Doctor Neutron removed the assumptions of infinitesimal pore/particle
sizes in his new nuclear micro-geophysical forward model called
Laminated Vuggy Porous Media (LVPM): 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.
LVPM computes these nuclear geophysical formation parameters:
GAMMA
(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, LVPM becomes the (non-linear) mixing rule generator
for all these physical quantities in laminated vuggy 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 LVPM/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 LVPM is provided below. LVPM 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 LVPM, 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.
