Multicomponent mass transport with homogeneous and heterogeneous chemical reactions: Effect of the chemistry on the choice of numerical algorithm: 1. Theory

Kirkner, David J.; Reeves, Howard W.

doi:10.1029/wr024i010p01719

Cited by 100 publications

(60 citation statements)

References 12 publications

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“…If we assume that the various aqueous species are in chemical equilibrium, it is possible to reduce the number of independent concentrations, that is, the number that actually need to be solved for. Mathematically, this means that in a system containing N tot aqueous species, the number of independent chemical components in the system N c is reduced from the total number of species by the N x linearly independent chemical reactions between them (for further discussion, see Aris (1965); Bowen (1968);Hooyman (1961); Kirkner and Reeves (1988);Lichtner (1985); Reed (1982); Van Zeggeren and Storey (1970). This leads to a natural partitioning of the system into N c primary or basis species, designated here as C j , and the N x secondary species, referred to as C i (Kirkner and Reeves, 1988;Lichtner, 1985;Reed, 1982).…”

Section: Process Model Equationsmentioning

confidence: 99%

“…Equation (5.2) implies that the rate of production of a primary component j due to homogeneous reactions, R aq j , can be written in terms of the sum of the total rates of production of the secondary species (Kirkner and Reeves, 1988)…”

Section: Process Model Equationsmentioning

confidence: 99%

“…then the governing differential equations can be written in terms of the total concentrations in the case where only aqueous (and therefore mobile) species are involved (Kirkner and Reeves, 1988)…”

Section: Process Model Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Mathematical Formulation Requirements and Specifications for the Process Models

Steefel¹,

Moulton²,

Pau³

et al. 2010

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Section: Process Model Equationsmentioning

confidence: 99%

Section: Process Model Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Mathematical Formulation Requirements and Specifications for the Process Models

Steefel¹,

Moulton²,

Pau³

et al. 2010

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“…Many transport codes have been written, as is evident from reviews (e.g. Kirkner and Reeves, 1988;Reeves and Kirkner, 1988;Kinzelbach et al, 1989). Numerical difficulties and long computation times have been addressed in various ways, depending on the choice of the geochemical problem.…”

Section: Introductionmentioning

confidence: 99%

Advective Transport of Interacting Solutes: The Chromatographic Model

Gruber¹

1996

Sediments and Toxic Substances

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Species on porous media surfaces exposed to aqueous solutions can still not yet be determined unambiguously. The influence of these ambiguities on contaminant transport needs to be understood. Here methods of multicomponent chromatography are presented that allow to visualize the effects of the ambiguities. The Riemann problem is solved to a large extent based on the mathematics of non-linear hyperbolic differential equations, before the problem is handed over to the computer. Since thereby the computational efforts are kept compatible with the corresponding limitations in a chemical laboratory, this method has been used for decades in chemical engineering. The method is illustrated for various multicomponent isotherms, e.g. the one underlying surface complexation models as implemented in the MINEQL family of programs.

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“…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, 1988; 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].…”

mentioning

confidence: 99%

Trace Metal Bioremediation: Assessment of Model Components from Laboratory and Field Studies to Identify Critical Variables

Jaffé¹,

Rabitz²

2003

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The objective of this project was to gain an insight into the modeling support needed for the understanding, design, and operation of trace metal/radionuclide bioremediation. To achieve this objective, a workshop was convened to discuss the elements such a model should contain. A "protomodel" was developed, based on the recommendations of the workshop, and was used to perform sensitivity analysis as well as some preliminary simulations in support for bioremediation test experiments at UMTRA sites.To simulate the numerous biogeochemical processes that will occur during the bioremediation of uranium contaminated aquifers, a time-dependent one-dimensional reactive transport model has been developed. The model consists of a set of coupled, steady state mass balance equations, accounting for advection, diffusion, dispersion, and a kinetic formulation of the transformations affecting an organic substrate, electron acceptors, corresponding reduced species, and uranium. This set of equations is solved numerically, using a finite element scheme. The redox conditions of the domain are characterized by estimating the pE, based on the concentrations of the dominant terminal electron acceptor and its corresponding reduced specie. This pE and the concentrations of relevant species are passed to a modified version of MINTEQA2, which calculates the speciation and solubilities of the species of interest. Kinetics of abiotic reactions are described as being proportional to the difference between the actual and 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. Results indicated that for the usually high nitrate contents found ate many DOE sites, overall bioremediation of trace metals was highly sensitive to the formulation of the denitrification process.Simulations were performed to illustrate the effect of biostimulation on the transport and precipitation of uranium in the subsurface, at conditions equivalent to UMTRA sites. These simulations predicted that uranium would precipitate in bands that are located relatively close to the acetate injection well. The simulations also showed the importance of properly determining U(IV) oxidative dissolution rates, in order to assess the stability of precipitates once oxygenated water reenters the aquifer after bioremediation is discontinued.The objective of this project was to provide guidance to NABIR's Systems Integration Element, on the development of models to simulate the bioremediation of trace metals and radionuclides. Such models necessarily need to integrate hydrological, geochemical, and microbiological processes. In order to gain a better understanding of the key processes that such a model should contain, it was deemed desirable to convene a worksh...

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Multicomponent mass transport with homogeneous and heterogeneous chemical reactions: Effect of the chemistry on the choice of numerical algorithm: 1. Theory

Cited by 100 publications

References 12 publications

Mathematical Formulation Requirements and Specifications for the Process Models

Mathematical Formulation Requirements and Specifications for the Process Models

Advective Transport of Interacting Solutes: The Chromatographic Model

Trace Metal Bioremediation: Assessment of Model Components from Laboratory and Field Studies to Identify Critical Variables

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