One of the most common debates in Petrophysics is whether to use Total or Effective Porosity. This article discusses the differences between the two. It explains why total porosities should always be calculated and why some companies use effective porosity to improve their insight into reservoir behaviour.

**Definitions**

**Core Calibration of Porosity**

**Calculating Total Porosity**

**Determining Effective Porosity**

**Porosity & Water Saturations**

**Effective Porosity, Permeability & Mobile Fluids**

**Summary**

**References**

Total porosity may be defined as all the pore space containing fluids (water, oil or gas), whether or not they are mobile. This pore space includes any hydrocarbon fluids, mobile water, capillary bound water and clay-bound water.

There are various definitions of 'effective' porosity e.g.Juhasz (1986), Hill-Shirley-Klein (1979), Clavier-Coates-Dumanoir (1977). However, the most common definition is:

phiE = phiT - Vd

where phiT is the total porosity of clean (clay free) sand and Vd is the volume of dispersed clay in the sand pore space expressed as a fraction of the bulk volume. In other words, effective porosity is total porosity less the volume of clay-bound water.

Of course, when you decrease porosity by converting from a total porosity to an effective porosity, the hydrocarbon saturations must increase, since the same amount of hydrocarbon is present. In other words, the hydrocarbon volumes estimated using either a total or effective porosity system are the same (i.e. ShT.phiT.h = ShE.phiE.h), it should make no difference which system is utilised.

To have the most confidence in your log evaluations, the core derived measurements should agree with those from your wireline logs. Since it is not possible to measure effective porosities in a reliable and repeatable manner, calibration with core analyses is best achieved by measuring total porosities on core plugs and comparing these with total porosities estimated from logs.

The best way to calculate total porosity is using the density log, correcting for lithology (using grain density) and fluid density (using invaded zone resistivity or neutron logs). For completeness the formula recommended is:

phiT = (RHOma - RHOB)/(RHOma - (RHOMF.SWXO+RHOHC.(1-SWXO)))

where RHOma is the grain density (normally determined from laboratory measurements on core material), RHOB is the density log measurement, RHOHC is the in-situ hydrocarbon density (from pressure data or sampling), RHOMF is the mud filtrate density (from correlation charts normally) and SWXO is the invaded zone water saturation.

Of course, solving this equation properly requires iteration since SWXO is dependent on phiT, no matter which saturation model you use (Archie, Dual-Water, Indonesia, Waxman-Smits etc.). Unfortunately, this requirement is also why this type of solution is not more commonly used. In actuality, the maths is very straightforward to program nowadays.

In the absence of density log (or NMR) data, total porosities are best calculated by empirical calibration to core data.

From the first equation, to estimate the effective porosity, some estimate of Vd must be made. Typically the density-neutron separation or the gamma ray logs are used to make this estimate. Actually, in the industry today, over 20 different models for the shale fraction Vd are in use. A lot of time is spent in discussions between personnel as to which model is most appropriate in any particular circumstance. This debate is another of the drivers for using total porosities.

Of course, once phiE is known, along with phiT and ShT, ShE can be readily calculated from the second equation.

Once a total or effective porosity has been determined, it must be used in a water saturation equation to determine hydrocarbon saturations. If you've used a total porosity model, then there's no concern about which shale fraction model you've used. If you've gone down the effective porosity route too early, you must adjust the saturation model to account for the conductivity of the clay-bound water that is measured by the resistivity logs, but not accounted for in the porosity.

So why bother with effective porosity at all? - There are a number of reasons:

- Effective porosity is primarily used as a tool to help people understand whether or not the hydrocarbons are likely to flow. In this respect, formation pressure tests or NMR measurements would be more diagnostic.

- Since effective porosity refers to the fluids that are not bound to the rock matrix, there is typically a better correlation between effective porosity and permeability than there is using total porosity - unless there is negligible shale present. Hence, if you're having trouble working out a decent porosity to permeability transform, effective porosity may reduce your difficulties.

Since a total porosity system is more reliably calibrated to core and simpler to work in, this is the approach recommended for petrophysical evaluation. If there are conductive shales present, correct for these using total porosity and either the Waxman-Smits or Dual Water models to get water saturations. Use effective porosity only to calibrate a permeability transform. If you need effective porosities and water saturations for some other reason (e.g. your volumetric model is "effective"), calculate them from your calibrated total porosity system.

- Clavier, C., Coates, G., and Dumanoir, J.: “Theoretical and Experimental Bases for the Dual-Water Model for Interpretation of Shaly Sands,” SPE-6859, 52nd annual meeting [Denver] preprint 16 p., 1977.
- Hill, H.J., Shirley, O.J., Klein, G.E.: “Bound Water in Shaley Sands - Its Relation to Qv and Other Formation Properties,” Log Analyst, May-June 1979.
- Juhasz, I.: "Assessment of the distribution of shale, porosity and hydrocarbon saturation in shaly sands,' paper AA, in 10th European formation evaluation symposium transactions, Society of Professional Well Log Analysts, Aberdeen Chapter, 15 p. 1986.
- Schlumberger Educational Services: “Log Interpretation Principles/Applications,” Schlumberger manual, 1989. Waxman, M.H., and Smits, L.J.M.; "Electrical conductivities in oil-bearing shaly sands," Society of Petroleum Engineers Journal, v. 8(2), p. 107-122, 1968.