Generalized Field-Development Optimization With Derivative-Free Procedures
- Obiajulu J. Isebor (BP) | David Echeverría Ciaurri (IBM) | Louis J. Durlofsky (Stanford University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- October 2014
- Document Type
- Journal Paper
- 891 - 908
- 2014.Society of Petroleum Engineers
- 1.6 Drilling Operations, 1.6.9 Coring, Fishing
- simulation-based optimization, mixed-integer nonlinear programming, field development optimization, derivative-free optimization
- 7 in the last 30 days
- 625 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
The optimization of general oilfield development problems is considered. Techniques are presented to simultaneously determine the optimal number and type of new wells, the sequence in which they should be drilled, and their corresponding locations and (time-varying) controls. The optimization is posed as a mixed-integer nonlinear programming (MINLP) problem and involves categorical, integer-valued, and real-valued variables. The formulation handles bound, linear, and nonlinear constraints, with the latter treated with filter-based techniques. Noninvasive derivative-free approaches are applied for the optimizations. Methods considered include branch and bound (B&B), a rigorous global-search procedure that requires relaxation of the categorical variables; mesh adaptive direct search (MADS), a local pattern-search method; particle swarm optimization (PSO), a heuristic global-search method; and a PSO-MADS hybrid. Four example cases involving channelized-reservoir models are presented. The recently developed PSO-MADS hybrid is shown to consistently outperform the standalone MADS and PSO procedures. In the two cases in which B&B is applied, the heuristic PSO-MADS approach is shown to give comparable solutions but at much lower computational cost. This is significant since B&B provides a systematic search in the categorical variables. We conclude that, although it is demanding in terms of computation, the methodology presented here, with PSO-MADS as the core optimization method, appears to be applicable for realistic reservoir development and management.
|File Size||1 MB||Number of Pages||18|
Audet, C. and Dennis Jr., J.E. 2004. A Pattern Search Filter Method for Nonlinear Programming Without Derivatives. SIAM J. on Optimization 14 (4): 980–1010.
Audet, C. and Dennis Jr., J.E. 2006. Mesh Adaptive Direct Search Algorithms for Constrained Optimization. SIAM J. on Optimization 17 (1): 188–217.
Bellout, M.C., Echeverría Ciaurri, D., Durlofsky, L.J. et al. 2012. Joint Optimization of Oil Well Placement and Controls. Computational Geosci. 16 (4): 1061–1079.
Bonami, P., Biegler L.T., Conn, A.R. et al. 2008. An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs. Discrete Optimization 5 (2): 186–204.
Brouwer, D.R. and Jansen, J.D. 2004. Dynamic Optimization of Waterflooding With Smart Wells Using Optimal Control Theory. SPE J. 9 (4): 391–402.
Cao, H. 2002. Development of Techniques for General Purpose Simulators. PhD thesis, Department of Petroleum Engineering, Stanford University.
Conn, A.R., Scheinberg, K., and Vicente, L.N. 2009. Introduction to Derivative-Free Optimization. Society for Industrial and Applied Mathematics.
Djerrah, A., Le Cun, B., Cung, V. et al. 2006. Bob++: Framework for Solving Optimization Problems With Branch-and-Bound Methods. Proceedings of the 15th IEEE International Symposium on High-Performance Distributed Computing, 369–370.
Eberhart, R.C. and Kennedy, J. 1995. A New Optimizer Using Particle Swarm Theory. Proceedings of the Sixth International Symposium on Micro Machine and Human Science, 39–43.
Echeverría Ciaurri, D., Conn, A.R., Mello, U.T. et al. 2012. Integrating Mathematical Optimization and Decision Making in Intelligent Fields. Paper SPE 149780 presented at the SPE Intelligent Energy Conference and Exhibition, Utrecht, The Netherlands. http://dx.doi.org/10.2118/149780-MS.
Echeverría Ciaurri, D., Isebor, O.J., and Durlofsky, L.J. 2011a. Application of Derivative-Free Methodologies for Generally Constrained Oil Production Optimization Problems. International J. Mathematical Modelling and Numerical Optimisation 2 (2): 134–161.
Echeverría Ciaurri, D., Mukerji, T., and Durlofsky, L.J. 2011b. Derivative-Free Optimization for Oil Field Operations, ed. X.S. Yang and S. Koziel, In Computational Optimization and Applications in Engineering and Industry, Studies in Computational Intelligence, 19–55. Springer.
Eckstein, J., Phillips, C., and Hart, W. 2001. PICO: An Object-Oriented Framework for Parallel Branch and Bound. Studies in Computational Mathematics 8: 219–265.
Fernández Martínez, J.L., García Gonzalo, E., and Fernández Alvarez, J.P. 2008. Theoretical Analysis of Particle Swarm Trajectories Through a Mechanical Analogy. International J. Computational Intelligence Research 4 (2): 93–104.
Forouzanfar, F., Li, G., and Reynolds, A.C. 2010. A Two-Stage Well Placement Optimization Method Based on Adjoint Gradient. Paper SPE 135304 presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy. 19–22 September. http://dx.doi.org/10.2118/135304-MS.
Gunnerud, V. and Foss, B. 2010. Oil Production Optimization—A Piecewise Linear Model, Solved With Two Decomposition Strategies. Computers & Chemical Engineering 34 (11): 1803–1812.
Humphries, T.D., Haynes, R.D., and James, L.A. 2013. Simultaneous and Sequential Approaches to Joint Optimization of Well Placement and Control. To appear in Computational Geosci. http://dx.doi.org/10.1007/s10596-013-9375-x.
Isebor, O.J. 2013. Derivative-Free Optimization for Generalized Oil Field Development. PhD thesis, Department of Energy Resources Engineering, Stanford University.
Isebor, O.J., Durlofsky, L.J., and Echeverría Ciaurri, D. 2013. A Derivative-Free Methodology With Local and Global Search for the Constrained Joint Optimization of Well Locations and Controls. To appear in Computational Geosci. http://dx.doi.org/10.1007/s10596-013-9383-x.
Kolda, T.G., Lewis, R.M., and Torczon, V. 2003. Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods. SIAM Review 45 (3): 385–482.
Kosmidis, V.D., Perkins, J.D., and Pistikopoulos, E.N. 2005. A Mixed Integer Optimization Formulation for the Well Scheduling Problem on Petroleum Fields. Computers & Chemical Engineering 29 (7): 1523–1541.
Land, A.H. and Doig, A.G. 1960. An Automatic Method of Solving Discrete Programming Problems. Econometrica 28 (3): 497–520.
Le Digabel, S. 2011. Algorithm 909: NOMAD: Nonlinear Optimization With the MADS Algorithm. ACM Trans. on Mathematical Software 37 (4): 44:1–44:15.
Li, L. and Jafarpour, B. 2012. A Variable-Control Well Placement Optimization for Improved Reservoir Development. Computational Geosci. 16 (4): 871–889.
Litvak, M.L., Hutchins, L.A., Skinner, R.C. et al. 2002. Prudhoe Bay E-Field Production Optimization System Based On Integrated Reservoir and Facility Simulation. Paper SPE 77643 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 29 September–2 October. http://dx.doi.org/10.2118/77643-MS.
Nocedal, J. and Wright, S.J. 2006. Numerical Optimization, second edition, Springer.
Onwunalu, J.E. and Durlofsky, L.J. 2010. Application of a Particle Swarm Optimization Algorithm for Determining Optimum Well Location and Type. Computational Geosci. 14 (1): 183–198.
Sarma, P. and Chen, W.H. 2008. Efficient Well Placement Optimization With Gradient-Based Algorithm and Adjoint Models. Paper SPE 112257 presented at the SPE Intelligent Energy Conference and Exhibition, Amsterdam, The Netherlands, 25–27 February. http://dx.doi.org/10.2118/112257-MS.
Sarma, P., Durlofsky, L.J., Aziz, K. et al. 2006. Efficient Real-Time Reservoir Management Using Adjoint-Based Optimal Control and Model Updating. Computational Geosci. 10 (1): 3–36.
Vaz, A.I.F. and Vicente, L.N. 2009. PSwarm: A Hybrid Solver for Linearly Constrained Global Derivative-Free Optimization. Optimization Methods and Software (24): 669–685.
Wang, C., Li, G., and Reynolds, A.C. 2007. Optimal Well Placement for Production Optimization. Paper SPE 111154 presented at the SPE Eastern Regional Meeting, Lexington, Kentucky, 17–19 October. http://dx.doi.org/10.2118/111154-MS.
Wang, H., Echeverría Ciaurri, D., Durlofsky, L.J. et al. 2012. Optimal Well Placement Under Uncertainty Using a Retrospective Optimization Framework. SPE J. 17 (1): 112–121.
Zandvliet, M., Handels, M., van Essen, G. et al. 2008. Adjoint-Based Well-Placement Optimization Under Production Constraints. SPE J. 13 (4): 392–399.