Doctor Neutron removed the assumptions of infinitesimal pore/particle sizes in his new nuclear micro-geophysical forward model called Laminated Vuggy Fractal Porous Media (LVFPM): pores / particles are permitted to have finite linear dimensions that range from 0.0001 cm to 1.0 cm and laminae with bed thicknesses from 0 to 10 cm. These laminae are composed of two interdependent media with separate bed thicknesses that can be oriented parallel or perpendicular to the borehole.
LVFPM computes these nuclear geophysical formation parameters:
(1) gamma hydrogen index (2) bulk density (RHOB), (3) electron density index (EDI) (4) apparent bulk density (RHOBapp) (5) photoelectric factor (Pe) (6) effective atomic number (Zeff) (7) linear absorption coefficients (8) density porosity (DPHI);
both for the homogeneous and the inhomogeneous cases.
In effect, LVFPM becomes the (non-linear) mixing rule generator for all these physical quantities in laminated vuggy fractal porous media with finite pore / particle sizes.
Gamma linear absorption coefficients are presented at 15 energies from 10 Kev to 10 Mev. These coefficients are critical to a proper understanding of both open hole and cased hole density logs and cased hole pulsed neutron decay and gamma ray spectroscopy logs in real porous media. Doctor Neutron's use of these coefficients to compute both the homogeneous and inhomogeneous bulk density and other gamma parameters is both accurate and innovative - it directly uses the NIST data tables prepared by Hubbell and Seltzer for each of seventeen elements commonly encountered in earth formations.
Neutron porosity values from several service companies are also presented. Model pores may contain salt water, oil, gas, Illite, Kaolinite, Montmorillonite and Barite. In addition to the standard formations (limestone, sandstone, dolomite), the matrix may contain Anhydrite, Aragonite, Cristobalite, Gypsum, Halite, Sulphur, Sylvite, Kaolinite, Illite, and Montmorillonite. Special help is provided to correctly handle the very important mixture, saltwater. Other minerals and fluids can be specified through the use of Microsoft EXCEL notebooks.
Differences in the above neutron and gamma ray parameters between the homogeneous case (infinitesimal pore sizes, no laminae) and the inhomogeneous case (finite pore sizes with laminae) are echoed in the responses of many commercially available logging tools such as dual-spaced neutron, dual-spaced density, and pulsed neutron tools like Thermal Multigate Decay and Thermal Decay Time .
Because the LVFPM/TPM derivations are symmetric in pore/particle properties and their software implementations are carefully controlled, a wide variety of 2 component mixture problems is actually supported:
(1) pores within a rock matrix; (2) particles and pebbles within a fluid bath, (3) structural clay globs within another solid matrix, and (4) other mineral inclusions within a rock matrix.
A block diagram for LVFPM is provided below. LVFPM is called micro to distinguish it from much larger scale seismic models; it is a forward model since its inputs and outputs are opposite to those needed to characterize reservoirs and mineral deposits from nuclear logs.
There are actually two code blocks inside LVFPM, called "FORMATION I" AND "FORMATION II". When MODE is set to HET, these blocks provide independent outputs for the two formations FORMATION I or FORMATION II; when mode is set to PARA or PERP, these blocks combine to provide outputs for parallel or perpendicular laminae: FORMATION I and FORMATION II.
See the page FRACTALS for a discussion of the inputs maximum pore radius and fractal dimension.