Page 95 - Percolation Models for Transport in Porous Media With

4.5 STABILITY 87

calculated value by several orders of magnitude. This is due to the fact that the
estimates in (4.53) and (4.55) are majorants, and therefore are rather overstated.
The closest proximity of the estimated and the exact values of the discussed coef-
ficient is observed in the case when the principal difference of j+(r) from f-(r)
takes place in the neighborhood of the minimal radius r = a* when a* -+ 0.
Concluding the topic, we would like to remind that other macro properties
of a porous medium can be calculated using a given f(r), just like the phase
permeabilities. The specific electric conductivity E of the medium in the case
when it is saturated by a conducting fluid, is an example of such a property. Since
the expression (1.11} for E is akin to (4.50} for Tk = 0, if the numerical factor
A' is replaced in the latter and r 4 in its denominator is replaced by r 2 , it follows
that all estimates presented above remain valid up to the numerical values of the
majorizing constants s_' s+' s~.
Thus it turns out that the calculation of the effective macro properties of porous
media, carried out in the percolation approach, is stable with respect to errors in
determining f ( r).