1. Retrospective Production Optimization Under Uncertainty Using Kernel Clustering Mehrdad Gharib Shirangi and Tapan Mukerji Department of Energy Resources Engineering Stanford University Stanford Center for Reservoir Forecasting 25 th Annual Meeting May 9-11, 2012

2. Production Optimization In Closed-loop Reservoir Management 2 Reservoir model Well controls

3. 3 Retrospective Optimization Approach k=1 k=2 k=3

4. Retrospective Optimization Yes No

5. 5 Choosing a Set of Representative Realizations at Each Subproblem

6. 6 Optimization a Weighted Objective function at each subproblem

7. 7 QIM-AG Optimization Algorithm  QIM-AG: Quadratic Interpolation Model using an Approximate Gradient (Zhao et al, 2011).  Build a quadratic model at each iteration  Quadratic model fits some interpolation points  Use an approximate gradient  A gradient-free optimization method,  Local optimizer, suitable for smooth functions  Computationally very efficient

8. 2D Example True Log-Permeability True Porosity

9. 9 porosity 3 Conditional Realizations to Pressure Data

10. NPV versus iterations of QIM-AG CaseSimulationsExpected NPV, M$True NPV, M$ full optimization 35400269257 2400256253 6600254251 Summary of the results K=1 K=2 K=3 K=1 K=2

11. MDS plots after Kernel Clustering

12. Clustering, Cumulative Production Curves in Time Cu. Water Prod. ($ value) Cu. Oil Prod. ($ value) Cu. Water Injec. ($ value)

13. Histograms of the final NPV distribution  The histograms are very similar and they show similar distributions of the NPV. Expected NPV is shown in green, while true NPV is shown in red

14. Computational Cost- Mean Weighted NPV Computational cost k=1 k=2 k=3 Mean Weighted NPV Iterations of QIM-AG

15. 3D Example

16. 16 Layer 1 A Conditional Realizations versus the True Model Layer 2Layer 3

17. 3D Example: NPV versus iterations full optimization CaseSimulationsExpected NPV, M$ full optimization 7600651.2 2939655.1 Computational cost k=1 k=2 k=3 Mean Weighted NPV

18. Histograms of the final NPV distribution  The histograms are very similar and show almost the same distribution of the NPV. Expected NPV shown in green, while true NPV shown in red

19. Undiscounted NPV: Weighted Sum of 3 Objective functions 19

20.  Applied retrospective production optimization.  Distance-kernel clustering to find sets of representative realizations at each subproblem.  Uncertainty in costs and prices affect the final solution. Need to use multiobjective optimization.  Need to investigate uncertainty in NPV when realizations are from multiple training images. 20 Conclusions & Future Work

21. Color code: iterations of QIM-AG

22. 22 Depending on the assigned costs of handling produced and injected water and the assigned oil revenue, different solutions are obtained.

24. Final Optimal Controls Producers Injectors Full Optimization