Optimal control of water flooding reservoir using proper orthogonal decomposition. (English) Zbl 1415.76204
Summary: Optimal control of water flooding reservoir is performed to calculate the optimal set of well controls to maximize economic profitability. However, calculating the optimal well controls requires major computational resources, which restricts its implementation in actual reservoir production. In this paper a reduced-order optimal control methodology mainly based on POD (Proper Orthogonal Decomposition) is proposed to optimize the operation of wells in water flooding reservoir. The methodology is decomposed into the ’offline’ and ’online’ calculations. The offline calculation consists in determining a reduced set of POD basis from several ’snapshots’ obtained using reservoir simulator over a pre-determined set of time instants and well control parameters. In the online calculation, knowing the current economic parameters, the optimal well controls are determined only using a nonlinear programming method and POD reconstruction. The methodology is approved on a small scale, two-dimensional, water flooding reservoir model. The results show that the NPV obtained by the reduced-order optimal control methodology is approached to within 99% of the NPV obtained by the adjoint-gradient based methodology, besides, it is quite fast, where the achieved increase in calculation speed is several dozens of times, and its advantage of calculation speed significantly increases as the number of grid blocks increases.
MSC:
| 76D27 | Other free boundary flows; Hele-Shaw flows |
| 76D55 | Flow control and optimization for incompressible viscous fluids |
| 76S05 | Flows in porous media; filtration; seepage |
Keywords:
water flooding reservoir; reduced-order model; optimal control; proper orthogonal decompositionReferences:
| [1] | Sarma, P.; Durlofsky, L.; Aziz, K., Efficient real-time reservoir management using adjoint-based optimal control and model updating, Comput. Geosci., 10, 1, 3-36 (2006) · Zbl 1161.86303 |
| [2] | Wang, C.; Li, G.; Reynolds, A., Production optimization in closed-loop reservoir management, SPE J., 14, 03, 506-523 (2009) |
| [3] | Chen, Y.; Oliver, D.; Zhang, D., Efficient ensemble-based closed-loop production optimization, SPE J., 14, 04, 634-645 (2009) |
| [4] | Peters, L.; Arts, R.; Brouwer, G., Results of the Brugge benchmark study for flooding optimization and history matching, SPE Reserv. Eval. Eng., 13, 03, 391-405 (2010) |
| [9] | Doublet, D.; Aanonsen, S.; Tai, X., An efficient method for smart well production optimization, J. Pet. Sci. Eng., 69, 1, 25-39 (2009) |
| [10] | Jansen, J., Adjoint-based optimization of multi-phase flow through porous media — a review, Comput. & Fluids, 46, 1, 40-51 (2011) · Zbl 1305.76107 |
| [11] | Forouzanfar, F.; Della, R.; Russo, R., Life-cycle production optimization of an oil field with an adjoint-based gradient approach, J. Pet. Sci. Eng., 112, 351-358 (2013) |
| [13] | Sirovich, L., Turbulence and the dynamics of coherent structures. Part I: Coherent structures, Quart. Appl. Math., 45, 3, 561-571 (1987) · Zbl 0676.76047 |
| [14] | Kunisch, K.; Volkwein, S., Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics, SIAM J. Numer. Anal., 40, 2, 492-515 (2002) · Zbl 1075.65118 |
| [15] | Utturkar, Y.; Zhang, B.; Shyy, W., Reduced-order description of fluid flow with moving boundaries by proper orthogonal decomposition, Int. J. Heat Fluid Flow, 26, 2, 276-288 (2005) |
| [16] | Weller, J.; Lombardi, E.; Bergmann, M., Numerical methods for low-order modeling of fluid flows based on POD, Internat. J. Numer. Methods Fluids, 63, 2, 249-268 (2010) · Zbl 1423.76356 |
| [17] | Fic, A.; Białecki, R.; Kassab, A., Solving transient nonlinear heat conduction problems by proper orthogonal decomposition and the finite-element method, Numer. Heat Transfer B, 48, 2, 103-124 (2005) |
| [18] | Krysl, P.; Lall, S.; Marsden, J., Dimensional model reduction in non-linear finite element dynamics of solids and structures, Internat. J. Numer. Methods Engrg., 51, 3, 479-504 (2001) · Zbl 1013.74071 |
| [19] | Han, S.; Feeny, B., Application of proper orthogonal decomposition to structural vibration analysis, Mech. Syst. Signal Process., 17, 4, 989-1001 (2003) |
| [21] | Banks, H.; Joyner, M.; Wincheski, B., Nondestructive evaluation using a reduced-order computational methodology, Inverse Problems, 16, 3, 929 (2000) · Zbl 0960.35107 |
| [22] | Ding, P.; Tao, W., An inverse analysis for the estimation of boundary heat flux in a circular pipe employing the proper orthogonal decomposition, Prog. Comput. Fluid Dyn., 9, 3-5, 231-246 (2009) |
| [23] | Winton, C.; Pettway, J.; Kelley, C., Application of Proper Orthogonal Decomposition (POD) to inverse problems in saturated groundwater flow, Adv. Water Resour., 34, 11, 1519-1526 (2011) |
| [24] | Ravindran, S., A reduced-order approach for optimal control of fluids using proper orthogonal decomposition, Internat. J. Numer. Methods Fluids, 34, 4, 425-448 (2000) · Zbl 1005.76020 |
| [25] | Ly, H.; Tran, H., Modeling and control of physical processes using proper orthogonal decomposition, Math. Comput. Modelling, 33, 1, 223-236 (2001) · Zbl 0966.93018 |
| [26] | Volkwein, S., Optimal control of a phase-field model using proper orthogonal decomposition, ZAMM J. Appl. Math. Mech., 81, 2, 83-97 (2001) · Zbl 1007.49019 |
| [27] | Tallet, A.; Allery, C.; Allard, F., POD approach to determine in real-time the temperature distribution in a cavity, Build. Environ., 93, 34-49 (2015) |
| [28] | My-Ha, D.; Lim, K.; Khoo, B., Real-time optimization using proper orthogonal decomposition: Free surface shape prediction due to underwater bubble dynamics, Comput. Fluids, 36, 3, 499-512 (2007) · Zbl 1177.76069 |
| [29] | Guha, P.; Nabi, M., Optimal control of a nonlinear induction heating system using a proper orthogonal decomposition based reduced order model, J. Process Control, 22, 9, 1681-1687 (2012) |
| [30] | Doren, J.; Markovinović, R.; Jansen, J., Reduced-order optimal control of water flooding using proper orthogonal decomposition, Comput. Geosci., 10, 1, 137-158 (2006) · Zbl 1161.86304 |
| [31] | Jansen, J.; Bosgra, O.; Van den Hof, P. M.J., Model-based control of multiphase flow in subsurface oil reservoirs, J. Process Control, 18, 9, 846-855 (2008) |
| [32] | Zhu, J.; Chew, D.; Lv, S., Optimization method for building envelope design to minimize carbon emissions of building operational energy consumption using orthogonal experimental design (OED), Habitat Int., 37, 148-154 (2013) |
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