Page 113 - Percolation Models for Transport in Porous Media With

106 CHAPTER 6. PORE SIZE DISTRIBUTION

ties (such as saturation) of such media are mainly determined by the volumes of
the pores, while their conducting characteristics depend primarily on the capil-
lary subsystem of the pore space. Usage of the conventional parametric methods
permits to study only the large-scale pore subsystem (73]. To determine the pa-
rameters of a capillary subsystem, it is necessary to gather information about the
subsystem using a quantity that does not depend strongly on sizes of the pores.
Electric conductivity is an example of such a quantity. Parameters can be found
based on electric surface measurements using electro-parametric methods in a core
partially saturated with a conducting electrolyte [74]. This method suggests that
the measurements of the specific electric conductivities for different parts of the
core saturated with a wetting electrolyte in the gravitational field be taken instead
of the measurements in the non-wetting mercury volume. The described approach
allows to get rid of the influence from the subsystem of the site pores. It is also
possible to determine the PDF for capillaries based on direct use of the percola-
tional formula for electric conductivity. This method suggests a combined scheme
of mercury and standard porometry.

6.1 Percolation Model for the Mercury Injection
Test

During the mercury injection test the displacement of gas from the core by a non-
wetting phase (mercury) takes place. As it fills the capillaries, the non-wetting
phase overcomes the capillary pressure

Pk = !l.p = P1- P2 = 2xcos8/rk. (6.1)
For small pressure differences at the initial stage of the process, pores with radii
greater than Tk do not form a connected system. They form finite clusters, only
those of which can be reached by mercury, that are adjacent to the outer cross-
section of the specimen. When the pressure difference reaches the breakthrough
value, large enough for mercury to appear in the outer cross-section of the core,
the pores filled with mercury form a connected system, i.e., an infinite cluster.
At the intervening stage of the process, as !l.p increases further, the density
of the infinite cluster of the pores filled with mercury goes up. When saturation
S reaches the second threshold value the connected system of the gas-saturated
pores breaks.
From this instant, during the final stage of the process, the gas stops coming
out of the core. Trapped in the finite clusters, the gas compresses as the pressure
in the non-wetting phase goes up.
Take a periodic network of cylindrical capillaries as a geometrical model of
the pore space and consider the outlined stages for the filling of the core with