Models reactive transport

Beginning in the late 1980s, a number of groups have worked to develop reactive transport models of geochemical reaction in systems open to groundwater flow. As models of this class have become more sophisticated, reliable, and accessible, they have assumed increased importance in the geosciences (e.g., Steefel et al., 2005). The models are a natural marriage (Rubin, 1983 Bahr and Rubin, 1987) of the local equilibrium and kinetic models already discussed with the mass transport... 

In a reactive transport model, the domain of interest is divided into nodal blocks, as shown in Figure 2.11. Fluid enters the domain across one boundary, reacts with the medium, and discharges at another boundary. In many cases, reaction occurs along fronts that migrate through the medium until they either traverse it or assume a steady-state position (Lichtner, 1988). As noted by Lichtner (1988), models of this nature predict that reactions occur in the same sequence in space and time as they do in simple reaction path models. The reactive transport models, however, predict how the positions of reaction fronts migrate through time, provided that reliable input is available about flow rates, the permeability and dispersivity of the medium, and reaction rate constants. 

Reactive transport models are, naturally, more challenging to set up and compute... 

Fig. 2.11. Configurations of reactive transport models of water-rock interaction in a system open to groundwater flow (a) linear domain in one dimension, (b) radial domain in one dimension, and (c) linear domain in two dimensions. Domains are divided into nodal blocks, within each of which the model solves for the distribution of chemical mass as it changes over time, in response to transport by the flowing groundwater. In each case, unreacted fluid enters the domain and reacted fluid leaves it.

Since a valid reaction model is a prerequisite for a continuum model, the first step in any case is to construct a successful reaction model for the problem of interest. The reaction model provides the modeler with an understanding of the nature of the chemical process in the system. Armed with this information, he is prepared to undertake more complex calculations. Chapters 20 and 21 of this book treat in detail the construction of reactive transport models. 

Such models are known as reactive transport models and are the subject of the next chapter (Chapter 21). We treat the preliminaries in this chapter, introducing the subjects of groundwater flow and mass transport, how flow and transport are described mathematically, and how transport can be modeled in a quantitative sense. We formalize our discussion for the most part in two dimensions, keeping in mind the equations we use can be simplified quickly to account for transport in one dimension, or generalized to three dimensions. 

Molecular diffusion (or self-diffusion) is the process by which molecules show a net migration, most commonly from areas of high to low concentration, as a result of their thermal vibration, or Brownian motion. The majority of reactive transport models are designed to simulate the distribution of reactions in groundwater flows and, as such, the accounting for molecular diffusion is lumped with hydrodynamic dispersion, in the definition of the dispersivity. 

To construct models of this sort, we combine reaction analysis with transport modeling, the description of the movement of chemical species within flowing groundwater, as discussed in the previous chapter (Chapter 20). The combination is known as reactive transport modeling, or, in contaminant hydrology, fate and transport modeling. 

A reactive transport model, as the name implies, is reaction modeling implemented within a transport simulation. It may be thought of as a reaction model distributed over a groundwater flow. In other words, we seek to trace the chemical reactions that occur at each point in space, accounting for the movement of reactants to that point, and reaction products away from it. 

A reactive transport model in a more general sense treats a multicomponent system in which a number of equilibrium and perhaps kinetic reactions occur at the same time. This problem requires more specialized solution techniques, a variety of which have been proposed and implemented (e.g., Yeh and Tripathi, 1989 Steefel and MacQuarrie, 1996). Of the techniques, the operator splitting method is best known and most commonly used. 

In this chapter, we build on applications in the previous chapter (Chapter 26), where we considered the kinetics of mineral dissolution and precipitation. Here, we construct simple reactive transport models of the chemical weathering of minerals, as it might occur in shallow aquifers and soils. 

In a first reactive transport model (Bethke, 1997), we consider the reaction of silica as rainwater infiltrates an aquifer containing quartz (SiC>2) as the only mineral. Initially, groundwater is in equilibrium with the aquifer, giving a SiC>2(aq) concentration of 6 mg kg-1. The rainwater contains only 1 mg kg-1 Si02(aq), so as it enters the aquifer, quartz there begins to dissolve,... 

Only for the intermediate cases - those with velocities in the range of about 100 m yr-1 to 1000 m yr-1 - does silica concentration and reaction rate vary greatly across the main part of the domain. Significantly, only these cases benefit from the extra effort of calculating a reactive transport model. For more rapid flows, the same result is given by a lumped parameter simulation, or box model, as we could construct in REACT. And for slower flow, a local equilibrium model suffices. 

Groundwater remediation is the often expensive process of restoring an aquifer after it has been contaminated, or at least limiting the ability of contaminants there to spread. In this chapter, we consider the widespread problem of the contamination of groundwater flows with heavy metals. We use reactive transport modeling to look at the reactions that occur as contaminated water enters a pristine aquifer, and those accompanying remediation efforts. 

Fig. 33.3. Steady-state distribution of microbial activity and groundwater composition in an aquifer hosting acetotrophic sulfate reduction and acetoclastic methanogenesis, obtained as the long-term solution to a reactive transport model.

Steefel, C. I., D. J. DePaolo and P. C. Lichtner, 2005, Reactive transport modeling An essential tool and a new research approach for the Earth sciences. Earth and Planetary Science Letters 240, 539-558. 

Since publication of the first edition, the held of reaction modeling has continued to grow and hnd increasingly broad application. In particular, the description of microbial activity, surface chemistry, and redox chemistry within reaction models has become broader and more rigorous. Reaction models are commonly coupled to numerical models of mass and heat transport, producing a classification now known as reactive transport modeling. These areas are covered in detail in this new edihon. 

At the same time, reaction modeling is now commonly coupled to the problem of mass transport in groundwater flows, producing a subfield known as reactive transport modeling. Whereas a decade ago such modeling was the domain of specialists, improvements in mathematical formulations and the development of more accessible software codes have thrust it squarely into the mainstream. 

I expand treatment of sorption, ion exchange, and surface complexation, in terms of the various descriptions in use today in environmental chemistry. And I integrate all the above with the principals of mass transport, to produce reactive transport models of the geochemistry and biogeochemistry of the Earth s shallow crust. As in the first edition, I try to juxtapose derivation of modeling principles with fully worked examples that illustrate how the principles can be applied in practice. 

Runkel, R.L. Kimball, B.A. 2002. Evaluating remedial alternatives for an acid mine drainage system - application of a reactive transport model. Environmental Science Technology, 36, 1093-1101. 

Chen, Y. 2003. Using reactive transport modeling to evaluate the source term at Yucca Mountain. Computers Geosciences, 29, 385-397. 

Decker, D.L., Tyler, S.W., Papelis, C. and Simunek, J. (1999) A reactive transport model for arsenic in unsaturated gold mine heap and waste rock structures. Abstracts with Programs-Geological Society of America, 31(7), 70. 

The most sophisticated models applied to FePRBs to date combine multiple ADEs (i.e., multicomponent transport) with coupled chemical reactions [184,186,208]. These multicomponent reactive transport models were used to simulate the geochemical evolution in FePRBs for the treatment of TCE [184] and for remediating mixtures of Cr(VI) and chlorinated solvents [186,208]. The models are capable of reproducing the spatial distribution of field-observable parameters such as the concentrations of the chlorinated solvents, pH, Eh, alkalinity, Mg2 +, S042-, and N03 ... 

Multicomponent reactive transport models can also be used to estimate the potential for barrier clogging due to secondary mineral formation... 

Blowes DW, Mayer KU. An in situ permeable reactive barrier for the treatment of hexavalent chromium and trichloroethylene in ground water Volume 3, Mulitcomponent Reactive Transport Modeling, U.S. Environmental Protection Agency, EPA/600/R-99/095c, Ada, OK, 1999. 

The first attempt to include emissions of biogases in a full transient, one-dimensional reactive transport model for estuaries was recently developed for the Scheldt estuary (The Netherlands). The CONTRASTE model is designed to provide a full description of estuarine residual circulation—daily freshwater discharge and tidal oscillations. 

Wang, Y., and van Capellen, P. (1996) A multicomponent reactive transport model of early diagenesis application to redox cycling in coastal marine sediments. Geochim. Cosmochim. Acta 60, 2993-3014. 

Suhr G. (1999) Melt migration under oceanic ridges inference from reactive transport modeling of upper mantle hosted dunites. J. Petrol. 40, 575—600. 

A second type of mass-balance approach is quantitative incorporation of mass balances within a reactive-transport model and could be applied to groundwaters, surface waters, and surface-water-groundwater interactions. Paces (1983, 1984) calls this the local mass-balance approach. There are numerous examples and explanations of this approach (e.g.. Freeze and Cherry, 1979 Domenico and Schwartz, 1990). 

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