[74.2.1.1] Local porosity distributions
and local percolation probabilities
have been introduced as a partial
geometric characterization
of the complex pore-space geometry
in porous media.
[74.2.1.2] From these well-defined
and experimentally accessible geometric quantities,
the dielectric response of general porous media
resulting from geometrical disorder
was calculated using simple effective-medium theory.
[74.2.1.3] It was found that the theory
predicts an underlying percolation transition,
which may or may not appear
as a porosity threshold for conduction.
[74.2.1.4] As a consequence, percolation scaling theory
can be applied to the case of porous media.
[74.2.1.5] This provides a theoretical framework
inside which Archie’s law can be understood
as a statement about the diagenesis of rocks.
[74.2.1.6] In particular, the universal applicability
of this phenomenological relationship
appears as a consequence
of the universality
of the percolation transition.
[74.2.1.7] Simplest mean-field theory
gives the value m=2
for the cementation exponent
in the low-porosity limit.
[74.2.1.8] A new scaling law for the divergence
of the real duelectric constant
is predicted in the high porosity limit.
[74.2.1.9] This law should be observable
in conductor-filled insulating pore
casts of systems obeying Archie’s law.
[74.2.1.10] Numerical solutions for the effective dielectric constant
show a surprising sensitivity
to geometric details whenever the dispersion becomes large.
[74.2.1.11] The present theory contains no adjustable
parameters or distribution functions.
[page 75, §0]
[75.1.0.1] The dielectric response is calculated
purely from geometrical quantities.
[75.1.0.2] Experimental observation
of local porosity distributions
and local percolation probabilities[27]
must answer the question
whether they are suitable geometric characteristics
for distinguishing different cases of porous media or not.
