WATER RESISTIVITY METHODS
 RW Basics
RW from Lab Data RW
from Catalogs
RW from Water Zone
RW from SP
Selecting RW
 
Formation Water Resistivity
Most methods for computing water saturation require knowledge
of formation water resistivity at the formation temperature (RW@FT).
There are four major sources of this data.
Laboratory Water Analysis
Drill stem test
or produced water recoveries in your well, or from nearby wells,
are analyzed for chemical content and water resistivity in the laboratory.
A sample analysis is shown below.
The
chemical analysis is recorded in milligrams per kilogram (mg/kg), or milligrams per
liter (mg/l).
Water analysis report from a drill
stem test recovery, showing chemical analysis, calculated and
measured water resistivity, and Stiff diagram of chemical analysis.
The
resistivity of a water sample can be calculated from its
chemical analysis. To do this, an equivalent NaCl concentration
must be determined based on the ionic activity of each ion.
Enter chart with total solids concentration of the sample in ppm
(mg/kg) to find weighting factors for each ion present. The
concentration of each ion is multiplied by its weighting factor, and
the products for all ions are summed to obtain equivalent NaCl
concentration.
WSe -
Equivalent NaCl Water Salinity
from Water Analysis
1: TDS = SUM (IONi)
2:
WSe = SUM (IONi * FACTRi)
WHERE:
TDS = total dissolved solids (NaCl equivalent ppm)
IONi = ion concentration of ith component (ppm)
FACTRi = multiplier factor for ith component (ppm)
WSe = equivalent NaCl concentration (ppm)
NUMERICAL EXAMPLE:
Assume formation-water sample analysis
460 ppm Ca,
1400 ppm SO4
19,000 ppm Na plus Cl.
Total dissolved solids concentration
WSe = 460 + 1400 + 19,000 = 20,860 ppm NaCl equivalent.
Entering the chart with this total solids concentration
Ca multiplier = 0.81
SO4 multiplier = 0.45
Na+CL multiplier = 1.00
Equivalent NaCl concentration = 460 ´ 0.81 + 1400 ´ 0.45 + 19,000 ´
1.0 = 20,000 ppm.
RW@FT_1 - Water Resistivity from Salinity
2:
FT1 = SUFT + (BHT - SUFT) / BHTDEP * DEPTH
3: IF LOGUNITS$ = "METRIC"
4: THEN FT1 = 9 / 5 * FT1 + 32
5: RW@FT = (400000 / FT1 / WSe) ^ 0.88
WHERE:
BHT = bottom hole temperature (degrees Fahrenheit or Celcius)
BHTDEP = depth at which BHT was measured (feet or meters)
FT1 = formation temperature (degrees Fahrenheit)
RW@FT = water resistivity at formation temperatures (ohm-m)
SUFT = surface temperature (degrees Fahrenheit or Celcius)
WS = water salinity (ppm NcCl)
COMMENTS:
Use this relation if salinity is known from laboratory measurements.
NUMERICAL
EXAMPLE:
1. Salinity to water resistivity.
RW@FT = (400000 / 102'F / 20,000 ppm) ^ 0.88 = 0.238 ohm-m @
102'F
(rounded to three significant digits)
2.
Water resistivity to salinity.
WS = 400,000 / 102'F / ((0.250 ohm-m) ^ 1.14) = 19,000 ppm NaCl
(rounded to three significant digits)
WSa - Water salinity from chloride content:
6: WSa = Ccl * 1.645
WHERE:
Ccl = water salinity (ppm Cl)
WSa = water salinity (ppm NaCl)
COMMENTS:
Use this relationship when chloride content of the water sample
is known. Usually Cl content is derived approximately at the
well site from a drill stem test recovery. It is useful as a
first approximation until the water sample is analyzed more
accurately at a laboratory. The relationship is for pure NaCl
solutions and the factor may be higher or lower if other ions
are present.
NUMERICAL
EXAMPLE:
1. Chloride concentration to salinity.
WS = 11,600 ppm Cl * 1.645 = 19,000 ppm NaCl
RW from Water Catalogs
The water catalogue published by your local well logging society
or similar catalogues created by searching in-house data bases.
A sample is shown below.
A sample of RW data from a water resistivity catalog, data is tabulated and also
posted on
a map, and is based on a standard temperature of 25 degrees Celcius
(77 degrees Fahrenheit).
The
following relationships are needed to manipulate water resistivity
data prior to calculations of water saturation.
RW@FT_2 - Water Resistivity at Formation Temperature
7:
FT = SUFT + (BHT - SUFT) / BHTDEP * DEPTH
8: RW@FT = RW@SUFT * (SUFT + KT1) / (FT +
KT1)
9: RMF@FT = RMF@SUFT * (SUFT +
KT1) / (FT + KT1)
10: RMC@FT = RMC@SUFT + (SUFT * KT1) / (FT + KT1)
WHERE:
BHT = bottom hole temperature (degrees Fahrenheit or Celcius)
BHTDEP = depth at which BHT was measured (feet or meters)
KT1 = 6.8 for English units
KT1 = 21.5 for Metric units
FT = formation temperature (degrees Fahrenheit or Celcius)
RMC@FT = mud cake resistivity at formation temperature (ohm-m)
RMC@SUFT = mud cake resistivity at surface temperature (ohm-m)
RMF@FT = mud filtrate resistivity at formation temperature (ohm-m)
RMF@SUFT = mud filtrate resistivity at surface temperature (ohm-m)
RW@FT = water resistivity at formation temperatures (ohm-m)
RW@SUFT = water resistivity at surface temperature (ohm-m)
SUFT = surface temperature (degrees Fahrenheit or Celcius)
COMMENTS:
Use this relation when RW@SUFT
is known from measured data. This transformation can be made on
the chart below. .
NUMERICAL
EXAMPLE:
1. Water resistivity at formation temperature.
English units example:
RW@FT = (0.32 ohm-m @ 77'F) * (77 + 6.8) / (102 + 6.8) = 0.25
ohm @ 102'F
Metric
units example:
RW@FT = (0.32 ohm-m @ 25'C) * (25 + 21.5) / (39 + 21.5) = 0.25
ohm-m @ 39'C
Water resistivity - Temperature - Salinity relationships
Typical Depth - Temperature profiles
Temperature gradient for USA -
degrees Celcius per 1000 meters,
North American Heat Floe Map
(3 MB)
Legible Legend for NA Map
Temperature at 5000 meters for
Australia
RW from a Water Zone
Back calculation of RW@FT from log data in a clean (non shaly)
zone - usually called the Rwa method, or the water zone (Ro or
R0) method is commonly used when obvious water zones exist near the
zone of interest.
RW@FT_3 - Water resistivity from water zone
The
following algorithm is used to back calculate water resistivity
from a known water zone.
11: RW@FT = (PHIt ^ M) * RESD / A
12: RMF@FT = (PHIt ^ M) * RESS / A
13: RMC@FT = 2.0 * RMF@FT
WHERE:
A = tortuosity exponent (unitless)
M = cementation exponent (unitless)
PHIt = total porosity found by log analysis (fractional)
RESD = deepest resistivity log reading (ohm-m)
RESS = shallowest resistivity log reading (ohm-m)
RMC@FT = mud cake resistivity at formation temperature (ohm-m)
RMF@FT = mud filtrate resistivity at formation temperature (ohm-m)
RW@FT = water resistivity at formation temperatures (ohm-m)
COMMENTS:
Use this relationship if no measured values of RW are available
and only if data from a clean water zone can be found. A nomographic
solution is given below.
This
method is often called the Rwa method
Porosity
should be greater than 0.06.
Note
that results are at the formation temperature. To compare these
values to catalog values at 25 degrees Celcius, use the temperature
transformation from the previous algorithm or the nomograph
below.
Water resistivity from water zone data (Rwa Method)
NUMERICAL
EXAMPLE:
1. Assume data for water zone
Sand A Sand B Sand
C Sand D
RESD
6 0 40 0.3 0.5
PHIt 0.33 0.14 0.30 0.11
A = 0.62
M = 2.15
RW@FT 0.89 0.94 0.036 0.007
Sample:
RW@FT = Rwa = (0.33 ^ 2.15) * 6.0 / 0.62 = 0.89
The
RW@FT values represent the first approximation to a value of water
resistivity for each of the four zones. The value for Sand D is
not very realistic, and a better one will be found later when
we look at shale corrections.
RW from SP Log
Calculation from knowledge of the SP value in a clean zone
has been a traditional method for finding RW. It works
best in clean water bearing zones, but the Rwa or R0 method
would be better in this case. Shale content and hydrocarbon
content reduce the SP value and cause RW to too high, giving
very pessimistic saturation results..
RW@FT_4 - Water resistivity from the SP log
14:
FT1 = SUFT + (BHT - SUFT) / BHTDEP * DEPTH
15: IF LOGUNITS$ = "METRIC"
16: THEN FT1 = 9 / 5 * FT1 + 32
17: KSP = 60 + 0.122 * FT1
18: RSP = 10 ^ (-SSP / KSP)
19: IF RMF@FT > 0.1
20: THEN RMFE = 0.85
RMF@FT
21: IF RMF@FT <= 0.1
22: THEN RMFE = (146 RMF@FT - 5) / (337
* RMF@FT + 77)
23: RWE = RMFE / RSP
24: IF RWE > 0.12
25: THEN RW@FT = - (0.58 - 10 ^ (0.69
* RWE - 0.24))
26: IF RWE <= 0.12
27: THEN RW@FT = (77 * RWE + 5) / (146 - 337
* RWE)
WHERE:
BHT = bottom hole temperature (degrees Fahrenheit or Celcius)
BHTDEP = depth at which BHT was measured (feet or meters)
FT1 = formation temperature (degrees Fahrenheit)
KSP = temperature factor (degrees Fahrenheit)
RSP = RWE / RMFE (fractional)
RMFE = equivalent mud filtrate resistivity (ohm-m)
RMF@FT = mud filtrate resistivity at formation temperature (ohm-m)
RWE = equivalent water resistivity (ohm-m)
RW@FT = water resistivity at formation temperatures (ohm-m)
SSP = static SP reading in clean zone (ohm-m)
SUFT = surface temperature (degrees Fahrenheit or Celcius)
COMMENTS:
This algorithm should only be used IF the SP log has sufficient
character, the zone of interest is a clean water bearing sandstone,
and the result is reasonable for the area. Use caution since many
SP logs are not calibrated, and RMF or RW can be measured carelessly.
Solution
of these formulae can be done on the two charts below. An Excel macro for RW from SP, published by SPWLA, is
located HERE.
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Nomographs for RW from SP |
NUMERICAL
EXAMPLE:
1. Data for Sand C:
SUFT = 25 degrees C
BHT = 65 degrees C
BHTDEP = 2225 m
DEPTH = 1000 m
RMF = 0.75 @ 25 degrees C
SP = -90 mv
FT
= 25 + (65 - 25) / 2225 * 1000 = 43 degrees C
FT = 9 / 5 * 43 + 32 = 109 degrees F
RMF@FT = 0.75 * (25 + 21.5) / (43 + 21.5) = 0.54
KSP = 60 + 0.122 * 109 = 73.3
RSP = 10 ^ (90 / 73.3) = 16.9
RMFE = 0.85 * 0.54 = 0.46
RWE = 0.46 / 16.9 = 0.027
RW@FT = (77 * 0.027 + 5) / (146 - 337 * 0.027) = 0.051
Selection of Rw from Various Sources
Water resistivity data can be sparse or overwhelming, depending
on where you are working at the moment. The usual sources in order
of preference are:
1.
Produced water from the zone being analyzed in the same well or
nearby offset wells, analyzed for Rw in the lab.
2.
Drill stem test or perf test water from the zone being analyzed
in the same well or nearby offset wells, analyzed for Rw in the
lab. The test should produce at least 1000 ft (300 m) of water
before using the data, to prevent mud filtrate contamination from
causing errors. The sample should be from the bottom of the test.
3.
Produced or DST water from a nearby zone in the same geologic
horizon (do not cross erosional boundaries), analyzed as above.
4.
Water catalogues produced by local well log societies or government
agencies.
5.
Back calculated from log data in clean water bearing zone in the
same well or nearby offset well (Rwa or Ro method).
6.
Back calculated from nearby water bearing zone in same geologic
horizon.
7.
Calculated from SP in clean water bearing zone in same or nearby
zone in same well or nearby offset well.
8.
If no water has ever been produced in the area, back calculated
from a laboratory measured or assumed PHIxSW product.
9.
Local rule of thumb for water resistivity versus depth or versus
geologic horizon.
Do
not use:
1.
Water from a DST or perf test that recovered mostly filtrate water
(check water chemistry) or recovered only a small amount of water.
2.
SP or Rwa in a shaly zone.
3.
SP or Rwa in a hydrocarbon bearing zone.
4.
SP in a carbonate or evaporite sequence.
5.
SP in a low porosity zone.
"META/RW" SPREADSHEET -- Water Resistivity Calculations
This spreadsheet calculates RW at formation temperature using 5
different methods.
Calculate RW at formation temperature.
Metric and English Units
Sample of "META/RW" for calculating water resistivity from various
methods.
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