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

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characteristic scales are very important in the study of the flow
of miscible fluids.
3c. Plow of miscible fluids and salt transport.
It was already argued that an important problem in the exploitation
of fresh groundwater lenses comes from the fact
that underground waters are typically salinity-stratified, and
thus miscible. Because they are miscible, the molecular diffusi-
vity k for a salinity-stratified fluid introduces a diffusion thickness
scale, Vfct, where t is the time. If it is assumed that there
are no chemical reactions between the moving fluid and the
porous medium matrix, the transport of dissolved salt by a moving
fluid basically arises from convection and molecular diffusion.
Their relative effects are measured, as was shown by
W o o d in g ( 3 6 a ) , by a Rayleigh number A,
A H
A = --------- »
K
where H is a characteristic length of the macroscopic flow,
such as the depth of the porous layer. It must be pointed out
that, when the fluid is moving, the effects of the coefficient
of molecular diffusivity are often minimal compared to the
effects of hydrodynamic dispersion as obtained from the equation
for the conservation of salt. That is to say, the observed
mixing rate or buoyancy flux at a given level in a stratified fluid
flowing through a porous medium, is generally found to be
much larger than the buoyancy flux due to molecular diffusion
alone. This dispersion destroys any sharp interface, whose presence
is characteristic of immiscible fluid displacements, and
replaces it by a mixing layer. Essentially, this mechanical dispersion
originates from the fact that individual fluid particles
travel at variables velocities through the irregularly shaped pore
channels of the medium. The random distribution and orientation
of these channels impose a tortuous pattern upon the
microscopic streamlines. These streamlines of course do not
intersect, as is sketched in figure 2.
A statistical approach to the problems of dispersion was undertaken
by Sc h e id e g g e r ( 2 8 ) , B ear and B a c h m a t (3 a ) which lead