Henderson  Petrophysics

Theory For the Overlay Water Saturation Model

Passey et. al. (1990) described the EXXON technique for creating resistivity and porosity baseline curves and estimating organic matter content (TOC) as a function of separation of the baseline curves. The EXXON method can be modified, as described below, to identify hydrocarbons and calculate water saturation (S_w) without explicit knowledge of porosity, water resistivity (R_w) or the Formation Factor parameters a and m.

Equation (1) after Passey describes the separation of baselined porosity and resistivity logs:

(1)

where;

	is separation of the baselined resistivity and porosity curves,
R	is measured resistivity,
Rns	is resistivity of non-source shales,
P	is porosity log reading,
Pns	is porosity log reading in non-source shales, and,
K	is a scale factor dependent on the porosity log measurement units.

Equation (1) can be re-arranged to individually describe deviation from baseline conditions for the resistivity log (Y_r) and porosity log (Y_p):

	(2)
	(3)

In the absence of solid organic matter or hydrocarbons, the baseline conditions for the resistivity and porosity logs are:

R = Rns

and

P = Pns

so;

Yr= Yp= 0

To calculate continuous Y_r and Y_p profiles through the full range of clean formations to shales, R_ns and P_ns in equations (2) and (3) can be treated as functions of shaliness:

	(4)
	(5)

where:

Rsd	is resistivity of clean (no shale) formation,
RSh-ns	is resistivity of non-source shale,
Psd	is porosity log reading in clean formation,
PSh-ns	is porosity log reading in non-source shale, and,
Vsh	is shale fraction

In non-reservoir intervals (silt and shale), anomalous resistivity (Y_r > Y_p) is associated with solid organic matter. In reservoirs, Y_r > Y_p indicates the presence of hydrocarbons.

Continuous profiles of Y_r and Y_p can be used to calculate expected "wet" resistivity (Ro) in water zones and non-source shales. In the absence of hydrocarbons and organic material:

(6)

and

(7)

The classical Archie equation can be written as:

(8)

Substituting DLOGR estimated Ro from (7) above;

(9)

Henderson Petrophysics Home Page

References

Archie, G. E.: "The Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics", Petroleum Transactions of the AIME 146 (1942).

Passey, Q. R., Creaney, S., Kulla, J. B., Moretti, F. J., Stroud, J. D.: "A Practical Model For Organic Richness From Porosity and Resistivity Logs", AAPG Bull., Dec. 1990.

"QUICKLOG" - Petrophysical software distributed by Henderson Petrophysics, 8 Debbie Street,  Brisbane Queensland, Australia 4061. Telephone: (61) 7  3300 3980. Facsimile (61) 7 3300 9342.

"TOCP" - Petrophysical software distributed by Henderson Petrophysics.