A parametric transfer function methodology for analyzing reactive transport in nonuniform flow

Temporal Variability in the Response of a Linear Time-Invariant Catchment System to a Non-Stationary Inflow Concentration Field

Predicting the effects of changes in dissolved input concentration on the variability of discharge concentration at the outlet of the catchment is essential to improve our ability to address the problem of surface water quality. The goal of this study is therefore dedicated to the stochastic quantification of temporal variability of concentration fields in outflow from a catchment system that exhibits linearity and time invariance. A convolution integral is used to determine the output of a linear time-invariant system from knowledge of the input and the transfer function. This work considers that the nonstationary input concentration time series of an inert solute to the catchment system can be characterized completely by the Langevin equation. The closed-form expressions for the variances of inflow and outflow concentrations at the catchment scale are derived using the Fourier–Stieltjes representation approach. The variance is viewed as an index of temporal variability. The closed-form expressions therefore allow to evaluate the impacts of the controlling parameters on the temporal variability of outflow concentration.

Stepwise superposition approach for the analytical solutions of multi-dimensional contaminant transport in finite- and semi-infinite aquifers

Analytical solutions of contaminant transport in multi-dimensional media are significant for theoretical and practical purposes. However, due to the problems for which the solutions are sought which are complex in most of the cases, most available analytical solutions in multi-dimensional media are not given in their closed forms. Integrals are often included in the solution expressions, which may limit the practitioners to use the solutions. In addition, available multi-dimensional solutions for the third-type sources in bounded media are fairly limited. In this paper, a stepwise superposition approach for obtaining approximate multi-dimensional transport solutions is developed. The approach is based on the condition that the one-dimensional solution along the flow direction is known. The solutions are expressed in their closed forms without integrals. The transport media to the solutions are flexible and can be finite, semi-infinite, or infinite in the transverse directions. The solutions subject to the first- and third-type boundary conditions at the inlet with a distributed source over the domain are obtained. The integrals in some known solutions can also be evaluated by the approach if they can be derived to include known longitudinal integrals with respect to time. The accuracy and efficiency of the solutions proposed in this paper are verified through test problems and calculation examples.

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.

Estimating kinetic mass transfer by resting-period measurements in flow-interruption tracer tests

Flow-interruption tracer test is an effective approach to identify kinetic mass transfer processes for solute transport in subsurface media. By switching well pumping and resting, one may alter the dominant transport mechanism and generate special concentration patterns for identifying kinetic mass transfer processes. In the present research, we conducted three-phase (i.e., pumping, resting, and pumping) field-scale flow-interruption tracer tests using a conservative tracer bromide in a multiple-well system installed at the US Department of Energy Site, Oak Ridge, TN. A novel modeling approach based on the resting-period measurements was developed to estimate the mass transfer parameters. This approach completely relied on the measured breakthrough curves without requiring detailed aquifer characterization and solving transport equations in nonuniform, transient flow fields. Additional measurements, including hydraulic heads and tracer concentrations in large pumping wells, were taken to justify the assumption that mass transfer processes dominated concentration change during resting periods. The developed approach can be conveniently applied to any linear mass transfer model. Both first-order and multirate mass transfer models were applied to analyze the breakthrough curves at various monitoring wells. The multirate mass transfer model was capable of jointly fitting breakthrough curve behavior, showing the effectiveness and flexibility for incorporating aquifer heterogeneity and scale effects in upscaling effective mass transfer models.

Diversity and distribution of anaeromyxobacter strains in a uranium-contaminated subsurface environment with a nonuniform groundwater flow

Versaphilic Anaeromyxobacter dehalogenans strains implicated in hexavalent uranium reduction and immobilization are present in the fractured saprolite subsurface environment at the U.S. Department of Energy Integrated Field-Scale Subsurface Research Challenge (IFC) site near Oak Ridge, TN. To provide insight into the in situ distribution of Anaeromyxobacter strains in this system with a nonuniform groundwater flow, 16S rRNA gene-targeted primers and linear hybridization (TaqMan) probes were designed for Oak Ridge IFC Anaeromyxobacter isolates FRC-D1 and FRC-W, along with an Anaeromyxobacter genus-targeted probe and primer set. Multiplex quantitative real-time PCR (mqPCR) was applied to samples collected from Oak Ridge IFC site areas 1 and 3, which are not connected by the primary groundwater flow paths; however, transport between them through cross-plane fractures is hypothesized. Strain FRC-W accounted for more than 10% of the total quantifiable Anaeromyxobacter community in area 1 soils, while strain FRC-D1 was not detected. In FeOOH-amended enrichment cultures derived from area 1 site materials, strain FRC-D1 accounted for 30 to 90% of the total Anaeromyxobacter community, demonstrating that this strain was present in situ in area 1. The area 3 total Anaeromyxobacter abundance exceeded that of area 1 by 3 to 5 orders of magnitude, but neither strain FRC-W- nor FRC-D1-like sequences were quantifiable in any of the 33 area 3 groundwater or sediment samples tested. The Anaeromyxobacter community in area 3 increased from <10(5) cells/g sediment outside the ethanol biostimulation treatment zone to 10(8) cells/g sediment near the injection well, and 16S rRNA gene clone library analysis revealed that representatives of a novel phylogenetic cluster dominated the area 3 Anaeromyxobacter community inside the treatment loop. The combined applications of genus- and strain-level mqPCR approaches along with clone libraries provided novel information on patterns of microbial variability within a bacterial group relevant to uranium bioremediation.

Estimating first-order reaction rate coefficient for transport with nonequilibrium linear mass transfer in heterogeneous media

A travel-time based approach is developed for estimating first-order reaction rate coefficients for transport with nonequilibrium linear mass transfer in heterogeneous media. Tracer transport in the mobile domain is characterized by a travel-time distribution, and mass transfer rates are described by a convolution product of concentrations in the mobile domain and a memory function rather than predefining the mass transfer model. A constant first-order reaction is assumed to occur only in the mobile domain. Analytical solutions in Laplace domain can be derived for both conservative and reactive breakthrough curves (BTCs). Temporal-moment analyses are presented by using the first and second moments of conservative and reactive BTCs and the mass consumption of the reactant for an inverse Gaussian travel-time distribution. In terms of moment matching, there is no need for one to specify the mass transfer model. With the same capacity ratio and the mean retention time, all mass transfer models will lead to the same moment-derived reaction rate coefficients. In addition, the consideration of mass transfer generally yields larger estimations of the reaction rate coefficient than models ignoring mass transfer. Furthermore, the capacity ratio and the mean retention time have opposite influences on the estimation of the reaction rate coefficient: the first-order reaction rate coefficient is positively linearly proportional to the capacity ratio, but negatively linearly proportional to the mean retention time.

Modeling in-situ uranium(VI) bioreduction by sulfate-reducing bacteria

We present a travel-time based reactive transport model to simulate an in-situ bioremediation experiment for demonstrating enhanced bioreduction of uranium(VI). The model considers aquatic equilibrium chemistry of uranium and other groundwater constituents, uranium sorption and precipitation, and the microbial reduction of nitrate, sulfate and U(VI). Kinetic sorption/desorption of U(VI) is characterized by mass transfer between stagnant micro-pores and mobile flow zones. The model describes the succession of terminal electron accepting processes and the growth and decay of sulfate-reducing bacteria, concurrent with the enzymatic reduction of aqueous U(VI) species. The effective U(VI) reduction rate and sorption site distributions are determined by fitting the model simulation to an in-situ experiment at Oak Ridge, TN. Results show that (1) the presence of nitrate inhibits U(VI) reduction at the site; (2) the fitted effective rate of in-situ U(VI) reduction is much smaller than the values reported for laboratory experiments; (3) U(VI) sorption/desorption, which affects U(VI) bioavailability at the site, is strongly controlled by kinetics; (4) both pH and bicarbonate concentration significantly influence the sorption/desorption of U(VI), which therefore cannot be characterized by empirical isotherms; and (5) calcium-uranyl-carbonate complexes significantly influence the model performance of U(VI) reduction.

Analyzing bank filtration by deconvoluting time series of electric conductivity

Knowing the travel-time distributions from infiltrating rivers to pumping wells is important in the management of alluvial aquifers. Commonly, travel-time distributions are determined by releasing a tracer pulse into the river and measuring the breakthrough curve in the wells. As an alternative, one may measure signals of a time-varying natural tracer in the river and in adjacent wells and infer the travel-time distributions by deconvolution. Traditionally this is done by fitting a parametric function such as the solution of the one-dimensional advection-dispersion equation to the data. By choosing a certain parameterization, it is impossible to determine features of the travel-time distribution that do not follow the general shape of the parameterization, i.e., multiple peaks. We present a method to determine travel-time distributions by nonparametric deconvolution of electric-conductivity time series. Smoothness of the inferred transfer function is achieved by a geostatistical approach, in which the transfer function is assumed as a second-order intrinsic random time variable. Nonnegativity is enforced by the method of Lagrange multipliers. We present an approach to directly compute the best nonnegative estimate and to generate sets of plausible solutions. We show how the smoothness of the transfer function can be estimated from the data. The approach is applied to electric-conductivity measurements taken at River Thur, Switzerland, and five wells in the adjacent aquifer, but the method can also be applied to other time-varying natural tracers such as temperature. At our field site, electric-conductivity fluctuations appear to be an excellent natural tracer.