Production optimization with adjoint models under nonlinear control-state path inequality constraints

SPE Reservoir Evaluation and Engineering

Volumn 11, Issue 2, 2008, Pages 326-339

  Sarma, Pallav ^a   Chen, Wen H ^a   Durlofsky, Louis J ^b,c   Aziz, Khalid ^b  

^a CHEVRON ENERGY TECHNOLOGY COMPANY   (United States)

^b STANFORD UNIVERSITY   (United States)

^c Chevron Energy Technology Company

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ITERATIVE METHODS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS; NONLINEAR PROGRAMMING; OPTIMIZATION;

PENALTY-FUNCTION METHOD; PETROLEUM-PRODUCTION OPTIMIZATION PROBLEM;

OIL WELL PRODUCTION;

ALGORITHMS; ITERATIVE METHODS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS; NONLINEAR PROGRAMMING; OIL WELL PRODUCTION; OPTIMIZATION;

ALGORITHM; GAS PRODUCTION; HYDROCARBON RESERVOIR; MODELING; NUMERICAL METHOD; OIL PRODUCTION; OPTIMIZATION;

EID: 44649087793     PISSN: 10946470     EISSN: None     Source Type: Journal    
DOI: 10.2118/99959-PA     Document Type: Article

References (31)

1. Agkun, M., Haftka, R.T., and Wu, K.C. 1999. Sensitivity of Lumped Constraints Using the Adjoint Method. 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, St. Louis, Missouri, 12-15 April.
2. Asheim, H. 1988. Maximization of Water Sweep Efficiency by Controlling Production and Injection Rates. Paper SPE 18365 presented at the SPE European Petroleum Conference, London, 16-19 October. DOI: 10.2118/ 18365-MS.
3. Brouwer, D.R. and Jansen, J.-D. 2004. Dynamic Optimization of Water Flooding With Smart Wells Using Optimal Control Theory. SPEJ 9 (4): 391-402. SPE-78278-PA. DOI: 10.2118/78278-PA.
4. Brouwer, D.R., Nævdal, G., Jansen, J.D., Vefring, E.H., and van Kruijsdiik, C.P.J.W. 2004. Improved Reservoir Management Through Optimal Control and Continuous Model Updating. Paper SPE 90149 presented at the SPE Annual Technical Conference and Exhibition, Houston, 26-29 September. DOI: 10.2118/90149-MS.
5. Bryson, A.E. and Ho, Y.C. 1975. Applied Optimal Control: Optimization, Estimation, & Control. New York City: Taylor & Francis.
6. Bryson, A.E., Denham, W.F. and Dreyfus, S.E. 1963. Optimal Programming Problems with Inequality Constraints I: Necessary Conditions for Extremal Solutions. AIAA Journal 1 (11): 2544-2550.
7. Cao, H. 2002. Development of Techniques for General Purpose Simulators. PhD dissertation. Stanford, California: Stanford University.
8. Chavent, G., Dupuy, M., and Lemonnier, P. 1975. History Matching by Use of Optimal Control Theory. SPEJ 15 (1): 74-86; Trans., AIME, 259. SPE-4627-PA. DOI: 10.2118/4627-PA.
9. Chen, W.H., Gavalas, G.R., Seinfeld, J.H., and Wasserman, M.L. 1974. A New Algorithm for Automatic History Matching. SPEJ 14 (6): 593-608; Trans., AIME, 257. SPE-4545-PA. DOI: 10.2118/ 4545-PA.
10. Denham, W.F. and Bryson, A.E. 1964. Optimal Programming Problems With Inequality Constraints II: Solution by Steepest-Descent. AIAA Journal 2 (11): 25-34.
11. ECLIPSE 100 Technical Description 2001A. 2001. Abingdon, UK: Schlumberger.
12. Feehery, W.F. 1998. Dynamic Optimization with Path Constraints. PhD dissertation, Cambridge, Massachusetts: Massachusetts Institute of Technology.
13. Fisher, M.E. and Jennings, L.S. 1992. Discrete-Time Optimal Control Problems With General Constraints. ACM Transactions on Mathematical Software 18 (4): 401-413. DOI: 10.1145/138351.138356.
14. Jacobson, D. and Lele, M. 1969. A Transformation Technique for Optimal Control Problems With a State Variable Inequality Constraint. IEEE Transactions on Automatic Control 14 (5): 457-464. DOI: 10.1109/TAC.1969.1099283.
15. Jansen, J.D., Brouwer, D.R., Naevdal, G., and van Kruijsdiik, C.P.J.W. 2005. Closed-Loop Reservoir Management. First Break 23: 43-48.
16. Kelley, C.T. 1999. Iterative Methods for Optimization. Philadelphia, Pennsylvania: Society for Industrial and Applied Mathematics.
17. Li, R., Reynolds, A.C., and Oliver, D.S. 2001. History Matching of Three-Phase Flow Production Data. Paper SPE 66351 presented at the SPE Reservoir Simulation Symposium, Houston, 11-14 February. DOI: 10.2118/ 66351-MS.
18. Liu, S.-Q., Shi, J., Dong, J., and Wang, S. 2004. A Modified Penalty Function Method for Inequality Constraints Minimization. http:// www.mmm.muroran-it.ac.jp/~shi/LiuShiDongWang.pdf.
19. Mehra, R.K. and Davis, R.E. 1972. A Generalized Gradient Method for Optimal Control Problems With Inequality Constraints and Singular Arcs. IEEE Transactions on Automatic Control 17 (1): 69-79. DOI: 10.1109/TAC.1972.1099881.
20. Rao, S.S. 1978. Optimization: Theory and Applications. New York City: John Wiley and Sons Ltd.
21. Sarma, P., Aziz, K., and Durlofsky, L.J. 2005a. Implementation of Adjoint Solution for Optimal Control of Smart Wells. Paper SPE 92864 presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 31 January-2 February. DOI: 10.2118/92864-MS.
22. Sarma, P., Chen, W.H., Durlofsky L.J., and Aziz, K. 2006a. Production Optimization With Adjoint Models Under Nonlinear Control-State Path Inequality Constraints. Paper SPE 99959 presented at the SPE Intelligent Energy Conference and Exhibition, Amsterdam, 11-13 April. DOI: 10.2118/ 99959-MS.
23. Sarma, P., Durlofsky L.J., and Aziz, K. 2005b. Efficient Closed-Loop Production Optimization Under Uncertainty. Paper SPE 94241 presented at the SPE Europec/EAGE Annual Conference, Madrid, Spain, 13-16 June. DOI: 10.2118/94241-MS.
24. Sarma, P., Durlofsky, L.J., Aziz, K., and Chen, W.H. 2006b. Efficient Real-Time Reservoir Management Using Adjoint-Based Optimal Control and Model Updating. Computational Geosciences 10 (1): 3-36. DOI: 10.1007/s10596-005-9009-z.
25. Sengul, M., Yeten, B., and Kuchuk, F. 2004. The Completion Challenge - Modeling Potential Well Solutions. Middle East and Asia Reservoir Review 5: 4-17.
26. Stengel, R.F. 1985. Optimal Control and Estimation. New York City: Dover Books on Advanced Mathematics.
27. Vironovsky, G.A. 1991. Waterflooding Strategy Design Using Optimal Control Theory. 6th European IOR Symposium, Stavanger, 21-23 May.
28. Wu, Z., Reynolds, A.C., and Oliver, D.S. 1999. Conditioning Geostatistical Models to Two-Phase Production Data. SPEJ 4 (2): 142-155. SPE-56855-PA. DOI: 10.2118/56855-PA.
29. Yeten, B. 2003. Optimum Deployment of Nonconventional Wells. PhD dissertation, Stanford, California: Stanford University.
30. Zakirov, I.S., Aanonsen, S.I., Zakirov, E.S., and Palatnik, B.M. 1996. Optimization of Reservoir Performance by Automatic Allocation of Well Rates. 5th European Conference on the Mathematics of Oil Recovery, Leoben, Austria, 3-6 September.
31. Zhang, F., Skjervheim, J.A., Reynolds, A.C., and Oliver, D.S. 2005. Automatic History Matching in a Bayesian Framework, Example Applications. SPEREE 8 (3): 214-223. SPE-84461-PA. DOI: 10.2118/84461-PA.