Numerical modeling of arsenic mobility - In-Situ Remediation of Arsenic-Contaminated Sites - page 42

Engesgaard, 2002). In the single-step approach, a redox reaction is modeled as an irreversible
kinetic reaction that simultaneously includes organic substrate oxidation and the reduction of a
predefined electron acceptor (such as oxygen or nitrate). In contrast, the two-step approach or
so-called partial equilibrium approach (PEA) separates the electron donating step (e.g., organic
matter degradation) from the electron accepting step. The first step is assumed to be the rate-
limiting step (kinetically controlled), and thus the second step can be simply modeled as an
equilibrium (instantaneous) reaction (Postma and Jakobsen, 1996; Prommer et al ., 2002). Using
the latter approach, redox reactions driven by organic matter degradation can be simulated using
e.g., PHREEQC-2 by simply adding inorganic carbon at the same rate (i.e., r DOC , Equation (2.2) )
at which the organic substrate is removed. Internally, redox equilibrium may be assumed among all
electron acceptors, which will then be automatically consumed in the order of their thermodynamic
favorability without the need to explicitly define specific electron accepting reactions and their
order of consumption. In contrast, alternative modeling approaches may assume and model the
redox reactions as a single, coupled reaction (e.g., Hunter et al ., 1998; MacQuarrie and Sudicky,
2001). Besides organic matter, pyrite and/or other reduced minerals may also affect the redox
zonation within the aquifer. Examples are for instance areas of elevated nitrate due to recharge
from agricultural sources due to overuse of fertilizers (Zhang et al ., 2009). Here, pyrite oxidation
may lead to acidification of the groundwater, if the aquifer contains insufficient amounts of
minerals that can act as pH buffers, such as calcite. Moreover, pyrite oxidation has often been
shown to be accompanied by the release of trace metals, including arsenic (e.g., Price and Pichler,
2006; Smedley and Kinniburgh, 2001; Zhang et al ., 2009).

2.3.3 Sorption and desorption
Once arsenic is mobilized, adsorption-desorption reactions are important processes that subse-
quently exert a major control on the effective transport rates of arsenic and on whether its mobility
becomes problematic for downstream receptors. A range of mathematical expressions for arsenic
adsorption-desorption reactions have been used in reactive transport models, from relatively sim-
ple empirical relationships, such as distribution coefficients and isotherm equations (Freundlich,
1926; Langmuir, 1918) to the more sophisticated surface complexation modeling approaches
(Appelo and Postma, 2005; Goldberg et al ., 2007).
When adsorption is represented by empirical approaches, the conceptual model for adsorption
is generally simplistic in that it ignores potential effects of variable chemical conditions, such as
changes in pH or solute concentration spatially or with time on the partitioning behavior (Davis
and Kent, 1990). The simplest empirical relationship for adsorption used in reactive transport
models is the linear equilibrium sorption model:

S = K d × C (2.3)

where K d is the distribution coefficient [L 3 /M], C is the concentration of the dissolved phase
[M/L 3 ] and S is the mass of the solute species (arsenic) adsorbed on the aquifer solids [M/M].
The so-called K d approach then describes a temporally constant ratio between dissolved solute
concentration in the groundwater and the concentration sorbed to the sediment, i.e., the latter is
linearly proportional to the former. The proportionality constant ( K d ) or slope of the isotherm
relates to the retardation that the solute experiences relative to a non-reactive tracer during ground-
water flow (Appelo and Postma, 2005). Note that in this formulation the adsorption capacity of
the aquifer is assumed to be infinite. This assumption is, however, not necessarily suitable for
simulating arsenic, since the number of sorption sites that can be occupied by arsenic and other
solutes that compete for these sites is often limited.
Somewhat more complex empirical relationships, i.e., Freundlich and/or Langmuir adsorption
isotherms are often employed to account for the finite adsorption capacity of the aquifer media in
describing the relationship between sorbed and dissolved solute concentrations. The Freundlich