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Stolen from Prof. Maurice Dusseault, U Waterloo, Canada
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Rune M Holt, NTNU & SINTEF, Trondheim Norway
Rock Physics & GeomechanicsAspects of
Seismic Reservoir Monitoring
Euroconference Rock Physics & GeomechanicsErice, Sicily; Italy 25 – 30 September 2007
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”Reservoirs are Dynamic Systems”*
* Citation from L. W. Teufel (early 90ties) – images from Phillips Norway
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... which permits us to monitor their performance
Monitoring tools:
Time-lapse (”4D”) Seismics
Passive seismics
Surface & In situ displacements
5
Why do we want to monitor?To improve recovery through
Identification of undepleted pocketsObserving the efficiency of enhanced recovery operations (e.g. water, gas, steam injection)Being able to drill future wells in the right positions
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4D
Main 4D Attributes:
TWT – Two Way Traveltime (from top and bottom of reservoir)
Reflectivity – Given by impedance (=ρv) contrast between overburden and reservoir
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What is changing?
FluidsFluid substitution due to water, gas or steam injection
Saturation change due to water / gas drive
Fluid properties change as a result of pressure and temperature changes
8
Fluid-induced changesPreceded by a
seismic pilot study by Britton et al
(1982), Nur et al at Stanford studied the influence of
temperature changes on
velocities and attenuation of heavy oil / tar
sands.1984:
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Fluid-induced changes
Reflection coefficients depend on [ρ⋅vP] - more affected by fluid substitution than travel time
2
P
1 ( )v
(1 )
f
f
fr
s
s
fH
K
KK
αϕ α ϕ
ϕρϕ ϕ ρ
++ −
=+ −
Fluid substitution:P-wave velocity is assumed to change according to the Biot-Gassmann equation
Hfr: P-wave modulus of dry rock frame
α: Biot coefficient
Ks: Bulk modulus of solid grains
ρs: Density of solid grains
ϕ: Porosity.
Kf: Bulk modulus of pore fluid
ρf: Density of pore fluid
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Fluid-induced changes
Fine-scale mixing: Pore pressure equilibrates within patches (saturation heterogeneities) -Low frequency limit.Patchiness reduces our ability to predict 4D response.
Knight & Nolen-Hoeksma, 1990
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What is changing?Rocks
Pore pressure reduction in reservoir leads to effective stress increase within the depleted regionStress arching around depleted regions Wave velocity stress sensitivity
⇒Fingerprints for 4D seismics!
CO2sequestration – the opposite situation
So we are also saving the World....
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4D – Depleting Reservoirs
Stress changes:
Effective Stress Increase (compaction) in Reservoir during depletion ⇒Speed-up?
Vertical Stress Reduction (stretching) in Overburden ⇒Slow-down?
!
13
Monitoring of Depleting Reservoirs: Field Observations
The response from a depleting reservoir itself is often small; larger response is obtained during inflation.The most significant 4D attribute appears to be a TWT increase (slow down) in the overburden.Also, stress-induced anisotropy associated with the stress concentration above the flanks of the depleting zone has been measured.
Hatchell & Bourne, TLE 2005;
Barkved & Kristiansen, TLE 2005
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So... Our challenges are:
Geomechanics:To estimate the stress [and strain] path within
and around a depleting reservoir.
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Tools for Geomechanical Modelling :
AnalyticalElastic; matched reservoir & surrounding rock properties –focus on overburden (Geertsma, 1973)Elastic contrast – focus on [ellipsoidal] reservoir (Rudnicki, 1999)
NumericalFEM (Morita et al., 1989; Mulders, 2003)DEM (Alassi et al., 2005)
Field MeasurementsSurface & / in situ displacement monitoringRepeated stress measurements (XLOT or minifrac)
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Our challenges are:
Geomechanics:To estimate the stress [and strain] path within
and around a depleting reservoir.Rock Physics:
To understand the mechanisms of stress sensitive wave propagation and quantify velocity changes associated with given stress changes in situ.
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Rock Physics Tools:Experimental Laboratory
We measure Ultrasonic Vertical & Horizontal P- & S-wave velocities &
Oblique P-waves in a triaxial cell under controlled conditions of stress,
pore pressure & temperature
Formation Physics Laboratory @ SINTEF Petroleum Research
σ=σ0ei2π·f·t
ε=ε0ei(2π·f·t-ϕ)
Ø= 75 mm
L= 5
0 m
m
σ=σ0ei2π·f·tσ=σ0ei2π·f·t
ε=ε0ei(2π·f·t-ϕ)ε=ε0ei(2π·f·t-ϕ)
Ø= 75 mmØ= 75 mm
L= 5
0 m
mL=
50
mm
Set-up for 10 Hz
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Rock Physics Tools:
AnalyticalCrack-Pore models (Shapiro, 2002; Fjær, 2006)Grain pack models based on Hertz-Mindlin (Walton, 1987)
NumericalDiscrete Particle Modelling
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Discrete Particle Modelling
Simulating mechanical and petrophysical behaviour of an assembly of spherical particles based on contact mechanics.
A normal & shear force - displacement law Bond shear & tensile strengthsForce and moment equilibrium ensured for each contact in a cycling
and time-stepping approach
Discrete Particle Modelling represents a fully dynamic approach to computing complex behaviour of bonded rock based on contact law between individual particles
Potyondy & Cundall, IJRM 2004
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Rock Physics Tools: Numerical Laboratory
Particle scale description of rock (from petrographical / 3D μCT analysis)
Computation of mechanical and petrophysical rock properties as function of external stress and pore pressure.
PFC3D model with clusters of spheres representing each grain
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Numerical Laboratory Experiments
Low Confining StressHigh Confining Stress
Li & Holt, Oil&Gas Sci&Tech 2002; Holt et al, IJRM 2005
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Rock-induced changesReservoir Stress Path:
hh
fpσγ Δ
=Δ
vv
fpσγ Δ
=Δ
The stress path is controlled byDepleting reservoir geometry (shape; inclination)Elastic contrast between reservoir and surroundingsNon-elastic / Failure processes
Conventional assumption:Uniaxial compactionStrictly true only if the depleting reservoir is infinitely wide and thinImplies no stress arching: γv=0; γh=α(1-2ν)/(1-ν)
Stress-path coefficients after Hettema & Schutjens
23
Reservoir Stress Path
Stress path coefficients from Rudnicki’s analytical model (1999); reservoir is elastically matched to the surroundings (Poisson’s ratio = 0.20)
Δh
Re=Δh/2R
h
e=h/2R
Only for [European] pancake shaped reservoir (e=0) is the uniaxial strain & no arching assumption fulfilled.
...varies between uniaxial strain and isotropic loading
24
0
500
1000
1500
0 5 10 15
Confining Pressure [MPa]
Wav
e Ve
loci
ties
[m/s
]Hydrostatic Stress
vP
vS
Walton limits; n = 6
No slip
No slip
Slip
Slip
0
500
1000
1500
0 5 10 15
Confining Stress [MPa]
Wav
e Ve
loci
ties
[m/s
]
vP LAB vP PFC
vS LAB vS PFC
Hydrostatic loading
vS
vP
Reservoir Rock Stress Sensitivity?Unconsolidated sand (and fractured rock) exhibits strongly stress sensitive velocities.
Stress sensitivity decreases with increasing stress
Glass Beads
25
Reservoir Rock Stress Sensitivity: Synthetic sandstoneStress increase within the reservoir may have small impact on seismic traveltime & reflectivity because
Cemented reservoir rock is ~ stress insensitive in compressionReservoir is thin
0.4
0.6
0.8
1
1.2
0 10 20 30 40 50 60
Effective vertical stress [MPa]
Ver
tical
P-w
ave
velo
city
[rel
.]
Field (depletion)
Field (injection/coring)
Laboratory (core test)
Holt et al., TLE 2005
Uniaxial compaction of Synthetic sandstone
cemented under stress
Stress sensitivity is larger during unloading (injection)
May be more significant in unconsolidated or fractured reservoirs
26
Reservoir Rock Stress Sensitivity: Numerical modelling of sandstone
1000
1500
2000
2500
3000
0 20 40 60 80 100
Axial Stress [MPa]
Velo
citie
s [m
/s]
vPz
• vPx
vSzx
vSxy
CompressionDecompression
PFC3D simulation performed with spherical particles; bonds inserted under 30 MPa axial & 15 MPa lateral stress
In situ Behaviour fromnumerical modelling We observe:
Qualitatively the same response to loading & unloading as seen in the physical experiments
Notice Stress-Induced Anisotropy (also in lab!), and velocity decrease at high stress due to bond breakage
Courtesy of Lars M Moskvil
27
Rock-induced changes
Note: The stress path coefficients refer to pore pressure change in the reservoir.The pore pressure response in the overburden is small (~ un-drained shear loading).The stress is altered in a very large volume of rock around the reservoir.
vv
f
hh
f
p
p
σγ
σγ
Δ=
ΔΔ
=Δ
Geertsma Model
vγ
hγ
Overburden Stress Path:
The γ’s are plotted along a vertical line through the centre of the reservoir
28
Rock-induced changes
0
500
1000
1500
2000
2500
3000
3500
-5 0 5
Effective stress change [MPa]
Dep
th [m
]
VerticalHorizontal
Mean
The stress path in the overburden is close to Constant Volume & Pure shear loading
Erling Fjær, 2006
Overburden Stress Path:
29
Relatively linear increase in velocity with increasing stress (unlike sand & sandstone)
Less stress sensitivity during unloading than loading
Significant temperature effect
Overburden Shale Stress Sensitivity
Johnston, 1987
Hydrostatic Loading
.. But Not 4D Relevant?..
30
-20
-10
0
10
20
30
40
0 5
Axial Stress Increase [MPa]
P-W
ave
Velo
city
Cha
nge
[m/s
]
10
Axial Velocity Increase
Radial Velocity Decrease
Constant Volume Test
Stress-Induced Anisotropy
Undrained axial loading (normal to bedding) &
radial unloading with zero volume deformation
Overburden Shale Stress Sensitivity
10% porosity field shale core
Constant Volume
Test
31
0.10
0.15
0.20
5 10 15 20
Mean Net Stress [MPa]
P-W
ave
Ani
sotr
opy
ε
0
10
20
30
40
50
Axi
al &
Rad
ial S
tres
s [M
Pa]
Hydrostatic loading to 40 MPa axial stressConstant Volume test dataAxial stressRadial stress
Notice: Lithological > Stress – induced anisotropy
Overburden Shale Stress Sensitivity
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Combined Seismics - Rock Physics –Geomechanics Simulation10 MPa pore pressure reduction in a 200 m thick reservoir section at 2400 m depth.
• Unconsolidated reservoir sand:vP ~σ0.20
•Well cemented reservoir rock: Stress sensitivity by porosity change only.
• Arching: Depleted zone radius = 400 m Limited arching: Depleted zone radius = 2000 m
-4000
-3000
-2000
-1000
0-20 -15 -10 -5 0 5
TWT shift [ms]
Dep
th [m
]
Well cemented reservoir rock; Arching - No fluid substitution
Unconsolidated reservoir sand; Arching - No fluid substitution
Unconsolidated reservoir sand; Limited Arching
Water replacing Oil
No fluid substitution
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-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 0.5 1 1.5 2
Relative distance from centre of drained area
Aver
age
diffe
renc
e in
hor
izon
tal s
tress
es[M
Pa]
From Fjær, 2006
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Length ∝ S-wave splitting
Orientation ↔ polarization of fastest S-wave
35
Valhall (1997)
Barkved et al, 2005
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Valhall (2003)Barkved et al, 2005
37
Summary of what we know
Time-lapse seismics shows pronounced effects of reservoir depletion on TWT and Anisotropy, caused mainly by stress changes around the reservoir.
Primarily shear stress evolution.Note: Thick zone of influence!
The reservoir is less visible.Loading along reservoir stress pathCemented rocks are ~ stress insensitive in situNote: Thin zone of influence
Fluid substitution effects in reservoir may be substantial, but not easily predictable / interpretable.
38
Summary of what we don’t know...
Stress path & Stress sensitivity in fractured or faulting reservoirs (beyond elasticity)Scale issues (Grain to Lab to Field...)Accounting for complexity in seismic modelling!Dispersion – in Shales?And what about temperature...?
But the Keys are: High Quality & Repeatable Seismic Data + Interdisciplinary communication
39
Dispersion in shales?
Modelled curves: Assuming bound water has a viscous
behaviour→ Shear modulus of bound
water is complex
10−3
10−2
10−1
100
101
102
103
104
0
500
1000
1500
2000
2500
3000
3500
4000
4500
frequency (kHz)
veloc
ity (m
/s)
From Suarez-Rivera et al., 2001
Is it real – and what is then the mechanism?
40
R
The R-factor is defined as
v 1v
(1 )
z
z z
R
TWT zRTWT z
εΔ
= ⋅
→Δ Δ
= +
From Hatchell & Bourne, TLE 2005
The 4D seismic response caused by reservoir depletion is mainly caused by slow-down in the overburden
Explanation: Stress Arching
Seismic data give typically R∼5 for vertical unloading and R∼1 for loading
41
R from Lab
Uniaxial Compaction test with Reservoir Sandstone Core
-20
0
20
40
60
25 50 75 100 125 150Axial Stress [MPa]
R [-
]
3300
3400
3500
3600
3700
3800
Axi
al P
-Wav
e Ve
loci
ty [m
/s]
42
Time
Vertical Stress
X
HorizontalStress
Str
ess
Vertical
Horizontal
This has a profound impact on rock mechanical and petrophysical laboratory measurements
compactionstrengthwave velocities Core alteration
also leads to Stress Memory!
Stress Release during Coring
43
R from Lab
0
10
20
30
40
30 40 50 60
Axial Stress [MPa]
R [-
]
3000
3100
3200
3300
3400
3500
Simulated Core Behaviour using Synthetic sandstone formed under Stress (30 MPa axial, 15 MPa radial).
K0
44
R from Lab
Simulated Virgin Rock Behaviour using Synthetic sandstone formed under Stress (30 MPa axial, 15 MPa radial).
y = 3.2x + 1.00R2 = 0.93
0.99
1.00
1.01
1.02
1.03
0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007
Axial Strain [milliStrain]
Rel
ativ
e A
xial
P-W
ave
Velo
city
[-]
R~3K0
45
R from Lab
Hydrostatic Loading of Shale
1.00
1.05
1.10
0.000 0.001 0.002Axial Strain [-]
Wav
e Ve
loci
ties
[m/s
]
R~48
46
R from Lab
Constant Volume Test with Shale
y = 12x + 1.00R2 = 0.98
0.995
1.000
1.005
1.010
1.015
1.020
-0.0010 -0.0005 0.0000 0.0005 0.0010 0.0015
Strain [-]
(Rel
.) W
ave
Velo
citie
s [-]
vPz
vPr
R~12