Simulating bioremediation of uranium-contaminated aquifers; uncertainty assessment of model parameters

Abstract

Bioremediation of trace metals and radionuclides in groundwater may require the manipulation of redox conditions via the injection of a carbon source. For example, after nitrate has been reduced, soluble U(VI) can be reduced simultaneously with other electron acceptors such as Fe(III) or sulfate to U(IV), which may precipitate as a solid (uraninite).

To simulate the numerous biogeochemical processes that will occur during the bioremediation of trace-metal-contaminated aquifers, a time-dependent one-dimensional reactive transport model has been developed. The model consists of a set of coupled mass balance equations, accounting for advection, hydrodynamic dispersion, and a kinetic formulation of the biological or chemical transformations affecting an organic substrate, electron acceptors, corresponding reduced species, and trace metal contaminants of interest, uranium in this study. This set of equations is solved numerically, using a finite difference approximation. The redox conditions of the domain are characterized by estimating the pE, based on the concentration of the dominant terminal electron acceptor and its corresponding reduced species. This pE and the concentrations of relevant species are then used by a modified version of MINTEQA2, which calculates the speciation/sorption and precipitation/dissolution of the species of interest under equilibrium conditions. Kinetics of precipitation/dissolution processes are described as being proportional to the difference between the actual and calculated equilibrium concentration. A global uncertainty assessment, determined by Random Sampling High Dimensional Model Representation (RS-HDMR), was performed to attain a phenomenological understanding of the origins of output variability and to suggest input parameter refinements as well as to provide guidance for field experiments to improve the quality of the model predictions. By decomposing the model output variance into its different input contributions, RS-HDMR can identify the model inputs with the most influence on various model outputs, as well as their behavior pattern on the model output. Simulations are performed to illustrate the effect of biostimulation on the fate of uranium in a saturated aquifer, and to identify the key processes that need to be characterized with the highest accuracy prior to designing a uranium bioremediation scheme.

Introduction

The fate of trace metals and radionuclides in the subsurface is affected by many biogeochemical interactions with a variety of organic and inorganic chemical species and minerals under different redox conditions. These interactions can affect the mobility of contaminants in the subsurface by altering their physical and chemical characteristics such as their speciation, sorption, and solubility. Due to their potential toxicity, the fate and transport of trace metals and radionuclides in subsurface systems are of great concern. Many researchers have focused on gaining a better understanding of the microbiological and/or geochemical reactions that affect the fate and transport of trace metals and radionuclides in the subsurface. In situ stimulation of microbially mediated redox reactions has drawn significant attention as a potentially safe and cost-effective strategy for remediating trace-metal and radionuclide contaminated aquifers.

Mathematical models have been developed to simulate the biodegradation of organic substrates in groundwater systems. In these models, the biodegradation of organic substrates and the corresponding utilization of electron acceptors, as well as bacterial dynamics such as growth, decay, and transport, have been incorporated into the advective–dispersive transport equations. Different chemical species have usually been simulated as either single or multiple limiting components Borden and Bedient, 1986, Molz et al., 1986, Widdowson et al., 1988. In recent years, models have been developed that included biologically mediated redox dynamics in terms of the sequential utilization of different electron acceptors during the degradation of an organic substrate Rabouille and Gaillard, 1991, Sweerts et al., 1991, Matsunaga et al., 1993, McNab and Narasimhan, 1994, Van Cappellen and Wang, 1995, Dhakar and Burdige, 1996, Park and Jaffé, 1996. Some of these models have been extended to include abiotic redox reactions and geochemical processes such as speciation and precipitation/dissolution Van Cappellen and Wang, 1996, Hunter et al., 1998, Smith and Jaffé, 1998.

Based on these biological and geochemical processes, trace metals dynamics in groundwater have been described by several authors (e.g., Yeh and Tripathi, 1991, Engesgaard and Kipp, 1992, Lensing et al., 1994). Although, in many of these studies, it was assumed that the metal is at equilibrium with the surrounding geochemistry, this is clearly not always the case. Nonequilibrium conditions have therefore been implemented in formulating the cycling of iron and manganese (i.e., McNab and Narasimhan, 1994, Hunter et al., 1998), and in the formulation of the dynamics of trace metals, where it has been assumed that the metals are driven kinetically towards chemical equilibrium (Smith and Jaffé, 1998).

Aqueous phase homogeneous reactions such as speciation, complexation, or acid–base reactions are usually described as instantaneous reactions. This is justified because their effect on the concentration of a chemical species is very fast compared to the change in concentration due to groundwater transport. These reactions are therefore represented in many models by thermodynamic equilibrium conditions Grove and Wood, 1979, Miller and Benson, 1983, Narasimhan et al., 1986, Kirkner and Reeves, 1988, Reeves and Kirkner, 1998, Engesgaard and Kipp, 1992. In contrast, biologically mediated reactions and heterogeneous reactions such as precipitation/dissolution are relatively slow and have been incorporated by several authors into transport models using kinetic relationships Steefel and Lasaga, 1994, Tebes-Stevens et al., 1998, VanBriesen and Rittmann, 1999.

In all areas of numerical modeling, the issue of predictive quality, in view of model input uncertainty, has been a topic of prime concern. Systematic uncertainty assessments can identify the inputs with the most influence and their behavior patterns on the model outputs. The resultant information can provide guidance for new experiments or parameter estimations to reduce the output uncertainty. A general set of quantitative model assessment and analysis tools, termed High Dimensional Model Representation (HDMR), has been introduced recently for improving the efficiency of deducing high-dimensional input–output system behavior Rabitz et al., 1999, Alis and Rabitz, 1999, Alis and Rabitz, 2001, Shorter et al., 1999, Shorter and Rabitz, 2000. HDMR is an efficient approach for global uncertainty assessment of a model. With a modest sampling effort, HDMR can provide reliable information by decomposing the model output variance into its different input contributions such as the independent input variable action, the pair correlated action of inputs, etc. This information is most valuable for attaining a physical understanding of the origins of output uncertainty as well as suggestions for additional laboratory/field studies or parameter refinements to best improve the quality of model predictions.

The overall goal of a uranium bioremediation scheme is the stabilization of the uranium as U(IV)-minerals. The goal of this work was to identify the key parameter interactions and uncertainties in trace metal bioremediation models, specifically applied to the immobilization of uranium, in order to provide guidance for further model development and to link model development to ongoing fieldwork. To accomplish this goal, a “proto model” to simulate trace metal bioremediation was developed and applied to study the biological immobilization of uranium in groundwater. The HDMR method was then applied to this model to assess the relationship between the different model input parameters and model outputs.

A model designed to simulate trace-metal/radionuclide bioremediation in aquifers can include different levels of detail, in terms of the relevant geochemistry and bacterial dynamics, at varying scales. It was decided here to develop a model where the biomass is incorporated into the overall kinetic coefficients, rather than simulating bacterial growth, decay, and transport separately. The rationale for this decision was that: (1) successful field techniques for the in situ measurement of rate coefficients, such as the Push–Pull Test (Schroth et al., 1998), yield bulk reaction rate coefficients that have the biomass incorporated; (2) during biostimulation, when a substantial amount of an easily degradable growth substrate is injected into the subsurface, one is likely to reach some maximum biomass level (Jaffé and Rabitz, 1988); and (3) by not including complex bacterial dynamics, this already complex “proto model” does not require an additionally large number of parameters that are difficult to characterize, specially for field conditions.

The model consists of a set of coupled, time-dependent one-dimensional mass balance equations, which include physical processes such as advection, diffusion, and dispersion, and biogeochemical processes such as biotic and abiotic redox reactions, speciation, adsorption, and precipitation/dissolution of minerals, all of which can affect either the organic substrate, the terminal electron acceptors (oxygen, nitrate, Mn(IV), Fe(III), and sulfate), the corresponding reduced species, and the trace metals/radionuclides of interest. The system of mass balance equations is solved numerically using a second-order-accurate finite difference scheme through a series of iterative routines. At each node and time step, the concentration profiles of chemical species are transferred to an equilibrium speciation model, which calculates the speciation and solubility of the species of interest.

The pH, along with other environmental variables such as temperature, is a key parameter that affects the fate of trace metals and other chemical constituents. The pH of a groundwater system may vary spatially and with time. During biostimulation, the different biotic and abiotic reactions may further affect the pH of the groundwater. For the purpose of this work, however, pH will not be calculated explicitly in the model but will be considered as a model input. Dissolved-organic carbon-enhanced transport was not accounted for in the simulations shown here, but can be easily included by allowing for a partitioning of the relevant species between the dissolved organic carbon and the aqueous phase.