As a simple extension to the work in this vuggy dolomite,
25% of the oil was replaced with barite and the various
physical variables are displayed as functions of formation
LVFPM model input porosity for several pore sizes.  Again
bed thickness is unused - the focus remains fixed on pore
size effects alone.   In Figure 1, the curve labeled
"homogeneous" is consistent with the classic linear
volumetric bulk density mixing rule:

That is, a formation's bulk density is equal to the sum of
the densities of the formation's materials linearly weighted
by their individual volume fractions.  Analyses show that the LVPM homogeneous mode output bulk density (red curve) is strictly linear.  The cyan curve is the above classic linear density mixing rule formula in which these density and saturation values were used: dolomite density = 2.87 g/cc; barite density = 4.48 g/cc; oil density = 1.05 g/cc; barite saturation = 0.25; and oil saturation = 0.75.  The two curves are indistinguishable.  This homogeneous/linear solution corresponds to that for infinitesimal pore sizes.

In this same Figure, the other curves represent the bulk
density outputs from LVPM in its heterogeneous mode of
operation for pore sizes of 0.0001 cm, 0.5 cm, and 1.0 cm. The exact same density and saturation values listed above apply to these curves and are input to program LVPM. The best fit to these output data for a pore size of 0.0001 is definitely quadratic, while the data for pore sizes of 0.5 cm and 1.0 cm can be quite well fit with a linear
relationship in porosity.  Thus pore size effects can not
only alter the relationship between bulk density and
porosity, they can also undermine the assumption of
linearity of the mixing rule for bulk density in terms of
a formation's constituent material densities and volume
fractions.  Figure 2 shows the impact of these features
on density porosity computed from bulk density.

These density effects arise from the application of the
transmission probability method (TPM) to vuggy porous media with finite pore sizes.  TPM more accurately details the propagation of neutrons and gamma rays in both vuggy porous media and in laminated vuggy porous media.

Figure 3 shows the rather strong effects of pore size on
neutron apparent limestone porosity for this example.
These effects arise from pore size effects on the neutron
slowing down length (Figure 4) and its use within an LVPM
proxy model for neutron porosity.

The remaining figures describe the effects of vuggy porosity on the thermal neutron diffusion length and thermal neutron diffusion coefficient.  In this example of a barite and oil saturated vuggy dolomite, although the effects of pore size on both of these quantities is quite strong, the direct effects on the thermal neutron capture cross section (sigma) remain quite small.  However, the indirect impact on sigma through its diffusion corrections will be significant.