(1973) n°3 - Royal Academy for Overseas Sciences

Streamline
— 590 —
Solid matrix
Streamline pattern in a porous medium matrix.
to a relation between the permeability and the dispersion coefficients.
However, the problem remains unsolved because the solution
still involves the knowledge of the detailed unknown
medium geometry. Another approach to the understanding of
dispersion was an analytical study by T a y l o r (32) who investigated
the dispersion of two fluids of the same physical properties
and with an initial longitudinal concentration gradient
of a passive contaminant, the fluids being contained in a straight
capillarly tube with steady fully developed laminar flow prevailing.
It was found that the dispersion coefficient which measures
the rate at which the contaminant will spread out axially,
increases with increasing velocity differences across the capillary
tube and with increasing dimensions of the tube. The results
were later applied (7, 26a, 26b) to a porous medium, assuming
that the porous medium can be modeled by a random array of
capillarly tubes. This application is somewhat speculative because
dispersion in a porous medium is not only created by
microscopic velocity differences in the interstices between particles,
but also by macroscopic effects such as channeling.
In practice, the relative importance of convection over dispersion
is measured by defining a Peclet number Pe,
Pe = vd/K
It was shown (18) that the coefficients of lateral dispersion and
of longitudinal dispersion both increase uniformly as values
of Pe increase from 0(10) and 0(1) respectively.