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Local Porosity Theory and Stochastic Reconstruction for Porous Media

R. Hilfer
ICA-1, Universität Stuttgart, 70569 Stuttgart, Germany
Institut für Physik, Universität Mainz, 55099 Mainz, Germany
Räumliche Statistik und Statistische Physik, Lecture Notes in Physics Vol. 554
D. Stoyan and K. Mecke (eds.), Springer, Berlin, 2000, pages 203-241

The paper reviews recent developments in local porosity theory, and discusses its application to the analysis of stochastic reconstruction models for sedimentary rocks. Special emphasis is placed on the geometric observables in local porosity theory and their relation with the Hadwiger theorem from stochastic geometry. In addition recent results for the exact calculation of effective physical transport properties are given for a Fontainebleau sandstone. The calculations pertain to potential type problems such as electrical conduction, dielectric relaxation, diffusion or Darcy flow. The exact results are compared to the approximate parameterfree predictions from local porosity, and are found to be in good agreement.