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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

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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

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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

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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?

!

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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

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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

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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

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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

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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

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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

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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:

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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?..

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-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

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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

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Valhall (1997)

Barkved et al, 2005

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Valhall (2003)Barkved et al, 2005

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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.

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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

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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?

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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

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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]

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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

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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

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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

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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

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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