longitudinal dispersion in nonuniform isotropic porous media

8
The typical experimental investigation of longitudinal dispersion
does not use an instantaneous slug, but displaces the resident fluid
with a solution of some constant solute concentration, Co (Rose,
1977). Again, assuming an infinite, one-dimensional medium, the
boundary conditions are
lim
x -+ _00
lim
x -+ +00
C(x,t)
C(x,t) o
and the initial condition is
C(x,O) = Co
C(x,O) = °
The solution to equation (1.3) under these initial and boundary
conditions is
C(x,t) erfc (1.5)
where erfc is the complementary error function.
The complementary error function solution, shown in Figure 1.3, is
commonly known as a breakthrough curve. Actually, breakthrough curves
are more often measured at a fixed location over time than as a spatial
profile at a fixed time. The difference between the two profiles is
small under the following condition (Fischer, 1964):