VIII Conclusion

[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 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.