367_AVO_Fluid_Inversion.pdf

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

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

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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 lithologies which could 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.

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

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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

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

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

IO

GO

FRM FRM==BRINE BRINE

IB

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

GB

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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

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

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The Basic Model

The Shales are characterized by:

Vp1, Vs1, r1

P-wave velocity S-wave velocity Density

Vp2, Vs2, r2

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

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The Basic Model

Vp1, Vs1, r1

Each parameter has a probability distribution:

Vp2, Vs2, r2

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

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The Basic Model The Sand is characterized by:

Shale

Sand

Shale

Brine Modulus Brine Density Gas Modulus Gas Density Oil Modulus Oil Density Matrix Modulus Matrix density Porosity Shale Volume Water Saturation Thickness

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

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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

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

1.9 DBSB (Km)

2.4

2.9

3.4 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

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

1.9 DBSB (Km)

2.4

2.9

3.4 11

Trend Analysis: Other Distributions 5000

Shale Velocity

4500 4000

3.0

3500

2.8

Sand Density

2.6 3.0 Shale Density 2.8 2500 2.4 40% 2.6 Sand Porosity 2000 2.2 35% 2.4 1500 2.0 30% 2.2 1000 1.8 2.0 25% 500 1.6 1.8 0 1.4 20% 0.41.2 1.6 0.9 1.4 1.9 2.4 2.9 3.4 15% 1.4 DBSB (Km) 1.0 10% 1.2 0.4 0.9 1.4 1.9 2.4 2.9 1.0 5% DBSB (Km) 0.4 0.9 1.4 1.9 2.4 2.9 0% DBSB (Km) 0.4 0.9 1.4 1.9 2.4 DBSB (Km) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 3000

3.4 3.4

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. 45o 0o

Top Shale

Sand

Base Shale

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

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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

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

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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

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

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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 ρGAS G

KOIL ρOIL G

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

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

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

Brine Oil Gas

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

@ 1000m

@ 1600m

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

@ 1200m

@ 1800m

@ 1400m

@ 2000m

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

2

6

5 3 1

Sand Impedance

4 3

Shale

2 5

6

1

Class 2

Class 3

Class 1

Burial Depth

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

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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 Fk is either brine, oil, gas; • p(I,G|Fk) are suitable distribution densities (eg. Gaussian) estimated from the stochastic simulation output.

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

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

Oil

OCCURRENCE

Brine

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

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

OCCURRENCE

100%

50%

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

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When the distributions overlap, the probabilities decrease:

OCCURRENCE

Even if we are right on the “Gas” peak, we can only be 60% sure we have gas.

100%

50%

VARIABLE

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

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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.

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

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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

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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.

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

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Example Probability Calculations

Gas

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

Oil

Brine

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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, Sglobal 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

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Fitting 6 Known Zones to the Model

4

4

5

5 6

6 3

1

3

1

2

2

3

2

1

4

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

5

6

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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.

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

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

Far Angle Stack 20-40 degrees

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

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One Line from the 3D Volume

Near Angle Stack 0-20 degrees

Shallow producing zone Deeper target zone

Far Angle Stack 20-40 degrees

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

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AVO Anomaly Near Angle Stack 0-20 degrees

Far Angle Stack 20-40 degrees

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

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

+189

-3500 Far Angle Stack 20-40 degrees

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

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Trend Analysis Sand and Shale Trends 3.00 5000

4000

2.75

Sand velocity

DENSITY

VELOCITY

4500

Sand density

2.50

3500

2.25

3000

2500

2.00

2000

1.75 1500

1000 500

700

900

1100

1300

1500

1700

1.50 500

1900

700

900

1100

1300

1500

1700

1900

4000 3.00

Shale velocity

2.75

DENSITY

VELOCITY

3500

3000

2500

2000

1500

1000 500

Shale density

2.50

2.25

2.00

1.75

700

900

1100

1300

1500

1700

1900

2100

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

2300

2500

1.50 500

700

900

1100

1300

1500

1700

1900

BURIAL DEPTH (m) 36

Monte Carlo Simulations at 6 Burial Depths -1400

-2000

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

-1600

-2200

-1800

-2400

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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

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

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Calibration Results at Defined Locations Wet Zone 1

Well 2

Wet Zone 2

Well 5

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

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Calibration Results at Defined Locations Well 3

Well 6

Well 4

Well 1

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

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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

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

1.0

.80

Probability of Gas .60

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

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Using Bayes’ Theorem at Target Horizon

Near angle amplitudes of second event

1.0

Probability of oil on second event

.80 .60

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

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Verifying Selected Locations at Target Horizon

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

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Summary By representing lithologic parameters as probability distributions we can calculate the range of expected AVO responses. This allows us to investigate the uncertainty in AVO predictions. Using Bayes’ theorem we can produce probability maps for different potential pore fluids. But: The results depend critically on calibration between the real and model data. And: The calculated probabilities depend on the reliability of all the underlying probability distributions. Last Updated: April 2005 Authors: Dan Hampson, Brian Russell

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