Contaminant Fate and Reactive Transport in Groundwater - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 865

Appropriate initial and boundary conditions, geometry of the model domain and
specified values of the physical coefficients together with the partial differential
equation for flow (Eq. ( 19.15 )) define an individual flow problem.
In a similar way the governing transport equation for a dissolved contaminant can
be derived based on the mass conservation of the contaminant through an aquifer
control volume. The partial differential equation describing the fate and transport
of a dissolved contaminant in a three-dimensional groundwater flow system can be
written as follows (Zheng and Bennet 2002 ):

nD ij ∂

R n

∂ ( nC )

∂

∂
∂

C ∂

∂

= − ( nv i C ) + q s C s + (19.16)

t x i ∂ x j x i

where:

n = porosity of the aquifer sediments [-];

contaminant concentration in groundwater [M L − 3 ];

C =

t time [T];

x i,j =

=

distance along the respective Cartesian coordinate axis [L];

hydrodynamic dispersion coefficient tensor [L 2 T − 1 ];

D ij =

average linear velocity [L T − 1 ]; v i =

q s = volumetric flow rate per unit volume of aquifer representing fluid sources

(positive) and sinks (negative) [T − 1 ];
C s = concentration of the source or sink flux [M L − 3 ];

chemical reaction term [M L − 3 T − 1 ].

Σ R n =

The chemical reaction term added to the general advective-dispersive equa-
tion allows us to describe the principal biogeochemical processes (e.g. sorption,
biodegradation, precipitation/dissolution, et cetera) taking place in the subsurface.
The mathematical problem of contaminant transport, expressed in terms of gov-
erning equations, initial and boundary conditions, together with the applicable flow
and transport parameters, and the information on sources and sinks and on the reac-
tion term, can be solved to obtain the concentration distribution in the modeled
region at a time of interest. Alternatively, the concentration breakthrough in time
can be calculated at a location of interest.

19.3.2 Mathematical Models

There are two main procedures for obtaining the solution of a mathematical model:
analytical and numerical methods. These methods result in two different types
of models used to solve groundwater flow and contaminant transport problems.
Generally, analytical models can be applied only under a number of simplifying
assumptions, whereas more complex groundwater flow and contaminant transport
problems require numerical solutions. Most of the practical applications at contam-
inated sites need numerical solutions of the groundwater flow and/or contaminant