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

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

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

Retrospective Optimization Yes No

5 Choosing a Set of Representative Realizations at Each Subproblem

6 Optimization a Weighted Objective function at each subproblem

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

2D Example True Log-Permeability True Porosity

9 porosity 3 Conditional Realizations to Pressure Data

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

MDS plots after Kernel Clustering

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

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

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

3D Example

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

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

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

Undiscounted NPV: Weighted Sum of 3 Objective functions 19

 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

Color code: iterations of QIM-AG

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

Final Optimal Controls Producers Injectors Full Optimization