longitudinal dispersion in nonuniform isotropic porous media

120
When one fluid displaces another immiscibly, the interface
velocity (or seepage velocity, V ) is greater than the Darcy velocity.
s
This is caused by a portion of the cross section's being occupied by
grains which reduces the available cross-sectional area for flow. The
average areal porosity is known to be equal to the volumetric porosity
(Bear, 1972), but flow takes place only in pores which interconnect.
Thus an effective porosity may be defined by,
a = VD/V
e s
The difference in effective porosity to total porosity gives an
estimate of the amount of fluid which is stagnant. If the miscible
(4.3)
displacement process follows advection-diffusion theory, the seepage
velocity is equal to the velocity of the 50% concentration point
(assuming adsorption is not significant). Using the conductivity
measurements, the velocity of the 50% concentration point is easily
found. Table 4.4 shows the variation in average effective porosity
between the top of the sand pack and each probe for both porous
materials. Experimental error for the effective porosity and total
porosity measurements is ±l%. The effective porosity at the first
probe, which measures over the top 7% of the column, is seen to be
higher than subsequent porosities further down the column. This effect
is most noticeable in the nonuniform medium, where the smaller grains
tend to filter down,leaving the top portion of the column with larger,
more uniform grain sizes. Porosities measured at the other two probes
show more uniformity, as expected, since these measurements average
over a much greater portion of the column. Comparison of the average