Practical Use of the Ensemble-Based Conjugate Gradient Method for Production Optimization in the Brugge Benchmark Study
- Y. T. Zhang (Universitetet i Stavanger/The National IOR Centre of Norway) | R. J. Lorentzen (International Research Institute of Stavanger) | A. S. Stordal (Institute of Marine Research)
- Document ID
- Society of Petroleum Engineers
- SPE Norway One Day Seminar, 18 April, Bergen, Norway
- Publication Date
- Document Type
- Conference Paper
- 2018. Society of Petroleum Engineers
- 3.2 Well Operations and Optimization, 3.2.7 Lifecycle Management and Planning, 7 Management and Information, 7.2 Risk Management and Decision-Making, 5 Reservoir Desciption & Dynamics, 3 Production and Well Operations, 5.4 Improved and Enhanced Recovery, 7.2.1 Risk, Uncertainty and Risk Assessment
- conjugate gradient, production optimization, Brugge, ensemble-based, trust-region
- 3 in the last 30 days
- 115 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 9.50|
|SPE Non-Member Price:||USD 28.00|
The concept of the ensemble-based optimization has matured over the last several years and is rooted in the field of reservoir-model-based production optimization. Usually, a backtracking line search scheme is used, but this approach often leads to inefficient searching path direction (e.g. zig-zag patterns). As such, it has some redundancies in finding an optimal solution effectively, increasing the computational overhead with greater risk of problematic numerical instability. Here, we introduce a trust-region conjugate gradient method embedded in EnOpt, motivated by the general applicability and the success in practice. The approach is tested on a synthetic truth model developed by TNO, namely the Brugge benchmark model. The optimization strategy is to control maximum allowed water cut in each connection at which control valves (ICVs) are closed, and the objective is to maximize the net-present-value (NPV). Injectors are controlled using voidage replacement. The methodology performs well on the case considered here. In particular, we use the entire ensemble of controls to adapt the covariance matrix. As such, the gradient estimate of EnOpt is statistically equivalent to that of a Gaussian Mutation Optimization (GMO) algorithm.
|File Size||1 MB||Number of Pages||13|
Amari, S.-I. 1998. Natural Gradient Works Efficiently in Learning. Neural Computation 10 (2): 251–276. https://doi.org/10.1162/089976698300017746.
Bonalde, I. and Ramones, M. 1994. A Robust Algorithm for Parameter Estimation in Well Tests. SPE Advanced Technology Series. 2 (1): 119–125. SPE-23656-PA. https://doi.org/10.2118/23656-PA.
Carter, R. G. 1991. On the Global Convergence of Trust Region Algorithms Using Inexact Gradient Information. SIAM Journal on Numerical Analysis 28 (1):251–265. https://doi.org/10.1137/0728014.
Chaudhri, M. M., Phale, H. A., Liu, N.. 2009. An Improved Approach for Ensemble-Based Production Optimization. Presented at the 2009 SPE Western Regional Meeting, San Jose, California, 24-26 March. SPE-121305-MS. https://doi.org/10.2118/121305-MS.
Chen, C., Li, G., and Reynolds, A. C. 2012. Robust Constrained Optimization of Short- and Long-Term Net Present Value for Closed-Loop Reservoir Management. SPE J. 17 (3):849–864. SPE-141314-PA. https://doi.org/10.2118/141314-PA.
Chen, Y. and Oliver, D. S. 2008. Efficient Ensemble-Based Closed-Loop Production Optimization. Presented at the 2008 SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma, 19-23 April. SPE-112873-MS. https://doi.org/10.2118/112873-MS.
Chen, Y. and Oliver, D. S. 2012. Localization of Ensemble Based Control Setting Updates for Production Optimization.SPE J. 17 (1): 122–136. SPE-125042-PA. https://doi.org/10.2118/125042-PA.
Conn, A. R., Gould, N. I. M., and Toint, P. L. 2000. Trust-RegionMethods, first edition, Philadephia, Pennsylvania: MPS- SIAM series on optimization. https://doi.org/10.1137/L9780898719857.
Do, S. T. and Reynolds, A. C. 2013. Theoretical Connections between Optimization Algorithms Based on an Approximate Gradient. Computational Geosciences 17 (6): 959–73. https://doi.org/10.1007/s10596-013-9368-9.
Eisenstat, S. C., Elman, H. C., and Schlutz, M. H. 1988. Block-Preconditioned Conjugate-Gradient-Like Methods for Numerical Reservoir Simulation. SPE Reservoir Engineering 3 (1): 307–312. SPE-13534-PA. https://doi.org/10.2118/13534-PA.
Erway, J. B., Gill, P. E., and Griffin, J. D. 2009. Iterative Methods for Finding a Trust-Region Step. SIAM Journal on Optimization 20 (2): 1110–1131. https://doi.org/10.1137/070708494.
Fonseca, R. M., Leeuwenburgh, O., van den Hof, P. M. J.. 2013. Improving the Ensemble Optimization Method Through Covariance Matrix Adaptation (CMA-EnOpt). Presented at the SPE Reservoir Simulation Symposium, Woodlands, Texas, 18-20 February. SPE-163657-MS. https://doi.org/10.2118/163657-MS.
Fonseca, R. M., Leeuwenburgh, O., van den Hof, P. M. J.. 2014. Ensemble-Based Hierarchical Multi-Objective Production Optimization of Smart Wells. Computational Geosciences 18 (3-4): 449–461. https://doi.org/10.1007/s10596-013-9399-2.
Forouzanfar, F., Poquioma, W. E., and Reynolds, A. C. 2016. Simultaneous and Sequential Estimation of Optimal Placement and Controls of Wells With a Covariance Matrix Adaptation Algorithm. SPE J. 21 (2): 501–521. SPE-173256-PA. https://doi.org/10.2118/173256-PA.
Foss, B. A. and Jensen, J. P. 2011. Performance Analysis for Closed-Loop Reservoir Management. SPE J. 16 (1):183–190. SPE-138891-PA. https://doi.org/10.2118/138891-PA.
Fu, J. and Wen. X.-H. 2017. Model-Based Multi-Objective Optimization Methods for Efficient Management of Subsurface Flow. SPE J. 22 (6): 1984–1998. SPE-182598-PA. https://doi.org/10.2118/182598-PA.
Gao, G., Jiang, H., van Hagen, P.. 2017. A Gauss-Newton Trust-Region Solver for Large-Scale History-Matching Problems. SPE J. 22 (6): 1999–2011. SPE-182602-PA. https://doi.org/10.2118/182602-PA.
Hanea, R. G., Casanova, P., Wilschut, F. H.. 2017. Well Trajectory Optimization Constrained to Structural Uncertainties. Presented at the SPE Reservoir Simulation Conference, Montgomery, Texas, 20-22 February. SPE- 182680-MS. https://doi.org/10.2118/182680-MS.
Jansen, J.-D., Brouwer, R., Douma, S. G.. 2009. Closed Loop Reservoir Management. Presented at the 2009 SPE Reservoir Simulation Symposium, Woodlands, Texas, 2-4 February. SPE-119098-MS. https://doi.org/10.2118/119098-MS.
Kaul, P. and Thrasher, R. L. 1996. A Parameter-Based Approach for Two-Phase-Equilibrium Prediction With Cubic Equations of State. SPE Reservoir Engineering. 11 (4): 273–279. SPE-26640-PA. https://doi.org/10.2118/26640-PA.
Liu, X. and Reynolds, A. C. 2016. Augmented Lagrangian Method for Maximizing Expectation and Minimizing Risk for Optimal Well-Control Problems With Nonlinear Constraints. SPEJ. 21 (5): 1830–1842. SPE-173274-PA. https://doi.org/10.2118/173274-PA.
Lorentzen, R. J., Shafieirad, A., and Nævdal, G. 2009. Closed Loop Reservoir Management Using the Ensemble Kalman Filter and Sequential Quadratic Programming. Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 2-4 February. SPE-119101-MS. https://doi.org/10.2118/119101-MS.
Lorentzen, R. J., Berg, A., Naevdal, G.. 2006. A New Approach For Dynamic Optimization Of Water Flooding Problems. Presented at Intelligent Energy Conference and Exhibition, Amsterdam, The Netherlands, 11-13 April. SPE- 99690-MS. https://doi.org/10.2118/99690-MS.
Nocedal, J. and Wright, S. J. 2006. Numerical Optimization, second edition, New York, New York: Springer Series in Operations Research and Financial Engineering, Springer-Verlag New York. https://doi.org/10.1007/978-0-387-40065-5
Northrup, E. J. and Woo, P. T. 1988. Application of Preconditioned Conjugate-Gradient-Like Methods in Reservoir Simulation. SPE Reservoir Engineering. 3 (1): 295–301.SPE-13532-PA. https://doi.org/10.2118/13532-PA.
Oliveria, D. F., Reynolds, A. C. 2015. Hierarchical Multiscale Methods for Life-Cycle-Production Optimization: A Field Case Study. SPE J. 20 (5):896–907. SPE-173273-PA. https://doi.org/10.2118/173273-PA.
Peters, L., Arts R., Brouwer, G.. 2010. Results of the Brugge Benchmark Study for Flooding Optimization and History Matching. SPE Reservoir Evaluation & Engineering. 13 (3): 391–405. SPE-119094-PA. https://doi.org/10.2118/119094-PA.
Powell, M. J. D. 1984. On the Global Convergence of Trust Region Algorithms for Unconstrained Minimization. Mathematical Programming 29 (3): 297–303. https://doi.org/10.1007/BF02591998.
Sefat, M. H., Muradov, K. M., Elsheikh, A. H.. 2016. Proactive Optimization of Intelligent-Well Production Using Stochastic Gradient-Based Algorithms. SPE J. 19 (2): 239–252. SPE-178918-PA. https://doi.org/10.2118/178918-PA.
Simon, H. D. 1988. Incomplete LU Preconditioners for Conjugate-Gradient-Type Iterative Methods. SPE Reservoir Engineering. 3 (1): 302–306. SPE-13533-PA. https://doi.org/10.2118/13533-PA.
Steihaug, T. 1983. The Conjugate Gradient Method and Trust Regions in Large Scale Optimization. SIAM Journal on Numerical Analysis 20 (3): 626–637. http://www.jstor.org/stable/2157277.
Stordal, A. S., Szklarz, S. P., and Leeuwenburgh, O. 2015. A Theoretical Look at Ensemble-Based Optimization in Reservoir Management. Math Geosci 48 (4): 399–417. https://doi.org/10.1007/s11004-015-9598-6.
Sun, Y, Wierstra, D., Schaul, T.. 2009. Efficient Natural Evolution Strategies. http://arxiv.org/abs/1209.5853.
Watts, J. W.III 1981. A Conjugate Gradient-Truncated Direct Method for the Iterative Solution of the Reservoir Simulation Pressure Equation. Society of Petroleum Engineers Journal. 21 (3): 345–353. SPE-8252-PA. https://doi.org/10.2118/8252-PA.
Winfield, D. 1973. Function Minimization by Interpolation in a Data Table. IMA Journal of Applied Mathematics. 12 (3): 339–347. https://doi.org/10.1093/imamat/12.3.339.
Ye, F., Liu, H., Zhou, S.. 2008. A Smoothing Trust-Region Newton-CG Method for Minimax Problem. Applied Mathematics and Computation 199 (2): 581–589. https://doi.org/10.1016/j.amc.2007.10.070.
Zaydullin, R., Voskov, D., and Tchelepi, H. A. 2012. Nonlinear Formulation Based on EoS-Free Method for Compositional Flow Simulation. SPE J. 18 (2): 264–273. SPE-146989-PA. https://doi.org/10.2118/146989-PA.