured geologic media contaminated with volatile organic compounds, and the success of this process depends on the coupled heat transfer, multiphase flow, and thermodynamics. This study analyzed field‐scale removal of trichloroethylene (TCE) and heat transfer behavior in boiling fractured geologic media using the multiple interacting continua method. This method can resolve local gradients in the matrix and is less computationally demanding than alternative methods like discrete fracture‐matrix models. A 2D axisymmetric model was used to simulate a single element of symmetry in a repeated pattern of extraction wells inside a large heated zone and evaluate effects of parameter sensitivity on contaminant recovery. The results showed that the removal of TCE increased with matrix permeability, and the removal rate was more sensitive to matrix permeability than any other parameter. Increasing fracture density promoted TCE removal, especially when the matrix permeability was low (e.g., <10^?17 m²). A 3D model was used to simulate an entire treatment zone and the surrounding groundwater in fractured material, with the interaction between them being considered. Boiling was initiated in the center of the upper part of the heated region and expanded toward the boundaries. This boiling process resulted in a large increase in the TCE removal rate and spread of TCE to the vadose zone and the peripheries of the heated zone. The incorporation of extraction wells helped control the contaminant from migrating to far regions. After 22 d, more than 99.3% of TCE mass was recovered in the simulation.     

Quantification of Advective Transport Phenomena to Better Understand Dispersion in the Field

Observation of dispersion in field situations has left three issues that may be better understood by applying advective transport phenomena. (1) In some experiments, the longitudinal dispersivity becomes constant with increasing pathlength and in other cases it remains growing. (2) Dispersivities reported from multiple comprehensive observations at a single site differ at similar pathlength in some cases more than a factor two. (3) The observed difference between the plume fronts and plume tails is not represented in the reported parameters. The analytic equations for advective transport phenomena at macroscale of De Lange (2020) describe the thickness of the affected flow-tube and the spread of the plume front and tail. The scale factor defines the size of the averaging domain and so of the initial phase. The new macroscale correlation coefficient relates the growth of the longitudinal dispersivity beyond the initial phase to the aquifer heterogeneity. Using stochastic parameters for the aquifer heterogeneity, the parameters are quantified at 14 field experiments in the United States, Canada and Europe enabling the comparison of calculated and reported final dispersivities. Using the quantified parameters, 146 reported and calculated dispersivities along the traveled paths show a good match. A dispersivity derived from the local plume growth may differ a factor of two from the aquifer-representative value. The growths of plume fronts and tails between two plume stages are assessed in 14 cases and compared to calculated values. Distinctive parameters for the plume front and tail support better understanding of field situations. A user-ready spreadsheet is provided.