Bang-bang control and singular arcs in reservoir flooding

Journal of Petroleum Science and Engineering

Volumn 58, Issue 1-2, 2007, Pages 186-200

  Zandvliet, M J ^a   Bosgra, O H ^a   Jansen, J D ^b,c   Van den Hof, P M J ^a   Kraaijevanger, J F B M ^c  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c NONE

Author keywords

Bang bang control; Optimal control; Reservoir flooding; Singular arcs

Indexed keywords

NET PRESENT VALUE; OPTIMAL INJECTION; SINGULAR ARCS;

BANG BANG CONTROL SYSTEMS; INJECTION (OIL WELLS); OIL WELL FLOODING; OPTIMAL CONTROL SYSTEMS;

PETROLEUM RESERVOIRS;

BANG BANG CONTROL SYSTEMS; INJECTION (OIL WELLS); OIL WELL FLOODING; OPTIMAL CONTROL SYSTEMS; PETROLEUM RESERVOIRS;

CONTROL SYSTEM; FLOOD CONTROL; OPTIMIZATION; RESERVOIR FLOODING;

NUCLEOPOLYHEDROVIRUS;

EID: 34547124352     PISSN: 09204105     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.petrol.2006.12.008     Document Type: Article

References (45)

1. Agrachev A., Stefani G., and Zezza P. Strong optimality for a bang-bang trajectory. SIAM J. Control Optim. 41 4 (2002) 991-1014
2. Aitokhuehi I., Durlofsky L.J., Artus V., Yeten B., and Aziz K. Optimization of advanced well type and performance. 9th European Conference on the Mathematics of Oil Recovery, Cannes (2004)
3. Asheim H. Optimal control of water drive. SPE J. (SPE 15978) (1987)
4. Asheim H. Maximization of water sweep efficiency by controlling production and injection rates. SPE European Petroleum Conference (SPE 18365), London (1988)
5. Athans M. The status of optimal control theory and applications for deterministic systems. IEEE Trans. Automat. Contr. 11 3 (1966) 580-596
6. Athans M., and Falb P.L. Optimal Control - An Introdution to the Theory and Its Applications (1966), McGraw-Hill
7. Aziz K., and Settari A. Petroleum Reservoir Simulation (1979), Applied Science Publishers
8. Bangerth W., Klie H., Wheeler M.F., Stoffa P., and Sen M. On optimization algorithms for the reservoir oil well placement problem. Comput. Geosci. 10 (2006) 303-319
9. Belghith S.F., Lamnabhi-Lagarrigue F., and Rosset M.M. Bang-bang solutions for a class of problems arising in thermal control. In: Reichel D. (Ed). Algebraic and Geometric Methods in Nonlinear Control Theory (1986) 623-632
10. Bellman R. On the "bang-bang" control problem. Q. Appl. Math. 14 (1956) 11-18
11. Blakemore N., and Aris R. Studies in optimization - v. the bang-bang control of a batch reactor. Chem. Eng. Sci. 17 (1962) 591-598
12. Bressan A. A high-order test for the optimality of bangbang controls. SIAM J. Control Optim. 23 (1985) 38-48
13. Brouwer D.R., and Jansen J.D. Dynamic optimization of waterflooding with smart wells using optimal control theory. SPE J. (SPE 78278-PA) 9 4 (2004) 391-402
14. Brouwer D.R., Naevdal G., Jansen J.D., and van Kruijsdijk C.P.J.W. Improved reservoir management through optimal control and continuous model updating. SPE Annual Technical Conference and Exhibition (90149-MS), Houston (2004)
15. Brouwer, D.R. (2004). Dynamic Water Flood Optimization With Smart Wells Using Optimal Control Theory. PhD thesis, Delft University of Technology.
16. Bryson A.E., and Ho Y.C. Applied Optimal Control: Optimization, Estimation and Control (1975), Hemisphere-Wiley
17. Clarke F.H. Optimization and Nonsmooth Analysis (1983), John Wiley & Sons
18. Fathi Z., and Ramirez W.F. Optimal injection policies for enhanced recovery: part 2 - surfactant flooding. SPE J. 24 3 (1984) 333-341
19. Fathi Z., and Ramirez W.F. Use of optimal control theory for computing optimal injection policies for enhanced oil recovery. Automatica 22 1 (1986) 33-42
20. Fathi Z., and Ramirez W.F. Optimization of an enhanced oil recovery process with boundary controls - a large-scale non-linear maximization. Automatica 23 3 (1987) 301-310
21. Glashoff K., and Sachs E. On theoretical aspects of the bang-bang principle. Numer. Math. 29 (1977) 93-113
22. Hubbert M.K. Darcy's law and the field equations of the flow of underground fluids. Petrol. Trans. AIME (749-G) 207 (1956) 222-239
23. Jansen J.D., Brouwer D.R., Naevdal G., and Kruijsdijk C.P.J.W.V. Closed-loop reservoir management. First Break 23 (2005) 43-48
24. Kawski M. High-order maximum principles. New Trends in Nonlinear Dynamics and Control (2003), Springer-Verlag 313-326
25. Kraaijevanger J.F.B.M., Egberts P.J.P., Valstar J.R., and Buurman H.W. Optimal waferflood design using the adjoint method. Reservoir Simulation Symposium (SPE 105764), Houston (2007)
26. Krener A.J. The high order maximum principle. In: Reidel D. (Ed). Geometric Methods in System Theory (1973) 174-184
27. Ledzewicz U., and Schattler H. Optimal bang-bang controls for a two-compartment model in cancer chemotherapy. J. Optim. Theory Appl. 114 3 (2002) 609-637
28. Liu W., Ramirez W.F., and Qi Y.F. Optimal control of steamflooding. SPE J. (SPE 21619) 1 2 (1993) 73-82
29. Lucas S.K., and Kaya C.Y. Switching-time computation for bang-bang control laws. IEEE American Control Conference (2001) 176-181 Arlington
30. Luenberger D.G. Introduction to Dynamic Systems: Theory, Models and Applications (1981), John Wiley & Sons
31. Maurer H., Buskens C., Kim J., and Kaya C. Optimization methods for the verification of second order sufficient conditions for bang-bang controls. Optim. Control Appl. Methods 26 (2005) 129-156
32. Mehos G.J., and Ramirez W.F. Use of optimal control theory to optimize carbon dioxide miscible-flooding enhanced oil recovery. J. Pet. Sci. Eng. 2 (1989) 247-260
33. Meier L., and Bryson A.E. Efficient algorithm for time-optimal control of a two-link manipulator. J. Guid. Control Dyn. 13 5 (1990) 859-866
34. Mohler R. Bilinear Control Processes (1973), Academic Press
35. Peaceman D.W. Fundamentals of Numerical Reservoir Simulation (1977), Elsevier Scientific
36. Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., and Mishchenko E.F. The Mathematical Theory of Optimal Processes (1962), John Wiley & Sons
37. Ramirez W.F., and Fathi Z. Optimal injection policies for enhanced recovery: part 1- surfactant flooding. SPE J. 24 3 (1984) 328-332
38. Sarma P., Aziz K., and Durlofsky L.J. Implementation of adjoint solution for optimal control of smart wells. SPE Reservoir Simulation Symposium (SPE 92864), Houston (2005)
39. Sarma P., Chen W.H., Durlofsky L.J., and Aziz K. Production optimization with adjoint models under nonlinear control-state path inequality constraints. SPE Intelligent Energy Conference and Exhibition, (SPE 99959-MS), Amsterdam (2006)
40. Stengel R.F. Stochastic Optimal Control - Theory and Application (1986), John Wiley & Sons
41. Sudaryanto B., and Yortsos Y. Optimization of fluid front dynamics in porous media using rate control 1. equal mobility fluids. Phys. Fluids 12 7 (2000) 1656-1670
42. Sudaryanto B., and Yortsos Y. Optimization of displacements in porous media using rate control. SPE Annual Technical Conference and Exhibition (SPE 71509) (2001)
43. Sussmann H. A bang-bang theorem with bounds on the number of switchings. SIAM J. Control Optim. 17 5 (1979) 629-651
44. Yeten B., Durlofsky L.J., and Aziz K. Optimization of nonconventional well type, location, and trajectory. SPE J. (SPE 86880-PA) 8 3 (2003) 200-210
45. Zandvliet M.J., Jansen J.D., Van den Hof P.M.J., Bosgra O.H., and Kraaijevanger J.F.B.M. Bang-bang control in reservoir flooding. 10th European Conference on the Mathematics of Oil Recovery, Amsterdam (2006)