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3. Analytic Solutions of Hydrodynamic Dispersion Equations
~
FIGURE 3.8. Mass transport in a single
fracture.
the porous matrix depends mainly on the molecular diffusion. Based on these
assumptions, the governing equation of the one-dimensional advectiondispersion in the fracture is
(3.2.52)
where eis the concentration distribution in the fracture, V is the longitudinal
dispersion coefficient, and q is the diffusive flux through the fracture walls
(MjUT).
The diffusion equation in the porous matrix is
(3.2.53)
where C is the concentration distribution, and V' is the diffusion coefficient
in the porous matrix. Eqs. (3.2.52) and (3.2.53) will be coupled by the diffusive
flux q. According to the law of the linear diffusion, we have
OCI
q= -nV'.
OX x=b
(3.2.54)
Substituting this equation into Eq. (3.2.54), we obtain the governing equation
for a fracture as
oe = V02;- _ voC + nV' OCI .
ot
oz
OZ
b OX x=b
(3.2.55)
This equation can be solved simultaneously with Eq. (3.2.53). The subsidiary