Reduced-order optimal control of water flooding using proper orthogonal decomposition
Tóm tắt
Từ khóa
Tài liệu tham khảo
H. Asheim, Maximization of water sweep efficiency by controlling production and injection rates, paper SPE 18365, in: Proc. SPE European Petroleum Conference, London, UK (1988).
K. Aziz and A. Settari, Petroleum Reservoir Simulation (Applied Science Publishers, London, UK, 1979).
D.R. Brouwer and J.D. Jansen, Dynamic optimisation of water flooding with smart wells using optimal control theory, SPE J. (2004) 391–402, December.
G.H. Golub and C. Van Loan, Matrix Computations, 3rd Edition (John Hopkins Univ. Press, Baltimore, MD, 1983).
T. Heijn, R. Markovinović and J.D. Jansen, Generation of low-order reservoir models using system-theoretical concepts, paper SPE 79674, in: Proc. Reservoir Simulation Symposium, Houston, TX, USA, 3–5 February (2003).
P. Holmes, J.L. Lumley and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge University Press, Cambridge, 1996).
http://www.mathworks.com .
H.V. Ly and H.T. Tran, Modeling and control of physical processes using proper orthogonal decomposition, Math. Comput. Model. 33 (2001) 223–236.
R. Markovinović, E.L. Geurtsen, T. Heijn and J.D. Jansen, Generation of low-order reservoir models using POD, empirical gramians and subspace identification, in: Proc. 8th European Conf. on the Mathematics of Oil Recovery (ECMOR VIII), Freiberg, Germany, E31 (2002) pp. 1–10.
M. Meyer and H.G. Matthies, Efficient model reduction in non-linear dynamics using the Karhunen–Loève expansion and dual-weighted-residual methods, Comput. Mech. (2003) 179–191.
G. Naevdal, D.R. Brouwer and J.D. Jansen, Water flooding using closed-loop control, Comput. Geosci. (2006), DOI: 10.1007/s10596-005-9010-6.
D.W. Peaceman, Fundamentals of Numerical Reservoir Simulation (Elsevier Scientific Publishing Company, Amsterdam, The Netherlands, 1977).
R.D. Prabhu, S.S. Collis and Y. Chang, The influence of control on proper orthogonal decomposition of wall-bounded turbulent flows, Phys. Fluids 13(2) (2001) 520–537.
S.S. Ravindran, Reduced-order adaptive controllers for fluid flows using POD, J. Sci. Comput. 14(4) (2000) 457–478.
P. Sarma, K. Aziz and L.J. Durlofsky, Implementation of adjoint solution for optimal control of smart wells, paper SPE 92864, in: Proc. SPE Reservoir Simulation Symposium, Houston, TX, USA (2005).
P. Sarma, L.J. Durlofsky, K. Aziz and W.H. Chen, Efficient real-time reservoir management using adjoint-based optimal control and model updating, Comput. Geosci. (2006), DOI: 10.1007/s10596-005-9009-z.
L. Sirovich, Turbulence and the dynamics of coherent structures. Part 1: Coherent structures, Q. Appl. Math. 45(3) (1987) 561–571.
B. Sudaryanto and Y.C. Yortsos, Optimization of fluid front dynamics in porous media using rate control. I. Equal mobility fluids, Phys. Fluids 12(7) (2000) 1656–1670.
P.T.M. Vermeulen, A.W. Heemink and C.B.M. Te Stroet, Reduced models for linear groundwater flow models using empirical orthogonal functions, Adv. Water Resour. 27 (2004) 54–69.
G.A. Virnovski, Water flooding strategy design using optimal control theory, in: Proc. 6th European Symposium on IOR, Stavanger, Norway (1991) pp. 437–446.