quantifying uncertainties associated with reservoir simulation … · 2007-09-27 · quantifying...

1Shahab D. Mohaghegh, WVU, ISI

Quantifying Uncertainties Associated with Reservoir Simulation Studies UsingSurrogate Reservoir Models

Shahab D. MohagheghWest Virginia University &Intelligent Solutions, Inc.

SPE 102492

2Shahab D. Mohaghegh, WVU, ISI SPE 102492

Outline

Reservoir Simulation & UncertaintySurrogate Reservoir ModelsCase Study: A Giant Oil Field In the Middle East.Quantifying Uncertainty, Using Surrogate Reservoir Model

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Sources of Uncertainty

Geological InterpretationsLog interpretationsCore measurements & AnalysisSCALRock TypingSeismic measurements and interpretations

THE EARTH MODEL

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Quantifying Uncertainty

Conventional Approach:Geo-StatisticsMultiple Realizations

Hundreds & sometimes thousands of simulation runsResponse Surface

New ApproachSurrogate Reservoir Model, SRM

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SRM Development

Main tolls for the development of Surrogate Reservoir models: Intelligent Systems

Artificial Neural NetworksGenetic AlgorithmsFuzzy Logic

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Surrogate Reservoir Models

A subset of a more general set of models called Surrogate Intelligent Models

Real-Time OptimizationReal-Time Decision MakingAnalysis of Uncertainty

An absolute essential tool for smart fields (i-fields)

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SRM an Engineering Tool

Are Surrogate Reservoir Models the same as “Response Surface” techniques?

NO. Unlike purely statistical techniques, SRMs are designed to be engineering tools.SRM is defined within the System Theory while Response Surface is a geostatisticalmethod.

INPUT OUTPUTSYSTEM

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SRM an Engineering Tool

Depending on the project objectives, SRMs are developed to preserve and respond to the physics of the problem.Honoring the physics is an important validation step in the development process of SRMs and their distinguishing feature from other (geostatistical) techniques.

SEE A DEMONSTRATION

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“Monte Carlo Simulations entails generating a large number of equally likely random realizations of the reservoir fields with parameter statistics derived from sampling, solving deterministic flow equations for each realization, and post-processing the results over all realizations to obtain sample moments of the solution. This approach has the advantages of applying to a broad range of both linear and nonlinear flow problems, but has a number of potential drawbacks … the computation effort for each realization is usually large, especially for large-scale reservoirs. As a result, a detailed assessment of the uncertainty associated with flow performance predictions is rarely performed.”

“Accurate, Efficient Quantification of Uncertainty for Flow in Heterogeneous Reservoirs Using the KLME Approach.” Z. Lu, Los Alamos Natl. Laboratory; D. Zhang, U. of Oklahoma. SPE 93452, SPE Reservoir Simulation Symposium, 31 January-2 February, The Woodlands, Texas.

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Objective

Quantify uncertainties associated with reservoir simulation studies, using Monte Carlo Simulation method.Develop a Surrogate Reservoir Model (SRM) based on a Full Field Model (FFM) for a giant oil field in the Middle East for Analysis of uncertainty.

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Methodology

Develop an SRM based on the Full Field model.Calibrate and validate the SRM.Select KPIs for uncertainty analysis.Assign PDF to each KPI.Perform Monte Carlo Simulation.

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FFM Characteristics

Full Field Model Characteristics:Underlying Complex Geological Model.ECLIPSETM

165 Horizontal Wells.Approximately 1,000,000 grid blocks.Single Run = 10 Hours on 12 CPUs.Water Injection for Pressure Maintenance.

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SRM Characteristics

Accurate replication of Full Field Model Results (for every well in the field):

Instantaneous Water CutCumulative Oil ProductionCumulative Water Production

Ability to run in real-time.Remove the bottleneck.

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Very Complex Geology

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Very Complex Geology

Reservoirs represented in the FFM.

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Curse of Dimensionality

Source of dimensionality:STATIC: Representation of reservoir properties associated with each well.DYNAMIC: Simulation runs to demonstrate well productivity.

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Curse of Dimensionality

Representing reservoir properties for horizontal wells.

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Curse of Dimensionality, Static

Potential list of parameters that can be collected on a “per-grid block” basis.

IMPORTANT NOTE: Specific objective of the surrogate model must be identified in advance.

Mid Depth Thickness

Relative Rock Ttype Porosity

Initial Water Saturations Stylolite Intensity

Horizontal Permeabil ity Vertical Permeabil ity

Sw @ Reference Point So @ Reference Point

Capil lary Pressure/Saturation Function Pressure @ Reference Point

Parameters Used on a per segment basis

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Curse of Dimensionality, StaticPotential list of parameters that can be collected on a “per-well” basis.

IMPORTANT NOTE: Specific objective of the surrogate model must be identified in advance.

Latitude Longitude

Deviation Azimuth

Horizontal Well Length Productivity Index

Distance to Free Water Level Water Cut @ Reference Point

Flowing BHP @ Reference Point Oil Prod. Rate @ Reference Point

Cum. Oil Prod. @ Reference Point Cum. Water Prod. @ Reference Point

Distance to Nearest Producer Distance to Nearest Injector

Distance to Major Fault Distance to Minor Fault

Parameters Used on a per well basis

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Curse of Dimensionality, Static

Total number of parameters that need representation during the modeling process:

12 parameters x 40 grid block/well = 480

16 parameter per well

Total of 496 parameter per well

Building a model with 496 parameters per well is not realistic, THE CURSE OF DIMENSIONALITY

Dimensionality Reduction becomes a vital task.

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Curse of Dimensionality, Dynamic

Well productivity is identified through following simulation runs:

All wells producing at 1500, 2500, 3500, & 4500 bpd (nominal rates)

Cap the field productivityNo cap on field productivity

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Curse of Dimensionality, Dynamic

Well productivity through following simulation runs:

Step up the rates for all wellsCap the field productivityNo cap on field productivity

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Curse of Dimensionality

In order to address the “Curse of Dimensionality” one must understand the behavior and contribution of each of the parameters to the process being modeled.Not a simple and straight forward task. !!!

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Curse of Dimensionality

To address this issue, we use Fuzzy Pattern Recognition technology, based on Fuzzy Cluster Analysis.

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Parameter: Pressure @ Reference

Key Performance Indicator

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Key Performance Indicator

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Please Note: The lower the bar, the higher the influence.

Key Performance Indicators

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Surrogate Modeling

40% of data was set aside as blind (verification) data.

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Surrogate Modeling

40% of data was set aside as blind (verification) data.

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Optimal Production Strategy

Well Ranked No. 1

IMPORTANT NOTE: This is NOT a Response Surface – SRM was run hundreds of times to generate these figures.

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Optimal Production Strategy

Well Ranked No. 100

IMPORTANT NOTE: This is NOT a Response Surface – SRM was run hundreds of times to generate these figures.

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Following are the steps involved:1. Identify a set of key performance indicators that

are most vulnerable to uncertainty.2. Define probability distribution function for each of

the performance indicators.a. Uniform distributionb. Normal (Gaussian) distributionc. Triangular distributiond. Discrete distribution

Analysis of Uncertainty

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Following are steps involved:3. Run the neural network model hundreds or

thousands of times using the defined probability distribution functions for the identified reservoir parameters. Performing this analysis using the actual Full Field Model is impractical.

4. Produce a probability distribution function for cumulative oil production and the water cut at different time and liquid rate cap.

Analysis of Uncertainty

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I-12

P-16

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Key Performance Indicators

40 producing layers.

One million grid blocks.

This is the distribution of the parameter being studied in the geologic model.

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Cumulative Oil ProductionUniform Distribution was assigned to the top 5 KPIs.

Gaussian Distribution was assigned to the top 5 KPIs.

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Instantaneous Water CutUniform Distribution was assigned to the top 5 KPIs.

Gaussian Distribution was assigned to the top 5 KPIs.

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B-91

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Cumulative Oil Production

Influence of uncertainties associated with top and low ranking KPIs on the well

output.

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Instantaneous Water Cut

Influence of uncertainties associated with top and low ranking KPIs on the well

output.

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CONCLUSIONS

A successful surrogate reservoir model was developed for a giant oil field in the Middle East.The surrogate model was able to accurately mimic the behavior of the actual full field flow model.

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CONCLUSIONS

The surrogate reservoir model would provide results in real time.The surrogate model was used to analyze uncertainties associated with the full field flow model.

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CONCLUSIONS

Development of successful surrogate reservoir model is an important and essential step toward development of next generation of reservoir management tools that would address the needs of smart fields.

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Analysis of Uncertainty

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Analysis of Uncertainty

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Average Sw @ Reference point in Top Layer II

Value in the model = 8%Lets use a minimum of 4% and a maximum of 15% with a triangular distribution

4 8 15

Analysis of Uncertainty

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Average Capillary Pressure @ Reference point in Top Layer III

Value in the model = 79 psiLets use a minimum of 60 psi and a maximum of 100 psi with a triangular distribution

60 80 100

Analysis of Uncertainty

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PDF for HB001 Cumulative Oil and Cumulative Water production at the rate of 3,000 blpd cap after 20 years.

Analysis of Uncertainty

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Such analysis can be performed for all wells at any rate and any number of years.There is a higher probability of acceptance of the ideas for rate increase by the management, if we show that:

We are aware of the uncertainties associated with our analysis.Uncertainties are being accounted for in our decision making process.

Analysis of Uncertainty