longitudinal dispersion in nonuniform isotropic porous media

100
screens are needed to characterize the grain S1ze distribution. A
series of 25 screens are needed to characterize the nonuniform grain
size distribution. The sieves are stacked and placed in the mechanical
shaker for 10 minutes. The sand retained on each screen is weighed to
give the fraction by weight of grains which are nominally larger than
the opening size of the given screen but less than the opening S1ze of
the screen immediately above. The results are generally given as a
cumulative distribution of grain size by weight and often follow a log-
normal distribution (Vanoni, 1975). If we let d 84 , d 50 , and d 16
represent the 84 th , 50 th , and 16 th percentile grain S1ze on the
cumulative distribution, respectively, then the geometric mean grain
size, d g , and the geometric standard deviation, 0g , are given by d 50
1/2
and (d 84 !d 16 ) ,respectively, for a log-normal distribution.
Figure 4.9 shows the grain S1ze distributions for the two porous
media. Both distributions are reasonably log-normal, the nonuniform
grain size distribution having a much greater geometric standard
deviation (0 g = 2.93) than the uniform medium (0 g = 1.15). The
nonuniform medium also has a much greater mean grain size, d g
compared to d = 0.382mm for the uniform medium.
g
As discussed in Chapter 3, the grain S1ze distribution 1S a
volume-weighted distribution (equation (3.51»
P d (d) '" f z;; 3hCl.;)dZ;;
o
d
1.26mm,
where h(d) is the probability density for the grain diameter according
to the frequency of occurrence of a given grain. Pd(d) is the