Pressure and Compaction in theRock Physics Space
Jack Dvorkin
June 2002
Compaction of Shales
Freshly deposited shales and clays may have enormous porosity of ~80%. The speed of sound is close to that in water ~ 1500 m/s. The S-wave velocity is small but not negligible. As a result, Poisson’s ratioapproaches 0.5.
As the overburden increases, the shale compacts. Porosity decreasesand velocity increases.
Compaction in on-shore shale andin GOM.
50 100 150
0
200
600
800
1000
GR
Dep
th (m
)
1.6 1.8 2.0 2.2 2.4
RHOB (g/cc)
2.0 2.5
Vp (km/s)
NPP
GOM
2
3
4
5
6
7
0.2 0.4 0.6
Ip (
km
/s
g/cc
)
NPP
GOM
Porosity
CompactionIp
(km
/s g
/cc)
Dep
th (
m)
Difference in Compaction of Shales and Sands
Sands are much less compactable than shales (unless the grains break ordiagenesis sets in).
Compaction in dry kaolinite,Ottawa sand, and a 50/50
mixture thereof (Yin, 1992).
1.0
1.5
2.0
0.1 0.2 0.3 0.4 0.5
Vp (
km
/s)
Porosity
10 MPa
40 MPa
Clay
Sand
50% Sand50% Clay
DRY
Vp
(km
/s)
2
3
4
5
6
7
0.2 0.4 0.6
Ip (
km
/s
g/cc
)
NPP
GOM
Porosity
Compaction
YIN 50/50
YINKaolinite
Compaction of Shales
As long as shale is load-bearing, the compaction trend in the impedance-porosity space seems to be universal among wells logs and lab data.
Compaction in on-shore shale and in GOM + Yin's clay andsand/clay data.
Ip (
km/s
g/c
c)
Compaction and Undercompaction Due to PorePressure
Abnormal pore pressure results in undercompaction and porosityand velocity reversals
0.2
0.3
0.4
Por
osit
y
SHALE: 120 > GR > 90
2
3
Vp (
km
/s)
SHALE: 120 > GR > 90
Porosity Reversal
Velocity Reversal
1 km
Po
rosi
tyV
p (
km/s
)
2
3
4
5
6
7
8
9
0 0.2 0.4 0.6
Ip (
km
/s
g/cc
)
GOM
Porosity
YIN 50/50
YINKaolinite
Compaction and Undercompaction Due to PorePressure -- Same Rock Physics Trend
Normally- and over-pressured parts of the well project onto thesame rock physics trend, same as the lab data.
Ip (
km/s
g/c
c)
Moreover, well log data from different wells worldwide fall onto thesame Ip-porosity trend. Different color means different well.
Universality of Compaction and Undercompactionin Rock Physics Space
50 100 150
500
1000
1500
2000
2500
3000
3500
GR
Dep
th (m
)
0 .2 .4 .6Porosity
3 4 5 6 7 8 9 10Ip (km/s g/cc)
3
4
5
6
7
8
9
0 0.1 0.2 0.3 0.4 0.5 0.6
Ip (
km
/s)
Porosity
Ip (
km/s
g/c
c)
Dep
th (m
)
Universality of Compaction and Undercompactionin Rock Physics Space
The curves are from “unconsolidated sediment” model that relates elasticproperties to porosity, lithology, and pore fluid compressibility.
0
2
4
6
8
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Sh
ear
Mod
ulu
s (G
Pa)
Porosity
NPPC =100%
30%50%
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Com
pre
ssio
nal
Mod
ulu
s (G
Pa)
Porosity
NPP
C =100%
30%
50%
Co
mp
ress
ion
al M
od
ulu
s (G
Pa)
Sh
ear
Mo
du
lus
(GP
a)
Rational Effective-Medium ModelUncemented Particles
Hertz-Mindlin Theory + Modified Lower Hashin-Shtrikman
Hertz-Mindlin theory provides expressions for the contact stiffness betweentwo elastic particles. Based on these expressions, we can derive the elasticmoduli for uncemented sediment at critical porosity depending on pressure
and pore fluid.
0
20
40
60
80
100
0 0.1 0.2 0.3 0.4
M-M
odu
lus
(GPa)
Porosity
SOLID
HERTZ-MINDLIN
IncreasingPressure
MODIFIEDLOWER
HASHIN-SHTRIKMANWITH
HERTZ-MINDLIN
Co
mp
ress
ion
al M
od
ulu
s (G
Pa)
Compaction and Undercompaction Due to PorePressure in AI-EI Space
Abnormal pore pressure also results in AI and Poisson's ratioreversals
Ip Reversal
PR Reversal
3
456
78
Ip (
km
/s
g/cc
)
ALL
0.2
0.3
0.4
10 15 20 25 30
Poi
sson
's R
atio
ALL
Differential Pressure (MPa)
PR Reversal
1 km
Hi-P Gas
Ip (
km/s
g/c
c)P
R
5
6
7
0.3 0.4 0.5
Ip (
km
/s
g/cc
)
Poisson's Ratio
PR is very sensitive to mineralogy. We may want to use it todetect mineralogical changes associated with onset ofoverpressure. May help resolve the non-uniqueness ofuniversality of Ip-φφφφ trends
Compaction and Undercompaction Due to PorePressure in AI-EI Space
AbovePressure
Zone
BelowPressure
Zone
PressureZone
JustShales
Ip (
km/s
g/c
c)
High pore pressure in rock with gas results in smaller Poisson’s ratio.Velocity may vary a lot among rocks but PR behavior is universal.
Plots based on lab data.
30 20 10 0Pp (MPa)
Sand35% Porosity
30 20 10 0Pp (MPa)
Sand27% Porosity
30 20 10 00
.1
.2
Pp (MPa)
PR
Sand36% Porosity
High Pressure in Gas SandsP
R
Normal Compaction in ShalesLog data show monotonic compaction versus depth.
0 50 100 150
2000
2500
3000
GR
Dep
th (m
)
2.0 2.2 2.4 2.6RHOB (g/cc)
2 3 4 5Vp (km/s)
Dep
th (
m)
Normal Compaction in ShalesLog data show monotonic compaction versus depth.
0 .1 .2 .3 .4 .53
4
5
6
7
8
9
10
11
12
13
Porosity
Ip (
km
/s
g/cc
)
GR
20
40
60
80
100
120
140
160
0 0.1 0.2 0.3 0.4 0.53
4
5
6
7
8
9
10
11
12
13
Porosity
Ip (
km
/s
g/cc
)
TVD
1800
2000
2200
2400
2600
2800
3000
3200
Left -- color coding by GR highlights compaction trends for shale and sand.Right -- color coding by depth shows porosity collapse and impedance increase.
Ip (
km/s
g/c
c)
Ip (
km/s
g/c
c)
0.1 0.2 0.3 0.44
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
Porosity
Ip (
km
/s
g/cc
)
TVD2500
2550
2600
2650
2700
2750
2800
2850
Undercompaction in ShalesLog data show reverse compaction versus depth.
Color coding by depth shows porosity and impedance reversal.Overpressured shales stay on the same rock physics trend as normally
pressured shales.
Reversal -- DeeperShale Plots to
Low-Right
Ip (
km/s
g/c
c)
40 60 80 100
8
9
10
11
12
13
14
15
16
GR
MD
(kft
)
AT_136_1
.2 .4 1 3
Rt
.1 .2 .3 .4
Porosity
UPS
CA
LE
D
2.0 2.5 3.0
Vp (km/s)
UPS
CA
LE
D
5 6 7
Ip (km/s g/cc)
UPS
CA
LE
D
10 11 12 13
MW (lb/gal)
Mudweight Steps Approximately Match Porosity and Velocity Flattening
4 5 6 7 8 9 10
Pp (kpsi)
1 2 3 4
Peff (kpsi)
2 kf
tUndercompaction in Shales -- Example 2
Undercompaction in Shales -- Example 2
0.15 0.2 0.25 0.3 0.35
4
4.5
5
5.5
6
6.5
7
7.5
Porosity
P-I
mped
ance
Depth (km)
2.5
3
3.5
4
4.5
SAND
OverpressuredShale
Color-Coded by Depth
Overpressured shales stay on the same rock physics trend as normallypressured shales.
Ip (
km/s
g/c
c)
Undercompaction and Vp/Vs Ratio
In overpressured (softer) sediments, the Vp/Vs ratio is high and deviatesfrom the established Vp/Vs relations.
In overpressured gas sands the opposite is true -- the Vp/Vs ratio is small.
1.5
2.0
2.5
3.0
3.5
2.0 2.5 3.0 3.5 4.0
Vp
/V
s
Vp (km/s)
Mudrock
WilliamsShale
WilliamsSand
OverpressuredGas Sand
OverpressuredShale
Pore PressureIncrease
Figure shows a Vp/Vs versusVp plot for a well with an
overpressured shale section(green) and overpressured
gas sand (red). Blacksymbols are for normallypressured shales. Blue
curves show establishedrelations for water-saturated
sediment.
Vp
/Vs
Compaction and Unloading in Sands
Loading and unloading produce different strain paths in sand
Compaction and elastic unloading in a sand.
0 5 10 15 200.39
0.4
0.41
0.42
0.43
Pressure (MPa)
Galveston
Por
osit
y
0.39 0.40 0.41 0.42 0.430
1
2
Porosity
Galveston
Envelope
Vp (
km
/s)
0.39 0.40 0.41 0.42 0.430
0.2
0.4
0.6
0.8
1.0
1.2
Porosity
Galveston
Envelope
Vs
(km
/s)
Po
rosi
ty
Vp
(km
/s)
Vs
(km
/s)
Compaction and Unloading in Sands
Static and Dynamic Moduli
StaticUnloading
StaticLoading
0
1
2
3
4
0 5 10 15 20
Bu
lk M
odu
lus
(GPa)
Effective Pressure (MPa)
Dynamic
Static
0 5 10 15 20Effective Pressure (MPa)
Dynamic
Static
StaticUnloading
StaticLoading
SAND 1 SAND 2
Bu
lk M
od
ulu
s (G
Pa)
Conclusion
The projection of compaction (loading) process intothe impedance-porosity plane produces a universaltrend typical for many soft shales and independentof depth.
AI/EI technique may help detect pressure-associated lithology changes in shales. But what todo in frontier areas where impedance inversion isdifficult?
Unloading (uplift) is different from loading(compaction) and will produce a different trendbecause of irreversible porosity reduction.
Pore Fluid and Pressure Diagnostic from AI and EI
The softer the rock with liquid the larger the Poisson’s Ratio. The softer therock with gas the smaller the Poisson’s ratio.
0
0.1
0.2
0.3
0.4
2 3 4 5 6
Poi
sson
's R
atio
P-Impedance (km/s g/cc)
BRINE
PorePressure
PorePressure
GAS
NORTH SEASAND
PR
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