longitudinal dispersion in nonuniform isotropic porous media

102
cumulative probability distribution shown in Figure 4.9. The influence
of each grain on the pore length distribution is expected to follow the
cumulative grain size distribution weighted by the area of a given
particle
J(d) - f 1:;2h (l:;)dl:;
o
d
To produce J(d) from Pd(d), we first interpolate the experimental data
to 1000 equally spaced probabilities on the cumulative distribution.
For probabilities beyond the range of the experimentally determined
values, the length is set to the maximum or minimum grain size. The
distribution is given by equation (3.52)
d
J(d)- J 1. dP (I:;)
o I:; d
where the values of J(d) are normalized such that the integral over the
entire domain is one. This integration is performed numerically
(trapezoidal integration). Figure 4.10 shows the final grain size
distribution from this calculation. The d 50 values for the uniform
and nonuniform media are 0.38Omm and 0.453mm, respectively, for the
area-weighted distributions shown in Figure 4.10. The nominal
geometric standard deviations «d 84 /d 16 )1/2) for the uniform and
nonuniform media (Figure 4.10) are 1.16 and 2.42, respectively. Table
4.1 presents a summary of the information on the grain size
distributions.