An Analysis of Complex Reaction Networks in Groundwater Modeling

Chilakapati, Ashok; Ginn, Timothy; Szecsody, James

doi:10.1029/98WR01041

Title: An Analysis of Complex Reaction Networks in Groundwater Modeling

Abstract

The complex chemistry describing the biogeochemical dynamics in the natural subsurface environments gives rise to heterogeneous reaction networks, the individual segments of which can feature a wide range of timescales. Here, this paper presents a formulation of the mass balance equations for the batch chemistry and the transport of groundwater contaminants participating in such arbitrarily complex networks of reactions. We formulate the batch problem as an initial-value differential algebraic equation (DAE) system and compute its "index", so that the ease of solvability of the system is determined. We show that when the equilibrium reactions obey the law of mass action, the index of this initial-value DAE system is always unity (thus solvable with well-developed techniques) and that the system can be decoupled into a set of linerly implicit ordinary differential equations and a set of explicit algebraic equations. The formulations for the transport of these reaction networks can take advantage of their solvability properties under batch conditions. To avoid the error associated with time splitting fast reactions from transport, we present a split-kinetics approach where the fast equilibrium reactions are combined with transport equations while only the slower kinetic reactions are time split. Lastly, these results are used to formulatemore »« less

Authors:

Chilakapati, Ashok ^[1]; Ginn, Timothy ^[1]; Szecsody, James ^[1]

Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

Publication Date:: 1998-07-01

Research Org.:: Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1491708

Report Number(s):: PNNL-SA-31798
Journal ID: ISSN 0043-1397

Grant/Contract Number:: AC05-76RL01830

Resource Type:: Accepted Manuscript

Journal Name:: Water Resources Research

Additional Journal Information:: Journal Volume: 34; Journal Issue: 7; Journal ID: ISSN 0043-1397

Publisher:: American Geophysical Union (AGU)

Country of Publication:: United States

Language:: English

Subject:: 58 GEOSCIENCES; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats


                    Chilakapati, Ashok, Ginn, Timothy, and Szecsody, James. An Analysis of Complex Reaction Networks in Groundwater Modeling.  United States: N. p., 1998. 
Web.  doi:10.1029/98WR01041.

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                    Chilakapati, Ashok, Ginn, Timothy, & Szecsody, James. An Analysis of Complex Reaction Networks in Groundwater Modeling.  United States.  https://doi.org/10.1029/98WR01041

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                    Chilakapati, Ashok, Ginn, Timothy, and Szecsody, James. Wed .  
"An Analysis of Complex Reaction Networks in Groundwater Modeling".  United States.  https://doi.org/10.1029/98WR01041.  https://www.osti.gov/servlets/purl/1491708.

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@article{osti_1491708,

  title        = {An Analysis of Complex Reaction Networks in Groundwater Modeling},

  author       = {Chilakapati, Ashok and Ginn, Timothy and Szecsody, James},

  abstractNote = {The complex chemistry describing the biogeochemical dynamics in the natural subsurface environments gives rise to heterogeneous reaction networks, the individual segments of which can feature a wide range of timescales. Here, this paper presents a formulation of the mass balance equations for the batch chemistry and the transport of groundwater contaminants participating in such arbitrarily complex networks of reactions. We formulate the batch problem as an initial-value differential algebraic equation (DAE) system and compute its "index", so that the ease of solvability of the system is determined. We show that when the equilibrium reactions obey the law of mass action, the index of this initial-value DAE system is always unity (thus solvable with well-developed techniques) and that the system can be decoupled into a set of linerly implicit ordinary differential equations and a set of explicit algebraic equations. The formulations for the transport of these reaction networks can take advantage of their solvability properties under batch conditions. To avoid the error associated with time splitting fast reactions from transport, we present a split-kinetics approach where the fast equilibrium reactions are combined with transport equations while only the slower kinetic reactions are time split. Lastly, these results are used to formulate and solve a simplified reaction network for the biogeochemical transformation of Co(II)ethylenediaminetetraacetic acid (EDTA) in the presence of iron-coated sediments.},

  doi          = {10.1029/98WR01041},

  journal      = {Water Resources Research},

  number       = 7,

  volume       = 34,

  place        = {United States},

  year         = {1998},

  month        = {7}

}

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Figure 1: Breakthrough of a Lungmuir solute with and without decay. Analytic solution and numerical solutions to (33b), (33d), and (33g). $Nx$ is the number of grid cells, and $dt$ is the time step size.

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Water Resources Research, Vol. 51, Issue 7
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Tansik, Anna L.; Fitt, William K.; Hopkinson, Brian M.
Coral Reefs, Vol. 34, Issue 3
DOI: 10.1007/s00338-015-1289-8

Reactive transport codes for subsurface environmental simulation
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Steefel, C. I.; Appelo, C. A. J.; Arora, B.
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Fractional advection-dispersion equation: A classical mass balance with convolution-Fickian Flux
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Cushman, John H.; Ginn, Tim R.
Water Resources Research, Vol. 36, Issue 12
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A general paradigm to model reaction-based biogeochemical processes in batch systems: A GENERAL PARADIGM TO MODEL BIOGEOCHEMICAL PROCESSES
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Title: An Analysis of Complex Reaction Networks in Groundwater Modeling

Abstract

Citation Formats

Figures / Tables:

Differential/Algebraic Equations are not ODE’ s journal, September 1982

On methods for reducing the index of differential algebraic equations journal, November 1990

Differential-Algebraic Equation Index Transformations journal, January 1988

Structural analysis of multicomponent reaction models: Part II. Formulation of mass balances and thermodynamic constraints journal, January 1980

Extent of reaction in open systems with multiple heterogeneous reactions journal, May 1991

Approximation Methods for the Consistent Initialization of Differential-Algebraic Equations journal, February 1991

Modelling for dynamic simulation of chemical processes: the index problem journal, April 1992

Adsorption and dissociation of Co-EDTA complexes in iron oxide-containing subsurface sands journal, December 1995

Modeling of chemically reactive groundwater transport journal, July 1994

RAFT: A simulator for ReActive Flow and Transport of groundwater contaminants report, July 1995

Dynamic Dimension Reduction in ODE Models book, January 1996

The environmental biogeochemistry of chelating agents and recommendations for the disposal of chelated radioactive wastes journal, January 1981

Solute transport with multiple equilibrium-controlled or kinetically controlled chemical reactions journal, July 1992

The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods book, January 1989

Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space journal, March 1992

The Consistent Initialization of Differential-Algebraic Systems journal, March 1988

ODE Methods for the Solution of Differential/Algebraic Systems journal, August 1984

KEMOD: A mixed chemical kinetic and equilibrium model of aqueous and solid phase geochemical reactions report, January 1995

A critical evaluation of recent developments in hydrogeochemical transport models of reactive multichemical components journal, January 1989

A proposed numerical algorithm for solving nonlinear index problems journal, July 1990

Speciation of EDTA in Natural Waters: Exchange Kinetics of Fe-EDTA in River Water journal, January 1995

Adsorption-Dissolution Reactions Affecting the Distribution and Stability of CoIIEDTA in Iron Oxide-Coated Sand journal, September 1994

Independence of Chemical Reactions journal, May 1963

Maple V Language Reference Manual book, January 1991

Accuracy of operator splitting for advection-dispersion-reaction problems journal, May 1992

Total Degradation of EDTA by Mixed Cultures and a Bacterial Isolate journal, January 1992

Organic contaminant transport and fate in the subsurface: Evolution of knowledge and understanding journal, July 2015

External carbonic anhydrase in three Caribbean corals: quantification of activity and role in CO2 uptake journal, April 2015

Reactive transport codes for subsurface environmental simulation journal, September 2014

Fractional advection-dispersion equation: A classical mass balance with convolution-Fickian Flux journal, December 2000

A general paradigm to model reaction-based biogeochemical processes in batch systems: A GENERAL PARADIGM TO MODEL BIOGEOCHEMICAL PROCESSES journal, April 2003

Differential/Algebraic Equations are not ODE’ s
journal, September 1982

On methods for reducing the index of differential algebraic equations
journal, November 1990

Differential-Algebraic Equation Index Transformations
journal, January 1988

Structural analysis of multicomponent reaction models: Part II. Formulation of mass balances and thermodynamic constraints
journal, January 1980

Extent of reaction in open systems with multiple heterogeneous reactions
journal, May 1991

Approximation Methods for the Consistent Initialization of Differential-Algebraic Equations
journal, February 1991

Modelling for dynamic simulation of chemical processes: the index problem
journal, April 1992

Adsorption and dissociation of Co-EDTA complexes in iron oxide-containing subsurface sands
journal, December 1995

Modeling of chemically reactive groundwater transport
journal, July 1994

RAFT: A simulator for ReActive Flow and Transport of groundwater contaminants
report, July 1995

Dynamic Dimension Reduction in ODE Models
book, January 1996

The environmental biogeochemistry of chelating agents and recommendations for the disposal of chelated radioactive wastes
journal, January 1981

Solute transport with multiple equilibrium-controlled or kinetically controlled chemical reactions
journal, July 1992

The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods
book, January 1989

Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space
journal, March 1992

The Consistent Initialization of Differential-Algebraic Systems
journal, March 1988

ODE Methods for the Solution of Differential/Algebraic Systems
journal, August 1984

KEMOD: A mixed chemical kinetic and equilibrium model of aqueous and solid phase geochemical reactions
report, January 1995

A critical evaluation of recent developments in hydrogeochemical transport models of reactive multichemical components
journal, January 1989

A proposed numerical algorithm for solving nonlinear index problems
journal, July 1990

Speciation of EDTA in Natural Waters: Exchange Kinetics of Fe-EDTA in River Water
journal, January 1995

Adsorption-Dissolution Reactions Affecting the Distribution and Stability of CoIIEDTA in Iron Oxide-Coated Sand
journal, September 1994

Independence of Chemical Reactions
journal, May 1963

Maple V Language Reference Manual
book, January 1991

Accuracy of operator splitting for advection-dispersion-reaction problems
journal, May 1992

Total Degradation of EDTA by Mixed Cultures and a Bacterial Isolate
journal, January 1992

Organic contaminant transport and fate in the subsurface: Evolution of knowledge and understanding
journal, July 2015

External carbonic anhydrase in three Caribbean corals: quantification of activity and role in CO2 uptake
journal, April 2015

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journal, September 2014

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A general paradigm to model reaction-based biogeochemical processes in batch systems: A GENERAL PARADIGM TO MODEL BIOGEOCHEMICAL PROCESSES
journal, April 2003