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.     

Effects of sorption on transverse mixing in transient flows

Transverse mixing has been identified as a potentially limiting factor for natural attenuation of plumes originating from continuously emitting sources. Under steady-state flow conditions, dispersion is the only process leading to lateral mixing. This process is very slow and cannot explain the lateral spread of plumes observed in the field. When the flow direction fluctuates with time, transverse dispersion is slightly enhanced, but not very pronounced. Under these flow conditions, however, sorption can contribute to mixing into the mean transverse direction. If the reacting compounds differ in their strength of sorption, chromatographic mixing and separation alternate in time-periodic flows. For instantaneous sorption, the plumes may overlap within a stripe of fixed width. In contrast to sorption in local equilibrium, kinetic sorption contributes to mixing also for compounds with identical sorption strength. I derive an analytical expression for the equivalent transverse dispersion coefficient of a kinetically sorbing compound in a spatially uniform flow field undergoing sinusoidal fluctuations in time. This expression may be used for reactive transport calculations in an equivalent domain with constant flow. The effects are the strongest for compounds with a dimensionless partitioning coefficient of about unity, slow sorption kinetics, and slowly fluctuating velocities. For realistic parameters, kinetic sorption contributes to transverse mixing in the same range as heterogeneity.     

Transport of volatile compounds in porous media in the presence of a trapped gas phase

The presence of an immobile gaseous phase in an otherwise-saturated porous medium affects the transport of volatile compounds. The linear theory of partitioning tracers suggests that a volatile tracer introduced into such a system should be retarded with a constant retardation factor. Using high concentrations, however, the saturation of the gaseous phase will change as an effect of the tracer test itself. Competitive gas transfer among all volatile compounds and the change of saturation may lead to tracer concentrations that are temporarily higher than those injected. We analyze the system in the framework of the coherence theory by Helfferich [Soc. Pet. Eng. J. 21 (1) (1981) 51]. The governing equations are formulated as functions of total concentration, i.e., the mass of solutes in all phases per pore volume. Neglecting dispersion and mass-transfer kinetics, we derive the characteristic form of the resulting system of hyperbolic equations. In a system with N volatile compounds, a variation of the concentrations splits up into N waves, each traveling with its own characteristic velocity. If the presence of a gaseous phase is sustained, one wave will be a standing one. We perform numerical model calculations for tracers with various Henry's law coefficients and show that the results agree with the semi-analytical solution obtained by coherence theory.     

Concentration statistics for mixing-controlled reactive transport in random heterogeneous media

Uncertainty in the distribution of hydraulic parameters leads to uncertainty in flow and reactive transport. Traditional stochastic analysis of solute transport in heterogeneous media has focused on the ensemble mean of conservative-tracer concentration. Studies in the past years have shown that the mean concentration often is associated with a high variance. Because the range of possible concentration values is bounded, a high variance implies high probability weights on the extreme values. In certain cases of mixing-controlled reactive transport, concentrations of conservative tracers, denoted mixing ratios, can be mapped to those of constituents that react with each other upon mixing. This facilitates mapping entire statistical distributions from mixing ratios to reactive-constituent concentrations. In perturbative approximations, only the mean and variance of the mixing-ratio distribution are used. We demonstrate that the second-order perturbative approximation leads to erroneous or even physically impossible estimates of mean reactive-constituent concentrations when the variance of the mixing ratio is high and the relationship between the mixing ratio and the reactive-constituent concentrations strongly deviates from a quadratic function. The latter might be the case in biokinetic reactions or in equilibrium reactions with small equilibrium constant in comparison to the range of reactive-constituent concentrations. When only the mean and variance of the mixing ratio is known, we recommend assuming a distribution that meets the known bounds of the mixing ratio, such as the beta distribution, and mapping the assumed distribution of the mixing ratio to the distributions of the reactive constituents.     

Experiments on vertical transverse mixing in a large-scale heterogeneous model aquifer

Vertical transverse mixing is known to be a controlling factor in natural attenuation of extended biodegradable plumes originating from continuously emitting sources. We perform conservative and reactive tracer tests in a quasi two-dimensional 14 m long sand box in order to quantify vertical mixing in heterogeneous media. The filling mimics natural sediments including a distribution of different hydro-facies, made of different sand mixtures, and micro-structures within the sand lenses. We quantify the concentration distribution of the conservative tracer by the analysis of digital images taken at steady state during the tracer-dye experiment. Heterogeneity causes plume meandering, leading to distorted concentration profiles. Without knowledge about the velocity distribution, it is not possible to determine meaningful vertical dispersion coefficients from the concentration profiles. Using the stream-line pattern resulting from an inverse model of previous experiments in the sand box, we can correct for the plume meandering. The resulting vertical dispersion coefficient is approximately approximately 4 x 10(-)(9) m(2)/s. We observe no distinct increase in the vertical dispersion coefficient with increasing travel distance, indicating that heterogeneity has hardly any impact on vertical transverse mixing. In the reactive tracer test, we continuously inject an alkaline solution over a certain height into the domain that is occupied otherwise by an acidic solution. The outline of the alkaline plume is visualized by adding a pH indicator into both solutions. From the height and length of the reactive plume, we estimate a transverse dispersion coefficient of approximately 3 x 10(-)(9) m(2)/s. Overall, the vertical transverse dispersion coefficients are less than an order of magnitude larger than pore diffusion coefficients and hardly increase due to heterogeneity. Thus, we conclude for the assessment of natural attenuation that reactive plumes might become very large if they are controlled by vertical dispersive mixing.     

Stochastic evaluation of mass discharge from pointlike concentration measurements

The contaminant mass discharge crossing a control plane is an important metric in the assessment of natural attenuation at contaminated sites. For risk-assessment purposes, the mass discharge must be estimated together with a level of uncertainty. We present a conditional Monte Carlo approach that allows estimating the statistical distribution of mass discharge. The approach is based on conditioning multiple realizations of the hydraulic conductivity field on all data available. We jointly determine a first-order decay coefficient in each realization, leading to conditional statistical distributions of all estimated parameters and the total mass discharge. The resulting statistical distribution of contaminant mass discharges can be used in the assessment of risks at the contaminated site. The method is applied to data of hypothetical test cases, which gives the opportunity to compare estimation results to the true field. As concentration data, we account for pointlike measurements obtained in multi-level sampling wells. The obtained empirical distribution of mass discharge crossing the multi-level sampling fence could be well fitted by a log-normal distribution.     

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

We analyze reactive transport during in-situ bioremediation in a nonuniform flow field, involving multiple extraction and injection wells, by the method of transfer functions. Gamma distributions are used as parametric models of the transfer functions. Apparent parameters of classical transport models may be estimated from those of the gamma distributions by matching temporal moments. We demonstrate the method by application to measured data taken at a field experiment on bioremediation conducted in a multiple-well system in Oak Ridge, TN. Breakthrough curves (BTCs) of a conservative tracer (bromide) and a reactive compound (ethanol) are measured at multi-level sampling (MLS) wells and in extraction wells. The BTCs of both compounds are jointly analyzed to estimate the first-order degradation rate of ethanol. To quantify the tracer loss, we compare the approaches of using a scaling factor and a first-order decay term. Results show that by including a scaling factor both gamma distributions and inverse-Gaussian distributions (transfer functions according to the advection-dispersion equation) are suitable to approximate the transfer functions and estimate the reactive rate coefficients for both MLS and extraction wells. However, using a first-order decay term for tracer loss fails to describe the BTCs at the extraction well, which is affected by the nonuniform distribution of travel paths.     

Choice of dispersion coefficients in reactive transport calculations on smoothed fields

Local dispersion dominates the mixing of compounds that are introduced separately into the subsurface and do not partition into any other than the aqueous phase. Thus, reactions between these compounds are controlled by dispersive mixing if they are not limited by kinetics. I quantify longitudinal dispersive mixing by the longitudinal effective dispersion coefficient of a conservative tracer introduced by a point-like injection [Water Resour. Res. 36 (12) (2000) 3591-3604]. In the upscaling of mixing-controlled reactive transport, I apply the mean velocity and the effective dispersion coefficient to the macroscopic transport calculations, whereas the reactive parameters on the macro-scale are identical to those on the local scale. The applicability of the approach is demonstrated for the transport of compounds undergoing a second-order irreversible bimolecular reaction. Ten realizations of a two-dimensional heterogeneous log-conductivity field are considered. Using the effective dispersion parameters, the overall mass balance is met in the ensemble average, whereas solute spreading is underestimated. I assess the lack of spreading by the difference between the expected macrodispersion and effective dispersion coefficients. I extend the approach to simulations on log-conductivity fields obtained by kriging of regularly spaced conductivity measurements. These fields contain the large-scale features of the true fields but do not resolve the small-scale variability. For the calculations on the kriged fields, the corresponding conditional covariance is substituted into the analytical expressions of effective dispersion, yielding a correction effective dispersion coefficient. The comparison between simulations on the fully resolved fields and on the kriged fields indicates that the approach is valid for wide plumes meeting the ergodicity condition. The high variability of mixing on small scales unresolved by kriging, however, leads to severe uncertainty when mixing-controlled reactions are predicted for narrow plumes.     

A high-resolution non-invasive approach to quantify oxygen transport across the capillary fringe and within the underlying groundwater

Oxygen transport across the capillary fringe is relevant for many biogeochemical processes. We present a non-invasive technique, based on optode technology, to measure high-resolution concentration profiles of oxygen across the unsaturated/saturated interface. By conducting a series of quasi two-dimensional flow-through laboratory experiments, we show that vertical hydrodynamic dispersion in the water-saturated part of the capillary fringe is the process limiting the mass transfer of oxygen. A number of experimental conditions were tested in order to investigate the influence of grain size and horizontal flow velocity on transverse vertical dispersion in the capillary fringe. In the same setup, analogous experiments were simultaneously carried out in the fully water-saturated zone, therefore allowing a direct comparison with oxygen transfer across the capillary fringe. The outcomes of the experiments under various conditions show that oxygen transport in the two zones of interest (i.e., the unsaturated/saturated interface and the saturated zone) is characterized by very similar transverse dispersion coefficients. An influence of the capillary fringe morphology on oxygen transport has not been observed. These results may be explained by the narrow grain size distribution used in the experiments, leading to a steep decline in water saturation at the unsaturated/saturated interface and to the absence of trapped gas in this transition zone. We also modeled flow (applying the van Genuchten and the Brooks-Corey relationships) and two-dimensional transport across the capillary fringe, obtaining simulated profiles of equivalent aqueous oxygen concentration that were in good agreement with the observations.