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