DENSITY, NEUTRON & PULSED NEUTRON
MEASUREMENTS IN A VUGGY DOLOMITE, II
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.