Numerical modeling of arsenic mobility - In-Situ Remediation of Arsenic-Contaminated Sites - page 43

isotherm has the form:

C n

S = K F × (2.4)

where K F [L 3 /M] and n [ − ] are empirical coefficients and S and C are defined as above.
If the coefficient n equals 1, the Freundlich isotherm reduces to the linear sorption model.
However, n is usually selected to be smaller than 1, so that the increase of sorbed concentrations
decreases as the solute concentration increases. As is the case of the linear sorption model, no
upper adsorption limit is simulated and sorption extends infinitely as dissolved concentrations
increase.
In contrast the Langmuir adsorption equation introduces an upper limit to adsorption:

QKC

S =

(2.5)

1 + KC

where K is the partition coefficient reflecting the extent of sorption, Q is the maximum sorption
capacity [M/M] and C is defined as above.
In this description, sorption still increases linearly at low dissolved solute concentrations.
However, as aqueous concentrations increase further, the distribution coefficient, i.e., the ratio
between the sorbed and dissolved concentration decreases gradually as surface sites become
increasingly occupied. Eventually the isotherm flattens out as the sorption sites become fully
saturated.
These empirical formulations assume that the ambient solution concentration is at equilibrium
with the sorbed phase concentration. However, the equilibrium assumption may not be valid during
transport, in which case kinetic expressions may be applied to describe the time-dependence
of adsorption-desorption process. The simplest kinetic expression of sorption is a first-order
reversible reaction:

∂t = β C −

ρ b ∂S

S
K d

(2.6)

where ρ b is the bulk density of the subsurface medium [M/L 3 ], β is the first-order mass transfer
rate [1/T] between the liquid and solid phases. Kinetic expressions describing nth-order reversible
adsorption have also been described (Darland and Inskeep, 1997).
The above mentioned empirical sorption models require knowledge of the mineral composi-
tion and are dependent on the observed relationships between aqueous and sorbed concentrations.
Sorption isotherms are generally measured in the laboratory using batch equilibrium or column
breakthrough experiments and these results are then applied within a solute transport model to
predict field-scale transport behavior. However, these empirically derived partitioning relation-
ships are only valid for the conditions under which they were determined and do not account
for potential impacts of spatial or temporal variability in mineralogy and/or hydrochemistry on
adsorption. Therefore empirical adsorption models are generally only appropriate when applied
under well-controlled laboratory conditions or where field-sites are characterized by relatively
constant geochemical conditions.
There are numerous examples where standard adsorption isotherm equations have been fitted
to replicate observed laboratory data sets on arsenic sorption onto a variety of sorbents (e.g., Hsia
et al. , 1992; Masue et al. , 2007; Nath, 2009; Wolthers, 2005). Such calculation can be performed
by batch-type geochemical models (see Table 2.1 ) .
Applications of numerical modeling studies in which empirical relationships have been used to
represent arsenic sorption behavior are also manifold. For example, work undertaken by DPHE
et al. (1999) combined results from groundwater flow models with estimates derived from sorp-
tion isotherms to assess and predict the rate of arsenic movement in typical Bangladesh aquifers.
Darland and Inskeep (1997) studied the applicability of equilibrium adsorption models (linear
and Freundlich) and kinetic adsorption models (first-order and nth-order reversible) for simu-
lating arsenic transport under varying pore water velocities. Decker et al. (2006) developed a