Evidence for a variable Archie porosity
exponent “m” and impact on saturation
calculations for Mesaverde tight gas
sandstones: Piceance, Uinta, Green River,
Wind River, and Powder River basins
Robert M Cluff, The Discovery Group Inc.
Alan P. Byrnes, Kansas Geological Survey1
1presently
with Chesapeake Energy
Stefani Whittaker, The Discovery Group Inc.
Dan Krygowski, The Discovery Group Inc.
AAPG Rocky Mountain Section meeting, Denver, Colorado
10 July 2008
US DOE Project Summary
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DOE Contract # DE-FC26-05NT42660
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completion date 30 June 2008
Organizations
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University of Kansas Center for Research, Inc.
Kansas Geological Survey, Lawrence, KS
The Discovery Group Inc., Denver, CO
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Principal Investigators: Alan P. Byrnes, KGS;
Bob Cluff, Discovery Group
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project website is http://www.kgs.ku.edu/mesaverde
Objectives of this task
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Characterize Mesaverde electrical
properties as a function of porosity and
salinity
z Archie
porosity (cementation) exponent “m”
z Investigate behavior at low porosity end
(<6%) not previously studied
z Evaluate excess conductivity effects
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Methods to compute accurate Sw from
logs
Sampling
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systematic
characterization of
Kmv lithofacies
over entire Rocky
Mtn region
44 wells/6 basins
Described ~7000
~
ft core (digital)
2200 core
samples
120-400 advanced
properties
samples
Powder
River
Wind River
Wyoming
Green River
N
Washakie
Utah
Colorado
Uinta
Piceance
Permeability vs Porosity
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Samples collected over a wide range of porosity and
permeability across 6 basins
0-24% porosity, spanning 1 nD to >100 mD
1000
Klinkenberg Permeability (4,000 psi, mD)
z
100
10
1
0.1
Green River
Piceance
Powder River
Uintah
Washakie
Wind River
logK=0.3Phi-3.7
logK=0.3Phi-5.7
0.01
0.001
0.0001
0.00001
0.000001
0.0000001
0
2
4
6
8
10
12
14
In situ calc Porosity (%)
16
18
20
22
24
Archie’s equation
Sw = (a / φ
n
z
z
* (Rw / Rt )
completely empirical – no theoretical basis
“m” is the porosity or cementation exponent
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z
m)
loosely related to tortuosity of the current flow path,
better thought of as electrical efficiency of the path
“n” is the saturation exponent
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related to change in conductivity path with changing
saturation
Archie porosity exponent
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for a simple bundle of capillary tubes
oriented parallel to current flow direction:
m→1
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insensitive to cross section shape, so
fractures act like capillary tubes
as porosity increases and less of it
participates in the conductive path, m ↑
z for an “average” sandstone comprised of
spherical grains, m → 2
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Resistivity of a simple rock model
0
∞
For straight capillary tubes:
Porosity (φ)
Resistivity (Ro)
F = Ro/Rw = 1/φ
For rock with tortuous pores:
F = Ro/Rw = 1/φ m
(after Doveton, 2005)
1
Rw
Capillary tube model for m
m
1.0
>1
~2
>2
m=1
after Herrick & Kennedy, 1993,
SPWLA Paper HH
A
Φ
Rw
L
high -P
core holder
electric
insulator
then we measure R0. F = R0/Rw.
brine in
Resistance
Reference
Cell
Frequency
Generator
brine of known Rw & φ
Core Plug
Start with core plug saturated with
high-P fluid
Micropipette
Core measurement
of the formation
factor, F
Plated electrodes
When F and φ are plotted log-log
1000
m= 2
m= 3
100
m= 1
F
10
1
0.01
0.1
φ
1
log F = -m log φ
Observed porosity dependence
of “m”
„
„
R2 = 0.63 (RMA)
40Kppm dataset is largest and used for base case
cap m at 1.95
40K ppm brine data
2.2
2.2
2.1
2.0
In situ Archie Cementaiton
Exponent
„
Empirical: m = 0.676 log φ + 1.22
each salinity is different
In situ Archie m
„
y = 0.5377x + 1.3313
R2 = 0.6331
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
-0.2 0.0
0.2
0.4
0.6
0.8
1.0
1.2
log In situ Porosity (%)
1.4
2.0
1.8
1.6
1.4
1.2
1.0
0
4
8
12
16
In situ Porosity (%)
20
24
Dual porosity model
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m = log[(φ-φ2)m1 + φ2m2]/log φ
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φ expressed as V/V
φ2 = 0.0035, m1=2, m2=1; SE both = 0.11
z rock behaves like a mixture of matrix porosity and cracks, with
cracks dominating low porosity end
cap at m = 1.95 (φ ~ 16%)
40K ppm brine data
both models fit data
2.2
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φ = bulk porosity
φ2 = fracture porosity
m1 = matrix cementation
exponent
m2 = fracture cementation
exponent
In situ Archie Cementaiton
Exponent
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2.0
1.8
1.6
1.4
1.2
1.0
0
4
8
12
16
In situ Porosity (%)
20
24
And a third way to look at it....
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Why is the minimum m ~ 1.2, instead of 1?
A – for a distribution of cracks of different crosssectional area, the largest (widest) cracks will
dominate the conductivity
The high tail of the distribution determines the
bulk conductivity,
while the rest of the cracks act like “excess”
porosity that do not participate (significantly) in
the conductivity.
Therefore m ↑
And are the “cracks” all fractures?
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Probably not..............
Slot-like pores oriented preferentially parallel to
bedding also act like conductive cracks
Thin parallel laminae of slightly coarser, more
permeable sand will be crack-like
Salinity dependence of “m”
„
„
tested plugs with 20K, 40K, 80K, and 200K ppm brines
Nearly all cores exhibit some salinity dependence
2.3
n=335
0.9
Core Conductivity (mho/m)
In situ Archie Cementation Exponent,
(m, A=1)
1.0
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
0
2
4
6
8
10
12
14
16
18
Brine Conductivity (mho/m)
20
22
0.01
0.1
Brine Resistivity (ohm-m)
1
All data, all salinities
Archie Cementaiton Exponent (m, a=1)
2.40
2.20
2.00
1.80
1.60
1.40
1.20
200K
80K
1.00
40K
20K
0.80
0
2
4
6
8
10 12 14 16 18 20 22
In situ Porosity (% )
Salinity dependence of “m”
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20K ppm
y = 0.2267Ln(x) + 2.2979
2
R = 0.6619
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1.50
Series1
Log. (Series1)
1.00
40K ppm
z
3.00
0.50
y = 0.2328Ln(x) + 2.409
2
R = 0.6547
2.50
0.050
0.100
0.150
0.200
0.250
2.00
insitu porosity (%)
Series1
1.50
Log. (Series1)
80K ppm
1.00
0.50
3.00
0.00
0.000
2.50
y = 0.2149Ln(x) + 2.4354
2
0.050
0.100
0.150
0.200
R = 0.5132
0.250
insitu porosity (%)
2.00
Axis Title
0.00
0.000
Axis Title
Axis Title
2.00
200K ppm
Series1
1.50
Log. (Series1)
1.00
3.00
0.50
2.50
y = 0.1621Ln(x) + 2.3222
0.00
0.000
2
R = 0.3633
2.00
0.050
0.100
0.150
insitu porosity (%)
0.200
0.250
Axis Title
2.50
m = a log φ + b
intercept b drops with
decreasing salinity
slope is ~ constant
Series1
1.50
Log. (Series1)
1.00
0.50
0.00
0.000
0.050
0.100
0.150
insitu porosity (%)
0.200
0.250
Simple procedure to compute Sw
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determine Rw @ Tf conventionally
Pickett plots – focus on the lower porosity,
wetter sandstones
z produced waters
z your best guess.......
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convert Rw to 75°F by chart lookup or
Arps equation
Pickett Plot example
Rw = 0.306
pick m at low porosity
end, where BVWirr ~ BVW
Williams PA 424-34
Piceance basin
Kmv above “top gas”
Pickett plot Rw 0.306 ohmm @ 160°F = 0.7 @ 75°F (9K ppm)
Our new procedure
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compute m at 40K ppm from RMA regression:
m40k = 0.676 log φ + 1.22
e.g. for 10% φ : m = 0.676 + 1.22 = 1.896
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correct m for salinity effect by
m = m40k + ((0.0118 φ – 0.355) * (log Rw + 0.758))
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e.g. for 10% φ, Rw = 0.7 @ 75°F
m = 1.896 + ((0.0118 * 10 – 0.355) * (log 0.7 +
0.758))
m = 1.896 + (-0.237 * 0.603) = 1.753
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cap m at 1.95 (~12% porosity)
Practical impact
Nominally, most of us use an m close to 2,
but usually slightly less, for tight gas sand
evaluations (e.g. 1.85, 1.90)
z Variable m that DECREASES with
decreasing porosity leads to lower Sw’s
z Therefore, there is more gas in the tight
rocks than we thought.
z Above 10% porosity there is very little
difference
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Example: Low porosity, wet zone
Moderate porosity, wet
“High” porosity gas zone
m is HIGHER than base case, so Sw is higher
20Kppm example, Natural Buttes
30K ppm example, Wamsutter
Summary & Conclusions
335 Kmv samples run at multiple salinities
z Archie porosity exponent m varies with
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porosity
z salinity
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m ↓ as porosity ↓
m ↓ as salinity ↓
behavior is consistent with increasing
electrical efficiency with decreasing
porosity, whatever the pore scale
architecture
variable m model can be implemented with
a simple equation relating m to porosity
and formation water salinity
z m is constant above ~12% porosity at 1.95
z lowering m at 5-12% φ increases GIP
z see no impact below ~5% porosity
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BVWirr is typically 3-5%
z no longer calculate Sw’s >> 1
z Sw = 1 at low φ validates Rw
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Visit our project website
http://www.kgs.ku.edu/mesaverde
Questions?