T.P. Clement

Theoretical analysis of the worthiness of Henry and Elder problems as benchmarks of density-dependent groundwater flow models

Computer models must be tested to ensure that the mathematical statements and solution schemes accurately represent the physical processes of interest. Because the availability of benchmark problems for testing density-dependent groundwater models is limited, one should be careful in using these problems appropriately. Details of a Galerkin finite-element model for the simulation of density-dependent, variably saturated flow processes are presented here. The model is tested using the Henry salt-water intrusion problem and Elder salt convection problem. The quality of these benchmark problems is then evaluated by solving the problems in the standard density-coupled mode and in a new density-uncoupled mode. The differences between the solutions indicate that the Henry salt-water intrusion problem has limited usefulness in benchmarking density-dependent flow models because the internal flow dynamics are largely determined by the boundary forcing. Alternatively, the Elder salt-convection problem is more suited to the model testing process because the flow patterns are completely determined by the internal balance of pressure and gravity forces.

Development of analytical solutions for multispecies transport with serial and parallel reactions

A direct method for transforming multiple solute transport equations, coupled by linear, series, and/or parallel first-order, irreversible reactions, into a series of simple transport equations having known solutions is developed. Using this method, previously published analytical solutions to single-species transport problems, in which the transported species reacts with first-order kinetics, can be used to derive analytical solutions to multispecies transport systems with parallel, serial, and combined reaction networks. This new method overcomes many of the limitations that were implicit in previously published methods. In particular, the number of species that can be described is unlimited, and the reaction stoichiometry does not have to be unimolar. To illustrate the method, an analytical solution is derived for a five-species serial-parallel reactive transport system. The analytical solution obtained for this problem is compared with a numerical solution obtained with a previously developed code. This analytical method is applicable to the verification of new numerical codes.

Analytical solutions for multiple species reactive transport in multiple dimensions

Many numerical computer codes used to simulate multi-species reactive transport and biodegradation have been developed in recent years. Such numerical codes must be validated by comparison of the numerical solutions with an analytical solution. In this paper, a method for deriving analytical solutions of the partial differential equations describing multiple species multi-dimensional transport with first-order sequential reactions is presented. Although others have developed specific solutions of multi-species transport equations, here a more general analytical approach, capable of describing any number of reactive species in multiple dimensions is derived. A substitution method is used to transform the multi-species reactive transport problem to one that can be solved using previously published single-species solutions for various initial and boundary conditions. One- and three-dimensional examples are presented to illustrate the steps involved in extending single-species solutions to a four-species system with sequential first-order reactions.

Microbial growth and transport in porous media under denitrification conditions : experiments and simulations

Abstract Soil column experiments were conducted to study bacterial growth and transport in porous media under denitrifying conditions. The study used a denitrifying microbial consortium isolated from aquifer sediments sampled at the U.S. Department of Energys Hanford site. One-dimensional, packed-column transport studies were conducted under two substrate loading conditions. A detailed numerical model was developed to predict the measured effluent cell and substrate concentration profiles. First-order attachment and detachment models described the interphase exchange processes between suspended and attached biomass. Insignificantly different detachment coefficient values of 0.32 and 0.43 day−1, respectively, were estimated for the high and low nitrate loading conditions (48 and 5 mg l−1 NO3, respectively). Comparison of these values with those calculated from published data for aerobically growing organisms shows that the denitrifying consortium had lower detachment rate coefficients. This suggests that, similar to detachment rates in reactor-grown biofilms, detachment in porous media may increase with microbial growth rate. However, available literature data are not sufficient to confirm a specific analytical model for predicting this growth dependence.

Modeling Bacterial Transport and Accumulation Processes in Saturated Porous Media: A Review

During the past few decades, leaking underground fuel storage tanks have created soil and groundwater contamination problem throughout the United States. In addition, defense nuclear production by the U.S. Department of Energy (DOE), its predecessor agencies, and its contractors has generated large volumes of hazardous and radioactive wastes. Discharge of these wastes to soils has resulted in extensive contamination around DOE sites. Harnessing the potential of in situ microorganisms to degrade these chemical contaminants in the subsurface has been widely studied in the past two decades. Soil microbiologists have been investigating the role of shallow, root-zone microbes in recycling nutrients since the early twentieth century. However, only during the early 1970s did it become evident that subsurface microbes have a potential to degrade contaminants in much deeper subsurface zones. Developments in subsurface aseptic sediment sampling methods played a major role in providing conclusive evidences for the presence of microbes in these zones (Dunlap et al., 1977). Later experimental studies conducted under controlled laboratory conditions have also showed that these organisms can mineralize many man-made chemicals (Vogel and Grbic-Galic, 1986). In the early 1980s, researchers started to develop methods to harness these natural degradation potential of microbes to cleanup subsurface contaminants. Currently, two types of bioremediation approaches are being considered for field-scale cleanup: intrinsic bioremediation and active bioremediation. The intrinsic remedial approach is a plume management strategy that relies on the inherent degradative capacity of native subsurface microbes (Chapelle et al., 1994; Semprini et al., 1995; Wiedemeier et al., 1995; Rice et al., 1995). In contrast, active bioremediation is an accelerated clean-up strategy that uses various nutrient-delivery strategies to enhance growth and degradative capacity of native microbes (Semprini et al., 1991; Truex, 1995). As a part of the active bioremediation strategy, a few researchers have also explored the possibility of introducing non-indigenous cultured microbial strains into the subsurface to remove specific Contaminants (Mayotte et al., 1996; Duba et al., 1996).

Modeling Microbial Transport and Biodegradation in a Dual-porosity System

A mathematical model describing microbial transport and growth in a heterogeneous aquifer domain, composed of overlapping subdomains of high-permeability and low-permeability materials, is developed. Each material is conceptually visualized as a continuum which occupies the entire considered spatial aquifer domain. Based on the assumption that advection in the low-permeability domain is negligible, the mathematical model is solved by using a publically available reactive transport code. The importance of modeling microbial transport and growth in such a dual-porosity system is demonstrated through a hypothetical case study.