integrating production and seismic data into gaussian and pluri-gaussian models with enkf(s)
DESCRIPTION
Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S). Yong Zhao Yudou Wang Gaoming Li Al Reynolds EnKF Workshop: Voss June 2008. Sequential Data Assimilation (Ensemble Kalman Filter). Update. EnKF Analysis (Bayesian Updating and Sampling). - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/1.jpg)
Integrating Production and Seismic Data
into Gaussian and Pluri-Gaussian
Models with EnKF(S)
Yong Zhao
Yudou Wang
Gaoming Li
Al Reynolds
EnKF Workshop: Voss June 2008
![Page 2: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/2.jpg)
Sequential Data Assimilation (Ensemble Kalman Filter)
jn
jjn p
my
,,
nth :t @member ensemble j The
pnnucDDDDYpn
an DDCCCYY
npn
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,
1Update
jn
jn
j
jn
d
p
m
y
,
,,
augmented data Or,
![Page 3: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/3.jpg)
EnKF Analysis (Bayesian Updating and Sampling)
Critical Assumptions:1. Predictions of state vectors are Gaussian;2. Covariances can be represented by ensemble members;3. Gaussian noise in data; 4. Predicted data are a linear function of the state vector.
Or, with data augmented state vector1. Predictions of augmented vector are Gaussian;2. Gaussian noise in data;3. Covariances can be represented by ensemble members.
![Page 4: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/4.jpg)
Potential Problems in EnKF
1. Each analyzed vector of model parameters is a linear combination of
initial ensemble.
2. Difficult to match large data sets, e.g., seismic data.
3. Non-Gaussianity.
4. Strong non-linearity.
5. Poor knowledge of measurement errors.
6. Modeling of modeling errors.
7. Sampling errors due to finite ensemble size.
8. Inconsistency: updated pressure and saturations are inconsistent with
the updated models (statistically different from those obtained by
simulating from time zero)
![Page 5: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/5.jpg)
Rescaling for Different Types of Data
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Tpn
pn
pjn
ajn ddCNDDDYyy
n ,,,
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tmeasuremen eachfor 1
e.g., matrix, diagonal :~
D
Assimilating production data:
pnnuce
Tpn
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DDDDCDNDDDDDDYYYn
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~1ˆˆˆ
~~~1
~~~
Assimilating with rescaled data:
Better conditioned
![Page 6: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/6.jpg)
Truncation of Singular Values, PUNQ, Est. Contact Depths
Truncated at 0.9999 Rescaled
![Page 7: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/7.jpg)
Channel Model
2-D case2-D case– 100 X 100 grid, 100 X 100 grid, – 4 producers and 1 injector are located in the channel facies4 producers and 1 injector are located in the channel facies– 360 days of production with BHP and WCT measurements360 days of production with BHP and WCT measurements– 300 days of prediction300 days of prediction– 100 ensemble members100 ensemble members
Z1 Z1 Truncation Facies
![Page 8: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/8.jpg)
Conditional Models and Sw
Facies En20
Sw from true model Sw En20
True facies
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EnKF Predictions
Prior prediction Prediction from EnKF Rerun from time zero
![Page 10: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/10.jpg)
Normal Score Transform
Sw
CDF
Sw
CDF
S’w
S’w
Before Analysis
After Analysis
Prediction Domain Analysis Domain
![Page 11: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/11.jpg)
Normal Score Transform
Standard EnKF Global Transform Local Transform
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Predictions From Transforms
No Transform Global LocalEnKF
Rerun
![Page 13: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/13.jpg)
HIEnKF Method
If model changes significantly, updated primary field may be more inconsistent with the updated model.
When the change of model is significant, rerun from zero; otherwise, we use the EnKS.
1it it0t
aiai pm ,, ,am ,0
aim ,
1it
EnKF
Model changes significantly EnKF
![Page 14: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/14.jpg)
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
20 40 60 80 100
20
40
60
80
100
0.20
0.37
0.55
0.73
0.90Y
X
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
20 40 60 80 100
20
40
60
80
100
X
Y
0
25
50
75
100
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
20 40 60 80 100
20
40
60
80
100
X
Y
0
25
50
75
100
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
20 40 60 80 100
20
40
60
80
100
Y
X
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
20 40 60 80 100
20
40
60
80
100
Y
X
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
20 40 60 80 100
20
40
60
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100
0.20
0.37
0.55
0.73
0.90Y
X
EnKF HIEnKF
True
![Page 15: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/15.jpg)
0 100 200 300 400 500 600 7000.0
0.2
0.4
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1.0
Prod 3
Wat
er C
ut
TIME (Day)
EnKF HIEnKF
EnKF vs. HIEnKF
0 100 200 300 400 500 600 700
2000
3000
4000
5000Prod 3
BH
P (
psi)
TIME (Day)0 100 200 300 400 500 600 700
2000
3000
4000
5000Prod 3
BH
P (
psi)
TIME (Day)
![Page 16: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/16.jpg)
Three-Facies Model
3-D case– 50 X 50X3 grid, – 4 producers and 1 injector– Total rate constraint for each well– Hard data: observed facies in well gridblocks– 360 days of production with BHP and WCT measurements (monthly)– 300 days of prediction– Seismic data (at time zero and 300 days)– 100 ensemble members– Fixed porosity and permeability
Permeability (11md, 100md, 528md); Porosity (0.06, 0.13, 0.21)
Layer 1 Layer 2 Layer 3
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Assimilating Dynamic Data While Satisfying Hard Data, SPE 113990
If does not satisfy the hard data:If does not satisfy the hard data:
)~~
()(ˆ,
1~~~~
pjjucDDDDY
pj
aj ddCCCyy
jucadjustwjuc dZd ,,, to add :~
ajy
Completely redo the assimilation step:
Expand data with pseudo data:
![Page 18: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/18.jpg)
EnKF Predictions
Prior prediction Prediction from EnKF state Rerun from time zero
![Page 19: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/19.jpg)
Acoustic Impedance
t = 0
Match seismic data at the time they are measuredMatch seismic data at the time they are measured
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
10 20 30 40 50
10
20
30
40
50
2.10E4
7.55E4
1.30E5
1.85E5
2.39E5Y
X
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
10 20 30 40 50
10
20
30
40
50
1.70E4
7.13E4
1.26E5
1.80E5
2.34E5Y
X
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
10 20 30 40 50
10
20
30
40
50
2.80E4
7.90E4
1.30E5
1.81E5
2.32E5Y
X
t = 300days
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
10 20 30 40 50
10
20
30
40
50
2.10E4
7.55E4
1.30E5
1.85E5
2.39E5Y
X
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
10 20 30 40 50
10
20
30
40
50
1.70E4
7.13E4
1.26E5
1.80E5
2.34E5Y
X
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
10 20 30 40 50
10
20
30
40
50
2.80E4
7.90E4
1.30E5
1.81E5
2.32E5Y
X
![Page 20: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/20.jpg)
Matching Seismic Data:Local Analysis of EnKF
Local analysis:– Analyzed models are not constrained to the
sub-space spanned by the initial ensemble
– Undesired roughness can be introduced into the analyzed models
NN NN NN NN NN
NN NN NN NN NN
NN NN XX NN NN
NN NN NN NN NN
NN NN NN NN NN
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dX
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X of oodneighbourh in themismatch data :
X of oodneighbourh in thematrix covariance :,,
Xcenter at located vector state predicted / update :,
,,
,
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XNDDDDY
pX
aX
DD
CCC
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pXN
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pX
![Page 21: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/21.jpg)
Projection Method for Local Analysis
mmm
m
mmm
pa
pa
ˆˆ
projectionafter :ˆ
projection before :
A large ensemble with 1200 realizations of model
that honors the hard data (M0)– Use the first 200 eigenvectors
mUUm Tpp ˆ
200:
1200:0
mp
m
NU
NMTppp
T VUVUM 0
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Assimilate Seismic Data- Local Analysis (2 seismic + prod)
True Facies
No projectionEn20
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
10 20 30 40 50
10
20
30
40
50
Y
X
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
10 20 30 40 50
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50
Y
X
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
10 20 30 40 50
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30
40
50
Y
X
With projectionEn20
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
10 20 30 40 50
10
20
30
40
50
Y
X
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
10 20 30 40 50
10
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30
40
50
Y
X
Prod-1
Prod-2 Prod-3
Prod-4
Inj-1
10 20 30 40 50
10
20
30
40
50
Y
X
![Page 23: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/23.jpg)
Assimilate Seismic Data- Local Analysis With Projection
First Seismic OnlyContinue EnKF for production data
Rerun from time zero
100 200 300 400 500 600 7000.0
0.2
0.4
0.6
0.8
1.0
Prod 1
Wat
er C
ut
TIME (Day)
0 100 200 300 400 500 600 7000.0
0.2
0.4
0.6
0.8
1.0
Prod 3
Wat
er C
ut
TIME (Day)
100 200 300 400 500 600 7000.0
0.2
0.4
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0.8
1.0
Prod 1
Wat
er C
ut
TIME (Day)
0 100 200 300 400 500 600 7000.0
0.2
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1.0
Prod 3
Wat
er C
ut
TIME (Day)
100 200 300 400 500 600 7000.0
0.2
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1.0
Prod 1
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er C
ut
TIME (Day)
0 100 200 300 400 500 600 7000.0
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Prod 3
Wat
er C
utTIME (Day)
1st seismic
2nd seismic
1st seismic
2nd seismic
![Page 24: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/24.jpg)
Structure Map of PUNQ-S3
grid.
Fault, gas cap, strong aquifer.
52819
Data: BHP GOR WCTMatch to 4032 days
![Page 25: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/25.jpg)
Estimate the Depths of Fluid Contacts with EnKS
State Vector y
Model parameters m Primary variables p Production data d
Po
rosi
ty
Pe
rme
ab
ility
Flu
id c
on
tact
de
pth
s
Pre
ssu
re
Wa
ter
sa
tura
tio
n
Ga
s s
atu
rati
on
So
luti
on
ga
s-o
il ra
tio
GO
R
BH
P
WC
T
![Page 26: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/26.jpg)
Introduction to HIEnKS Method
If model changes significantly, updated primary field may be more inconsistent with the updated model.
Only use HIEnKS when the change of model is significant. otherwise, we use the EnKS.
1it it0t
aiai pm ,, ,am ,0
aim ,
1it
EnKS
Model changes significantly EnKS
![Page 27: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/27.jpg)
Examples
Example A:• Prior mean of OWC shifted up 20 feet
• Prior mean of GOC shifted down 20 feet.
True GOC
True OWC
Prior Mean of GOC
Prior Mean of OWC
Example A, prior oil column too thin
True GOC
True OWC
Prior Mean of GOC
Prior Mean of OWC
Example B, prior contact depths too deep
Example B:• Prior mean of OWC shifted down 20 feet
• Prior mean of GOC shifted down 20 feet.
20ft
20ft
20ft
20ft
STD: 20 ft
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Comparison of Estimates of Fluid Contacts Example A Example B
HIE
nK
SE
nK
S
En
KS
HIE
nK
S
![Page 29: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/29.jpg)
Consistency of Prediction, Example A
EnKS HIEnKS
EnKS: Future predictions poor, inconsistent. HIEnKS: Data matches good, consistent.
Du
rin
g D
ata
Ass
imil
atio
nR
eru
n f
rom
Tim
e 0
![Page 30: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/30.jpg)
Consistency of Prediction, Example A
EnKS
EnKS: Assimilation good, prediction poor, inconsistent. HIEnKS: Assimilation/Prediction good, roughly consistent.
Du
rin
g D
ata
Ass
imil
atio
nR
eru
n f
rom
Tim
e 0
HIEnKS
![Page 31: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/31.jpg)
Rock Property Fields- 4th, 5th layersT
ruth
En
KS
Vertical Permeability
HIE
nK
S
Horizontal Permeability
![Page 32: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/32.jpg)
Comments
Iteration can improve reliability of data match,
predictions and consistency between parameters
and dynamical variables but is expensive.
Scaling can be critical if SVD is used.
EnKF combined with pluri-Gaussian gives
reasonable results (3D - rock properties – hard
data).
![Page 33: Integrating Production and Seismic Data into Gaussian and Pluri-Gaussian Models with EnKF(S)](https://reader036.vdocuments.mx/reader036/viewer/2022062808/5681540c550346895dc20a89/html5/thumbnails/33.jpg)
Comments
Pluri-Gaussian inappropriate for fluvial systems
– Cosine transforms, MRFs, KPCA?
Seismic: local analysis with projection seems
feasible but is currently ad hoc.