HOW the FRACTAL DIMENSION of a POROUS MEDIUM EFFECTS the RESPONSES of STANDARD NUCLEAR LOGGING TOOLS
Program LVPM has been modified to accept fractal dimension INPUT information about porous media. This information could come from laboratory measurements on soil/rock samples or from log analyses. Previous versions of LVPM used a single pore size to describe earth formations. The main objective is to provide even more realistic and accurate reservoir analyses from nuclear logs both by accounting for fractal properties during fundamental tool calibrations and for developing environmental corrections for fractal properties during logging and post-processing.
The seminal papers of Michel Rieu and Garrison Sposito, "Fractal Fragmentation, Soil Porosity, and Soil Water Properties: I. Theory and II. Applications," SOIL SCI. AM. J., SEP-OCT, (1991), pp. 1231-1238 and 1239-1244 have been very widely read but they can be difficult to follow. A non-printable pdf of these very important and influential papers is included just below. A more extensive list of references is also provided at the end of this section.
Doctor Neutron's activities with fractals have been guided by the work of Allen G. Hunt. See his book "Percolation Theory for Flow in Porous Media", Springer, 2005, ISBN: 3-540-26110-9. Pages 44 - 49 provide an exceptionally clear explanation of the partial volume expansion of Rieu and Sposito and its extension to continuous pore size distributions.
For Doctor Neutron, clearly the most important and useful result from these references is exemplified by Hunt's equation (2.16):