An Overview of

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An Overview of Smart Fields at Stanford
University
D. Echeverría Ciaurri Smart Fields
Consortium Stanford University
October 18, 2007
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(No Transcript)
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(No Transcript)
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Outline

• Smart Fields Consortium
• Useful Mathematical Tools
• Smart Fields Related Projects
• Conclusions

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Outline

• Smart Fields Consortium
• Useful Mathematical Tools
• Smart Fields Related Projects
• Conclusions

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Closing the Loop
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Closing the Loop
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Closing the Loop
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Closing the Loop
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Closing the Loop
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Closing the Loop
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Closing the Loop
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Closing the Loop
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Closing the Loop
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Closing the Loop
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Stanford Smart Fields
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Stanford Smart Fields

• Stanford University

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Stanford Smart Fields

• Stanford University
• Energy Resources Engineering
• Geophysics
• Management Sciences and Engineering
• CEES
• Geology, Electrical Engineering,

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Stanford Smart Fields

• Stanford University
• Current consortium members

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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

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Scope of Work
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Scope of Work

• Optimization techniques

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Scope of Work

• Optimization techniques
• well placement
• well type
• reservoir and
  production
  system
  operations

Oilfield Review 2006
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Scope of Work

• Optimization techniques

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Scope of Work

• Optimization techniques
• Data filtering and integration

www.halliburton.com
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Scope of Work

• Optimization techniques
• Data filtering and integration

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Scope of Work

• Optimization techniques
• Data filtering and integration
• History matching

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Scope of Work

• Optimization techniques
• Data filtering and integration
• History matching
• Fast reservoir modeling and proxies

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Scope of Work

• Optimization techniques
• Data filtering and integration
• History matching
• Fast reservoir modeling and proxies
• Uncertainty propagation

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Scope of Work

• Optimization techniques
• Data filtering and integration
• History matching
• Fast reservoir modeling and proxies
• Uncertainty propagation
• Decision making

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Outline

• Smart Fields Consortium
• Useful Mathematical Tools
• Smart Fields Related Projects
• Conclusions

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Optimization
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Optimization

• Local optimization

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Optimization

• Local optimization
• exact / approximate / no gradients

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Optimization

• Local optimization
• exact / approximate / no gradients
• gradients are faster

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Optimization

• Local optimization
• exact / approximate / no gradients
• gradients are faster
• no gradients are robust

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Optimization

• Local optimization
• exact / approximate / no gradients
• gradients are faster
• no gradients are robust
• exact non trivial implementation

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Optimization

• Local optimization
• exact / approximate / no gradients
• gradients are faster
• no gradients are robust
• exact non trivial implementation
• direct methods easier but much slower

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Optimization

• Local optimization
• Global optimization

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Optimization

• Local optimization
• Global optimization
• when gradients make no sense

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Optimization

• Local optimization
• Global optimization
• when gradients make no sense

(from Onwunalu et al., 2007)
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Optimization

• Local optimization
• Global optimization
• when gradients make no sense

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Optimization

• Local optimization
• Global optimization
• when gradients make no sense
• most of them stochastic

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Optimization

• Local optimization
• Global optimization
• when gradients make no sense
• most of them stochastic
• DIRECT, genetic, particle swarm, differential
  evolution, simulated annealing

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Optimization

• Local optimization
• Global optimization
• when gradients make no sense
• most of them stochastic
• DIRECT, genetic, particle swarm, differential
  evolution, simulated annealing
• amenable to parallelization

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Optimization

• Local optimization
• Global optimization
• Local faster than global

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Optimization

• Local optimization
• Global optimization
• Local faster than global
• Hybridization

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Difficulties

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Difficulties

• Non-uniqueness in optimization

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Difficulties
(from Caers et al., 2002)

• Non-uniqueness in optimization

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Difficulties
(from Caers et al., 2002)

• Non-uniqueness in optimization

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Difficulties
(from Caers et al., 2002)

• Non-uniqueness in optimization

?
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Difficulties

• Non-uniqueness in optimization
• select a solution that honors geology
• KPCA

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Difficulties

• Non-uniqueness in optimization
• honors geology, KPCA
• Large-scale optimization
• from thousands to millions of variables
• reduce number of variables
• KPCA

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Difficulties

• Non-uniqueness in optimization
• honors geology, KPCA
• Large-scale optimization
• reduce number of variables, KPCA

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Difficulties

• 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

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Kernel PCA
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Kernel PCA

• PCA captures linear dependence

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Kernel PCA

• PCA captures linear dependence

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Kernel PCA

• PCA captures linear dependence

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Kernel PCA

• PCA captures linear dependence

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Kernel PCA

• PCA captures linear dependence

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Kernel PCA

• PCA captures linear dependence

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Kernel PCA

• PCA captures linear dependence
• Nonlinear is more flexible

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Kernel PCA

• PCA captures linear dependence
• Nonlinear is more flexible
• PCA preserves 2nd order statistics

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Kernel PCA

• PCA captures linear dependence
• Nonlinear is more flexible
• PCA preserves 2nd order statistics

requires more than 2nd order
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Kernel PCA

• PCA captures linear dependence
• Nonlinear is more flexible
• PCA preserves 2nd order statistics

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Kernel PCA

• PCA captures linear dependence
• Nonlinear is more flexible
• PCA preserves 2nd order statistics
• Higher dimensions preserve higher order
  statistics

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KPCA in Action
(from Sarma et al., 2006)
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KPCA in Action
(from Sarma et al., 2006)
PCA analysis (n 30)
KPCA analysis (n 30)
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KPCA in Action
(from Sarma et al., 2006)
PCA analysis (n 30)
KPCA analysis (n 30)
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KPCA in Action
(from Sarma et al., 2006)
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KPCA in Action
(from Sarma et al., 2006)
PCA analysis (n 30)
KPCA analysis (n 30)
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KPCA in Action
(from Sarma et al., 2006)
PCA analysis (n 30)
KPCA analysis (n 30)
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Exact Flow Gradients
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Exact Flow Gradients

• Cost function J flow others

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Exact Flow Gradients

• Cost function J flow others
• Example history matching

m model
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Exact Flow Gradients

• Cost function J flow others
• Example history matching
• Constraints (reservoir flow equations)

m model
x states
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Exact Flow Gradients

• Cost function J flow others
• Cost function and constraints
• Optimality

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Exact Flow Gradients

• Cost function J flow others
• Cost function and constraints
• Optimality

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Adjoint Equations

• Adjoint equations directly obtained from
  reservoir simulator
• Store Jacobians and
• Nontrivial implementation
• Other nonlinear constraints can be considered

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Outline

• Smart Fields Consortium
• Useful Mathematical Tools
• Smart Fields Related Projects
• Conclusions

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Smart Fields
SF
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Smart Data Analysis
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Smart Data Analysis

• Data from permanent downhole gauges

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Smart Data Analysis

• Data from permanent downhole gauges
• Pressure p(t) and flow rate q(t)

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Smart Data Analysis

• Data from permanent downhole gauges
• Pressure p(t) and flow rate q(t)
• Assume the model
• where k(t) is the reservoir response

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Smart Data Analysis

• Data from permanent downhole gauges
• Pressure p(t) and flow rate q(t)
• Assume the model
• where k(t) is the reservoir response

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Smart Data Analysis

• Data from permanent downhole gauges
• Pressure p(t) and flow rate q(t)
• Assume the model
• where k(t) is the reservoir response

measured
unknown
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Deconvolution
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Deconvolution

• Model

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Deconvolution

• Model

measured
estimated
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Deconvolution

• Model

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Deconvolution

• Model
• Assume k(t) convex efficient optimizer

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An Example
(from Ahn et al., 2007)
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An Example
(from Ahn et al., 2007)
(from Nomura et al., 2006)
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An Example
(from Ahn et al., 2007)
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An Example
(from Ahn et al., 2007)
reservoir response k(t)
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An Example
(from Ahn et al., 2007)
reservoir response k(t)
error RMSE 1.25
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Smart Fields
SF
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Genetic Algorithms
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Genetic Algorithms

• Analogy to Darwinian natural selection

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Genetic Algorithms

• Analogy to Darwinian natural selection
• Survival of the fittest

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Genetic Algorithms

• Analogy to Darwinian natural selection
• Survival of the fittest
• Fitness evaluation by simulator

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Genetic Algorithms

• Analogy to Darwinian natural selection
• Survival of the fittest
• Fitness evaluation by simulator
• Reproducing generations

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Genetic Algorithms

• Analogy to Darwinian natural selection
• Survival of the fittest
• Fitness evaluation by simulator
• Reproducing generations
• Crossover and mutation

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Genetic Algorithms
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Genetic Algorithms

• Individual chromosome (binary)

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Genetic Algorithms

• Individual chromosome (binary)

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Genetic Algorithms

• Individual chromosome (binary)

heel
101111110111100011101110011010001
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Genetic Algorithms

• Individual chromosome (binary)

heel
toe
101111110111100011101110011010001
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Genetic Algorithms

• Individual chromosome (binary)

heel
toe
jct
101111110111100011101110011010001
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Genetic Algorithms

• Individual chromosome (binary)

heel
toe
jct
toe
101111110111100011101110011010001
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Genetic Algorithms

• Individual chromosome (binary)

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Genetic Algorithms

• Individual chromosome (binary)
• Well type can evolve

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Genetic Algorithms

• Flowchart of a generation
• compose, evaluate, select,
• reproduce and mutate
• GA optimization typically requires thousands of
  simulations
• Need for fast proxies
• Principal Component Analysis helpful

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Single Well Optimization
(from Yeten et al., 2003)
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Single Well Optimization
(from Yeten et al., 2003)

• Maximize NPV, constraints GOR/WOR

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Single Well Optimization
(from Yeten et al., 2003)

• Maximize NPV, constraints GOR/WOR

optimum well (quad-lateral)
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Dealing with Uncertainty
(from Artus, Onwunalu et al., 2006)
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Dealing with Uncertainty
(from Artus, Onwunalu et al., 2006)

• Objective function NPV

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Dealing with Uncertainty
(from Artus, Onwunalu et al., 2006)

• Objective function NPV
• Multiple model realizations NPVi

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Dealing with Uncertainty
(from Artus, Onwunalu et al., 2006)

• Objective function NPV
• Multiple model realizations NPVi
• Average objective function NPVi

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Dealing with Uncertainty
(from Artus, Onwunalu et al., 2006)

• Objective function NPV
• Multiple model realizations NPVi
• Average objective function NPVi
• Introduce a risk attitude
• NPVi

NPVi
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Dealing with Uncertainty
(from Artus, Onwunalu et al., 2006)

• Objective function NPV
• Multiple model realizations NPVi
• Average objective function NPVi
• Introduce a risk attitude
• NPVi

NPVi
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Risk Neutral (r 0)
(from Artus, Onwunalu et al., 2006)
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Risk Neutral (r 0)
(from Artus, Onwunalu et al., 2006)
NPVi
Realization
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Risk Averse (r -0.5)
(from Artus, Onwunalu et al., 2006)
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Risk Averse (r -0.5)
(from Artus, Onwunalu et al., 2006)
NPVi
Realization
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Risk Attitude
(from Artus, Onwunalu et al., 2006)

• Risk neutral (r 0)
• NPVi 4.6
• 1.2

NPVi

• Risk averse (r -0.5)
• NPVi 4.5
• 0.5

NPVi
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Distributed Optimization
(from Grant et al., 2007)

• Distributing simpler than parallelizing
• Run generation simultaneously
• generation 24 simulations
• 50 generations (1200 simulations)
• Cluster can be remote

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Distributed Optimization
(from Grant et al., 2007)

• Single vertical well placement problem

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Distributed Optimization
(from Grant et al., 2007)

• Single vertical well placement problem

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Distributed Optimization
(from Grant et al., 2007)

• Single vertical well placement problem

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Distributed Optimization
(from Grant et al., 2007)

• Single vertical well placement problem
• 40x40x7 (10000) cells

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Distributed Optimization
(from Grant et al., 2007)

• Single vertical well placement problem
• 40x40x7 (10000) cells
• Speed-up obtained x6 (from 6h to 1h)

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Distributed Optimization
(from Grant et al., 2007)

• Single vertical well placement problem
• 40x40x7 (10000) cells
• Speed-up obtained x6 (from 6h to 1h)
• Why not x24?
• job submission time simulation time
• average vs. peak simulation time

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Model Order Reduction
(from Cardoso et al., 2007)
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Model Order Reduction
(from Cardoso et al., 2007)

• x pressure and saturation (N 800)

PCA
Injec. 1
Injec. 2
Prod. 1
Prod. 2
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Model Order Reduction
(from Cardoso et al., 2007)

• x pressure and saturation (N 800)

PCA
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Model Order Reduction
(from Cardoso et al., 2007)

• x pressure and saturation (N 800)

PCA
full model N 800 n 1 7 8 n 2
7 9 n 8 26 34 n 23 47
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Model Order Reduction
(from Cardoso et al., 2007)

• x pressure and saturation (N 800)

PCA
full model N 800 n 1 7 8 n 2
7 9 n 8 26 34 n 23 47
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Model Order Reduction
(from Cardoso et al., 2007)

• x pressure and saturation (N 800)

PCA
full model N 800 n 1 7 8 n 2
7 9 n 8 26 34 n 23 47
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Model Order Reduction
(from Cardoso et al., 2007)

• x pressure and saturation (N 800)

PCA
full model N 800 n 1 7 8 n 2
7 9 n 8 26 34 n 23 47
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23
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Model Order Reduction
(from Cardoso et al., 2007)

• x pressure and saturation (N 800)

PCA
full model N 800 n 1 7 8 n 2
7 9 n 8 26 34 n 23 47
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Uncertainty Assessment
(from Scheidt et al., 2007)
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Uncertainty Assessment
(from Scheidt et al., 2007)
N45E
N
N45W
channel sand
channel orientation
mud
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Uncertainty Assessment
(from Scheidt et al., 2007)
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40
30
channel sand
facies proportion
mud
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Uncertainty Assessment
(from Scheidt et al., 2007)
small
large
medium
channel sand
channel sinuosity
mud
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Uncertainty Assessment
(from Scheidt et al., 2007)
narrow
medium
wide
channel sand
channel width
mud
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Methodology
(from Scheidt et al., 2007)
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Methodology
(from Scheidt et al., 2007)
model distance
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Methodology
(from Scheidt et al., 2007)
distance matrix
model distance
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Methodology
(from Scheidt et al., 2007)
distance matrix
model distance
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Methodology
(from Scheidt et al., 2007)
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Methodology
(from Scheidt et al., 2007)
nonlinear features
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Methodology
(from Scheidt et al., 2007)
nonlinear
nonlinear features
linear features
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Methodology
(from Scheidt et al., 2007)
linear features
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Methodology
(from Scheidt et al., 2007)
KPCA
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Methodology
(from Scheidt et al., 2007)
KPCA
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Methodology
(from Scheidt et al., 2007)
oil production
KPCA
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An Example
(from Suzuki et al., 2006)
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An Example
(from Suzuki et al., 2006)

• Facies model
• data at the 6 wells
• facies permeability know

channel sand
mud
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An Example
(from Suzuki et al., 2006)

• Facies model
• Flow model
• 3 producers, 3 injectors
• 20 years simulation

channel sand
mud
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An Example
(from Suzuki et al., 2006)

• Facies model
• Flow model
• 405 reservoir models
• 3x3x3x3 81 geological scenarios
• 5 realizations/scenario

channel sand
mud
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An Example
(from Suzuki et al., 2006)
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An Example
(from Suzuki et al., 2006)

• 15 reservoir models selected (from 405)

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An Example
(from Suzuki et al., 2006)

• 15 reservoir models selected (from 405)

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An Example
(from Suzuki et al., 2006)

• 15 reservoir models selected (from 405)

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An Example
(from Suzuki et al., 2006)

• 15 reservoir models selected (from 405)

oil rate for 15 realizations
oil rate for 405 realizations
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An Example
(from Suzuki et al., 2006)

• 15 reservoir models selected (from 405)

P10, P50, P90
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Smart Fields
SF
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Closed-Loop Management
(from Sarma et al., 2006)
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Closed-Loop Management
(from Sarma et al., 2006)

• Model (sector)
• 32x46x8 (12000) cells
• 3 injectors and 4 producers, BHP control

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Closed-Loop Management
(from Sarma et al., 2006)

• Control problem
• permeability field unknown (model update)
• maximize NPV in 8 years (costly water)

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Closed-Loop Management
(from Sarma et al., 2006)

• Constraints
• bounds for controls
• total injection ? 20,000 STBD, watercut ? 0.95

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Closed-Loop Management
(from Sarma et al., 2006)

• Reference model
• producer BHP 4500 psi
• injection water distributed by kh

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Oil Saturations
(from Sarma et al., 2006)
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Oil Saturations
(from Sarma et al., 2006)
reference
optimized (known permeability)
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Oil Saturations
(from Sarma et al., 2006)
optimized (known permeability)
optimized (unknown permeability)
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Production Data
(from Sarma et al., 2006)
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Production Data
(from Sarma et al., 2006)
optimized
Cumulatives (STB)
reference
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Production Data
(from Sarma et al., 2006)
optimized
Cumulatives (STB)
reference
16 increase in oil production
30
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Production Data
(from Sarma et al., 2006)
optimized
Cumulatives (STB)
reference
50 decrease in water production
30
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Production Data
(from Sarma et al., 2006)
optimized
Cumulatives (STB)
reference
25 increase in NPV
30
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GPRS and ECLIPSE
(from Rousset et al., 2007)
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GPRS and ECLIPSE
(from Rousset et al., 2007)

• Model 1
• 10x10x5 cells
• 1 injector and 1 producer, BHP control
• 10 design variables
• Control problem 1
• homogeneous known permeability
• maximize cumulative oil production

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GPRS and ECLIPSE
(from Rousset et al., 2007)
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GPRS and ECLIPSE
(from Rousset et al., 2007)

• Model 2
• 10x10x5 cells
• 2 injectors and 2 producer, BHP control
• 20 design variables
• Control problem 2
• heterogeneous known permeability
• maximize cumulative oil production

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GPRS and ECLIPSE
(from Rousset et al., 2007)
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Smart Fields
SF
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History Matching
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History Matching
m
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History Matching
observe
m
32
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History Matching
observe
m
32
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History Matching
observe
m
32
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Workflow

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Workflow

m
facies
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Workflow

m
facies
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Workflow

m
facies
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Workflow
m

m
facies
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Workflow
m

m
facies
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Workflow
m

to optimizer
m
facies
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Workflow
m

to optimizer
m
facies
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Workflow
m

many parameters
to optimizer
m
facies
33
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Workflow
m

many parameters
fewer parameters
to optimizer
m
x
facies
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Workflow
m

many parameters
less parameters
gradients
to optimizer
m
x
facies
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Fractured Reservoirs
(from Rojas et al., 2007)
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Fractured Reservoirs
(from Rojas et al., 2007)

• History matching for naturally fractured
  reservoirs

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Fractured Reservoirs
(from Rojas et al., 2007)

• History matching for naturally fractured
  reservoirs

training image
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Fractured Reservoirs
(from Rojas et al., 2007)

• History matching for naturally fractured
  reservoirs
• m binary, fracture y/n

training image
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Fractured Reservoirs
(from Rojas et al., 2007)

• History matching for naturally fractured
  reservoirs
• m binary, fracture y/n
• 80x60 variables

training image
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Fractured Reservoirs
(from Rojas et al., 2007)

• History matching for naturally fractured
  reservoirs
• m binary, fracture y/n
• 80x60 variables
• KPCA (order 2) adjoints

training image
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Fractured Reservoirs
(from Rojas et al., 2007)

• History matching for naturally fractured
  reservoirs
• m binary, fracture y/n
• 80x60 variables
• KPCA (order 2) adjoints
• 40 coefficients retained

training image
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Matching Results
(from Rojas et al., 2007)
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Matching Results
(from Rojas et al., 2007)
true
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Matching Results
(from Rojas et al., 2007)
true
initial
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Matching Results
(from Rojas et al., 2007)
true
matched
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Matching Results
(from Rojas et al., 2007)
35
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Matching Results
(from Rojas et al., 2007)
injector 3
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Matching Results
(from Rojas et al., 2007)
producer 4
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Matching Results
(from Rojas et al., 2007)
producer 4
less than 100 flow simulations needed
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Integrating Data
(joint work with Mukerji and Santos)
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Integrating Data
(joint work with Mukerji and Santos)

• Production data and seismics

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Integrating Data
(joint work with Mukerji and Santos)

• Production data and seismics
• Stanford VI reservoir

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Integrating Data
(joint work with Mukerji and Santos)

• Production data and seismics
• Stanford VI reservoir
• three zones
• prograding fluvial channel
• an asymmetric anticline
• 6 million cells
• 4D seismic data set

zone 3
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Integrating Data
(joint work with Mukerji and Santos)

• Production data and seismics
• Stanford VI reservoir

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Integrating Data
(joint work with Mukerji and Santos)

• Production data and seismics
• Stanford VI reservoir
• Tomographies, 4D

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Integrating Data
(joint work with Mukerji and Santos)

• Production data and seismics
• Stanford VI reservoir
• Tomographies, 4D
• Flexible optimization
• alternating matching production/seismics
• cumulative match from tn to tn1

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Preliminary Results
(joint work with Mukerji and Santos)
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Preliminary Results
(joint work with Mukerji and Santos)

• 20x20x10 sector from zone 3

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Preliminary Results
(joint work with Mukerji and Santos)

• 20x20x10 sector from zone 3
• m facies

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Preliminary Results
(joint work with Mukerji and Santos)

• 20x20x10 sector from zone 3
• m facies
• k, f regression from well location

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Preliminary Results
(joint work with Mukerji and Santos)

• 20x20x10 sector from zone 3
• m facies
• k, f regression from well location
• VP and VS as seismics

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Preliminary Results
(joint work with Mukerji and Santos)

• 20x20x10 sector from zone 3
• m facies
• k, f regression from well location
• VP and VS as seismics
• PCA 30 coefficients retained

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Preliminary Results
(joint work with Mukerji and Santos)

• 20x20x10 sector from zone 3
• m facies
• k, f regression from well location
• VP and VS as seismics
• PCA 30 coefficients retained
• Measured data only after 3 months

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237
Preliminary Results
(joint work with Mukerji and Santos)
38
238
Preliminary Results
(joint work with Mukerji and Santos)

• Alternating optimization strategy
• production ( 2 iter)
• production seismics ( 2 iter)
• seismics (10 iter)

38
239
Preliminary Results
(joint work with Mukerji and Santos)

• Alternating optimization strategy

38
240
Preliminary Results
(joint work with Mukerji and Santos)

• Alternating optimization strategy
• Optimizer SQP numerical gradients

38
241
Preliminary Results
(joint work with Mukerji and Santos)

• Alternating optimization strategy
• Optimizer SQP numerical gradients
• True model m original sector projected over
  truncated PCA basis

38
242
Preliminary Results
(joint work with Mukerji and Santos)

• 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

38
243
Production Data
(joint work with Mukerji and Santos)
39
244
Production Data
(joint work with Mukerji and Santos)
injector
producer
5 spot
39
245
Oil Production
(joint work with Mukerji and Santos)
39
246
Oil Production
(joint work with Mukerji and Santos)
39
247
Oil Production
(joint work with Mukerji and Santos)
39
248
Oil Production
(joint work with Mukerji and Santos)
39
249
Water Injection
(joint work with Mukerji and Santos)
39
250
Water Injection
(joint work with Mukerji and Santos)
39
251
Water Injection
(joint work with Mukerji and Santos)
39
252
Water Injection
(joint work with Mukerji and Santos)
39
253
Seismic Data
(joint work with Mukerji and Santos)
injector
producer
5 spot
40
254
Seismic Data
(joint work with Mukerji and Santos)
injector
producer
5 spot
40
255
Velocities (VP)
(joint work with Mukerji and Santos)
true (projected)
initial guess
matching production (2 iter)
alternating matching
40
256
Velocities (VP)
(joint work with Mukerji and Santos)
true (projected)
initial guess
matching production (2 iter)
alternating matching
40
257
Velocities (VP)
(joint work with Mukerji and Santos)
initial guess
matching production (2 iter)
alternating matching
40
258
Velocities (VP)
(joint work with Mukerji and Santos)
z
z
true
initial
x
y
after production
alternating
40
259
Facies
(joint work with Mukerji and Santos)
41
260
Facies
(joint work with Mukerji and Santos)
true (projected)
initial guess
matching production (2 iter)
alternating matching
41
261
Facies
(joint work with Mukerji and Santos)
y
true
initial
x
LAYER 1
after production
alternating
41
262
Facies
(joint work with Mukerji and Santos)
y
true
initial
x
LAYER 1
after production
alternating
41
263
Facies
(joint work with Mukerji and Santos)
y
true
initial
x
LAYER 4
after production
alternating
41
264
Facies
(joint work with Mukerji and Santos)
y
true
initial
x
LAYER 4
after production
alternating
41
265
Facies
(joint work with Mukerji and Santos)
y
true
initial
x
LAYER 6
after production
alternating
41
266
Facies
(joint work with Mukerji and Santos)
y
true
initial
x
LAYER 6
after production
alternating
41
267
Facies
(joint work with Mukerji and Santos)
y
true
initial
x
LAYER 10
after production
alternating
41
268
Facies
(joint work with Mukerji and Santos)
y
true
initial
x
LAYER 10
after production
alternating
41
269
Outline

• Smart Fields Consortium
• Useful Mathematical Tools
• Smart Fields Related Projects
• Conclusions

O
270
C
271
Conclusions

• Smart Fields closed-loop paradigm

C
272
Conclusions

• Smart Fields closed-loop paradigm
• Multidisciplinary approach

C
273
Conclusions

• Smart Fields closed-loop paradigm
• Multidisciplinary approach
• Optimization is important

C
274
Conclusions

• Smart Fields closed-loop paradigm
• Multidisciplinary approach
• Optimization is important
• KPCA reduces number of optimization variables and
  honors geology

C
275
Conclusions

• Smart Fields closed-loop paradigm
• Multidisciplinary approach
• Optimization is important
• KPCA reduces number of optimization variables and
  honors geology
• Smart Fields has just started

C
276
Acknowledgement

• K. Aziz, J. Caers, L. Durlofsky and R.
  Horne
• T. Mukerji and E. Santos
• S. Ahn, M. Cardoso, M. Grant, M. Lee,
  J. Onwunalu, D. Rojas, M. Rousset, P. Sarma,
  C. Scheidt and B. Yeten
• Others at the Smart Field Consortium

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277

Thank you for your attention!
D. Echeverría Ciaurri Smart Fields
Consortium Stanford University
October 18, 2007
278

An Overview of Smart Fields at Stanford
University
D. Echeverría Ciaurri Smart Fields
Consortium Stanford University
October 18, 2007