3-snesim

Stanford Geostatistical Earth Modeling

Software

SGeMS :: SNESIM

@ Austin, Texas, 2007

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Training image (TI)

Geological analogs, outcrops

Sequence stratigraphy

Object-based modeling

Process-based modeling

Physical rule-based modeling

A training image is a visually explicit model of heterogeneity/ continuity without any attempt at local accuracy

A TI generator is available in SGeMS, coded by Amisha Maharaja

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P(sand)=3/4P(shale)=1/4 Draw simulated value

Updated simulation

Simulation grid

u2 u4

u3

u1

u?

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Look for patterns matching the conditioning data

Training image

Go to next grid node along random path...

• Stochastic (multiple realizations)• Easy to condition (pixel-based)• General (not specific to channels)• But slow

u?

Pixel-based approach building on sequential simulation paradigm(Journel, Srivastava, 1992)

Original MPS implementation

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IM Store and classify occurrences of all training patterns (for a given data search neighborhood or data template)

Construction requires scanning training image only once (fast)

Read the facies probabilities from search tree during simulation

u

1

3 24

(Strebelle, 2000)Introduction of search tree

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IM Generic sequential simulation algorithm

(1) Relocate any hard data to grid cells if required

(2) Define a random path

(3) Loop over all grid cells (1) Extract local data event (B) with a template

B=any data and previously simulated values(2) Read P(A|B) from search tree(3) Draw from P(A|B) a value(4) Add that value to the data set

multiple-pointdata event

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Single grid algorithm

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TI (250X250)80 condition data(9X9)120 seconds

150 condition data(12X12)450 seconds

Simulation (250X250)

(P4, 3GHz CPU, 512 RAM)

Single-grid unconditional simulation

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Empty

Full

Coarse gridtemplate

Fine gridtemplate

In 1994, Tom Tran suggested multiple-grids as a solution ::Instead of using one large and dense template, utilizea series of cascading coarse grids and sparse templates.

Multiple-grid approach

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Scan the training image using the coarse template. Performa coarse grid simulation. Copy the content of the coarse grid to the fine grid and perform another ( fine grid ) simulation.

Coarse grid Fine grid


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TI(250x250)

60 condition data36 seconds(3 grids)

150 condition data450 seconds(single grid)

(P4, 3GHz CPU 512 RAM)

Multiple-grid unconditional simulation

80 condition data, 1 grid120 seconds

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IM Load “facies_5.prj” (3/5 facies TI) Single and multiple-grid unconditional simulation

Load “facies_2.prj” (2 facies channel TI) single and multiple-grid simulation with and

without well data conditioning

Exercise :: single/multiple grids

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IM Load “facies_2.prj” (2 facies channel TI) simulation conditional to soft data (Pmud, Psand) 10 simulations + E-type; compare to the soft data

Exercise :: soft data conditioning

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Reference, p=0.375

East

Nor

th

0.0 250.0000.0

250.000

shale

sand

True reference used as Ti

Local non-stationary

Non-stationary patterns can NOT be simulated by a non-stationary TI

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0 250

250

Training image deposition direction

Reservoir actual deposition direction

θ

Rotate training image by θto look for conditioning data

Build one searching tree for each rotation angle θ

Non-stationary :: rotate TI

original TI

new TI

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0 250

250 original TI

Non-stationary :: rescale TI

125

125

500

500

X2

X0.5

new TI

new TI

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Non-stationary example

Realization with fetures (p=0.41)

East

Nor

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0.0 250.0000.0

250.000

shale

sand

Simulated realization

25 hard data locations, p=0.40

0. 50. 100. 150. 200. 250.

0.

50.

100.

150.

200.

250.

shale

sand

SeismicChannel thickness Channel orientation25 hard data

Fluvial fan deposit simulation:

45o

0o

90o

x2

x1

x0.5

(TI manipulation internally)

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250

250

250

250

100

100

100

100

200

100

300

100

R1 R2 R3

R1 R1+R2 R1+R2+R3

R4

Non-stationary example(TI manipulation externally)

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IM Load “fan_snesim.prj” (2 facies, 2D channel TI) Orginal TI → TI | ti3

Run SNESIM simulation on “sim_grid” conditioning to Hard + Soft (Pmud, Psand)

Use rotation and affinity region (TI manipulation internally)

Exercise :: rotation/affinity

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IM Load “fan_snesim.prj” (2 facies, 2D channel TI) Orginal TI → TI | ti3 Squeeze (2) → TI | ti4 Rotate 900 TI → TI | ti5 Rotate 900 TI + squeeze (2) → TI | ti6 Rotate 450 TI → TI | ti1 Rotate 450 + expansion (2) TI → TI | ti0 Rotate 450 + squeeze (2) TI → TI | ti2

Hard + Soft (Pmud, Psand) simulationUse region (TI manipulation externally)

Exercise :: rotation/affinity

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3D examples

3D 3 facies channel TI (150x195x30) SNESIM realization

(100x130x10)

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SNESIM

Categorical variables (<5)

Simple structures

Honor hard, soft, geology

Statistics

Pixel-wise simulation

Good target control

Soft data as probability

Non-stationary

Fast, but memory demanding

Summary

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A C

C

C

C A

B

B

A C

C BA C C C C

C C C C

C B C B C B C B

A A A

A A A A

C C C C

C B C B C B C B

A A A A

C C C C

C B C B C B C B

A A A A

C B C B C B C B

3rd grid

2nd grid

A : 1st sub-gridB : 2nd sub-gridC : 3rd sub-grid

Subgrid

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A

B B B B

A A A

A A A A

B B B B

A A A A

B B B B

A A A A

B B B B

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maximum number of conditioning data = 14 + 4

3rd grid

2nd grid

A : 1st sub-grid

B : 2nd sub-grid

C : 3rd sub-grid

basic node

added node

A C

C B

Subgrid

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A C C C C

C C C C

C B C B C B C B

A A A

A A A A

C C C C

C B C B C B C B

A A A A

C C C C

C B C B C B C B

A A A A

C B C B C B C B

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maximum number of conditioning data = 14 + 4

3rd grid

2nd grid

A : 1st sub-grid

B : 2nd sub-grid

C : 3rd sub-grid

basic node

added node

A C

C B

Subgrid 2

3-snesim

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