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Jean-Marc Chautru, Geovariances, France,Laurent Fontanelli, Repsol (Móstoles), Spain,Noelia Rodríguez-Morillas, Repsol (Móstoles), Spain,Taoufik Aït-Ettajer, Repsol (Houston), United States

MODELING COMPLEX

PETROPHYSICAL PROPERTIES TRANSITION ACROSS FACIES BORDERS

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THE ISSUE

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MODELING COMPLEX TRENDSPetrophysical properties may be poorly correlated to the facies 3D model : → Causes

– Sedimentological def inition of facies– Electrofacies poorly characterized in Permeability– …

→ Consequences– Properties histogram overlap from one facies to another– Smooth transition of properties from one facies to another

How to detect, characterize and account for such effects?

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SOLVING THE ISSUEHow to detect and characterize properties correlations across facies borders?

→ Use of domaining tools commonly used in mining industry

Consider 2 points (x+h) and x in different facies

– Mean difference: E[Z(x+h)-Z(x)]

– Conditional mean: E[Z(x+h) |Z(x)]A B

hxx+h

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BORDER EFFECTS

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Different types of border effect

case1

case2

case3

case4

Facies A Facies B

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Conditional mean (domain A)

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Case2

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Conditional mean (domain B)

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• Case 1: Independent distributions of Property in Facies A and Facies B.

• Case 2: Distributions of Property in Facies A and Facies B with different means and smooth transition. Property in A and B depends on the distance to the other facies.

• Case 3: Distributions of Property in Facies A and Facies B are partially independent, partially correlated (jump at border + trend effect.

• Case 4: Distributions of Property in Facies A and Facies B with different means and border effect in B only. Property in A does not depend of B, but property in B depends on the distance to A.

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CHARACTERIZING BORDER EFFECT

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EXAMPLES (SYNTHETIC DATA)Examples of typical Porosity distributions are compared:

→ Global Porosity– Continuity at f ield scale, independence from Facies

→ Facies dependent Porosity distribution– Specif ic Property histogram in each Facies, with or without overlap– Porosity distributions in different Facies are not correlated

→ Facies dependent Porosity distribution + border effect– Specif ic Property histogram in each Facies, with or without overlap– Porosity distributions in different Facies are linked

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EXAMPLE 1

Conditional mean

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Fre

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Porosity (%)

Poro_Global

Poro_Global

Global Porosity, independent of facies→ Same mean

→ No border effect

x+h in F1 x+h in F2 x+h in F3x outside F1 x in F1 x in F1

x+h in F2x outside F2

x+h in F1x in F2

x+h in F1x in F3

x+h in F3x in F2

x+h in F2x in F3

x+h in F3x outside F3

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EXAMPLE 1

Mean difference

Global Porosity, independent of facies→ Same mean of difference

→ No border effect

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Porosity (%)

Poro_Global

Poro_Global

x+h in F1 x+h in F2 x+h in F3x outside F1 x in F1 x in F1

x+h in F2x outside F2

x+h in F1x in F2

x+h in F1x in F3

x+h in F3x in F2

x+h in F2x in F3

x+h in F3x outside F3

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EXAMPLE 2

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Fre

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Porosity (%)

Poro_Facies1

Poro_Facies2

Poro_Facies3

3 independent facies→ Different means

→ No border effect

Conditional mean

x+h in F1

x+h in F2 x+h in F3

x outside F1

x in F1 x in F1

x+h in F2x outside F2

x+h in F1x in F2

x+h in F1x in F3

x+h in F3x in F2

x+h in F2x in F3

x+h in F3x outside F3

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EXAMPLE 2

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Porosity (%)

Poro_Facies1

Poro_Facies2

Poro_Facies3

3 independent facies→ Different means of difference

→ No border effect

Mean difference

x+h in F1

x+h in F2 x+h in F3

x outside F1

x in F1 x in F1

x+h in F2x outside F2

x+h in F1x in F2

x+h in F1x in F3

x+h in F3x in F2

x+h in F2x in F3

x+h in F3x outside F3

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EXAMPLE 3Trend from Facies1 to Facies3Facies2 independent

→ Flat conditional mean for F2– Value of F2 mean

→ From F3 to F1– Trend from 15% (at border)

to Facies mean

Conditional mean

x+h in F1

x+h in F2 x+h in F3

x outside F1

x in F1 x in F1

x+h in F2x outside F2

x+h in F1x in F2

x+h in F1x in F3

x+h in F3x in F2

x+h in F2x in F3

x+h in F3x outside F3

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EXAMPLE 3Trend from Facies1 to Facies3

Facies2 independent

→ Flat mean difference for F2

→ From F3 to F1

– Trend from 0% (at border)

to Facies means difference

Mean difference

x+h in F1

x+h in F2 x+h in F3

x outside F1

x in F1 x in F1

x+h in F2x outside F2

x+h in F1x in F2

x+h in F1x in F3

x+h in F3x in F2

x+h in F2x in F3

x+h in F3x outside F3

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PRACTICAL APPLICATION EXAMPLE

Validation of a genetic sedimentological model: → Border effect calculation based on acoustic impedance

with reference to genetic facies model

→ Test of relationship between facies and seismic properties– Independence -> facies model is not representative of the f ield

– Facies dependent statistics of properties -> facies model is representative of the f ield• Presence of property trend in facies indicates partial correlation between

facies and properties

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MODELING BORDER EFFECT

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MODELING BORDER EFFECT

Distanceto domainB (m)

Simulationwith distance asexternal drift

Calculate parameter drift from distance to

border and border effect analysis

Use this driftin KED or UK

Use each geobodyas a mask

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CONCLUSION

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CONCLUSION

→ Border effect analysis is a good tool for geological model QC

→ It allows characterizing complex petrophysicalproperties in Facies

→ It allows validating sedimentological models when coupled with seismic data

→ The tools are immediately available

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THANK YOU FOR YOUR ATTENTION