# Use of Resistivity Logs To Calculate Water Saturation at Prudhoe Bay

- Authors
- D.D. McCoy (Exxon Production Research Co.) | W.A. Grieves (Exxon Co. U.S.A.)
- DOI
- https://doi.org/10.2118/28578-PA
- Document ID
- SPE-28578-PA
- Publisher
- Society of Petroleum Engineers
- Source
- SPE Reservoir Engineering
- Volume
- 12
- Issue
- 01
- Publication Date
- February 1997

- Document Type
- Journal Paper
- Pages
- 45 - 51
- Language
- English
- ISSN
- 0885-9248
- Copyright
- 1997. Society of Petroleum Engineers
- Disciplines
- 5.6.1 Open hole/cased hole log analysis, 4.3.4 Scale, 2.4.3 Sand/Solids Control, 1.11 Drilling Fluids and Materials, 5.1 Reservoir Characterisation, 5.2 Reservoir Fluid Dynamics, 1.2.3 Rock properties, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 1.6.9 Coring, Fishing
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Summary

At the time of this work, induction- and porosity-log measurements were available in more than 180,000 ft of hydrocarbon column from 428 wells. Water saturations were determined from this areally and vertically extensive database after calibration to oil-base-core (OBC) -derived water saturations. This paper presents the method used to calibrate the log data to the OBC water saturations and reviews the methods used to derive resistivity and formation factor values. It also presents field measurements of as-received core-plug resistivity and water-saturation values from two oil-base-mud (OBM) -cored wells. Comparisons are presented with both field water saturations and "routine" electrical-property measurements on extracted plugs.

Introduction

Calculation of water saturation from logging measurements does not result in a precise determination of the distribution of the water saturation in a single well or across a given reservoir. The imprecision in the calculated values of water saturation is a result of both the application of models, such as the Archie equation, that cannot account for all factors affecting the relationship between formation resistivity and water saturation and uncertainty in the parameters used within the equation.

More than 450 wells at Prudhoe Bay had deep-induction-log data. The objective of calibrating the log-derived water saturations was to extend the accuracy of the OBC water saturations to the larger and more areally extensive database of logged wells. There are two key requirements for calibration. The first is the need for a representative sample of the distribution of water saturation in the reservoir. The other key factor is the accuracy of these water-saturation values. The OBC water-saturation database was extensive and, in general, met the criteria for adequately sampling the water-saturation distribution in the reservoir, despite the variability of those values. In a given zone within a well, there were, on average, approximately 50 water-saturation measurements used in the calibration. Overall, there were nearly 7,000 independent measurements and all lithologies were sampled by the OBC data set.

This work will review the derivation of the parameters used to calculate water saturations from the Archie equation. Further, it will discuss the major factors that led to the need for calibration of the Archie equation through use of the OBC water-saturation values. Finally, it will attempt to verify the calibration method by direct comparison with a laboratory determination of the calibrating parameter from an on-site testing program.

Derivation of the Archie Parameters

**Model Selection.**

The Archie equation was selected for the calculation of water saturation in the Ivishak formation. There are six parameters in the Archie equation:

Equation 1

where *a,m*=electrical parameters; *n*=saturation exponent; f=porosity, fraction; *R _{t}*=true or formation resistivity, O·m; and

*R*=water resistivity, O·m.

_{ w}The Archie equation was selected because of the generally low level of conductive matrix effects within the Ivishak and because it had been applied and documented in numerous other fields.^{1}

Each parameter other than the saturation exponent was estimated and evaluated from independent sources of information and will be discussed in this paper. Later in this paper, it is demonstrated that derivation of saturation exponents from laboratory data yielded unreliable parameter values. Because only one parameter in the Archie equation was unknown, the saturation exponent was chosen as the calibration parameter.

**Resistivity Values.**

The dual induction log was the standard log for resistivity logging at Prudhoe Bay. Although resistivities in the upstructure areas of the field are higher than normally considered appropriate for the induction log, comparisons with laterologs run in three wells indicate that the induction log is capable of better performance at high resistivities than is normally considered possible. However, because the induction log measures conductivity, small errors in the conductivity zero setting can be significant at low conductivities (high resistivities). Consequently, it was necessary to develop a method to detect these calibration errors and to correct for them in an appropriate manner.

Mapping was chosen as the method to compare conductivity values on an areal basis (this method works best when there are two smoothly varying values of key petrophysical properties). The value chosen for mapping is the log (base 10) of the conductivity corresponding to the 95th percentile of resistivity, after eliminating nonpay intervals, pyritic intervals, bad data, and water-influx intervals. This value was intended to represent the maximum resistivity level in a thick bed and be the value most sensitive to conductivity zero errors.

A map of the conductivity value described previously was developed. A number of areas with closely spaced and irregular contours were noted, especially in the east-central and north areas of the field. The tentative calibration correction was determined as the amount of conductivity to be added or subtracted to bring the well's logarithm of conductivity to within one standard deviation of the conductivity of nearby wells as recorded by the deep induction log.

A total of 62 wells was identified as potential candidates for correction with this procedure. However, the following criteria were set up to limit corrections to reasonable values.

1. No correction less than 0.5 m /m. Correction is too small to consider.

2. No correction greater than 10 m /m. Correction should be less than anticipated sonde error.

3. No correction if fewer than five wells within 1-mile radius. Too few wells to apply technique.

4. No correction if 95th percentile resistivity is less than 40 O·m. Hard to recognize errors in low-resistivity areas.

Wells chosen for calibration corrections are listed in **Table 1** along with the corrections. Corrections range from 0.5 to 6.4 m /m. Eleven negative corrections average -2.4 m /m and 19 positive corrections average +1.8 m /m. The average absolute correction is 2.0 m /m. The fact that the average correction is close to the published accuracy of the induction log also lends credence to the corrections as a whole. The corrected conductivity map is given in **Fig. 1**.

**Derivation of**

*a*and*m*Values.Two sources of data were evaluated for determination of the relationships between formation factor, *F*, (*F=a*f^{-m} ) and porosity in the Ivishak reservoir. Laboratory measurements of porosity and resistivity on representative core samples were selected for the final calculation of these relationships. Logging measurements of resistivity and porosity were also available in water-saturated intervals; however, use of this source of data led to less consistent predictions of the formation factor.

Model Selection.

The Archie equation was selected for the calculation of water saturation in the Ivishak formation. There are six parameters in the Archie equation:

Equation 1

where *a,m*=electrical parameters; *n*=saturation exponent; f=porosity, fraction; *R _{t}*=true or formation resistivity, O·m; and

*R*=water resistivity, O·m.

_{ w}The Archie equation was selected because of the generally low level of conductive matrix effects within the Ivishak and because it had been applied and documented in numerous other fields.^{1}

Each parameter other than the saturation exponent was estimated and evaluated from independent sources of information and will be discussed in this paper. Later in this paper, it is demonstrated that derivation of saturation exponents from laboratory data yielded unreliable parameter values. Because only one parameter in the Archie equation was unknown, the saturation exponent was chosen as the calibration parameter.

**Resistivity Values.**

The dual induction log was the standard log for resistivity logging at Prudhoe Bay. Although resistivities in the upstructure areas of the field are higher than normally considered appropriate for the induction log, comparisons with laterologs run in three wells indicate that the induction log is capable of better performance at high resistivities than is normally considered possible. However, because the induction log measures conductivity, small errors in the conductivity zero setting can be significant at low conductivities (high resistivities). Consequently, it was necessary to develop a method to detect these calibration errors and to correct for them in an appropriate manner.

Mapping was chosen as the method to compare conductivity values on an areal basis (this method works best when there are two smoothly varying values of key petrophysical properties). The value chosen for mapping is the log (base 10) of the conductivity corresponding to the 95th percentile of resistivity, after eliminating nonpay intervals, pyritic intervals, bad data, and water-influx intervals. This value was intended to represent the maximum resistivity level in a thick bed and be the value most sensitive to conductivity zero errors.

A map of the conductivity value described previously was developed. A number of areas with closely spaced and irregular contours were noted, especially in the east-central and north areas of the field. The tentative calibration correction was determined as the amount of conductivity to be added or subtracted to bring the well's logarithm of conductivity to within one standard deviation of the conductivity of nearby wells as recorded by the deep induction log.

A total of 62 wells was identified as potential candidates for correction with this procedure. However, the following criteria were set up to limit corrections to reasonable values.

1. No correction less than 0.5 m /m. Correction is too small to consider.

2. No correction greater than 10 m /m. Correction should be less than anticipated sonde error.

3. No correction if fewer than five wells within 1-mile radius. Too few wells to apply technique.

4. No correction if 95th percentile resistivity is less than 40 O·m. Hard to recognize errors in low-resistivity areas.

Wells chosen for calibration corrections are listed in **Table 1** along with the corrections. Corrections range from 0.5 to 6.4 m /m. Eleven negative corrections average -2.4 m /m and 19 positive corrections average +1.8 m /m. The average absolute correction is 2.0 m /m. The fact that the average correction is close to the published accuracy of the induction log also lends credence to the corrections as a whole. The corrected conductivity map is given in **Fig. 1**.

**Derivation of a and m Values.**

Two sources of data were evaluated for determination of the relationships between formation factor, *F*, (*F=a*f^{-m} ) and porosity in the Ivishak reservoir. Laboratory measurements of porosity and resistivity on representative core samples were selected for the final calculation of these relationships. Logging measurements of resistivity and porosity were also available in water-saturated intervals; however, use of this source of data led to less consistent predictions of the formation factor.

Resistivity Values.

The dual induction log was the standard log for resistivity logging at Prudhoe Bay. Although resistivities in the upstructure areas of the field are higher than normally considered appropriate for the induction log, comparisons with laterologs run in three wells indicate that the induction log is capable of better performance at high resistivities than is normally considered possible. However, because the induction log measures conductivity, small errors in the conductivity zero setting can be significant at low conductivities (high resistivities). Consequently, it was necessary to develop a method to detect these calibration errors and to correct for them in an appropriate manner.

Mapping was chosen as the method to compare conductivity values on an areal basis (this method works best when there are two smoothly varying values of key petrophysical properties). The value chosen for mapping is the log (base 10) of the conductivity corresponding to the 95th percentile of resistivity, after eliminating nonpay intervals, pyritic intervals, bad data, and water-influx intervals. This value was intended to represent the maximum resistivity level in a thick bed and be the value most sensitive to conductivity zero errors.

A map of the conductivity value described previously was developed. A number of areas with closely spaced and irregular contours were noted, especially in the east-central and north areas of the field. The tentative calibration correction was determined as the amount of conductivity to be added or subtracted to bring the well's logarithm of conductivity to within one standard deviation of the conductivity of nearby wells as recorded by the deep induction log.

A total of 62 wells was identified as potential candidates for correction with this procedure. However, the following criteria were set up to limit corrections to reasonable values.

1. No correction less than 0.5 m /m. Correction is too small to consider.

2. No correction greater than 10 m /m. Correction should be less than anticipated sonde error.

3. No correction if fewer than five wells within 1-mile radius. Too few wells to apply technique.

4. No correction if 95th percentile resistivity is less than 40 O·m. Hard to recognize errors in low-resistivity areas.

Wells chosen for calibration corrections are listed in **Table 1** along with the corrections. Corrections range from 0.5 to 6.4 m /m. Eleven negative corrections average -2.4 m /m and 19 positive corrections average +1.8 m /m. The average absolute correction is 2.0 m /m. The fact that the average correction is close to the published accuracy of the induction log also lends credence to the corrections as a whole. The corrected conductivity map is given in **Fig. 1**.

Derivation of *a* and *m* Values.

Two sources of data were evaluated for determination of the relationships between formation factor, *F*, (*F=a*f^{-m} ) and porosity in the Ivishak reservoir. Laboratory measurements of porosity and resistivity on representative core samples were selected for the final calculation of these relationships. Logging measurements of resistivity and porosity were also available in water-saturated intervals; however, use of this source of data led to less consistent predictions of the formation factor.

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