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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 » and solve a simplified reaction network for the biogeochemical transformation of Co(II)ethylenediaminetetraacetic acid (EDTA) in the presence of iron-coated sediments.« less

Authors:
 [1];  [1];  [1]
+ Show Author Affiliations
  1. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Publication Date:
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. doi: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. doi: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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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI:  10.1029/98WR01041
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Cited by: 48 works
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Figures / Tables:

Figure 1 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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    Works referencing / citing this record:

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    journal, September 2014

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

    • Essaid, Hedeff I.; Bekins, Barbara A.; Cozzarelli, Isabelle M.
    • Water Resources Research, Vol. 51, Issue 7
    • DOI: 10.1002/2015wr017121

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

    • Fang, Yilin; Yeh, Gour-Tsyh; Burgos, William D.
    • Water Resources Research, Vol. 39, Issue 4
    • DOI: 10.1029/2002wr001694

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

    • Cushman, John H.; Ginn, Tim R.
    • Water Resources Research, Vol. 36, Issue 12
    • DOI: 10.1029/2000wr900261

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

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