Abstract

As has been reported by numerous authors since 1945 that resistivity logs are insensitive to the presence of hydrocarbon or water filled vuggy porosity (Guyod, 1945; Nugent and others, 1978; Rasmus, 1987; and Asquith, 2005).

Rasmus(1987) reported that the Maxwell-Garnett Equation which is designed to model low frequency resistivity response in a series of large spherical pores (vugs) within finer spherical matrix pores can be used to model resisitivity in vuggy carbonates. The equation is listed below:

Ct = Cm {1+{2V[(Cv-Cm)/(Cv+2Cm)]}/1-{V[Cv-Cm)/(Cv+2Cm)]}}

Rt = 1/Ct

Where:

Ct = total conductivity

Rt = total resistivity

Cm = matrix conductivity

Cm = [Φ(matrix)∧2 * Sw(matrix)∧2]/Rw

Φ(matrix) = Φ( sonic) & Sw(matrix) = {[1/Φ(sonic)∧2] * (Rw/Rt)}∧0.5

Cv = vug conductivity

Cv = Sw(vug)/Rw

V = percent vugs [V = Φ(total) - Φ(matrix)] or V = Φnd - Φ (sonic)

The Maxwell-Garnett Equation can then applied to the determination cementation (m), saturation (n) exponent and water saturation (Sw) in a Permian Clear Fork vuggy dolostone. The first step is to determine a value for Ro [wet resistivity] as shown below:

Co = Cm {1+{2V[(Cv-Cm)/(Cv+2Cm)]}/1-{V[Cv-Cm)/(Cv+2Cm)]}}

Ro = 1/Co

Where:

Co = total wet conductivity

Ro = total wet resistivity

Cm = matrix conductivity

Cm = [Φ(matrix)∧2 * Sw(matrix)∧2]/Rw w/ Sw(matrix) = 1.0

Φ(matrix) = Φ(sonic) & Sw(matrix) = {[1/Φ(sonic)∧2] * (Rw/Rt)}∧0.5

Cv = vug conductivity

Cv = Sw(vug)/Rw w/ Sw(vug) = 1.0

Therefore:

Fr (Formation Resistivity Factor) = Ro/Rw

I (Resistivity Index) = Rt/Ro Rt = (2*LLD) - LLS

Φ(total) = Φnd

Sw(total) = [BVW(matrix) + BVW(vug)/Φ(total)]

BVW(matrix) = Φ(sonic) * Sw(matrix)

BVW(vug) = 0.0 [i.e hydrocarbon filled]

When Φ(nd) [Φ(total)] is cross plotted versus Fr (Ro/Rw) and a line fitted to the data with the origin at Φ(total) = 1.0 and Fr(Ro/Rw) = 1.0 the cementation exponent (m) is 2.30. When Sw(total) is cross plotted versus reisitivity index I (Rt/Ro) and a line fitted to the data with the origin at Sw(total) = 1.0 and I = 1.0 the saturation exponent (n) is 1.54. In order to calculate water saturation (Sw) the correct equation would be:

Sw(total) = {[1/Φ(total)∧2.30] * (Rw/Rt)}∧(1/1.54)

Note from this work that in a vuggy reservoir like our Clear Fork example that both cementation (m) and saturation (n) exponents are changed. This example illustrates what was reported by Rasmus (1987) that changing only the cementation exponent (m) in a vuggy reservoir is not sufficient to determine the correct water saturation (Sw), because both m and n vary.

You will note in this example that it was assumed that the vugs contained hydrocarbons [Sw(vug) = 0.0]. So without core data to obtain m and n values the geologist or engineer can obtain a reasonable value for Sw in a vuggy reservoir by:

Sw(total) = {[1/Φ(total)∧2] * (Rw/Rt)}∧0.5

Clear Fork Water Saturation [5350’ to 5400’]

Sw(m = 2.30 & n = 1.54) 24.6%

Sw(m = 2.30 & n = 2.00) 34.5%

Sw(m = 2.00 & n = 2.00) 22.1%

In both Archie Equations it is assumed that Sw (vug) = 0.0, because the resistivity logs are insensitive to either hydrocarbon [Sw(vug) = 0.0] or water [Sw(vug) = 1.0] filled vugs. I have listed below some of the logging methods that can be used to indicate if the vugs contain hydrocarbons or water:

1. Φd > Φn [on correct matrix] gas effect in gas-bearing reservoirs

2. Dielectric Water-Filled Porosity (Φw) < Φnd

3. Rt/Rw versus Rxo/Rmf data plot in the productive region and correct pore type (vug+intercrystalline/intergranular porosity) of a DEW Plot.

4. Hydrocarbon indicated on a NMR Log

This exercise was only intended to illustrate the problem in dealing with the log analysis of vuggy carbonates, and is not intended to be a substitute for core derived m and n values. However, I hope it illustrates the importance of obtaining both m and n when analyzing vuggy carbonates.