FIGURE 2.13. Diagram for ExampIe 2.
2.6. Extensions
47
where () is the porosity, a and bare the length and width of the rectangular
aquifer, respectively, and () is the Dirac-{) function.
The initial condition is
C(x, y, 0) = 0,
and the boundary conditions are
(x,y) E rectangle OABD
Example 2
C(a, y, t) = Co, along BD
C(O, y, t) = 0,
along 0 A
~CI = 0, along OD·
y (x,O,/)
~C I = 0, along AB
y (x,b,/)
(2.6.36)
(2.6.37)
Consider a two-dimensional groundwater pollution problem on a vertical
profile. Figure 2.13 shows an unconfined aquifer, where water is recharged
from BC and flows into a river via the aquifer. Assurne that a steady flow has
been reached. Starting from an instant t = 0, the recharge source changes
from clean water to polluted water with a radioactive tracer concentration of
Co. Now let us build up a mathematical model for this hydrodynamic dispersion problem.
Assurne that the water head distribution is known from the steady unconfined aquifer model, and, by means of Darcy's Law, the velocity components V x and v.. are also known. Ignoring molecular diffusion, the coefficients
of hydrodynamic dispersion can be calculated by the following equations:
{
Dxx = (IXL v,,2 + IX T v.. 2 )/V
Dxz = Dzx = (IXL - IXT) v" Vz/V
(2.6.38)
Dzz = (IXT v,,2 + IXL v.. 2 )jV