Contaminant Fate and Reactive Transport in Groundwater - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 864

The development and application of contaminant transport models are motivated
by fundamental questions such as the need to assess the impact of the contamination
on environmentally important receptors located down-gradient of the source zone,
to estimate time-scales and optimal design of a remediation scheme and its sensitiv-
ity to changes in physical or biogeochemical conditions (Prommer and Barry 2005 ).
The results of transport models always bear a degree of uncertainty that originates
from the usually sparse dataset available and from the incomplete hydrogeologi-
cal and hydrogeochemical site characterization, lack in process understanding and
parameter ambiguity due to spatial heterogeneity. Nonetheless, transport models are
characterized by high flexibility and allow a quick investigation of a number of pos-
sible scenarios. Therefore, they remain an indispensable tool to gain an improved
understanding of factors controlling the contaminant fate and transport.

19.3.1 Governing Equations

Because of the impossibility of mathematically describing the complicated geome-
try of the solid surfaces that delimit the flow domain in a natural porous medium,
the vast majority of groundwater flow and transport models are based on the con-
tinuum approach (Bear 1972 ). According to this mathematical approach, the actual
multiphase porous medium is substituted with a fictitious continuum, a structure-
less substance to any point of which kinetic and dynamic variables and parameters
can be assigned. These properties, averaged over a representative elementary vol-
ume (REV), are a continuous function of the spatial coordinates of a point and of
time and allow the description of flow and transport phenomena in porous media by
means of partial differential equations (PDEs). The selected REV should be much
larger than the microscopic scale of heterogeneity associated with the presence of
solid particles and pore spaces in the porous medium and much smaller than the
considered domain.
The governing groundwater flow equation can be derived by applying the mass
conservation principle to an aquifer control volume (Bear 1972 , 1979 ; Zheng and
Bennet 2002 ) and can be written as:

K ij ∂

∂
∂

h

S s ∂

h
∂

+ q s = (19.15)

x i ∂ x j t

where:

x i,j = distance along the respective Cartesian coordinate axis [L];

t time [T];

K ij =

=

tensor of hydraulic conductivity [L T − 1 ];

h hydraulic head [L];

q s =

=

fluid source/sink term [L 3 L − 3 T − 1 ];

specific storage [L 3 L − 3 L − 1 ]; S s =