Use of PP and PS time-lapse stacks Use of PP and PS time-lapse stacks for fluid-pressure discrimination.for fluid-pressure discrimination.
ALEXEY STOVAS ALEXEY STOVAS 11,, MARTIN LANDRØ MARTIN LANDRØ 11
& BØRGE ARNTSEN & BØRGE ARNTSEN 22
11NTNU, Dept. of Petroleum Engineering NTNU, Dept. of Petroleum Engineering and Applied Geophysics, Trondheim, and Applied Geophysics, Trondheim,
NorwayNorway
22 Statoil R&D centre Statoil R&D centre, Trondheim, Norway, Trondheim, Norway
OutlineOutline
Change in PP and PS reflectivity due to Change in PP and PS reflectivity due to change in pressure and saturation change in pressure and saturation (reflection pattern)(reflection pattern)
Pressure-saturation discrimination and Pressure-saturation discrimination and uncertaintiesuncertainties
Application on the Gullfaks synthetic data Application on the Gullfaks synthetic data set set
ConclusionsConclusions AcknowledgmentsAcknowledgments
MethodMethod
Methodology (Stovas & Landrø, 2002a,b)Methodology (Stovas & Landrø, 2002a,b) Water saturation model (Gassmann, 1951)Water saturation model (Gassmann, 1951) Pressure model (Mindlin, 1949)Pressure model (Mindlin, 1949) Reflection coefficients (Ursin & Stovas, Reflection coefficients (Ursin & Stovas,
2002)2002) The Gullfaks synthetic data set (Arntsen, The Gullfaks synthetic data set (Arntsen,
2002)2002)
Gassmann and Hertz-Mindlin models giveGassmann and Hertz-Mindlin models give
Reflectivity versus saturation and Reflectivity versus saturation and pressure (1)pressure (1)
MS
GHMP
Reflection coefficients versus incident Reflection coefficients versus incident angleangle
Reflectivity versus saturation and Reflectivity versus saturation and pressure (2)pressure (2)
PP
PS
M
MR
R
A
Stacked reflection coefficients versus Stacked reflection coefficients versus opening angle (opening angle ())
Reflectivity versus saturation and Reflectivity versus saturation and pressure (3)pressure (3)
PP
PS
M
MR
R
A
Basic principle (1)Basic principle (1)
We establish relationship between the We establish relationship between the change in the PP and PS stack change in the PP and PS stack amplitudes and the change in water amplitudes and the change in water saturation and pressuresaturation and pressure
PP
PP
R S
P PR
B
where operator maps the input vector of the change in saturation and pressure into the output vector of the change in the stacks amplitudes
B
MappingMapping
One point from PP&PS stacks
RPP
RPS
July, 2001
June, 1999
PP
am
plit
ud
e
PS amplitude
One point from PP&PS stacks
P
S
July, 2001
June, 1999
Pre
ssu
reWater saturation
Opening angle (ray tracing)Opening angle (ray tracing)
-1000 -800 -600 -400 -200 0 200 400 600 800 1000
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0
PS PP
ReservoirShetland
Rogaland
Hordaland
Nedre Nordaland
Nordaland
max
=62o
Dep
th, m
Inline distance, m
Basic principle (2)Basic principle (2)
The procedure:The procedure: Compute elastic parametersCompute elastic parameters Compute PP&PS reflection coefficientsCompute PP&PS reflection coefficients Evaluate min/max opening angleEvaluate min/max opening angle Compute stacked PP&PS reflection coefficientsCompute stacked PP&PS reflection coefficients Build up the reflection patternsBuild up the reflection patterns Compute PP&PS calibration factors Compute PP&PS calibration factors Compute the difference PP&PS stacksCompute the difference PP&PS stacks Place amplitudes into corresponding reflection Place amplitudes into corresponding reflection
patternspatterns
Uncertainties in Uncertainties in saturation&pressure from saturation&pressure from uncertainties in PP&PS stacked uncertainties in PP&PS stacked amplitudesamplitudes
RPP
2P/P0
2S
RPP
- RPP
RPP
+ RPP
RPS
- RPS
RPS
+ RPS
RPS
Pre
ssu
re
Water saturation
= discrimination angle
Weighting factors for Weighting factors for uncertaintiesuncertainties
22 PP 12 PS1
S b R b Rdet
B
21 PP 11 PS0
P 1b R b R
P det
B
Gullfaks synthetic dataGullfaks synthetic data
Data set includes:Data set includes: 8 types of reservoir rock (Tarbert and 8 types of reservoir rock (Tarbert and
Ness formations) overlaid by shale Ness formations) overlaid by shale (Shetland formation)(Shetland formation)
3 time-lapse models with PP and PS 3 time-lapse models with PP and PS seismic dataseismic data
Saturation-pressure condition is known for Saturation-pressure condition is known for Model I and has to be predicted for Model Model I and has to be predicted for Model II and Model IIIII and Model III
P-wave Gullfaks modelP-wave Gullfaks model T
ime,
ms
Distance, m
Oil water contact
Top reservoir
Reservoir rock physics Reservoir rock physics
parametersparameters 0s frK(GPa) maK (GPa) (GPa) ma 3gcm
SM1 T3 0.18 3.27 23.5 3.76 2.52 0.30
SM2 T-2B2+T-2B1 0.11 3.69 22.5 4.14 2.49 0.27
SM3 T-2A+T-1C+T-1B(øvre) 0.29 4.70 29.0 3.91 2.62 0.29
SM4 T-1B(nedre)+T-1A+N-3D 0.43 3.93 27.3 4.11 2.60 0.30
SM5 N-3C+N-3B+N-3A+N-2C 0.69 3.08 29.0 4.82 2.62 0.34
SM6 N-2C(nedre)+N-2B2 0.48 5.40 24.0 4.83 2.52 0.23
SM7 N-2B1+N-2A 0.31 4.02 19.0 3.80 2.42 0.23
SM8 N-1 0.74 5.24 23.0 4.55 2.90 0.37
P- and S-wave velocities for P- and S-wave velocities for reservoir rock SM1reservoir rock SM1
0,00,2
0,40,6
0,81,0
2,0
2,2
2,4
2,6
2,8
3,0
0,0050,010
0,0150,020
0,025
SM1
, km
/s
Effect
ive
pres
sure
, GPa
Water saturation
0,00,2
0,40,6
0,81,0
1,0
1,2
1,4
1,6
1,8
0,0050,010
0,0150,020
0,025
SM1
, km
/s
Effect
ive
pres
sure
, GPa
Water saturation
Isolines for reflectivity changes Isolines for reflectivity changes for the interface Shetland/SM1for the interface Shetland/SM1
0,0 0,2 0,4 0,6 0,8 1,0
0,005
0,010
0,015
0,020
0,025
0,0 0,2 0,4 0,6 0,8 1,0
0,005
0,010
0,015
0,020
0,025
RPP
RPS
Shetland/SM1
Eff
ecti
ve p
ress
ure
, GP
a
Water saturation
PP&PS stacks for Gullfaks Model PP&PS stacks for Gullfaks Model II
-2,5
-2,4
-2,3
-2,2
-2,1
-2,0
-1,9
-1,8
-1,7
-1,6
-1,5
-2,5
-2,4
-2,3
-2,2
-2,1
-2,0
-1,9
-1,8
-1,7
-1,6
-1,5
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
Top reservoir
PP stack, Model I
Tim
e, s
-4,8
-4,7
-4,6
-4,5
-4,4
-4,3
-4,2
-4,1
-4,0
-3,9
-3,8
-3,7
-3,6
-3,5
-3,4
-3,3
-3,2
-4,8
-4,7
-4,6
-4,5
-4,4
-4,3
-4,2
-4,1
-4,0
-3,9
-3,8
-3,7
-3,6
-3,5
-3,4
-3,3
-3,2
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
Top reservoir
PS stack, Model I
Tim
e, s
PP&PS stacks for Gullfaks Model PP&PS stacks for Gullfaks Model IIII
-2,5
-2,4
-2,3
-2,2
-2,1
-2,0
-1,9
-1,8
-1,7
-1,6
-1,5
-2,5
-2,4
-2,3
-2,2
-2,1
-2,0
-1,9
-1,8
-1,7
-1,6
-1,5
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
Top reservoir
PP stack, Model II
Tim
e, s
-4,8
-4,7
-4,6
-4,5
-4,4
-4,3
-4,2
-4,1
-4,0
-3,9
-3,8
-3,7
-3,6
-3,5
-3,4
-3,3
-3,2
-4,8
-4,7
-4,6
-4,5
-4,4
-4,3
-4,2
-4,1
-4,0
-3,9
-3,8
-3,7
-3,6
-3,5
-3,4
-3,3
-3,2
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
Top reservoir
PS stack, Model II
Tim
e, s
PP&PS stacks for Gullfaks Model PP&PS stacks for Gullfaks Model IIIIII
-2,5
-2,4
-2,3
-2,2
-2,1
-2,0
-1,9
-1,8
-1,7
-1,6
-1,5
-2,5
-2,4
-2,3
-2,2
-2,1
-2,0
-1,9
-1,8
-1,7
-1,6
-1,5
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
Top reservoir
PP stack, Model III
Tim
e, s
-4,8
-4,7
-4,6
-4,5
-4,4
-4,3
-4,2
-4,1
-4,0
-3,9
-3,8
-3,7
-3,6
-3,5
-3,4
-3,3
-3,2
-4,8
-4,7
-4,6
-4,5
-4,4
-4,3
-4,2
-4,1
-4,0
-3,9
-3,8
-3,7
-3,6
-3,5
-3,4
-3,3
-3,2
500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
Top reservoir
PS stack, Model III
Tim
e, s
0,0 0,2 0,4 0,6 0,8 1,0
0,005
0,010
0,015
0,020
0,025
* *
Model IS=0.18P=0.0065 GPaModel IIS = 0.77, = 0.039P = 0.0065 GPa, = 0.0004 GPaModel IIIS = 0.805, = 0.03P = 0.0142 GPa, = 0.0006 GPa
Model II
Model III
Model I
****** * **
**
*** *
**
****
*
** ******
ooooooooo
oooooooo
oooo oo oooo oooooooooo
Shetland/SM1
Eff
ecti
ve p
ress
ure
, GP
a
Water saturation
Saturation-pressure prediction Saturation-pressure prediction for reservoir rock SM1for reservoir rock SM1
Seismic amplitudes Seismic amplitudes and saturation-pressure and saturation-pressure uncertaintiesuncertainties
800 1000 1200 1400 1600
0,004
0,006
0,008
0,010
0,012
0,014
0,016
Model I
Model II
Seismic line, m
Pre
ssu
re, G
Pa
0,0
0,2
0,4
0,6
0,8
1,0
Model I
Model II
Sat
ura
tio
n
0,00
0,01
0,02
0,03
0,04
0,05
Model II vs. model I
RPS
RPP
Sei
smic
am
plit
ud
es
800 1000 1200 1400 1600
0,004
0,006
0,008
0,010
0,012
0,014
0,016
Model III
Model I
Seismic line, m
Pre
ssu
re, G
Pa
0,00,10,20,30,40,50,60,70,80,91,0
Model I
Model III
Sat
ura
tio
n
0,01
0,02
0,03
0,04
0,05
0,06
0,07
Model III vs. model I
RPS
RPP
Sei
smic
am
plit
ud
es
Weighting factors for Weighting factors for uncertaintiesuncertainties
1 2 3 4 5 6 7 80
20
40
60
80
100
120
140
b11
/ det B
1 2 3 4 5 6 7 80
20
40
60
80
100
120
140 b12
/ det B
1 2 3 4 5 6 7 8
-140
-120
-100
-80
-60
-40
-20
0
Model I Model II Model III
b21
/ det B
SMj
1 2 3 4 5 6 7 80
20
40
60
80
100
120
140
b22
/ det B
SMj
22 PP 12 PS1
S b R b Rdet
B 21 PP 11 PS
0
P 1b R b R
P det
B
Uncertainties vs. opening Uncertainties vs. opening angle (water saturation)angle (water saturation)
0 5 10 15 20 25 30 35 40 45 50 55 60
0,00
0,05
0,10
0,15
P/P
0
Opening angle, degrees
0 5 10 15 20 25 30 35 40 45 50 55 60
0,0
0,1
0,2
0,3
S
Opening angle, degrees
0 5 10 15 20 25 30 35 40 45 50 55 60
0,00
0,05
0,10
0,15
P/P
0
Opening angle, degrees
0 5 10 15 20 25 30 35 40 45 50 55 60
0,0
0,1
0,2
0,3
S
Opening angle, degrees
Uncertainties vs. opening Uncertainties vs. opening angle angle (gas saturation)(gas saturation)
0 5 10 15 20 25 30 35 40 45 50 55 60
0,00
0,05
0,10
0,15
0,20
P/P
0
Opening angle, degrees
0 5 10 15 20 25 30 35 40 45 50 55 60
0,00
0,05
0,10
0,15
0,20
S
Opening angle, degrees
0 5 10 15 20 25 30 35 40 45 50 55 60
0,00
0,05
0,10
0,15
0,20
Un
cert
ain
ty in
pre
ssu
re
Opening angle, degrees
0 5 10 15 20 25 30 35 40 45 50 55 60
0,00
0,05
0,10
0,15
0,20 shale
=0.29 S=0.2, P=0.01 GPa S=0.8, P=0.02 GPa
shale
=0.50 S=0.2, P=0.01 GPa S=0.8, P=0.02 GPa
Un
cert
ain
ty in
satu
rati
on
Opening angle, degrees
ConclusionsConclusions
Method of fluid-pressure discrimination from Method of fluid-pressure discrimination from PP and PS stacks is developed PP and PS stacks is developed
Method is applied on synthetic data set from Method is applied on synthetic data set from Gullfaks model which consists of three time-Gullfaks model which consists of three time-lapse situations. The results of water lapse situations. The results of water saturation and pressure prediction are very saturation and pressure prediction are very close to the modelled data (2-3% error in close to the modelled data (2-3% error in average).average).
The analysis of weighting factors for The analysis of weighting factors for uncertainties in water saturation and pressure uncertainties in water saturation and pressure shows that for all reservoir rocks representing shows that for all reservoir rocks representing Gullfaks Field the relative uncertainties in Gullfaks Field the relative uncertainties in saturation are bigger than the corresponding saturation are bigger than the corresponding uncertainties in pressure.uncertainties in pressure.
AcknowledgmentsAcknowledgments
We want to acknowledge the financial We want to acknowledge the financial support from the EC project ENK6-CT-support from the EC project ENK6-CT-2000-00108, ATLASS and Statoil. 2000-00108, ATLASS and Statoil.