Page 126 - Percolation Models for Transport in Porous Media With

6.3 MERCURY ELECTRIC POROMETRY 119

Substitute the integral in the left side of the equation (6.21) by an integral
sum according to some quadrature formula. For example, if we divide the interval
[a., a*] with the grid {r; = r;-1 + h, h =(a*- a.)/(n- 1), i = 1, ... ,n} and use
the trapezoid formula, we obtain
n
LfiAik = 1/3 (6.26)
i=l
where

Now the system (6.26) can be solved using the regularization method, as de-
scribed above. As a result, the values {f(r;)} of the sought PDF at the chosen set
of points are obtained.

6.3 Percolation Model for the Combined Mercu-

ry and Electric Porometry Method

The method of determining the PDF for capillaries using the data of electric
porometry presented in §6.2 is more exact and well-defined than the analytical
formula (6.18) based on the model ofiCP. However this method, in its turn, carries
an error due to the use of the effective medium model, the latter being merely a
limiting case of the exact percolation model. The EMM describes the properties of
the medium well enough only at some distance from the percolation threshold ec
and brings an error of ~ 20% into the calculations of the percolation parameters in
the vicinity of ec· Therefore the interval ofradii where f(r) is determined with due
reliability bevomes smaller. Also, when a wetting fluid is used as an electrolyte
in the electric porometry method according to the scheme in fig. 36, the most
significant interval, i.e., that of small radii, is not scanned because the conducting
IC breaks up. Furthermore in practice, to obtain representative experimental
information about the studied core, its vertical dimension should be big enough
(1 - 10 meters), which is much larger than the cores actually studied.
Overcoming of these drawbacks is possible in the development of a combined
method, that of mercury electric porometry, which integrates positive features of
mercury porometry and the standard electric porometry (see fig. 41). The use of
a non-wetting conducting fluid, which is injected in the medium under pressure,
takes care of the problem of core size and allows to scan the interval of small radii.
It is most natural to use mercury as such a fluid. As for the mathematical methods
to be used for processing the experimental data, they may be upgraded with