Should Petrophysics Calculate Total or Effective Porosity?

Petrophysicists define two porosities, the total porosity (PHIT) that includes isolated pores and the space occupied by clay-bound water and the effective porosity (PHIE) which excludes isolated pores and pore volume occupied by water adsorbed on clay minerals.??

Density Porosity (PHID) is not PHIT as it represents a porosity somewhere between PHIT and PHIE.? This is because the matrix (Rhoma) and fluid (Rhofl) densities used for PHID are picked for clean formations and may be different in the shales.?

PHID =?(Rhoma - Rhob)/(Rhoma - Rhofl)

Consequently, it is necessary to calibrate PHID to the core porosity.??

• PHIT = PHID x Constant
• PHIE = PHIT – VSH*PHISH

Without core, it is necessary to first calculate PHIE using an appropriate density response equation like:

Rhob = (1 - PHIE - VSH) * Rhoma + VSH * Rhosh + PHIE * Rhofl)

To calculate PHIT from PHIE requires knowledge of the shale porosity (PHISH) due to clay bound water, which can be calculated from:

PHISH = (Rhodsh - Rhosh) / (Rhodsh - Rhow)

Where: Rhodsh (Dry shale density) Rhosh?(Shale density) Rhow?(Shale water density)

The dry shale point (Rhodsh) does not exist on the logs, as they are always wet insitu. Rhodsh can be determined from the density vs. neutron porosity (PHIN) crossplot.

• Dry clay density can be inferred from knowledge of the clay mineralogy
• The wet shale point is at the end of the data boomerang
• The dry shale is the extrapolation of the shale line to the dry line

Water Saturation

Reservoirs with a high formation water salinity and a low clay mineral content are called Archie reservoirs, where the effective and total porosities are essentially the same, because there are negligible clay bound water effects.? Otherwise, they are called non-Archie reservoirs, because there can be a significant clay bound water saturation.? Non-Archie reservoirs can be evaluated in terms of either effective or total porosity.

Different water saturation (Sw) equations use different porosities.?In clean formations the Archie equation can be used, as it is assumed PHIT is equal to PHIE. ?In shaly formations the water saturation equation must correct for the shale’s excess conductivity.? Waxman-Smits, Juhasz and Dual Water use PHIT, whereas Simandoux and Indonesia use PHIE.?

It is essential that the shaly sand water saturation equation be selected to correct for the shale’s excess conductivity.

This equation can be confirmed using a crossplot where ‘unlimited’ Sw is plotted against the volume of shale (Vsh) in the water leg.??

• Rw confirmed in clean intervals (Vsh<10%)
• Sw should average 1 as shaliness increases

Conclusions

• Petrophysicists should calculate both PHIT and PHIE.?
• Density Porosity PHID is not PHIT, as it is somewhere between PHIT and PHIE.
• If core data is available calculate PHIT, then PHIE.
• If no core data is available calculate PHIE, then PHIT.
• Confirm Sw equation by plotting ‘unlimited’ Sw vs. Vsh in the water leg.?