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.