581 AVO Fluid Inversion

AFI (AVO Fluid Inversion) Uncertainty in AVO: How can we measure it? Dan Hampson, Brian Russell Hampson-Russell Hampson -Russell Software, Calgary

Last Updated: Updated: April 2005 Authors: Dan Hampson, Brian Russell

1

Overview AVO Analysis is now routinely used for exploration and development. But: all AVO attributes contain a great deal of “uncertainty” – there is a wide range of of lithologies which could account account for any AVO response. In this talk we present a procedure for analyzing and quantifying AVO uncertainty.

As a result, we will calculate probability maps for hydrocarbon detection.


2

Overview AVO Analysis is now routinely used for exploration and development. But: all AVO attributes contain a great deal of “uncertainty” – there is a wide range of of lithologies which could account account for any AVO response. In this talk we present a procedure for analyzing and quantifying AVO uncertainty.

As a result, we will calculate probability maps for hydrocarbon detection.


2

AVO Uncertainty Analysis: The Basic Process

G CALIBRATED: !

GRADIENT ! INTERCEPT ! BURIAL DEPTH AVO ATTRIBUTE MAPS ISOCHRON MAPS


I

STOCHASTIC AVO MODEL FLUID PROBABILITY MAPS

!

PBRI

!

POIL

!

PGAS 3

“Conventional” AVO Modeling: Creating 2 pre-stack synthetics IN INSITU SITU==OIL OIL

IO

GO

FRM FRM==BRINE BRINE

IB


GB

4

Monte Carlo Simulation: Creating many synthetics

I-G DENSITY FUNCTIONS BRINE

OIL

GAS

75

50

25

0

Last Updated: April 2005 Authors: Dan Hampson, Brian Russell

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The Basic Model

Shale

We assume a 3-layer model with shale enclosing a sand (with various fluids).

Sand

Shale


6

The Basic Model

The Shales are characterized by:

Vp1, Vs1, r1

P-wave velocity S-wave velocity Density

Vp2, Vs2, r2


7

The Basic Model

Vp1, Vs1, r1

Each parameter has a probability distribution:

Vp2, Vs2, r2


8

The Basic Model The Sand is characterized by: Brine Modulus Brine Density

Shale

Gas Modulus Gas Density Oil Modulus

Sand

Oil Density Matrix Modulus Matrix density

Shale

Porosity Shale Volume Water Saturation Thickness

Each of these has a probability distribution. Last Updated: April 2005 Authors: Dan Hampson, Brian Russell

9

Trend Analysis Some of the statistical distributions are determined from well log trend analyses: 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 0.4

0.9

1.4

1.9

2.4

2.9

3.4

DBSB (Km) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell

10

Determining Distributions at Selected Locations Assume a Normal distribution. Get the Mean and Standard Deviation from the trend curves for each depth: 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 0.4

0.9

1.4

1.9

2.4

2.9

3.4

DBSB (Km) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell

11

Trend Analysis: Other Distributions 5000

Shale Velocity

4500 4000

3.0

Sand Density

3500

2.8

3000

2.6 3.0

2500

2.4

2000

2.2

1500

2.0

1000

1.8

500

1.6

0

1.4

2.8

Shale Density 40%

2.6

Sand Porosity

35%

2.4 2.2

30%

2.0

25%

1.8 0.4

1.2 1.0

1.6

20% 0.9

1.4

15%

1.4

1.9

2.4

2.9

3.4

DBSB (Km)

10%

1.2 0.4 1.0

0.9 5% 0.4

0%

1.4 0.9

1.9 1.4

2.4

DBSB (Km)

1.9

2.9 2.4

3.4 2.9

3.4

DBSB (Km) 0.4

0.9


1.4

1.9

DBSB (Km)

2.4

2.9

3.4 12

Practically, this is how we set up the distributions: Shale: Vp Vs Density Sand: Brine Modulus Brine Density Gas Modulus Gas Density Oil Modulus Oil Density Matrix Modulus Matrix density Dry Rock Modulus Porosity Shale Volume Water Saturation Thickness Last Updated: April 2005 Authors: Dan Hampson, Brian Russell

Trend Analysis Castagna’s Relationship with % error Trend Analysis

Constants for the area

Calculated from sand trend analysis Trend Analysis Uniform Distribution from petrophysics Uniform Distribution from petrophysics Uniform Distribution 13

Calculating a Single Model Response From a particular model instance, calculate two synthetic traces at different angles.

Note that a wavelet is assumed known. 0o 45o

Top Shale

Sand

Base Shale


14

Calculating a Single Model Response On the synthetic traces, pick the event corresponding to the top of the sand layer:

Note that these amplitudes include interference from the second interface.

0o

45o

Top Shale P1

P2

Sand

Base Shale


15

Calculating a Single Model Response Using these picks, calculate the Intercept and Gradient for this model: I G

= P1 = (P2-P1)/sin2(45)

0o

45o

Top Shale P1

P2

Sand

Base Shale


16

Using Biot-Gassmann Substitution Starting from the Brine Sand case, the corresponding Oil and Gas Sand models are generated using Biot-Gassmann substitution. This creates 3 points on the I-G cross plot:

BRINE

GAS

OIL

KGAS

KOIL

ρGAS

ρOIL

G

G I


G I

I 17

Monte-Carlo Analysis By repeating this process many times, we get a probability distribution for each of the 3 sand fluids:

G

I


Brine Oil Gas

18

The Results are Depth Dependent Because the trends are depth-dependent, so are the predicted distributions:

@ 1000m

@ 1600m


@ 1200m

@ 1800m

@ 1400m

@ 2000m

19

The Depth-dependence can often be understood using Rutherford-Williams classification 4

2

6

5 3 1

Sand

4

e c n a d e p m I

3

Shale

2

5

6

1

Class 2

Class 3

Class 1

Burial Depth


20

Bayes’ Theorem Bayes’ Theorem is used to calculate the probability that any new (I,G) point belongs to each of the classes (brine, oil, gas):

~ P F I , G

(

)=

~ ~ p I , G F * P ( F )

∑

k

p ( I , G F k )* P ( F k

)

where: • •

P(Fk) represent a priori probabilities and F k is either brine, oil, gas; p(I,G|Fk) are suitable distribution densities (eg. Gaussian) estimated from the stochastic simulation output.


21

How Bayes’ Theorem works in a simple case: Assume we have these distributions: Gas

Oil

Brine E C N E R R U C C O

VARIABLE Last Updated: April 2005 Authors: Dan Hampson, Brian Russell

22

How Bayes’ Theorem works in a simple case: This is the calculated probability for (gas, oil, brine). 100%

E C N E R R U C C O

50%

VARIABLE Last Updated: April 2005 Authors: Dan Hampson, Brian Russell

23

When the distributions overlap, the probabilities decrease: Even if we are right on the “Gas” peak, we can only be 60% sure we have gas. E C N E R R U C C O

100%

50%

VARIABLE


24

Showing the Effect of Bayes’ Theorem This is an example simulation result, assuming that the wet shale VS and VP are related by Castagna’s equation.


25

Showing the Effect of Bayes’ Theorem This is an example simulation result, assuming that the wet shale VS and VP are related by Castagna’s equation.

This is the result of assuming 10% noise in the VS calculation Last Updated: April 2005 Authors: Dan Hampson, Brian Russell

26

Showing the Effect of Bayes’ Theorem Note the effect on the calculated gas probability

1.0

0.5

0.0

Gas Probability By this process, we can investigate the sensitivity of the probability distributions to individual parameters.


27

Example Probability Calculations

Gas


Oil

Brine

28

Real Data Calibration #

In order to apply Bayes’ Theorem to (I,G) points from a real seismic data set, we need to “calibrate” the real data points.

#

This means that we need to determine a scaling from the real data amplitudes to the model amplitudes.

#

We define two scalers, S global and Sgradient , this way: Iscaled Gscaled

= Sglobal *Ireal = Sglobal * Sgradient * Greal

One way to determine these scalers is by manually fitting multiple known regions to the model data. Last Updated: April 2005 Authors: Dan Hampson, Brian Russell

29

Fitting 6 Known Zones to the Model

4

4

5

5 6

6 3

1

3

1

2

2

3

2

1

4


5

6

30

Real Data Example – West Africa

This example shows a real project from West Africa, performed by one of the authors (Cardamone). There are 7 productive oil wells which produce from a shallow formation. The seismic data consists of 2 common angle stacks. The object is to perform Monte Carlo analysis using trends from the productive wells, calibrate to the known data points, and evaluate potential drilling locations on a second deeper formation.


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One Line from the 3D Volume Near Angle Stack 0-20 degrees

Far Angle Stack 20-40 degrees


32

One Line from the 3D Volume

Near Angle Stack 0-20 degrees

Shallow producing zone Deeper target zone



33

AVO Anomaly Near Angle Stack 0-20 degrees



34

Amplitude Slices Extracted from Shallow Producing Zone Near Angle Stack 0-20 degrees

+189

-3500



35

Trend Analysis Sand and Shale Trends 3.00 5000

4500

Y T I C O L E V

4000

2.75

Sand velocity

Sand density

Y T I S N E D

2.50

3500

2.25

3000

2500

2.00

2000

1.75 1500

1000

1.50

500

700

900

1100

1300

1500

1700

1900

500

700

900

1100

1300

1500

1700

1900

4000 3.00

3500

Y T I C O L E V

Shale velocity

2.75

Y T I S N E D

3000

Shale density

2.50

2500

2.25

2000

2.00

1500

1.75

1000 500

1.50

700

900

1100

1300

1500

1700

1900

2100

BURIAL DEPTH (m) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell

2300

2500

500

700

900

1100

1300

1500

1700

1900

BURIAL DEPTH (m) 36

Monte Carlo Simulations at 6 Burial Depths -1400

-2000


-1600

-2200

-1800

-2400

37

Near Angle Amplitude Map Showing Defined Zones Wet Zone 1 Well 6 Well 3

Well 5 Well 1

Well 7

Well 2 Well 4

Wet Zone 2


38

Calibration Results at Defined Locations Wet Zone 1

Wet Zone 2


Well 2

Well 5

39

Calibration Results at Defined Locations Well 3

Well 4


Well 6

Well 1

40

Using Bayes’ Theorem at Producing Zone: OIL Near Angle Amplitudes

1.0

.80

Probability of Oil .60

.30 Last Updated: April 2005 Authors: Dan Hampson, Brian Russell

41

Using Bayes’ Theorem at Producing Zone: GAS Near Angle Amplitudes

1.0

.80

Probability of Gas .60


42

Using Bayes’ Theorem at Target Horizon

Near angle amplitudes of second event

1.0

Probability of oil on second event

.80 .60


43

Verifying Selected Locations at Target Horizon


44

581 AVO Fluid Inversion

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