# A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions

## Abstract

This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing NE equilibrium reactions and a set of reactive transport equations of M-NE kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kineticmore »

- Authors:

- ORNL
- University of Central Florida, Orlando

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 931723

- DOE Contract Number:
- DE-AC05-00OR22725

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Contaminant Hydrology; Journal Volume: 92; Journal Issue: 1-2

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 54 ENVIRONMENTAL SCIENCES; 97; KINETIC EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; ENVIRONMENTAL TRANSPORT; WATER QUALITY; GROUND WATER; CHEMICAL REACTIONS; EQUILIBRIUM; MATHEMATICAL MODELS; URANIUM; SOILS; RADIONUCLIDE MIGRATION

### Citation Formats

```
Zhang, Fan, Yeh, Gour-Tsyh, Parker, Jack C, Brooks, Scott C, Pace, Molly, Kim, Young Jin, Jardine, Philip M, and Watson, David B.
```*A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions*. United States: N. p., 2007.
Web. doi:10.1016/j.jconhyd.2006.11.007.

```
Zhang, Fan, Yeh, Gour-Tsyh, Parker, Jack C, Brooks, Scott C, Pace, Molly, Kim, Young Jin, Jardine, Philip M, & Watson, David B.
```*A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions*. United States. doi:10.1016/j.jconhyd.2006.11.007.

```
Zhang, Fan, Yeh, Gour-Tsyh, Parker, Jack C, Brooks, Scott C, Pace, Molly, Kim, Young Jin, Jardine, Philip M, and Watson, David B. Mon .
"A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions". United States.
doi:10.1016/j.jconhyd.2006.11.007.
```

```
@article{osti_931723,
```

title = {A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions},

author = {Zhang, Fan and Yeh, Gour-Tsyh and Parker, Jack C and Brooks, Scott C and Pace, Molly and Kim, Young Jin and Jardine, Philip M and Watson, David B},

abstractNote = {This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing NE equilibrium reactions and a set of reactive transport equations of M-NE kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.},

doi = {10.1016/j.jconhyd.2006.11.007},

journal = {Journal of Contaminant Hydrology},

number = 1-2,

volume = 92,

place = {United States},

year = {Mon Jan 01 00:00:00 EST 2007},

month = {Mon Jan 01 00:00:00 EST 2007}

}