Stochastic Modeling and Data Integration

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Analogue: Is Powerball Random? 80 Million Possibilities. 49! 42. 80M. (49 - 5)! * 5! 1. 1 x. ≈. Simulation Realizations: B: 1. 2. 3. 4. 5. 6. A: 6. 13 22 39 47 41.
Integrated Stochastic Modeling For Reservoir Characterization Y. Z. Ma

SEG Summer Workshop, June 2001, Taos, New Mexico

Integrated Stochastic Modeling Data Integration

Integrated Team Expertise

Stochastic Modeling For Reservoir Characterization

Inconsistency Resolution

Uncertainty Analysis

Prediction and Uncertainty truth

Accurate & Precise Most liked or most likely?

Inaccurate & Precise

Accurate & Imprecise Accurate & Relatively Precise

Inaccurate & Imprecise

Stochastic Modeling and Data Integration Geological

Petrophysical

Seismic (Derived)

Engineering Pressure

w1

w2

Time, days

Integrated Stochastic Modeling Multiple Disciplines Uncertainty in GM to Risk Analysis in Production

Rate

GM: (Framework), Facies, f , k, SW, ...

Production profile

Time

Stochastic Modeling of Interpreted Geologic Data Fluvial Channel Outcrop

Interpretation

Geologic Model

Data

Stochastic Modeling With Well Data: Facies Example Fluvial Channel Model

Fluvial Channel Model Conditioned with 6 Wells

6 Wells

Stochastic Simulation, Well & Seismic Integration

SGS with Nugget

SGS with 13 Wells

SGS with spherical range of 1.3km

CoCoSim with Seis-Attr (-0.73)

Well locations

Seismic Attribute

Inconsistency Resolution Ex1: Correlation Enhancement

Noisy Attribute

Variograms in EW

Wells r=0.52

r=0.79

Factorial Kriging Attribute

Variogram of Factorial Kriging Attr.

Correlations

Inconsistency Resolution Ex2: Calibration-Implied Rock Stats Seismic Attribute

=

Porosity Logs

25%

0.5

Porosity Average: 20% Porosity

0.4 0.3 0.2 0.1 0.0 -400

-200

0

Impedance

200

Stochastic Simulation, Data Integration & Uncertainty Analysis Thickness

Without data integration

Porosity

......

Quantification 375

400

425

450

475

500M

hcpv = 433 M. m3, s = 18.5 M. m3

Uncertainty With data integration

HCPV Example

HC Saturation

Reduction

Reduction

...... Quantification 350

375

400

425

450

475M

hcpv = 412 M. m3, s = 3.8 M. m3

Integrated Modeling with Many Attributes or Data Types

Attribute 1

CoCoSim with Attribute 1

Attribute 2

CoCoSim with Attribute 2

Composite Attribute

CoCoSim with Composite Attr.

Analogue: Is Powerball Random? 80 Million Possibilities

(49 - 5)! * 5!

1



x

49!

1

42

80M

Simulation Realizations: A:

6

13

22

39

47

41

B:

1

2

3

4

5

6

C:

10

12

17

25

40

20 W

Data, Data, Help me For a Big Hit! C:

(10) 12

17

(25) 40

20 W

If you could play after 1st 2 draws (25), (10):

(47 - 3)! * 3!

1 x

47!

42



1

680K

Well, Well, I Want a Big Gusher!

Is Geology Random? Lottery

Geologic Modeling

1. Purely Random

Correlated Properties (Physics Law)

2. No Data

Well, Seismic, Outcrop Etc.

3. Match Numbers Exactly

Mimics the “truth”

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