581 avo fluid inversion

Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 1

AFI(AVO Fluid Inversion)

Uncertainty in AVO:How can we measure it?

Dan Hampson, Brian RussellHampson-Russell Software, Calgary


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.


AVO Uncertainty Analysis:The Basic Process

AVO ATTRIBUTEAVO ATTRIBUTEMAPSMAPSISOCHRONISOCHRONMAPSMAPS

!! GRADIENTGRADIENT!! INTERCEPTINTERCEPT!! BURIAL DEPTHBURIAL DEPTH

CALIBRATED:CALIBRATED:

STOCHASTIC STOCHASTIC AVOAVOMODELMODEL

GG

IIFLUIDFLUID

PROBABILITYPROBABILITYMAPSMAPS

!! PPBRIBRI

!! PPOILOIL

!! PPGASGAS


“Conventional” AVO Modeling: Creating 2 pre-stack synthetics

IO GO

IB GB

IN SITU = OILIN SITU = OIL

FRM = BRINEFRM = BRINE


Monte Carlo Simulation: Creating many synthetics

0

25

50

75

II--G DENSITY FUNCTIONS G DENSITY FUNCTIONS BRINE OIL GAS


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

Shale

Shale

Sand

The Basic Model


The Shales are characterized by:

P-wave velocity S-wave velocityDensity

Vp1, Vs1, r1

Vp2, Vs2, r2

The Basic Model


Each parameter has a probability Each parameter has a probability distribution:distribution:

Vp1, Vs1, r1

Vp2, Vs2, r2

The Basic Model


The Sand is characterized by:

Brine ModulusBrine DensityGas ModulusGas DensityOil ModulusOil DensityMatrix ModulusMatrix densityPorosityShale VolumeWater SaturationThickness

Each of these has a probability distribution.Each of these has a probability distribution.

Shale

Shale

Sand

The Basic Model


0500

100015002000250030003500400045005000

0.4 0.9 1.4 1.9 2.4 2.9 3.4DBSB (Km)

Some of the statistical distributions are determined from well log trend analyses:

Trend Analysis


Determining Distributions at Selected Locations

0500

100015002000250030003500400045005000

0.4 0.9 1.4 1.9 2.4 2.9 3.4DBSB (Km)

Assume a Normal distribution. Get the Mean and Standard Deviation from the trend curves for each depth:


Trend Analysis: Other Distributions

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0.4 0.9 1.4 1.9 2.4 2.9 3.4DBSB (Km)

Shale Velocity

1.01.2

1.41.6

1.82.0

2.22.4

2.62.8

3.0

0.4 0.9 1.4 1.9 2.4 2.9 3.4DBSB (Km)

Sand Density

1.01.21.41.61.82.02.22.42.62.83.0

0.4 0.9 1.4 1.9 2.4 2.9 3.4DBSB (Km)0%

5%

10%

15%

20%

25%

30%

35%

40%

0.4 0.9 1.4 1.9 2.4 2.9 3.4DBSB (Km)

Shale Density

Sand Porosity


Shale:Shale:VVpp Trend AnalysisTrend AnalysisVVss Castagna’sCastagna’s Relationship with % errorRelationship with % errorDensityDensity Trend AnalysisTrend Analysis

Sand:Sand:Brine ModulusBrine ModulusBrine DensityBrine DensityGas ModulusGas ModulusGas DensityGas DensityOil ModulusOil Modulus Constants for the areaConstants for the areaOil DensityOil DensityMatrix ModulusMatrix ModulusMatrix densityMatrix densityDry Rock Modulus Dry Rock Modulus Calculated from sand trend analysisCalculated from sand trend analysisPorosityPorosity Trend AnalysisTrend AnalysisShale VolumeShale Volume Uniform Distribution from Uniform Distribution from petrophysicspetrophysicsWater SaturationWater Saturation Uniform Distribution from Uniform Distribution from petrophysicspetrophysicsThicknessThickness Uniform DistributionUniform Distribution

Practically, this is how we set up the distributions:


Top Shale

Base Shale

Sand

From a particular model instance, calculate two synthetic traces at different angles.

0o 45o

Note that a wavelet is assumed known.

Calculating a Single Model Response


Top Shale

Base Shale

Sand

0o 45o

On the synthetic traces, pick the event corresponding to the top of the sand layer:

P1P2

Note that these amplitudes include interference from the second interface.



Top Shale

Base Shale

Sand

0o 45o

P1P2

Using these picks, calculate the Intercept and Gradient for this model:

I = P1G = (P2-P1)/sin2(45)



GI

GI

GI

OILOIL

KKOILOIL

ρρOILOIL

GASGAS

KKGASGAS

ρρGASGAS

BRINEBRINE

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:

Using Biot-Gassmann Substitution


I

G

BrineOilGas

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

Monte-Carlo Analysis


@ 1000m@ 1000m @ 1200m@ 1200m @ 1400m@ 1400m

@ 1600m@ 1600m @ 1800m@ 1800m @ 2000m@ 2000m

Because the trends are depth-dependent, so are the predicted distributions:

The Results are Depth Dependent


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

classification

SandSand

Burial DepthBurial Depth

Impe

danc

eIm

peda

nce ShaleShale

1

1

2

2

3

3

4

4

5

5

6

6

Class 3

Class 2Class 1


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):

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.

( ) ( )( ) ( )∑

=k kk FPFGIp

FPFGIpGIFP

*,

)~(*~,,~


How Bayes’ Theorem works in a simple case:

VARIABLEVARIABLE

OC

CU

RR

ENC

EO

CC

UR

REN

CE

Assume we have these distributions:

Gas Oil

Brine

Last Updated: April 2005 Authors: Dan Hampson, Brian Russell 23VARIABLEVARIABLE

OC

CU

RR

ENC

EO

CC

UR

REN

CE

100%

50%

This is the calculated probability for (gas, oil, brine).

How Bayes’ Theorem works in a simple case:


When the distributions overlap, the probabilities decrease:

VARIABLEVARIABLE

OC

CU

RR

ENC

EO

CC

UR

REN

CE

100%

50%

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


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

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



Note the effect on the calculated gas probability

0.0

0.5

1.0

Gas Probability

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



Example Probability Calculations

Gas Oil Brine


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 = Sglobal *IrealGscaled = Sglobal * Sgradient * Greal

One way to determine these scalers is by manually fitting multiple known regions to the model data.


Fitting 6 Known Zones to the Model

1

4

2

3

56

1

4

2

3

56

1 2

4 5 6

3


This example shows a real project from West Africa, performed byone 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.

Real Data Example – West Africa


Near Angle Stack0-20 degrees

Far Angle Stack20-40 degrees

One Line from the 3D Volume




Shallow producing zone

Deeper target zone

One Line from the 3D Volume




AVO Anomaly




-3500

+189

Amplitude Slices Extracted fromShallow Producing Zone


Trend AnalysisSand and Shale Trends

1000

1500

2000

2500

3000

3500

4000

4500

5000

500 700 900 1100 1300 1500 1700 1900

VELO

CIT

Y

1.50

1.75

2.00

2.25

2.50

2.75

3.00

500 700 900 1100 1300 1500 1700 1900

DEN

SITY

1000

1500

2000

2500

3000

3500

4000

500 700 900 1100 1300 1500 1700 1900 2100 2300 2500

BURIAL DEPTH (m)

VELO

CIT

Y

1.50

1.75

2.00

2.25

2.50

2.75

3.00

500 700 900 1100 1300 1500 1700 1900

BURIAL DEPTH (m)

DEN

SITY

Sand velocity

Shale velocity

Sand density

Shale density


Monte Carlo Simulations at 6 Burial Depths

-1400 -1600 -1800

-2000 -2200 -2400


Near Angle Amplitude Map Showing Defined Zones

Wet Zone 1

Wet Zone 2

Well 6

Well 7Well 3 Well 5

Well 1

Well 2

Well 4


Calibration Results at Defined Locations

Wet Zone 1

Wet Zone 2

Well 2

Well 5


Well 3

Well 4

Well 6

Well 1

Calibration Results at Defined Locations


.30

.60

1.0

Probability of Oil.80

Near Angle Amplitudes

Using Bayes’ Theorem at Producing Zone: OIL


.30

.60

1.0

Probability of Gas.80

Near Angle Amplitudes

Using Bayes’ Theorem at Producing Zone: GAS


Near angle amplitudes of second event

.30

.60

1.0

.80Probability of oil on second event

Using Bayes’ Theorem at Target Horizon


Verifying Selected Locationsat Target Horizon


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 allthe underlying probability distributions.

581 avo fluid inversion

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