Numerical modeling of arsenic mobility - In-Situ Remediation of Arsenic-Contaminated Sites - page 40

such as flow velocities and their variations in space and time and, linked to that, hydrodynamic
mixing and dilution effects. In cases where active remediation requires addition of specific
amendments to the aquifer, the rate of delivery of such reactants via advective-dispersive transport
can often be the limiting factor in the progress of in-situ treatment. In such cases developing a
good understanding (and associated model) of the groundwater flow processes, subsurface mixing
of multiple solutes induced by hydrodynamic dispersion, and contact times between solutes and
minerals, can be key to successful remediation. A detailed understanding and quantification of the
natural groundwater dynamics as well as the dynamics induced by the extraction and/or injection
itself are essential for optimizing engineered schemes or predicting natural attenuation rates.
An equation describing the transport and dispersion of a single, dissolved conservative species
in flowing groundwater within a homogeneous porous medium may be derived based on the prin-
ciple of mass balance (e.g., Domenico and Schwartz, 1998). The mass balance statement requires
that the change in mass storage of a species within a representative elementary aquifer volume
(REV) during a given time interval is equal to the difference in the mass inflows and outflows
due to dispersion, advection and external sinks and sources over the same interval. Mathemati-
cally, this mass balance is most frequently described by the advection-dispersion equation (ADE)
(Bear, 1972; Bear and Verruijt, 1987; Zheng and Wang, 1999):

D ij ∂C
∂x j

∂C
∂t =

∂
∂x i

∂
∂x i (v i C)

q s
θ C q

− + (2.1)

where C [ML − 3 ] is the dissolved concentration of a chemical species, v i [LT − 1 ] is the seepage
or linear pore water velocity in direction x i [L], D ij [L 2 T − 1 ] is the hydrodynamic dispersion
coefficient tensor (summation convention assumed), θ is the porosity of the subsurface medium,
q s [L 3 L − 3 T − 1 ] is the volumetric flow rate per unit volume of water representing external fluid
sources and sinks and C q [ML − 3 ] is the concentration of a species within this flux if q s is positive
(injection), otherwise C q = C .
The first term on the right side of the ADE represents the rate of change in concentration
due to dispersion, whereby the dispersion term represents two processes: molecular diffusion as
well as mechanical dispersion. Mechanical dispersion results from the microscopic fluctuation of
streamlines in space with respect to the mean groundwater flow direction and small-scale changes
of porosity and hydraulic conductivity. Mechanical dispersion is assumed to be scale-independent
within the ADE and often initially estimated, for example, on the basis of literature values and
subsequently optimized during the model calibration for which concentration data of conservative
solutes most commonly serve as calibration constraints (e.g., Fiori and Dagan, 1999; Greskowiak
et al ., 2005; Jensen et al. , 1993; Wallis et al. , 2010). This pragmatic approach appears in many
cases to produce a reasonable description of solute spreading and mixing behavior, especially for
local-scale problems and for aquifers that are relatively homogeneous. However, it should be noted
that this approach can be too simplistic and, while perhaps still capturing the general patterns, may
sometimes not satisfactorily reproduce the spreading behavior observed at larger scales (Konikow,
2010). This will also depend on the level of detail at which larger-scale geological features and
structures and their impact on groundwater flow are represented within the numerical model.
The second term on the right side of the ADE describes advective transport. Thereby it is
assumed that the dissolved species is transported at the same mean velocity as the flowing ground-
water, which, in field-scale contaminant problems within the saturated groundwater zone, does
represent the dominant physical transport process. The average seepage velocity of the flowing
groundwater, i.e., v i in Equation (2.1) , is derived from Darcy's law and the three-dimensional
flow equation for saturated groundwater.
The last term on the right hand side of the ADE represents the effects of mixing of waters
from external sources and sinks with different solute concentrations. For non-conservative solute
transport, additional terms can be added to the right side of the ADE to account for geochemical
reactions, such as sorption, precipitation/dissolution of minerals, decay etc. The geochemical