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An Adaptive Hierarchical Multiscale Algorithm for Estimation of Optimal Well Controls
- Diego F. Oliveira (University of Tulsa) | Albert Reynolds (University of Tulsa)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- October 2014
- Document Type
- Journal Paper
- 909 - 930
- 2014.Society of Petroleum Engineers
- 6.8 Fundamental Research in Reservoir Description and Dynamics, 6.5 Reservoir Simulation, 6 Reservoir Description and Dynamics
- Production Optimization, Multiscale Optimization, Closed-loop reservoir management
- 14 in the last 30 days
- 273 since 2007
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In determining the optimal well controls by maximizing net present value (NPV) for the remaining life of a reservoir, one typically defines the length of the control steps a priori. Moreover, these control steps are often the same for all wells. We provide a scale-splitting/merging method for adaptively selecting the number and the lengths of control steps as the overall optimization proceeds. We start with a reasonably small number of control steps and find the associated optimal controls by maximizing NPV. Both the adjoint-gradient-based steepest-ascent method and ensemble-based optimization (EnOpt) are considered as optimization algorithms. Because the correlation length used to generate the ad hoc covariance matrix indigenous to EnOpt affects the results, we implement a simple method to reduce the correlation length as the optimization proceeds. This enables EnOpt to generate a good approximation for well-control problems in which the optimal solution is bang-bang. The adaptive approach is applied to two example problems, and the results are compared with those obtained with a predetermined number of control steps.
Asadollahi, M. and Nævdal, G. 2010. Selection of Decision Variables for Large-Scale Production Optimization Problems Applied to Brugge Field. Paper SPE 136378 in Proceedings of the SPE Russian Oil & Gas Technical Conference and Exhibition. http://dx.doi.org/10.2118/136378-MS.
Asheim, H. 1988. Maximization of Water Sweep Efficiency by Controlling Production and Injection Rates. Paper SPE 18365 in Proceedings of the SPE European Petroleum Conference. http://dx.doi.org/10.2118/18365-MS.
Ben Ameur, H., Chavent, G., and Jaffré, J. 2002. Refinement and Coarsening Indicators for Adaptive Parameterization: Application to the Estimation of Hydraulic Transmissivities. Inverse Problems 18: 775–794.
Brouwer, D.R. and Jansen, J.D. 2004. Dynamic Optimization of Water Flooding With Smart Wells Using Optimial Control Theory. SPE J. 9 (4): 391–402. http://dx.doi.org/10.2118/78278-PA.
Brouwer, D.R., Nævdal, G., Jansen, J.D. et al. 2004. Improved Reservoir Management Through Optimal Control and Continuous Model Updating. Paper SPE 90149 in Proceedings of the SPE Annual Technical Conference and Exhibition, Houston, Texas, 26–29 September. http://dx.doi.org/10.2118/90149-MS.
Chavent, G.M. and Bissell, R. 1998. Indicators for the Refinement of Parameterization. In Inverse Problems in Engineering Mechanics, ed. M. Tanaka and G.S. Dulikravich. Amsterdam: Elsevier.
Chen, C. 2011. Adjoint-Gradient-Based Production Optimization With the Augmented Lagrangian Method, PhD thesis, University of Tulsa, Tulsa, Oklahoma.
Chen, C., Li, G., and Reynolds, A. 2012. Robust Constrained Optimization of Short- and Long-Term Net Present Value for Closed-Loop Reservoir Management. SPE J. 17 (3): 849–864. http://dx.doi.org/10.2118/141314-PA.
Chen, Y., Oliver, D.S., and Zhang, D. 2009. Efficient Ensemble-Based Closed-Loop Production Optimization. SPE J. 14 (4): 634–645. http://dx.doi.org/10.2118/112873-PA.
Conn, A., Gould, N., and Toint, P. 1992. LANCELOT: A Fortran Package for Large-Scale Nonlinear Optimization (Release A), New York: Springer-Verlag.
Conn, A.R., Scheinberg, K., and Vicente, L.N. 2008. Introduction to Derivative-Free Optimization, Philadelphia: SIAM.
Do, S.T. 2012. Application of SPSA-Type Algorithms to Production Optimization, PhD thesis, The University of Tulsa, Tulsa, Oklahoma.
Gao, G. and Reynolds, A.C. 2006. An Improved Implementation of the LBFGS Algorithm for Automatic History Matching. SPE J. 11 (1): 5–17. http://dx.doi.org/10.2118/90058-PA.
Grimstad, A.A., Mannseth, T., Nævdal, G. et al. 2003. Adaptive Multiscale Permeability Estimation. Computational Geosci. 7: 1–25.
Hager, W.W., Huang, S.J., Pardalos, P.M. et al. (eds.) 2006. Multiscale Optimization Methods and Applications, Vol. 82 of Nonconvex Optimization and Its Applications (Closed), Springer.
Hayek, M., Ackerer, P., and Sonnendrücker, E. 2009. A New Refinement Indicator for Adaptive Parameterization: Application to the Estimation of the Diffusion Coefficient in an Elliptic Problem. J. Computational and Applied Math. 224: 307–319.
Jansen, J.D., Brouwer, D.R., Naevdal, G. et al. 2005. Closed-Loop Reservoir Management. First Break 23: 43–48.
Kraaijevanger, J.F.B.M., Egberts, P.J.P., Valstar, J.R. et al. 2007. Optimal Waterflood Design Using the Adjoint Method. Paper SPE 105764 in Proceedings of the SPE Reservoir Simulation Symposium, Houston, Texas, 26–28 February. http://dx.doi.org/10.2118/105764-MS.
Lien, M., Brouwer, D.R., Mannseth, T. et al. 2008. Multiscale Regularization of Flooding Optimization for Smart Field Management. SPE J. 13 (2): 195–204. http://dx.doi.org/10.2118/99728-PA.
Lorentzen, R.J., Berg, A.M., Nævdal, G. et al. 2006. A New Approach for Dynamic Optimization of Waterflooding Problems. Paper SPE 99690 in Proceedings of the SPE Intelligent Energy Conference and Exhibition. http://dx.doi.org/10.2118/99690-MS.
Nocedal, J. and Wright, S.J. 2006. Numerical Optimization, New York: Springer.
Nwaozo, J. 2006. Dynamic Optimization of a Water Flood Reservoir, MS thesis, University of Oklahoma, Norman, Oklahoma.
Oliver, D.S., Reynolds, A.C., and Liu, N. 2008. Inverse Theory for Petroleum Reservoir Characterization and History Matching, Cambridge, UK: Cambridge University Press.
Peters, L., Arts, R., Brouwer, G. et al. 2010. Results of the Brugge Benchmark Study for Flooding Optimization and History Matching. SPE Res Eval & Eng 13 (3): 391–405. http://dx.doi.org/10.2118/119094-PA.
Powell, M.J.D. 2009. The BOBYQA Algorithm for Bound Constrained Optimization Without Derivatives, Technical Report DAMTP 2009/NA06, Centre for Mathematical Sciences, University of Cambridge, UK.
Press, W.H., Teukolsky, S.A., Vetterling, W.T. et al. 1992. Numerical Recipes in FORTRAN: The Art of Scientific Computing, Cambridge, England: Cambridge University Press.
Sarma, P., Chen, W., Durlofsky, L. et al. 2008. Production Optimization With Adjoint Models Under Nonlinear Control-State Path Inequality Constraints. SPE Res Eval & Eng 11 (2): 326–339. http://dx.doi.org/10.2118/99959-PA.
Sarma, P., Durlofsky, L., and Aziz, K. 2005. Implementation of Adjoint Solution for Optimal Control of Smart Wells. Paper SPE 92864 in Proceedings of the SPE Reservoir Simulation Symposium. http://dx.doi.org/10.2118/92864-MS.
Sarma, P., Durlofsky, L., Aziz, K. et al. 2006. Efficient Real-Time Reservoir Management Using Adjoint-Based Optimal Control and Model Updating. Computational Geosci. 10: 3–36.
Schlumberger. 2011. Eclipse Reservoir Simulation Software: Reference Manual, London, UK: Schlumberger Software. www.slb.com, version 2011.2 edn.
Shuai, Y., White, C.D., Zhang, H. et al. 2011. Using Multiscale Regularization to Obtain Realistic Optimal Control Strategies. Paper SPE 142043 in Proceedings of the SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, 21–23 February. http://dx.doi.org/10.2118/142043-MS.
Sudaryanto, B. and Yortsos, Y.C. 2000. Optimization of Fluid Front Dynamics in Porous Media Using Rate Control. I. Equal Mobility Fluids. Physics of Fluids 12 (7): 1656–1670.
van Essen, G.M., den Hof, P.M.J.V., and Jansen, J.D. 2011. Hierarchical Long-Term and Short-Term Production Optimization. SPE J. 16 (1): 191–199. http://dx.doi.org/10.2118/124332-PA.
van Essen, G.M., Zandvliet, M.J., den Hof, P.M.J.V. et al. 2009. Robust Waterflooding Optimization of Multiple Geological Scenarios. SPE J. 14 (1): 202–210. http://dx.doi.org/10.2118/102913-PA.
Wang, C., Li, G., and Reynolds, A.C. 2009a. Production Optimization in Closed-Loop Reservoir Management. SPE J. 14 (3): 506–523.
Wang, Y., Li, G., and Reynolds, A.C. 2009b. Estimation of Depths of Fluid Contacts by History Matching Using Iterative Ensemble Kalman Smoothers Paper SPE 119056 in Proceedings of the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 2–4 February. http://dx.doi.org/10.2118/119056-MS.
Zakirov, I.S., Aanonsen, S.I., Zakirov, E.S. et al. 1996. Optimizing Reservoir Performance by Automatic Allocation of Well Rates. In Proceedings of the 5th European Conference on the Mathematical Oil Recovery—Leoben, Austria, 3–5 September.
Zandvliet, M., Bosgra, O., Jasen, J. et al. 2007. Bang-Bang Control and Singular Arcs in Reservoir Flooding. J. Pet. Sci. Eng. 58 (1): 186–200. http://dx.doi.org/10.1016/j.petrol.2006.12.008.
Zhao, H., Chen, C., Do, S. et al. 2013. Maximization of a Dynamic Quadratic Interpolation Model for Production Optimization. SPE J. 18 (6): 1012–1025. http://dx.doi.org/10.2118/141317-PA.
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