Capillary
Capillary Pressure
Pressure Properties
Properties of
of
Mesaverde
Mesaverde Group
Group Low-Permeability
Low-Permeability
Sandstones
Sandstones in
in Six
Six Basins,
Basins, Western
Western U.S.
U.S.
Alan P. Byrnes
(KGS- now Chesapeake Energy)
Robert M. Cluff
John C. Webb
(The Discovery Group Inc)
(KGS Student Research Assts.)
Daniel S. Osburn
Andrew Knoderer
Owen Metheny
Troy Hommertzheim
http://www.kgs.ku.edu/mesaverde
Joshua Byrnes
US DOE # DE-FC26-05NT42660
US DOE # DE-FC26-05NT42660
US DOE Project Summary
• Solicitation DE-PS26-04NT42072-0
– subtopic area 1: Understanding Tight Gas Resources
– Award Date: October 1, 2005
– Completion Date: June 30, 2008
– Contract # DE-FC26-05NT42660
• Organization: University of Kansas, Kansas
Geological Survey
• Principal Investigator: Alan P. Byrnes, KGS
• KGS-Discovery Group, Inc. co-participants
• DOE share $411,030 (80%)
• Industry share $102,804 (20%)
Objectives
• The project will provide petrophysical tools
that address:
– 1) minimum gas flow, critical and residual gas
saturation, Sgc=f(lithofacies, Pc, architecture)
– 2) capillary pressure, Pc=f(P), Pc=f(lithofacies, k,
φ, architecture)
– 3) electrical properties, m*
– 4) facies and upscaling issues
– 5) wireline log interpretation algorithms
– 6) providing a web-accessible database of advanced
rock properties.
Sampling
Powder
River
Wind River
• 44 wells/6 basins
• Describe ~7000 ft
core
• 2200 core samples
• 120-400 advanced
properties samples
Wyoming
Green River
N
Washakie
Utah
Colorado
Uinta
Piceance
Sampled across
wide range of
lithofacies
Sampled over wide range
of porosity and permeability
Klinkenberg Permeability (4,000 psi, mD)
1000
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
Capillary Pressure in Uniformly
Variable Capillary
• Pc = 2τ cosθ/r
Pc = capillary pressure
τ = interfacial tension
θ = contact angle
r = pore radius
(after Lake, 2005)
Mercury Capillary Pressure
(after Jennings, 1981)
Depth
(after Doveton, 1999)
Capillary Pressure Equations
• Pc = 2τ cosθ/r
• r = 2τ cosθ/Pc
where:
Pc = capillary pressure
τ = interfacial tension
θ = contact angle
r = pore radius
• H=
Pcres
.
(σbrine-σoil,gas) x 0.433
• Pcres = Pcair-Hg τcosθres
τcosθair-hg
Capilary Pressure Measurement
In situ Mercury Intrusion
high-P fluid
• Drainageimbibition
(n=37)
• Drainage only
(n=90)
• NES = 4000 psi
high -P
core holder
electric
insulator
Pressure
transducer
Core Plug
Core Plug
– Unconfined
(n=150)
– In situ
Resistance
Reference
Cell
• Three different
air-Hg
measurements
Unconfined (routine) Mercury Intrusion
high -P
core holder
Pressure
transducer
mercury in
mercury in
9000
8000
7000
6000
5000
4000
3000
Air-Hg Capillary Pressure (psia)
2000
• Capillary Pressure
Varies with
Lithofacies and
associated pore size
distribution and
permeability
10000
Unconfined
Capillary
Pressure
1000
0
100
90
80
70
60
50
40
30
20
10
0
Wetting Phase Saturation (%)
Pc Normalization - Leverett J
function
• J(Sw) = C Pc (k/φ)0.5/τcosθ
– J = dimensionless Pc function,
function of Sw
– C = conversion constant =
0.2166
– Pc = capillary pressure (psi)
–
τcosθ = interfacial tension
(dyne/cm) X cosine of the
contact angle (degrees)
– k = permeability (md)
–φ
= porosity (fraction)
Normalization: Leverett J Function
9
0.00025md
8
0.00049md
0.0012md
0.0017md
7
Leverett J Function
• J function
works poorly
for mixed
lithofacies and
between basins
• Does work OK
for single
lithofacies in a
small area
0.0018md
0.0030md
6
0.0040md
0.0057md
5
0.0085md
0.012md
4
0.013md
0.032md
0.046md
3
0.085md
0.25md
2
0.41md
0.56md
1
0.84md
2.24md
0
0
10
20 30
40
50
60
70 80
Wetting Phase Saturation (%)
90 100
Air-Hg Capillary Pressure (psia)
10000
Normalization: BrooksCorey Capillary Pressure
9000
8000
7000
•
•
•
6000
5000
4000
3000
2000
1000
Transform taking logarithm of Pc and Sw
λ represents pore throat size distribution
Standard unimodal curves can be reduced
to intercept (Pce = extrapolated threshold
entry) and slope (λ)
0
0
10
20
30
40
50
60
70
80
90 100
10000
Air-Hg Capillary Pressure (psia)
Wetting Phase Saturation (%)
Air-Hg Capillary Pressure (psia)
10000
1000
-2.05
Pc = 1.54E+07Sw
2
R = 0.997
Pce
λ
1000
100
100
0
10
20
30
40
50
60
70
80
Wetting Phase Saturation (%)
90
100
10
100
Wetting Phase Saturation (%)
Stress effect on Pc
113 mD
10000
Air-Hg Capillary Pressure (psia)
Air-Hg Capillary Pressure (psia)
10000
1000
100
10
R091 1
255.9 ft
0
k = 113 mD
φ = 24.5%
10
20
30
40
50
60
70
80
90
100
Wetting Phase Saturation (%)
0.6 mD
100
10
10
20
30
40
50
60
70
80
90 100
Wetting Phase Saturation (%)
100
10
E946 1
6530.3 ft
k = 0.04160mD 10
φ = 9.5%
20
30
40
50
60
70
80
90
100
30
40
50
60
70
80
90
100
8 mD
90
100
0.2 mD
Wetting Phase Saturation (%)
Wetting Phase Saturation (%)
10
10
20
30
40
50
60
70
80
Wetting Phase Saturation (%)
100
10
20
30
40
50
60
70
80
Wetting Phase Saturation (%)
90
100
100
10
20
30
40
50
60
70
80
90
100
0.02 mD
90
100
0.00007 mD
Wetting Phase Saturation (%)
1000
100
10
B029 1
13672.5 ft
0 mD10
k = 0.000065
φ = 2.6%
• no significant difference
in high-low pairs at high
K
• increasing Pce separation
with decreasing K
• merging of curves at 3550% Sw
• smaller pores are in
protected pore space
1000
10000
1000
PA424 1
4606.5 ft
0 mD10
k = 0.00107
φ = 12.7%
100
B029 1
11460.6 ft
k = 0.02550mD 10
φ = 4.4%
Air-Hg Capillary Pressure (psia)
Air-Hg Capillary Pressure (psia)
20
1000
LD43C 1
4013.25 ft
0
k = 0.190 mD
φ = 12.9%
Air-Hg Capillary Pressure (psia)
Air-Hg Capillary Pressure (psia)
1000
10000
0.001 mD
10
10000
10000
0.04 mD
10
10000
1000
E946 1
6486.4 ft
0
k = 0.637 mD
φ = 12.2%
100
R780 1
2729.9 ft
0
k = 7.96 mD
φ = 19.2%
Air-Hg Capillary Pressure (psia)
Air-Hg Capillary Pressure (psia)
10000
1000
20
30
40
50
60
70
80
Wetting Phase Saturation (%)
• users of Winland R35
need to adjust for
confining stress
Threshold Entry Pore Diame ter
(µ m)
100
0.50
y = 11.77x
2
R = 0.77
10
1
y = 11.28x0.50
R2 = 0.93
0.1
A
0.01
1E-06 0.00001 0.0001
0.001
0.01
0.1
1
10
100
Klinkenberg Permeability/Porosity (mD/%)
Threshold Entry Gas Column
Height (ft)
10000
C
1000
y = 6.75x-0.50
R2 = 0.93
100
10
1
1E-06
-0.50
y = 6.48x
2
R = 0.77
1E-05 0.0001 0.001
0.01
0.1
1
10
Klinkenberg Permeability/Porosity (mD/%)
100
• threshold entry
pressure is
predictable from
√K/φ at any
confining
pressure
• correct
unconfined Pce
to insitu Pce
based on perm
change with
stress
Brooks-Corey Slope
• PSD expressed by Pcslope
• Pcslope = f (k)
• Pcslope ↓ with P ↑
Leverett J(Sw) =
Pc (k/φ)0.5/τcosθ
Poor fit because
Pcslope ≠ C = f(k, lith)
5
Brooks-Corey Capillary
Pressure Slope
Implicitly assumes
Pcslope = Constant
in situ
unconfined
y = -0.0304Ln(x) + 1.87
4
2
R = 0.0216
y = -0.037Ln(x) + 1.256
2
3
R = 0.052
2
1
0
1E-05 0.0001 0.001
0.01
0.1
1
10
100
In situ Klinkenberg Permeability (mD)
1000
1000
900
800
700
600
Modeled Pc
Curves
k=0.0001 mD
k=0.001 mD
k=0.01 mD
k=0.1 mD
k=1 mD
k=10 mD
500
400
300
200
100
0
Modeled Pc curves
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1000
Water Saturation (fraction)
Pc properties evolve
over time as
diagenesis changes
porosity and pore
architecture
Height above free water (ft)
Height above free water (ft)
Modeled Pc curves
100
k=0.0001 mD
k=0.001 mD
k=0.01 mD
10
k=0.1 mD
k=1 mD
k=10 mD
1
0.0
0.1
Water Saturation (fraction)
1.0
Drainge-Imbibition
• what is the residual trapped gas when a reservoir
leaks or along a gas migration path?
Approx. Height above Free Water
Level (ft)
10000
Primary Drainage
First Imbibition
Secondary Drainage
Second Imbibition
Tertiary Drainage
Third Imbibition
1000
100
10
1
0.1
0
10
20
30
40
50
60
70
80
Wetting Phase Saturation (%)
90
100
Trapping increases with
increasing initial saturation
(after Lake 2005)
Air-Hg Capillary Pressure (psia)
100
10
1
0
10
20
30
40
50
60
70
80
90
100
Wetting Phase Saturation (%)
Air-Hg Capil lary Pressure (psia)
Air-Hg Capillary Pressure (psia)
100
10
10
20
30
40
50
60
70
80
90
100
Wetting Phase Saturation (%)
20
30
40
50
60
70
80
90
100
Wetting Phase Saturation (%)
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
100
10
10
20
30
40
50
60
70
80
90
100
Wetting Phase Saturation (%)
1.0
10
10
20
30
40
50
60
70
80
90
100
Wetting Phase Saturation (%)
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
100
10
1
S685
6991.2 ft (B)0
φ = 8.6%
= 0.0063 mD
10
20
30
40
50
60
70
80
90
100
Wetting Phase Saturation (%)
10000
1000
Air-Hg Capillary Pressure (psia)
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
100
10
10
20
30
40
50
60
70
80
Wetting Phase Saturation (%)
90
100
C = 1/[(Snwr-Swi)-1/(Snwi-Swi)]
Snwr = 1/[C + 1/Snwi]
C = 0.55 (min ε); Swi = 0
100
Air-Hg Capillary Pressure (psia)
Air-Hg Capillary Pressure (psia)
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
10000
Air-Hg Capillary Pressure (psia)
10
10000
1000
1
E458
6404.8 ft (A) 0
φ = 9.5%
= 0.0019 mD
10
1
R829
5618.3 ft (B)0
φ = 9.2%
= 0.287 mD
10000
1
B646
8294.4 ft (B)0
φ = 7.6%
= 0.022 mD
100
10000
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
1
E393
7027.2 ft
0
φ = 15.0%
= 1.93 mD
1000
1
B049
9072.1 ft (A) 0
φ = 12.3%
= 6.74 mD
10000
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
Primary Drainage
Primary Imbibition
Second Drainage
Second Imbibition
Third Drainage
Third Imbibition
1000
100
10
KM360 1
8185.7 ft (B)0
φ = 5.9%
= 0.00070 mD
Residual Nonwetting Phase Saturation
(Snwr)
Air-Hg C apillary Pressure (psia)
Primary Drainage
First Imbibition
Secondary Drainage
Second Imbibition
Tertiary Drainage
Third Imbibition
1000
E393
7001.1ft
φ = 17.4%
= 28.9 mD
Residual Gas Saturation
10000
10000
kik
0.9
0.8
0.7
unconfined
confined
Land C=0.66, Swi=0
Land C =0.54, Swi=0
0.6
0.5
0.4
0.3
0.2
0.1
0.0
10
20
30
40
50
60
70
80
Wetting Phase Saturation (%)
90
100
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Initial Nonwetting Phase Saturation (Snwi)
• Trapping
constant, C
consistent
with
cemented
sandstone
1.0
Complete trapping, C=0
Vuggy, isolated moldic, C=0.3
Mesaverde high C =0.35
Mesaverde Ss, C=0.55
Mesaverde low, C=0.9
Cemented Ss, C=0.7
Berea, C=1.7
Unconsolidated, sucrosic, oolitic, C=3
0.9
Residual Nonwetting Phase Saturation (Snwr)
Residual
gas
saturation
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Initial Nonwetting Phase Saturation (Snwi)
0.9
1
Conclusions
• Drainage capillary pressure (Pc) can be modeled using
equations for threshold entry pressure (Pte) and BrooksCorey λ slopes.
• Confining pressure decreases largest pores consistent with
permeability decrease but has little influence on smaller
pores (pores largely protected by matrix)
• Snwr ↑ with Snwi ↑ Land-type relation: Snwr = 1/[0.55 +
1/Snwi]
• Mesaverde Project website is
http://www.kgs.ku.edu/mesaverde