longitudinal dispersion in nonuniform isotropic porous media

137
Monte Carlo integration technique described 1n Section 3.5. The pore
size distribution used for the calculations is shown in Figure 4.12.
Although the same number of pores leading to and from a junction are
required for a given unit cell (see Figure 3.2), it is possible to have
a continuous range of junction connectivity for the network. This 1S
accomplished by using the two nearest even connectivities, say C1 and
C2, in proportion a, such that the connectivity for the network, C,
is,
C aC1 + (1-a)C2
Table 5.1 shows the computed and measured permeabi1ities using the
"best fit" junction connectivity, C = 16. This parameter was set
primarily to adjust the calculated permeability of the nonuniform
medium, since the uniform medium was fairly insensitive to the junction
connectivity parameter. Table 5.1 also shows the permeability
calculations when network effects are ignored (C -+ (0). As expected, the
permeability of the nonuniform medium is significantly higher when the
network effects are not taken into account. Convergence of the Monte
Carlo integration scheme for the nonuniform medium is slower than for
the uniform medium, as shown in Figures 5.1 and 5.2. The nonuniform
medium required 400,000 iterations (unit cells) , while the uniform
medium permeability was calculated using 100,000 iterations to get
within 2:1% of the final asymptotic value. Permeability as computed
from equation (3.11) 1S seen in Table 5.1 to do reasonably well (within
15%) for both the uniform and nonuniform medium. The Haring and