In this second example of laminated beds, LVPM was used to
model limestone laminae whose pores alternately contain oil
and then montmorillonite. The oil + limestone pore size was
fixed at 0.0001 cm and the montmorillonite + limestone pore
size was fixed at a much larger value of 0.1 cm. Significant
differences appear between the parallel and perpendicular
laminar orientations.

The bed thicknesses of both types of laminae were varied from
0.01 cm to 10 cm. In the figures of this section, the far
left always refers to mainly montmorillonite saturated
limestone and the far right refers to mainly oil saturated
limestone. Specifically, from left to center, the limestone
+ montmorillonite bed thickness is fixed at 10 cm. Then,
from center to right, this bed thickness drops from 10 cm to
0.01 cm. For the limestone and oil, its bed thickness varies
from 0.01 cm to 10 cm from left to center and then from center
to right, it is fixed at 10 cm. Thus, at the center of all
these figures, both bed thicknesses are equal to 10 cm.

Again in this section, homogeneous refers to the application
of classic volumetric mixing rules governed by bed thickness
weighting for homogeneous media with infinitesimal pore sizes.
Heterogeneous again refers to the exclusive use of the
transmission probability method within LVPM to compute all
physical properties for both media with finite limestone pore
sizes. LVPM more accurately details the propagation of
neutrons and gamma rays in these heterogeneous media.
Corrections need to be applied to the apparent density and
neutron logging values to properly account for finite pore
sizes and bed thickness effects.

In Figure 1, note that the homogeneous/classic bulk densities
and the LVPM parallel orientation bulk densities are about the
same whereas the LVPM perpendicular orientation bulk densities
are much lower, by an average of 0.047 g/cc, than the other two.
In this example, bulk density log readings in perpendicular and
parallel laminated beds need to be increased to correct for the
propagation of gamma rays in these laminae.  For the parallel
laminae these increases are equal to those expected from
classic bed thickness weighting.  However, for the perpendicular
lamine, such corrections are much larger.

Increases in LVPM neutron porosity in laminated beds are
observed in Figure 3 as the oil and limestone bed thickness
increases; these increases continue as the montmorillonite
and limestone bed thickness is reduced.   These porosity values
are derived from a proxy model based on the neutron slowing
down length (Figure 6).  In this example, LVPM neutron
porosities for both the parallel and perpendicular cases are
about the same and  both are larger than those predicted from
classic bed thickness weighting.  These overly optimistic
neutron porosity values must be decreased to improve porosity
measurement accuracy.