Post on 22-Jul-2018
Smart Fields, Stanford UniversityIntegrated Operations 200707
Semi-automatic history matchingapplying
parameter estimation techniques
October 3, 2007
D. EcheverrD. Echeverríía Ciaurria Ciaurri
Smart Fields ConsortiumStanford University
Smart Fields, Stanford UniversityIntegrated Operations 200707
Outline
O
• Smart Fields Consortium
• The History Matching Problem
• Challenges and Trends
• History Matching at Smart Fields
• Conclusions
Smart Fields, Stanford UniversityIntegrated Operations 200707
Outline
O
• Smart Fields Consortium
• The History Matching Problem
• Challenges and Trends
• History Matching at Smart Fields
• Conclusions
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closing the Loop
1
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closing the Loop
1
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closing the Loop
1
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closing the Loop
1
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closing the Loop
1
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closing the Loop
1
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closing the Loop
1
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closing the Loop
1
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closing the Loop
1
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closing the Loop
Field Development Optimization
1
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closing the Loop
Field Development Optimization
1
Smart Fields, Stanford UniversityIntegrated Operations 200707
Stanford Smart Fields
2
Smart Fields, Stanford UniversityIntegrated Operations 200707
Stanford Smart Fields
• Stanford University
2
Smart Fields, Stanford UniversityIntegrated Operations 200707
Stanford Smart Fields
• Stanford University
– Energy Resources Engineering
– Geophysics
– Management Sciences and Engineering
– CEES
– Geology, Electrical Engineering, …
2
Smart Fields, Stanford UniversityIntegrated Operations 200707
Stanford Smart Fields
• Stanford University
• Current consortium members
2
Smart Fields, Stanford UniversityIntegrated Operations 200707
Stanford Smart Fields
• Stanford University
• Current consortium members
– BP, Chevron, CMG, Conoco Phillips,
ExxonMobil, Landmark, NTNU, Petrobras,
Shell, Saudi Aramco, Statoil, Total
– in discussions with several others
2
Smart Fields, Stanford UniversityIntegrated Operations 200707
Scope of Work
3
Smart Fields, Stanford UniversityIntegrated Operations 200707
Scope of Work
• Optimization techniques
3
Smart Fields, Stanford UniversityIntegrated Operations 200707
Scope of Work
Oilfield Review 2006
• Optimization techniques– well placement
– well type
– reservoir and production system operations
3
Smart Fields, Stanford UniversityIntegrated Operations 200707
Scope of Work
• Optimization techniques
3
Smart Fields, Stanford UniversityIntegrated Operations 200707
Scope of Work
• Optimization techniques
• Data filtering and integration
www.halliburton.com
3
Smart Fields, Stanford UniversityIntegrated Operations 200707
Scope of Work
• Optimization techniques
• Data filtering and integration
3
Smart Fields, Stanford UniversityIntegrated Operations 200707
Scope of Work
• Optimization techniques
• Data filtering and integration
• History matching
3
Smart Fields, Stanford UniversityIntegrated Operations 200707
Scope of Work
• Optimization techniques
• Data filtering and integration
• History matching
• Fast reservoir modeling and proxies
3
Smart Fields, Stanford UniversityIntegrated Operations 200707
Scope of Work
• Optimization techniques
• Data filtering and integration
• History matching
• Fast reservoir modeling and proxies
• Uncertainty propagation
3
Smart Fields, Stanford UniversityIntegrated Operations 200707
Scope of Work
• Optimization techniques
• Data filtering and integration
• History matching
• Fast reservoir modeling and proxies
• Uncertainty propagation
• Decision making
3
Smart Fields, Stanford UniversityIntegrated Operations 200707
Model Order Reduction
4
(from Cardoso et al., 2007)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Model Order Reduction
4
• PCA, original model size N = 800
Injec. 1 Injec. 2
Prod. 1 Prod. 2
(from Cardoso et al., 2007)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Model Order Reduction
4
• PCA, original model size N = 800
(from Cardoso et al., 2007)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Model Order Reduction
4
• PCA, original model size N = 800
full model N = 800n = 1 + 7 = 8n = 2 + 7 = 9n = 8 + 26 = 34n = 23 + 47 = 61
(from Cardoso et al., 2007)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Model Order Reduction
4
• PCA, original model size N = 800
full model N = 800n = 1 + 7 = 8n = 2 + 7 = 9n = 8 + 26 = 34n = 23 + 47 = 61
(from Cardoso et al., 2007)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Model Order Reduction
4
• PCA, original model size N = 800
full model N = 800n = 1 + 7 = 8n = 2 + 7 = 9n = 8 + 26 = 34n = 23 + 47 = 61
(from Cardoso et al., 2007)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Model Order Reduction
4
• PCA, original model size N = 800
full model N = 800n = 1 + 7 = 8n = 2 + 7 = 9n = 8 + 26 = 34n = 23 + 47 = 61
(from Cardoso et al., 2007)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Model Order Reduction
4
• PCA, original model size N = 800
full model N = 800n = 1 + 7 = 8n = 2 + 7 = 9n = 8 + 26 = 34n = 23 + 47 = 61
(from Cardoso et al., 2007)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Outline
O
• Smart Fields Consortium
• The History Matching Problem
• Challenges and Trends
• History Matching at Smart Fields
• Conclusions
Smart Fields, Stanford UniversityIntegrated Operations 200707
History Matching
5
Smart Fields, Stanford UniversityIntegrated Operations 200707
History Matching
m**
5
Smart Fields, Stanford UniversityIntegrated Operations 200707
History Matching
m**observe
5
( )** mO
Smart Fields, Stanford UniversityIntegrated Operations 200707
m
History Matching
m**observe
( )mO
5
( )** mO
Smart Fields, Stanford UniversityIntegrated Operations 200707
m
History Matching
( ) ( ) ||mOmO|| minargm̂ **
Mm−=
∈
m**observe ( )** mO
( )mO
5
Smart Fields, Stanford UniversityIntegrated Operations 200707
A Different Perspective
6
Smart Fields, Stanford UniversityIntegrated Operations 200707
A Different Perspective
6
• Data filtering– solution quality ~– use observations to improve estimation– when noise/uncertainty is significant
||mm̂|| *−
Smart Fields, Stanford UniversityIntegrated Operations 200707
A Different Perspective
6
• Data filtering
• Example: Kalman Filter
Smart Fields, Stanford UniversityIntegrated Operations 200707
A Different Perspective
6
• Data filtering
• Example: Kalman Filter
• Original idea: linear systems only
Smart Fields, Stanford UniversityIntegrated Operations 200707
A Different Perspective
6
• Data filtering
• Example: Kalman Filter
• Original idea: linear systems only
• Extended Kalman Filter– linearization around current estimate
– problematic with high nonlinearities
Smart Fields, Stanford UniversityIntegrated Operations 200707
A Different Perspective
6
• Data filtering
• Example: Kalman Filter
• Original idea: linear systems only
• Extended Kalman Filter
• Ensemble Kalman Filter
Smart Fields, Stanford UniversityIntegrated Operations 200707
A Different Perspective
6
• Data filtering
• Example: Kalman Filter
• Original idea: linear systems only
• Extended Kalman Filter
• Ensemble Kalman Filter– see next presentation!
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization– exact / approximate / no gradients
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization– exact / approximate / no gradients– gradients are faster
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization– exact / approximate / no gradients– gradients are faster– no gradients are robust
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization– exact / approximate / no gradients– gradients are faster– no gradients are robust– exact non trivial implementation
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization– exact / approximate / no gradients– gradients are faster– no gradients are robust– exact non trivial implementation– direct methods easier but much slower
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization
• Global optimization
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization
• Global optimization– when gradients make no sense
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization
• Global optimization– when gradients make no sense
(from Onwunalu et al., 2007)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization
• Global optimization– when gradients make no sense
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization
• Global optimization– when gradients make no sense– most of them stochastic
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization
• Global optimization– when gradients make no sense– most of them stochastic– DIRECT, genetic, particle swarm,
differential evolution, simulated annealing
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization
• Global optimization– when gradients make no sense– most of them stochastic– DIRECT, genetic, particle swarm,
differential evolution, simulated annealing– amenable to parallelization
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization
• Global optimization
• Local faster than global
Smart Fields, Stanford UniversityIntegrated Operations 200707
Optimization
7
• Local optimization
• Global optimization
• Local faster than global
• Hybridization
Smart Fields, Stanford UniversityIntegrated Operations 200707
Workflow
8
Smart Fields, Stanford UniversityIntegrated Operations 200707
m
Workflow
8
facies
Smart Fields, Stanford UniversityIntegrated Operations 200707
Workflow
8
facies
rock properties
m
Smart Fields, Stanford UniversityIntegrated Operations 200707
Workflow
8
facies
O1 (m)
O2 (m)
rock properties
m
Smart Fields, Stanford UniversityIntegrated Operations 200707
Workflow
8
facies
O1 (m)
O2 (m)
m**
rock properties
m
Smart Fields, Stanford UniversityIntegrated Operations 200707
Workflow
8
facies
O1 (m)
O2 (m)||.||
m**
rock properties
m
Smart Fields, Stanford UniversityIntegrated Operations 200707
Workflow
8
facies
O1 (m)
O2 (m)||.||
m**
tooptimizerrock
propertiesm
Smart Fields, Stanford UniversityIntegrated Operations 200707
Workflow
8
facies
flow
seis||.||
m**
tooptimizerrock
propertiesm
Smart Fields, Stanford UniversityIntegrated Operations 200707
Workflow
8
facies
flow
seis||.||
m**
tooptimizer
manyparameters
rock properties
m
Smart Fields, Stanford UniversityIntegrated Operations 200707
Workflow
8
facies
flow
seis||.||KPCA
m**
tooptimizer
manyparameters
fewerparameters
rock properties
mξ
Smart Fields, Stanford UniversityIntegrated Operations 200707
Workflow
8
facies
flow
seis||.||KPCA
m**
tooptimizer
manyparameters
lessparameters
rock properties
mξ
gradients
Smart Fields, Stanford UniversityIntegrated Operations 200707
Outline
O
• Smart Fields Consortium
• The History Matching Problem
• Challenges and Trends
• History Matching at Smart Fields
• Conclusions
Smart Fields, Stanford UniversityIntegrated Operations 200707
Challenges and Trends
9
Smart Fields, Stanford UniversityIntegrated Operations 200707
Challenges and Trends
9
• Non-uniqueness in optimization
Smart Fields, Stanford UniversityIntegrated Operations 200707
Challenges and Trends
9
• Non-uniqueness in optimization
0.0
0.2
0.4
0.6
0.8
1.0
Wat
erC
ut
0 200 400 600 800 1000tim e, days
a a a a a a a a a
a
a
a
a
a
a
a
a
a
a
a
a
aa
a
a
a
aa
aa a a a a a a a a a a a a a
a a a a a a a a a
a
a
a
a
a
a
a
a
a
a
a
a
a
aa
aa
aa
aa
aa
aa a a a a a a a a a
a
a
In itia l Perm eab
Wat
er c
ut
t (days)
(from Caers et al., 2002)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Challenges and Trends
9
• Non-uniqueness in optimization
0.0
0.2
0.4
0.6
0.8
1.0
Wat
erC
ut
0 200 400 600 800 1000tim e, days
a a a a a a a a a
a
a
a
a
a
a
a
a
a
a
a
a
aa
a
a
a
aa
aa a a a a a a a a a a a a a
a a a a a a a a a
a
a
a
a
a
a
a
a
a
a
a
a
a
aa
aa
aa
aa
aa
aa a a a a a a a a a
a
a
In itia l Perm eab
Wat
er c
ut
t (days)
East
Nor
th
0.0 50.00.0
50.0
0.0
200.0
400.0
600.0
800.0
1000.0
East
Nor
th
0.0 50.00.0
50.0
0.0
200.0
400.0
600.0
800.0
1000.0
East
Nor
th
0.0 50.00.0
50.0
0.0
200.0
400.0
600.0
800.0
1000.0
East
Nor
th
0.0 50.00.0
50.0
0.0
200.0
400.0
600.0
800.0
1000.0
(from Caers et al., 2002)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Challenges and Trends
9
• Non-uniqueness in optimization
0.0
0.2
0.4
0.6
0.8
1.0
Wat
erC
ut
0 200 400 600 800 1000tim e, days
a a a a a a a a a
a
a
a
a
a
a
a
a
a
a
a
a
aa
a
a
a
aa
aa a a a a a a a a a a a a a
a a a a a a a a a
a
a
a
a
a
a
a
a
a
a
a
a
a
aa
aa
aa
aa
aa
aa a a a a a a a a a
a
a
In itia l Perm eab
Wat
er c
ut
t (days)
East
Nor
th
0.0 50.00.0
50.0
0.0
200.0
400.0
600.0
800.0
1000.0
East
Nor
th
0.0 50.00.0
50.0
0.0
200.0
400.0
600.0
800.0
1000.0
East
Nor
th
0.0 50.00.0
50.0
0.0
200.0
400.0
600.0
800.0
1000.0
East
Nor
th
0.0 50.00.0
50.0
0.0
200.0
400.0
600.0
800.0
1000.0
(from Caers et al., 2002)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Challenges and Trends
9
• Non-uniqueness in optimization– select a solution that honors geology
– KPCA
Smart Fields, Stanford UniversityIntegrated Operations 200707
Challenges and Trends
9
• Non-uniqueness in optimization– honors geology, KPCA
• Large-scale optimization– from thousands to millions of variables
– reduce number of variables
– KPCA
Smart Fields, Stanford UniversityIntegrated Operations 200707
Challenges and Trends
9
• Non-uniqueness in optimization– honors geology, KPCA
• Large-scale optimization– reduce number of variables, KPCA
Smart Fields, Stanford UniversityIntegrated Operations 200707
Challenges and Trends
9
• Non-uniqueness in optimization– honors geology, KPCA
• Large-scale optimization– reduce number of variables, KPCA
• Cost functions expensive to compute– reduce number of function calls, gradients
Smart Fields, Stanford UniversityIntegrated Operations 200707
More Trends
10
Smart Fields, Stanford UniversityIntegrated Operations 200707
More Trends
10
• Global methods
Smart Fields, Stanford UniversityIntegrated Operations 200707
More Trends
10
• Global methods– dealing with uncertainty and noise
Smart Fields, Stanford UniversityIntegrated Operations 200707
More Trends
10
• Global methods– dealing with uncertainty and noise
– when a good initial guess is not available
Smart Fields, Stanford UniversityIntegrated Operations 200707
More Trends
10
• Global methods– dealing with uncertainty and noise
– when a good initial guess is not available
– combined with proxies
Smart Fields, Stanford UniversityIntegrated Operations 200707
More Trends
10
• Global methods– dealing with uncertainty and noise
– when a good initial guess is not available
– combined with proxies
– hybridize with local methods
Smart Fields, Stanford UniversityIntegrated Operations 200707
More Trends
10
• Global methods– dealing with uncertainty and noise
– when a good initial guess is not available
– combined with proxies
– hybridize with local methods
• Data filtering
Smart Fields, Stanford UniversityIntegrated Operations 200707
Workflow
8
facies
flow
seis||.||KPCA
m**
tooptimizer
manyparameters
lessparameters
rock properties
mξ
gradients
Smart Fields, Stanford UniversityIntegrated Operations 200707
Kernel PCA
12
Smart Fields, Stanford UniversityIntegrated Operations 200707
Kernel PCA
11
• PCA captures linear dependence
Smart Fields, Stanford UniversityIntegrated Operations 200707
Kernel PCA
11
• PCA captures linear dependence
Smart Fields, Stanford UniversityIntegrated Operations 200707
Kernel PCA
11
• PCA captures linear dependence
Smart Fields, Stanford UniversityIntegrated Operations 200707
Kernel PCA
11
• PCA captures linear dependence
Smart Fields, Stanford UniversityIntegrated Operations 200707
Kernel PCA
11
• PCA captures linear dependence
Smart Fields, Stanford UniversityIntegrated Operations 200707
Kernel PCA
11
• PCA captures linear dependence
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
+=
=
21
212
1
12
yxyxyarctanx
Smart Fields, Stanford UniversityIntegrated Operations 200707
Kernel PCA
11
• PCA captures linear dependence
• Nonlinear is more flexible
Smart Fields, Stanford UniversityIntegrated Operations 200707
Kernel PCA
11
• PCA captures linear dependence
• Nonlinear is more flexible
• PCA preserves 2nd order statistics
Smart Fields, Stanford UniversityIntegrated Operations 200707
Kernel PCA
11
• PCA captures linear dependence
• Nonlinear is more flexible
• PCA preserves 2nd order statistics
requires more than 2nd order
Smart Fields, Stanford UniversityIntegrated Operations 200707
Kernel PCA
11
• PCA captures linear dependence
• Nonlinear is more flexible
• PCA preserves 2nd order statistics
Smart Fields, Stanford UniversityIntegrated Operations 200707
Kernel PCA
11
• PCA captures linear dependence
• Nonlinear is more flexible
• PCA preserves 2nd order statistics
• Higher dimensions preserve
higher order statistics
Smart Fields, Stanford UniversityIntegrated Operations 200707
KPCA in Action(from Sarma et al., 2006)
12
Smart Fields, Stanford UniversityIntegrated Operations 200707
KPCA in Action
12
-1 0 1 20
0.5
1Approximate pdf
-2 -1 0 1 2 30
0.2
0.4
0.6
0.8Approximate pdf
-0.5
0
0.5
1
1.5 Perm Field from KLE
10 20 30 40
10
20
30
40
0
1
2Perm Field from KPCA
10 20 30 40
10
20
30
40
PCA analysis (n = 30)
(from Sarma et al., 2006)
KPCA analysis (n = 30)
Smart Fields, Stanford UniversityIntegrated Operations 200707
KPCA in Action
12
-1 0 1 20
0.5
1Approximate pdf
-2 -1 0 1 2 30
0.2
0.4
0.6
0.8Approximate pdf
-0.5
0
0.5
1
1.5 Perm Field from KLE
10 20 30 40
10
20
30
40
0
1
2Perm Field from KPCA
10 20 30 40
10
20
30
40
PCA analysis (n = 30)
(from Sarma et al., 2006)
KPCA analysis (n = 30)
Smart Fields, Stanford UniversityIntegrated Operations 200707
KPCA in Action
12
(from Sarma et al., 2006)
Smart Fields, Stanford UniversityIntegrated Operations 200707
-1 0 1 20
0.5
1Approximate pdf
-2 -1 0 1 2 30
0.2
0.4
0.6
0.8Approximate pdf
-0.5
0
0.5
1
Perm Field from KLE
10 20 30 40
10
20
30
40
-0.5
0
0.5
1
1.5
Perm Field from KPCA
10 20 30 40
10
20
30
40
KPCA in Action
12
PCA analysis (n = 30)
(from Sarma et al., 2006)
KPCA analysis (n = 30)
Smart Fields, Stanford UniversityIntegrated Operations 200707
-1 0 1 20
0.5
1Approximate pdf
-2 -1 0 1 2 30
0.2
0.4
0.6
0.8Approximate pdf
-0.5
0
0.5
1
Perm Field from KLE
10 20 30 40
10
20
30
40
-0.5
0
0.5
1
1.5
Perm Field from KPCA
10 20 30 40
10
20
30
40
KPCA in Action
12
PCA analysis (n = 30)
(from Sarma et al., 2006)
KPCA analysis (n = 30)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Flow Gradients
13
Smart Fields, Stanford UniversityIntegrated Operations 200707
Flow Gradients
13
• Cost function = flow + seismic
Smart Fields, Stanford UniversityIntegrated Operations 200707
Flow Gradients
13
• Cost function = flow + seismic
• Flow cost function
( ) ( )∑−
=
=1N
0nn mLmJ m: model
( ) ( ) ||mOmO|| J(m) **11 −=
Smart Fields, Stanford UniversityIntegrated Operations 200707
Flow Gradients
13
• Cost function = flow + seismic
• Flow cost function
• Constraints (reservoir flow equations)
( ) 0m,x,xg n1nn =+ x: states
( ) ( )∑−
=
=1N
0nn mLmJ m: model
Smart Fields, Stanford UniversityIntegrated Operations 200707
Flow Gradients
13
• Cost function = flow + seismic
• Cost function and constraints
• Optimality
( ) 0m,x,xg ,0mJ
n1nnA ==
∂∂
+
( ) ( ) ( )m,x,xg m,xL,mJ n1nnT
1n
1N
0n1nnA ++
−
=+ λ+=λ ∑
( ) ( )λ=λλ
,mJ minargˆ,m̂ A,m
ff
Smart Fields, Stanford UniversityIntegrated Operations 200707
Flow Gradients
13
• Cost function = flow + seismic
• Cost function and constraints
• Optimality
( ) 0m,x,xg ,0mJ
n1nnA ==
∂∂
+
( ) ( ) ( )m,x,xg m,xL,mJ n1nnT
1n
1N
0n1nnA ++
−
=+ λ+=λ ∑
( ) ( )λ=λλ
,mJ minargˆ,m̂ A,m
ff
Smart Fields, Stanford UniversityIntegrated Operations 200707
Adjoint Equations
• Adjoint equations directly obtained from reservoir simulator
• Store Jacobians: and
• Nontrivial implementation
• Other nonlinear constraints can be considered
n
1n
xg∂∂ −
n
n
xg∂∂
14
Smart Fields, Stanford UniversityIntegrated Operations 200707
Outline
O
• Smart Fields Consortium
• The History Matching Problem
• Challenges and Trends
• History Matching at Smart Fields
• Conclusions
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
random
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
random
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
random
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
curve optimumrandom
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
curve optimumrandom
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
curve optimumrandom
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
curve optimumrandom
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
curve optimumrandom
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
curve optimumrandom
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
curve optimumrandom
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
curve optimumrandom
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
curve optimumrandom
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
curve optimumrandom
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
high
low
cost function
curve optimumrandom
(from Caers et al., 2003)
15
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
(from Caers et al., 2003)
16
Smart Fields, Stanford UniversityIntegrated Operations 200707
Probability Perturbation
• Global Optimization
• Related projects (Jef Caers)– History matching based on multiple alternative
geological scenarios
– Modeling of hydrogeological deposits constrained to pressure data
– Integration of 4D seismics and production data
– just to name a few...
(from Caers et al., 2003)
16
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closed-Loop Management
17
(from Sarma et al., 2006)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closed-Loop Management
• Model (sector)
– 32x46x8 (~12000) cells– 3 injectors and 4 producers, BHP control
(from Sarma et al., 2006)
17
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closed-Loop Management
• Control problem– permeability field unknown (model update)– maximize NPV in ~ 8 years (costly water)
(from Sarma et al., 2006)
17
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closed-Loop Management
• Constraints– bounds for controls– total injection ≤
20,000 STBD, watercut ≤
0.95
(from Sarma et al., 2006)
17
Smart Fields, Stanford UniversityIntegrated Operations 200707
Closed-Loop Management
• Reference model– producer BHP = 4500 psi– injection water distributed by kh
(from Sarma et al., 2006)
17
Smart Fields, Stanford UniversityIntegrated Operations 200707
Oil Saturations(from Sarma et al., 2006)
18
Smart Fields, Stanford UniversityIntegrated Operations 200707
Oil Saturations(from Sarma et al., 2006)
reference optimized(known permeability)
18
Smart Fields, Stanford UniversityIntegrated Operations 200707
Oil Saturations(from Sarma et al., 2006)
optimized(known permeability)
optimized(unknown permeability)
18
Smart Fields, Stanford UniversityIntegrated Operations 200707
Production Data(from Sarma et al., 2006)
19
Smart Fields, Stanford UniversityIntegrated Operations 200707
Production Data(from Sarma et al., 2006)
base case
Cum
ulat
ives
(STB
)
optimized
reference
19
Smart Fields, Stanford UniversityIntegrated Operations 200707
Production Data(from Sarma et al., 2006)
base case
Cum
ulat
ives
(STB
)
16% increase in oil production
optimized
reference
19
Smart Fields, Stanford UniversityIntegrated Operations 200707
Production Data(from Sarma et al., 2006)
base case
Cum
ulat
ives
(STB
)
50% decrease in water production
optimized
reference
19
Smart Fields, Stanford UniversityIntegrated Operations 200707
Production Data(from Sarma et al., 2006)
base case
Cum
ulat
ives
(STB
)
25% increase in NPV
optimized
reference
19
Smart Fields, Stanford UniversityIntegrated Operations 200707
Integrating Data
20
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Integrating Data
• Production data and seismics
20
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Integrating Data
• Production data and seismics
• Stanford VI reservoir
20
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Integrating Data
• Production data and seismics
• Stanford VI reservoir– three zones
zone 3
20
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Integrating Data
• Production data and seismics
• Stanford VI reservoir– three zones
– prograding fluvial channel
zone 3
20
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Integrating Data
• Production data and seismics
• Stanford VI reservoir– three zones
– prograding fluvial channel
– an asymmetric anticline
zone 3
20
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Integrating Data
• Production data and seismics
• Stanford VI reservoir– three zones
– prograding fluvial channel
– an asymmetric anticline
– 6 million cellszone 3
20
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Integrating Data
• Production data and seismics
• Stanford VI reservoir– three zones
– prograding fluvial channel
– an asymmetric anticline
– 6 million cells
– 4D seismic data set zone 3
20
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Integrating Data
• Production data and seismics
• Stanford VI reservoir
20
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
• Production data and seismics
• Stanford VI reservoir
• Tomographies, 4D
Integrating Data
20
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
• Production data and seismics
• Stanford VI reservoir
• Tomographies, 4D
• Flexible optimization– alternating matching production/seismics
– cumulative match from tn to tn+1
Integrating Data
20
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Preliminary Results
21
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Preliminary Results
• 20x20x10 sector from zone 3
21
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Preliminary Results
• 20x20x10 sector from zone 3
• m: facies
21
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Preliminary Results
• 20x20x10 sector from zone 3
• m: facies
• k, φ: regression from well location– k from Kozeny-Carman’s
21
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Preliminary Results
• 20x20x10 sector from zone 3
• m: facies
• k, φ: regression from well location
• VP and VS as seismics
21
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Preliminary Results
• 20x20x10 sector from zone 3
• m: facies
• k, φ: regression from well location
• VP and VS as seismics– Gassmann fluid substitution
– Batzle-Wang fluid properties
21
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Preliminary Results
• 20x20x10 sector from zone 3
• m: facies
• k, φ: regression from well location
• VP and VS as seismics
• PCA: 30 coefficients retained
21
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Preliminary Results
• 20x20x10 sector from zone 3
• m: facies
• k, φ: regression from well location
• VP and VS as seismics
• PCA: 30 coefficients retained– 1000 realizations
21
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Preliminary Results
• 20x20x10 sector from zone 3
• m: facies
• k, φ: regression from well location
• VP and VS as seismics
• PCA: 30 coefficients retained
• Measured data only after 3 months
21
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
22
Preliminary Results(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
• Alternating optimization strategy– production ( 2 iter)
– production + seismics ( 2 iter)
– seismics (10 iter)
22
Preliminary Results(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
• Alternating optimization strategy
22
Preliminary Results(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
• Alternating optimization strategy
• Optimizer: SQP + numerical gradients
22
Preliminary Results(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
• Alternating optimization strategy
• Optimizer: SQP + numerical gradients
• True model m*: original sector projected over truncated PCA basis
*m
22
Preliminary Results(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
• Alternating optimization strategy
• Optimizer: SQP + numerical gradients
• True model m*: original sector projected over truncated PCA basis
• Initial guess m0*: random realization
taken from the 1000 for the PCA
*m
m̂
22
Preliminary Results(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Production Data
23
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Production Data
5 spot
injector
producer
23
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Oil Production
23
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Oil Production
23
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Oil Production
23
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Oil Production
23
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Water Injection
23
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Water Injection
23
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Water Injection
23
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Water Injection
23
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Seismic Data
5 spot
injector
producer
24
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
5 spot
injector
producer
24
(joint work with Mukerji and Santos)
Seismic Data
Smart Fields, Stanford UniversityIntegrated Operations 200707
Velocities (VP )
true(projected)
initialguess
matchingproduction
(2 iter)
alternatingmatching
24
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Velocities (VP )
true(projected)
initialguess
matchingproduction
(2 iter)
alternatingmatching
24
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Velocities (VP )
initialguess
matchingproduction
(2 iter)
alternatingmatching
24
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Velocities (VP )
x
z
y
z
24
true
after production
initial
alternating
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Facies
25
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Facies
true(projected)
initialguess
matchingproduction
(2 iter)
alternatingmatching
25
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Facies
x
y
LAYER 125
true
after production
initial
alternating
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Facies
x
y
LAYER 125
true
after production
initial
alternating
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Facies
x
y
LAYER 425
true
after production
initial
alternating
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Facies
x
y
LAYER 425
true
after production
initial
alternating
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Facies
x
y
LAYER 625
true
after production
initial
alternating
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Facies
x
y
LAYER 625
true
after production
initial
alternating
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Facies
x
y
LAYER 1025
true
after production
initial
alternating
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Facies
x
y
LAYER 1025
true
after production
initial
alternating
(joint work with Mukerji and Santos)
Smart Fields, Stanford UniversityIntegrated Operations 200707
Outline
O
• Smart Fields Consortium
• The History Matching Problem
• Challenges and Trends
• History Matching at Smart Fields
• Conclusions
Smart Fields, Stanford UniversityIntegrated Operations 200707
Conclusions
• Semi-automatic history matching
• Seen as an optimization problem
• Local vs. global optimization
• KPCA reduces number of optimization variables and honors geology
• Different types of data integrated
C
Smart Fields, Stanford UniversityIntegrated Operations 200707
Acknowledgement
• Khalid Aziz, Jef Caers, Lou Durlofsky, Roland Horne, Tapan Mukerji and Eduardo Santos
• Marco Cardoso, Jerome Onwunalu, Danny Rojas and Pallav Sarma
• Others at the Smart Field Consortium
A
Smart Fields, Stanford UniversityIntegrated Operations 200707
Thank youfor
your attention!
October 3, 2007
D. EcheverrD. Echeverríía Ciaurria Ciaurri
Smart Fields ConsortiumStanford University
Smart Fields, Stanford UniversityIntegrated Operations 200707
Semi-automatic history matchingapplying
parameter estimation techniques
October 3, 2007
D. EcheverrD. Echeverríía Ciaurria Ciaurri
Smart Fields ConsortiumStanford University