8.1. Simulation and Prediction of Groundwater Pollution
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FIGURE 8.2. An idealized geometrie structure
of fractures-pores.
FIGURE 8.3. One-dimensional flow and
solute transport in a porous block.
ac
- = 0
1!' _ _
1 - -
z'=a ________ ~~--~7--------~
c=c
where V' is the one-dimensional velocity in the porous blocks, D' is the
dispersion coefficient and the definitions of a, land d are shown in Figure 8.2.
The rate of the volume occupied by fractures can be seen from the figure as
8 = bj(a + b).
(8.1.14)
In the porous blocks, C must satisfy the following one-dimensional
advection-dispersion equation:
ac a (ac)
ac
Tt = az' D' az' - V' az'
subject to the following subsidiary conditions:
c = C~, t = 0;
C' = C, z' = a;
ac
az' = 0, z' = o.
(8.1.15)
(8.1.16)
We first solve the one-dimensional problem to obtain C, then substitute C
into Eq. (8.1.13) to determine rand substitute it into Eq. (8.1.12). With
appropriate initial and boundary conditions, the concentration distribution
in the continuous fractured medium can be solved by the usual way. Because
the average velocity in the fractured media is large, the numerical methods
for advection-dominated problems are often used to avoid oscillations of
the numerical solution. For instance, Noorishad and Mehran (1982), and