11-16 July, 1999 © 2001 Earthworks Environment & Resources Ltd. All Rights Reserved 1

Post-Processing Geostatistical Realisations - the Spillpoint

ashley.francis@sorviodvnvm.co.uk

http://www.sorviodvnvm.co.ukPresented at SEG Development & Production Forum,

11-16th July 1999, Kananaskis, Calgary, Canada

11-16 July, 1999 © 2001 Earthworks Environment & Resources Ltd. All Rights Reserved 2

Prospect Generation

• Interpret 2D seismic - horizon and faults

• Map TWT

• Map Stacking Velocity

• Depth Convert

• Find lowest closing contour

• Report volumes

• Propose well location

11-16 July, 1999 © 2001 Earthworks Environment & Resources Ltd. All Rights Reserved 3

Variograms

Stacking Velocity Variogram

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Separation (m )V

aria

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ty (

m/s

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Seismic Horizon Time Variogram

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11-16 July, 1999 © 2001 Earthworks Environment & Resources Ltd. All Rights Reserved 4

Observed VariogramsTime Velocity Depth

X =

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Observed VariogramsProspect Analysis

• Spillpoint : 1844 m

• Volume :882.2 x 106 m3

• Area : 34.7 x 106 m2

• Thickness: 25.4 m

• Prognosis : 1775 m

• Connection: 100%?

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Observed VariogramsConditional Simulation/Spillpoint

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Observed VariogramsIsoprobability Map/GRV Curve

• Spillpoint : 1834 m

• Volume :717.3 x 106 m3

• Area : 23.1 x 106 m2

• Thickness: 30.4 m

• Prognosis : 1776 m

• Connection: 79%GRV Distribution (Observed Variogram)

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GRV (m ^3 x 10^6)

Cu

mu

lati

ve P

rob

abili

ty (

%)

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Observed VariogramsIsoprobability Map/GRV Curve (all)

• Spillpoint : 1834 m

• Volume :791.5 x 106 m3

• Area : 25.8 x 106 m2

• Thickness: 30.1 m

• Prognosis : 1776 m

• Connection: 79%GRV Distribution (Observed Variogram)

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GRV (m ^3 x 10^6)

Cu

mu

lati

ve P

rob

abili

ty (

%)

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Variogram Problems

• Horizon time data - Gaussian model variogram?– Parabolic variogram behaviour at origin

– Horizon times continuous surfaces?

– Fresnel zone spatial averaging - “support effect”

• Stacking velocity data is noisy– Large nugget component on variogram

– Expect Stacking Velocities to be noisy

– Nugget inferred to be random error

– Filter nugget during kriging or simulation

11-16 July, 1999 © 2001 Earthworks Environment & Resources Ltd. All Rights Reserved 10

DEM DATA for SE England

(Data courtesy Nigel Press Associates. EuroDEM ©NPA 1997)

11-16 July, 1999 © 2001 Earthworks Environment & Resources Ltd. All Rights Reserved 11

DEM Variogram

Raw Data

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Smoothed Data

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DEM Variogram (Detail)

Raw Data

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Smoothed Data

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DEM Smoothing Correction

Correcting for Smoothing

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DEM Smoothing Correction (detail)

Correcting for Smoothing

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Fresnel Zone Support Effect

Seismic Horizon Time Variogram (detail)

y = 0.4721x - 503.82

-1000

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ms

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)

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“Support” Effect

• Support is a sample volume concept

• Variance decreases with increasing sample volume

• “Regularisation” - no overlap between samples

• Fresnel zone/Vertical resolution is spatial mixing

• Not strictly “support”.

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Time Variogram CorrectedTime Velocity Depth

X =

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Time Variogram CorrectedProspect Analysis

• Spillpoint : 1844 m

• Volume :886.6 x 106 m3

• Area : 34.7 x 106 m2

• Thickness: 25.5 m

• Prognosis : 1775 m

• Connection: 100%?

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Time Variogram CorrectedConditional Simulation/Spillpoint

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Time Variogram CorrectedIsoprobability Map/GRV Curve

• Spillpoint : 1834 m

• Volume :654.8 x 106 m3

• Area : 20.6 x 106 m2

• Thickness: 31.4 m

• Prognosis : 1774 m

• Connection: 68%GRV Distribution (Time Variogram Corrected)

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GRV (m ^3 x 10^6)

Cu

mu

lati

ve P

rob

abili

ty (

%)

11-16 July, 1999 © 2001 Earthworks Environment & Resources Ltd. All Rights Reserved 21

Time Variogram CorrectedIsoprobability Map/GRV Curve (All)

• Spillpoint : 1834 m

• Volume :802.0 x 106 m3

• Area : 25.5 x 106 m2

• Thickness: 30.8 m

• Prognosis : 1774 m

• Connection: 68%GRV Distribution (Time Variogram Corrected)

0%10%

20%30%40%50%

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90%100%

0 500 1000 1500 2000

GRV (m ^3 x 10^6)

Cu

mu

lati

ve P

rob

abili

ty (

%)

11-16 July, 1999 © 2001 Earthworks Environment & Resources Ltd. All Rights Reserved 22

Time/velocity Variograms CorrectedTime Velocity Depth

X =

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Time/velocity Variograms CorrectedProspect Analysis

• Spillpoint : 1843 m

• Volume :849.5 x 106 m3

• Area : 33.8 x 106 m2

• Thickness: 25.1 m

• Prognosis : 1772 m

• Connection: 100%?

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Time/velocity Variograms CorrectedConditional Simulation/Spillpoint

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Time/velocity Variograms CorrectedIsoprobability Map/GRV Curve

• Spillpoint : 1839 m

• Volume :807.8 x 106 m3

• Area : 28.9 x 106 m2

• Thickness: 27.5 m

• Prognosis : 1774 m

• Connection: 92%GRV Distribution (Time/velocity Variograms Corrected)

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90%100%

0 500 1000 1500 2000

GRV (m ^3 x 10^6)

Cu

mu

lati

ve P

rob

abili

ty (

%)

11-16 July, 1999 © 2001 Earthworks Environment & Resources Ltd. All Rights Reserved 26

Time/velocity Variograms CorrectedIsoprobability Map/GRV Curve (All)

• Spillpoint : 1939 m

• Volume :844.2 x 106 m3

• Area : 30.3 x 106 m2

• Thickness: 27.5 m

• Prognosis : 1774 m

• Connection: 92%GRV Distribution (Time/velocity Variograms Corrected)

0%10%

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90%100%

0 500 1000 1500 2000

GRV (m ^3 x 10^6)

Cu

mu

lati

ve P

rob

abili

ty (

%)

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Volume Summary

Seed Variogram P90 P10 Mean ChangeKriged Any Observed n/a n/a 882.2 0.0%Kriged Any Time n/a n/a 886.6 0.5%Kriged Any Time + Velocity n/a n/a 849.5 -3.7%Simulation single Observed 190.3 1132.6 717.3 -18.7%Simulation single Time 218.3 1133.1 654.8 -25.8%Simulation single Time + Velocity 515.9 1125.5 807.8 -8.4%Simulation independent Observed 510.2 1132.6 791.5 -10.3%Simulation independent Time 508.6 1151.2 802.0 -9.1%Simulation independent Time + Velocity 607.5 1125.5 844.2 -4.3%

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Recovering the Variogram

• Smoothing will be a function of:– Frequency/Bandwidth

– Migration (Collapse of Fresnel zone)

• Smoothing effect is “locked in” to data set.

• Correction is not a nugget - additional variance is spatially correlated

• Effect of smoothing is quite small in this example

• Effect of spillpoint criteria is more significant

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How can we condition to a known hydrocarbon contact?

• Discard realisations with “wrong” spillpoint?– Discard all realisations? (Precision)

• Discard realisations with too deep spillpoint?

• Discard realisations with too shallow spillpoint?

• Condition to a spillpoint level?

• How do we know the control on spillpoint?