Applying the distance-based approach to model flow uncertainty in

Annual Meeting 2011
Stanford Center for Reservoir Forecasting
Applying the distance‐based approach to model flow uncertainty in structurally complex reservoirs
Aaditya Satija, Jef Caers
Motivation
• Structural Uncertainty remains a challenge
– Computational complexity of Structural Modeling
– Difficulty in automation
• manual consistency checks needed
– Multiple levels of uncertainty
– Many independent parameters
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Distance Kernel Methods
Generation
Generation of
of multiple
multiple models
models
Definition
Definition of
of aa distance
distance
Kernel
Kernel
Transformation
Transformation
Representation
Representation
of
of Uncertainty
Uncertainty
MDS
MDS
Clustering
Clustering
Model
Model Selection
Selection
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Applying DKM to Structural Models
• Challenges
– Constructing multiple structural models
• Surface interactions: Consistency checks needed
– Multiple uncertain input parameters
• Fault Geometry
– Orientation
– Hierarchy
• Fault Placement
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Elements of DKM
1. Model of structural uncertainty
– Fault Geometry
– Placement
2. Constructing multiple structural models – gOcad FaultMod
3. Fast flow simulation (3DSL)
– Sensitive parameters to 3DSL response
4. Select models
5. Eclipse flow simulation on selected models
– Sensitive parameters to Eclipse response
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Modeling Structural Uncertainty • Fault Geometry
– Strike and Dip
– Hierarchy
– Well defined distance metrics
• Fault placement
– Not even a parameter
– What to do with this one?
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Fault Placement
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Fault Placement
Distances between fault origins
Distance between fault models
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Fault Placement
• From distance to parameter
– distance matrix Æ MDS, Kernel transformation
– Clusters Æ Categorical Parameter
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Fault Placement w.r.t wells
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Fault Placement w.r.t. wells
Distance between Injector and Fault Origin
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Constructing multiple structural models
• gOcad FaultMod
–
–
–
–
Models fault surfaces as isovalues on continuous function
Define dip and strike distributions, number of faults
FaultMod generates 3D structural models
Extract hierarchy from simulated model
• gOcad SKUA
– Define common volume of interest for all models
– Make flow simulation grid • Layer‐cake model for petrophysical properties
• Faults: transmissibility multiplier of 0.1
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3DSL Simulation
Range of Total Oil Production
• Sensitivity of total oil production
Fault strike angles
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3DSL Simulation
• Sensitivity without Interactions
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3DSL Simulation
• Sensitivity with Interaction
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DKM for Structural Models
Total Oil Production
MDS
Simulation Time Step
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DKM for Structural Models
MDS
Clustering
Kernel Transformation
Selected Models
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Estimating Quantiles
• Using difference in 3DSL response to select models for Eclipse simulation
Total Oil Production
True
Estimate
p90
p50
p10
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Estimating Sensitivity
• Eclipse Simulations
– Around 8 days for 50 simulations
– Not complete sensitivity picture in reality
– Sensitivity Analysis using 10 selected models
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Reference Sensitivity
• Sensitivity using a broader set of 50
models
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Exception Case
• Horizontal faults
• Close‐together wells
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Exception Case
• Response
– 3DSL water saturation in production well block
• Multiway Sensitivity
– Order of 10‐15
– Not sensitive
• Why?
– Conduit Effect
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Conclusions
• Applied Distance Kernel workflow to structural
models
– Generated multiple structural models
– Converted parameters (geometric and placement) to
categorical variables
• Analysed sensitivity of flow response to
parameters
• Estimated the uncertainty in flow response of
structural models using DKM
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Acknowledgements
• Nicolas Cherpeau
– faultMod
• Darryl Fenwick
– StreamSim 3DSL
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