581 AVO Fluid Inversion
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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
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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 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.
Last Updated: Updated: April 2005 Authors: Dan Hampson, Brian Russell
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.
Last Updated: 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
Last Updated: Updated: April 2005 Authors: Dan Hampson, Brian Russell
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
Last Updated: Updated: April 2005 Authors: Dan Hampson, Brian Russell
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
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
Vp2, Vs2, r2
Each parameter has a probabilit distribution:
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
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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
1.9
2.4
2.9
3.4
DBSB (Km) Last Updated: April 2005 Authors: Dan Hampson, Brian Russell
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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
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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
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell
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
Trend Analysis Castagna’s Relationship with % error Trend Analysis
Constants for the area
Calculated from sand trend analysis Trend Analysis Uniform Distribution from petrophysics
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
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
KOIL
ρGAS
ρOIL
G
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
4
e c n a d e p m I
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 F k 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
Brine E C N E R R U C C O
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). 100%
E C N E R R U C C O
50%
VARIABLE Last Updated: April 2005 Authors: Dan Hampson, Brian Russell
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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
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, 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
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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
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
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
Wet Zone 2
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell
Well 2
Well 5
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Calibration Results at Defined Locations Well 3
Well 4
Last Updated: April 2005 Authors: Dan Hampson, Brian Russell
Well 6
Well 1
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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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