Chapter 5

Determination of Rw

Lecture notes for PET 370

Spring 2012

Prepared by: Thomas W. Engler,

Ph.D., P.E.

Determination of Rw

1. Archie’s Equation

a. if water zone is present.

b. Rwa Approach

c. Resistivity - Porosity Crossplots

2. Laboratory

a. Direct measurement of representative

water sample.

b. Chemical analysis of water sample.

3. Databases

a. Published regional water catalogs

b. online:http://octane.nmt.edu/waterquality/

4. SP log

5. Guess?

Name Five Methods to determine Rw.

k

SSP

mfeR

weR 10*

Determination of Rw

Preliminary Concepts

Total conductivity is influenced by:

– porosity

– water saturation

– salinity

– salt composition

– temperature

– shale content

– metallic minerals; e.g., pyrite

Water

conductivity

metXshXF

nwSwC

tC

Which directly related to water conductivity?

Determination of Rw

Preliminary Concepts

Temperature Effects

ionic conductivity - as temp. increases the

conductivity increases. True or False?

True

Salinity Effects

As salinity increases the conductivity will

increase. True or False?

Solution ppm NaCl resistivity,-m

oil or gas - 1.0 E6

Potable water 500 10.0

Fresh mud filtrate < 5,000 1.0 - 5.0

Sea water 35,000 0.2

Salt mud filtrate 75,000 0.1

Saturated salt water 250,000 0.04

Determination of Rw

How to determine formation temperature?

The formation of interest is at 6500 ft. What is the formation

temperature?

Tf = 112 F

What is the geothermal gradient, (gG), in {deg.F/100 ft}?

gG = 0.80 F/100 ft

Lea County ,NM

Determination of Rw

How to determine formation temperature?

Near surface temperature, (To), is given regionally by:

Gulf Coast 80 deg. F

Oklahoma 60

California 60

Permian Basin 60

Rocky Mtns. 50

Alberta 35

Determination of Rw

Location To, C

Ankara, Turkey 6.7

Aswan, Egypt 26.7

Aberdeen, Scotland 8.9

Bogota, Columbia 14.3

Bombay, India 27.1

Calgary, Alberta 5.4

Caracas, Venezuela 20.5

Changha, China 18.0

Gabon, Africa 26.0

Great Yarmouth, England 8.9

Location To, C

Jakarta, Indonesia 26.7

Lima, Peru 20.0

Mendoza, Argentina 16.0

Natal, Brazil 23.0

Perth, Australia 18.0

Prince George, B.C. 3.6

Rio De Janeiro, Brazil 23.0

Santa Cruz, Bolivia 15.0

Siberia (west), Russia -4.0

Trinidad, W.I. 29.7

How to determine formation temperature?

Determination of Rw How to determine resistivity at Tf?

Courtesy of Schlumberger

Given a Resistivity = 0.1 ohmm at 75F what is

The resistivity at 125 ?

Determination of Rw How to determine resistivity at Tf?

Courtesy of Schlumberger

Given a mud resistivity = 1.1 ohmm at 66F

what is the resistivity at 140 ?

Determination of Rw

1. Archie’s Equation

a. if water zone is present.

b. Rwa Approach

c. Resistivity - Porosity Crossplots

2. Laboratory

a. Direct measurement of representative

water sample.

b. Chemical analysis of water sample.

3. Databases

a. Published regional water catalogs

b. online:http://octane.nmt.edu/waterquality/

4. SP log

5. Guess?

Methods

F

oR

wR

k

SSP

mfeR

weR 10*

Determination of Rw

How to determine resistivity if a chemical

composition is available?

When drilling in evaporite and carbonate formations, the

following type of problem can occur. A recovered water

sample is classified as 200,000 ppm of saturated brine;

i.e., only NaCl ions are present. At a formation

temperature of 275 F what is the Rw?

Rw = 0.013 ohmm

Using this Rw in log evaluations indicated the presence

of oil; however, numerous production tests produced

only water!

Determination of Rw

How to determine resistivity if a chemical

composition is available?

Consider the effect of Mg++ and Ca++ ions, which are common

in carbonates, on the computed values of Rw. Assuming a

concentration of 50,000 ppm of Mg++ and Ca++ ions and

100,000 ppm of Na Cl what is the Rw?

Rw = 0.024 ohmm

What is the increase in water saturation due to this variation in

Rw?

Ion Concentration Multiplier Equiv NaCl

conc.

Na+ and Cl- 100,000

Ca++ 50,000

Mg++ 50,000

Total 200,000

Ion Concentration Multiplier Equiv NaCl

conc.

Na+ and Cl- 100,000 1.00 100,000

Ca++ 50,000 0.35 17,500

Mg++ 50,000 -0.50 -25,000

Total 200,000 92,500

If n=2 in the Archie saturation equation, then

2/1

1

2*12

wR

wR

wS

wS

Therefore for this example Sw2 = 1.36*Sw1 or a 36% increase in water saturation.

Determination of Rw

How to determine resistivity if a chemical

composition is available?

Empirical Ion Multiplier Chart

Schlumberger

Determination of Rw

1. Archie’s Equation

a. if water zone is present.

b. Rwa Approach

c. Resistivity - Porosity Crossplots

2. Laboratory

a. Direct measurement of representative

water sample.

b. Chemical analysis of water sample.

3. Databases

a. Published regional water catalogs

b. online:http://octane.nmt.edu/waterquality/

4. SP log

5. Guess?

Methods

F

oR

wR

k

SSP

mfeR

weR 10*

Determination of Rw

waR

wR

wS

:by saturation water Determine

)minimum(waRwR

:find zones, of series afor Calculate

F

tR=waR

thusincrease; Rt will but the

same theis iprelationsh F thezone, HC ain If

F

)oRor(tR

wR

then100%), = (Sw zone water ain If

F

tR2wS

wR

:Equation sArchie' Rearrange

Rwa Technique

Requirements:

1. Rw is constant

2. Lithology is constant

3. A water zone exists and is identifiable

Procedure:

Determination of Rw

Rwa Technique Example

Problem 2.13

= 32.8%

= 26.4%

= 28%

= 30.3% A

B

C

D

E

Ct = 2000

Ct = 3000

Ct = 3800

Ct = 2400

Zone F Ct,

millimhos/m

Rt, ohm-m Rwa,ohm-m Sw, %

A 30.3 8.82 2000 0.50 0.057 65

B 30.3 8.82 2000 0.50 0.057 65

C 26.4 11.62 3000 0.33 0.028 92

D 28.0 10.33 3800 0.25 0.024 100

E 32.8 7.53 2400 0.42 0.056 65

Determination of Rw

Rwa Technique Example

Problem 2.13

= 32.8%

= 26.4%

= 28%

= 30.3% A

B

C

D

E

Ct = 2000

Ct = 3000

Ct = 3800

Ct = 2400

Zone F Ct,

millimhos/m

Rt, ohm-m Rwa,ohm-m Sw, %

A 30.3 8.82 2000 0.50 0.057 65

B 30.3 8.82 2000 0.50 0.057 65

C 26.4 11.62 3000 0.33 0.028 92

D 28.0 10.33 3800 0.25 0.024 100

E 32.8 7.53 2400 0.42 0.056 65

Determination of Rw

1. Archie’s Equation

a. if water zone is present.

b. Rwa Approach

c. Resistivity - Porosity Crossplots

2. Laboratory

a. Direct measurement of representative

water sample.

b. Chemical analysis of water sample.

3. Databases

a. Published regional water catalogs

b. online:http://octane.nmt.edu/waterquality/

4. SP log

5. Guess?

Methods

F

oR

wR

k

SSP

mfeR

weR 10*

Determination of Rw

Resistivity – Porosity Crossplots

Pickett Plot

Rearrange Archie’s Equation:

wSlogn)

waRlog(logm

tRlog

Determination of Rw

Resistivity – Porosity Crossplots

Pickett Plot Example

Pickett Plot

y = 0.3007x-0.5267

R2 = 0.7674

0.01

0.10

1.00

0.10 1.00 10.00 100.00

Rt,ohm-m

Po

rosit

y

aRw=0.10

Rw=0.12

m=1/.5267=1.90

Sw=50%

Results:

m = 1.90

Rw = 0.12 ohm-m

Determination of Rw

Resistivity – Porosity Crossplots

Hingle Plot

m/1

waR

n

wSm/1

]t

R[

Rearrange Archie’s Equation

Determination of Rw

Resistivity – Porosity Crossplots

Hingle Plot Example

Hingle Plot, m=1.90

y = 3.4858x

R2 = 0.9836

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.00 0.05 0.10 0.15 0.20

Porosity

Rt-

1/m

Sw = 50%

At= 10% y = 0.35

Ro = 7.4 ohmm

F = 64

Rw = 0.115 ohmm

OOIP = 118 Mstb

Determination of Rw

Determination of Rw

Bassiouni, Z: Theory, Measurement, and Interpretation of

Well Logs, SPE Textbook Series, Vol. 4, (1994)

Chapter 4, Sec 4.5-4.6

Chapter 12, Sec 12.2

Chapter 13

Schlumberger, Log Interpretation Chartbook, (1995)

References

Determination of Rw

How to determine formation temperature?

During logging operations record the maximum temperature

(TTD) at the bottom of the well (DTD).

Assume a linear geothermal gradient, (gG), {deg.F/100 ft}

Region of Diurnal and

Annual Variations

To Ta

TEMPERATURE

DE

PT

H

100’

gG

{F/100’}

TTD, DTD

Tf, Df

oT

TDD

fD

)o

TTD

(Tf

T