Bulk Density, Density Porosity, Neutron Porosity,
Capture Cross Section, Diffusion Length, Diffusion
Coefficient, and Slowing Down Length -
All versus Laminated Bed Thickness
In every case, the classic mixing rules predict a smooth,
gradual (albeit non-linear) transition from oil sand
properties to oil sand + montmorillonite properties, whereas
the LVPM heterogeneous calculations predict a much larger
and stronger non-linear approach from oil sand properties to
oil sand + montmorillonite properties. For example, Figure 1
indicates that the heterogeneous bulk density increases from
2.332 g/cc at a montmorillonite bed thickness of 0.01 cm to
2.401 c/cc at a thickness of just 1 cm, an increase of
0.069 g/cc. Compare this with the homogeneous/classic
values: 2.330 g/cc to 2.345 g/cc, an increase of just
0.015 g/cc. Figure 2 echoes these features in the density
porosity.
The bulk density differential between the homogeneous and
heterogeneous methods reaches its maximum near a
montmorillonite bed thickness of 2 cm: it amounts to
0.057 g/cc and corresponds to a porosity differential of
3.4 pu! As the montmorillonite bed thickness continues to
increase, the heterogeneous density remains larger than the
homogeneous density, but their differential continues to
decrease.
Figure 3 details the neutron porosity as a function of
montmorillonite bed thickness. See Figure 7 for the
underlying neutron slowing-down length. As the
montmorillonite bed thickness increases, the homogeneous
neutron porosity remains greater than the heterogeneous
porosity and this difference increases throught the entire
bed thickness range.
Surprisingly, Figure 4 indicates no difference between the
homogeneous and heterogeneous neutron capture cross section
as the montmorillonite bed thickness increases out to
10 cm! Similar results hold for the thermal neutron
diffusion length, as seen in Figure 5. Small differences
between the homogeneous and heterogeneous thermal neutron
diffusion coefficient are shown in Figure 6.
