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?

Methods

F

oR

wR

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

Determination of Rw

Preliminary Concepts

Temperature Effects

ionic conductivity - as temp. increases the

conductivity increases. Why?

Salinity Effects

As salinity increases the conductivity will

increase.

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?

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

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

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

Direct measurement

Obtain water sample and corresponding temperature.

Representative sample:

Pumping well with high WOR

Flowing well with high WOR

Drill stem test

Not Useful:

Flowing well with high GOR

Condensate - gas well

Well with casing leak

Tank bottoms

Determination of Rw

How to determine resistivity if a chemical

composition is available?

Calculate equivalent NaCl concentration by

using ion multipliers.

Use salinity - temperature - resistivity

relationships to find Rw.

Example

Ion ppm multiplier Equiv NaCl

ppm Na+ and Cl- 25,000 1.00 25,000

CO3- 2,000 0.42 840

SO4++ 5,000 0.40 2,000

HCO3- 10,000 0.23 2,300

Mg++ 4,000 0.93 3,720

TDS = 46,000 33,860

T = 200 deg. F => Rw = ohm-m

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

Determination of Rw

Rwa Technique Example

Strawn Sandstone Evaluation Rwa Approach

average Rwa = Sw =

Interval Ca, mmho/m Rt, ohm-m t,microsec/ft porosity F Rt/F (Rw/Rwa)1/2

3562-64 110 9.1 65 0.097 85.9 0.106 0.942 tight

3564-66 90 11.1 76 0.179 25.4 0.438 0.463 pay

3566-68 90 11.1 71 0.143 39.5 0.281 0.578 pay

3568-70 100 10.0 62 0.072 155.1 0.064 1.000 tight

3570-72 125 8.0 70 0.136 43.9 0.182 0.718 tight/wet

3572-74 130 7.7 76 0.179 25.4 0.303 0.557 pay

3574-76 125 8.0 72 0.151 35.7 0.224 0.648 wet

3576-78 125 8.0 68 0.121 55.6 0.144 0.808 tight

3578-80 120 8.3 70 0.136 43.9 0.190 0.704 wet

3580-82 115 8.7 71 0.143 39.5 0.220 0.653 wet

3582-84 115 8.7 70.5 0.140 41.6 0.209 0.671 wet

3584-86 120 8.3 72 0.151 35.7 0.233 0.635 wet

3586-88 120 8.3 71 0.143 39.5 0.211 0.667 wet

3588-90 130 7.7 71 0.143 39.5 0.195 0.695 wet

3590-92 145 6.9 73 0.158 32.6 0.212 0.666 wet

3592-94 200 5.0 70 0.136 43.9 0.114 0.908 shaly

3594-96 270 3.7 75 0.172 27.4 0.135 0.834 shaly

3596-98 280 3.6 74.5 0.168 28.6 0.125 0.867 shaly

3598-3600 260 3.8 71 0.143 39.5 0.097 0.982 wet

3600-02 280 3.6 73 0.158 32.6 0.110 0.926 wet

3602-04 320 3.1 75 0.172 27.4 0.114 0.908 wet

3604-06 355 2.8 74 0.165 29.8 0.094 0.997 wet

3606-08 360 2.8 76 0.179 25.4 0.110 0.926 wet

3608-10 350 2.9 75 0.172 27.4 0.104 0.950 wet

3610-12 340 2.9 74 0.165 29.8 0.099 0.976 wet

3612-14 350 2.9 74 0.165 29.8 0.096 0.990 wet

3614-16 325 3.1 74 0.165 29.8 0.103 0.954 wet

3616-18 275 3.6 72 0.151 35.7 0.102 0.961 wet

3618-20 200 5.0 73 0.158 32.6 0.154 0.782 wet

3620-22 120 8.3 66 0.105 73.3 0.114 0.909 wet

Rw=0.094

depth h Sw h hSw

3564-66 2 0.179 0.463 0.358 0.166

3566-68 2 0.143 0.578 0.286 0.165

3572-74 2 0.179 0.557 0.358 0.199

6 1.002 0.530

average porosity in pay zones = 0.167 Area = 40 acres

average Sw in pay zones = 0.529 Boi = 1.5 rbbl/stb

OIP = 97,551 stb

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