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A Bootstrap Procedure for Estimation of Parameter Sensitivity from Proxy Flow Models

Learn efficient methods for estimating parameter sensitivity in reservoir forecasting using proxies to save computational time. Explore the benefits of model selection and sensitivity analysis techniques.

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A Bootstrap Procedure for Estimation of Parameter Sensitivity from Proxy Flow Models

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  1. Annual Meeting 2013 Stanford Center for Reservoir Forecasting A Bootstrap Procedure for Estimation of Parameter Sensitivity from Proxy Flow Models Ogy Grujić, Jef Caers

  2. Computational Time • Sensitivity Analysis: • Uncertainty Quantification; • History Matching; • Requires large number of flow simulations; • Time consuming. How can we save computational time? SCRF 2013

  3. How do we save time? • Use Proxies - fast approximations to fine full physics reservoir simulation responses. • Model Selection - run fine full physics flow simulation on a small sub-set of models. SCRF 2013

  4. Reservoir case study • dGSA with 5 Parameters: • TI – Geological Scenarios [1,2,3] • Thickness [50,100] ft; • Swir [0.2,0.35]; • Corey’s Coefficient [2,4]; • Perm_A; • Ensemble size: 750 models; SCRF 2013

  5. dGSA – Proxies vs. Fine Proxy Flow Responses Fine Full physics Flow Responses Inaccurate and Misleading SCRF 2013

  6. Proxy Misclassifies Models SCRF 2013

  7. How do we save time? • Use Proxies - fast approximations to fine full physics reservoir simulation responses. • Model Selection - run fine full physics flow simulation on a small sub-set of models. Sample from Proxy Simulate with Fine SCRF 2013

  8. How many runs is enough? How can we estimate These confidence intervals? SCRF 2013

  9. How to Estimate Confidence Intervals? • In dGSA workflow we got 2 important categories associated with each model: • Model Classification; • Associated Parameters; • Single-variate bootstrap procedure is not appropriate for this type of problem. • Another way would be Bivariate Bootstrap; SCRF 2013

  10. Bivariate Bootstrap

  11. Bivariate Bootstrap F(p|x) Fb(x) F(p|x) Fr(x)

  12. Bivariate Bootstrap

  13. Bivariate Bootstrap Bias Correction TrueSensitivity True Sensitivity Estimated Sensitivity Estimated Sensitivity

  14. How many runs is enough? SCRF 2013

  15. Stopping Criteria • Two ways of establishing stopping criteria: • Based on the boundary line (sensitive/non-sensitive); • Based on desired width of confidence interval; • It is important to observe confidence intervals and behavior of sensitivity estimate on all parameters. • Always observe all parameters! SCRF 2013

  16. Stopping Criteria

  17. Future Work • Model Selection – Improve model sampling procedure. • Expand the workflow to study parameter interactions • Proxy Confidence Intervals – Estimation of Accuracy in dGSA results achieved with proxy flow simulation. SCRF 2013

  18. Conclusions • A robust tool for estimation number of necessary simulation run; • Completely independent of: • Type of proxy, • Prior, • Number of parameters… SCRF 2013

  19. Backup Slides

  20. Sampling the Proxy • Cluster each side into “many” sub-clusters; • Medoids are used as “candidates” for fine flow full physics simulations; SCRF 2013

  21. dGSA - How many flow simulations do we actually need? Computationally Expensive! How Many Do We Need? dGSA - Revisited SCRF 2013

  22. Bivariate Bootstrap-Step by Step- Step 1 Sample for classification Sample for parameters Step 2 SCRF 2013

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