SUN Xian-hang, XU Ming-hai, GONG Liang, JIA Xin-xin, ZHOU Hui. A Fast POD-Based Method for Predicting Oil and Water Flow in Water-Drive Reservoir[J]. Applied Mathematics and Mechanics, 2015, 36(12): 1228-1237. doi: 10.3879/j.issn.1000-0887.2015.12.002
 Citation: SUN Xian-hang, XU Ming-hai, GONG Liang, JIA Xin-xin, ZHOU Hui. A Fast POD-Based Method for Predicting Oil and Water Flow in Water-Drive Reservoir[J]. Applied Mathematics and Mechanics, 2015, 36(12): 1228-1237.

# A Fast POD-Based Method for Predicting Oil and Water Flow in Water-Drive Reservoir

##### doi: 10.3879/j.issn.1000-0887.2015.12.002
Funds:  The National Natural Science Foundation of China(51276199); The National Science and Technology Major Project of China(2011ZX05017_004_HZ01)
• Rev Recd Date: 2015-09-30
• Publish Date: 2015-12-15
• A fast method based on the proper orthogonal decomposition (POD) technique for predicting oil and water flow in water-drive reservoir was proposed. The reduced order model of oil and water flow in water-drive reservoir was generated with the POD. An ensemble of 100 samples of pressure and water saturation snapshots in the time range of [0 d, 500 d] with an interval step of 5 d for the 2D water-drive reservoir model was obtained through numerical reservoir simulation, and the POD was applied to extract a reduced set of POD basis functions from these snapshots. After the injection and production parameters were changed continuously, the obtained POD basis functions combined with the reduced order model were used to predict the new physical fields. The research results show that fast and accurate predictions can be achieved with the proposed POD-based method, for the given example, the prediction errors of pressure and water saturation are less than 1.2% and 1.5%, respectively. What’s more, this POD-based method is 50 times faster in calculation than the traditional numerical reservoir simulation.
•  [1] Brouwer D R, Jansen J D. Dynamic optimization of water flooding with smart wells using optimal control theory[J].SPE Journal,2004,9(4): 391-402. [2] 张凯, 李阳, 姚军, 刘均荣, 闫霞. 油藏生产优化理论研究[J]. 石油学报, 2010,31(1): 78-82.（ZHANG Kai, LI Yang, YAO Jun, LIU Jun-rong, YAN Xia. Theoretical research on production optimization of oil reservoirs[J].Acta Petrolei Sinica,2010,31(1): 78-82.（in Chinese）） [3] ZHU Yan, XIE Jin-zhuang, YANG Wei-hua, HOU Lian-hua. Method for improving history matching precision of reservoir numerical simulation[J].Petroleum Exploration and Development,2008,35(2): 225-229. [4] Marcé R, Moreno-Ostos E, García-Barcina J M, Armengol J. Tailoring dam structures to water quality predictions in new reservoir projects: assisting decision-making using numerical modeling[J].Journal of Environmental Management,2010,91(6): 1255-1267. [5] Berkooz G, Holmes P, Lumley J L. The proper orthogonal decomposition in the analysis of turbulent flows[J].Annual Review of Fluid Mechanics,1993,25(1): 539-575. [6] Singh S J, Chatterjee A. Galerkin projections and finite elements for fractional order derivatives[J].Nonlinear Dynamics,2006,45(1/2): 183-206. [7] Matre O P, Mathelin L. Equation-free model reduction for complex dynamical systems[J].International Journal for Numerical Methods in Fluids,2010,63(2): 163-184. [8] di Mare F, Knappstein R. Statistical analysis of the flow characteristics and cyclic variability using proper orthogonal decomposition of highly resolved LES in internal combustion engines[J].Computers & Fluids,2014,105: 101-112. [9] Weller J, Lombardi E, Bergmann M, Iollo A. Numerical methods for low-order modeling of fluid flows based on POD[J].International Journal for Numerical Methods in Fluids,2010,63(2): 249-268. [10] 腾飞, 罗振东. 非饱和土壤水流问题的降阶外推仿真模型[J]. 应用数学和力学, 2014,35(2): 148-161.(TENG Fei, LUO Zhen-dong. A reduced-order and extrapolation simulation model for unsaturated soil water flow equation[J].Applied Mathematics and Mechanics,2014,35(2):148-161.(in Chinese)) [11] 丁鹏, 陶文铨. 求解对流换热反问题的低阶模型[J]. 西安交通大学学报, 2009,43(3): 14-16.（DING Peng, TAO Wen-quan. Reduced order model based algorithm for inverse convection heat transfer problem[J].Journal of Xi’an Jiaotong University,2009,43(3): 14-16.(in Chinese)) [12] Van Doren J F M, Markovinovi? R, Jansen J D. Reduced-order optimal control of water flooding using proper orthogonal decomposition[J].Computational Geosciences,2006,10(1): 137-158. [13] Ly H V, Tran H T. Modeling and control of physical processes using proper orthogonal decomposition[J].Mathematical and Computer Modelling,2001,33(1): 223-236. [14] Sirovich L. Turbulence and the dynamics of coherent structures： I—coherent structures； II—symmetries and transformations； III—dynamics and scaling[J].Quarterly of Applied Mathematics,1987,45(1): 561-571. [15] 李淑霞, 谷建伟. 油藏数值模拟基础[M]. 山东: 中国石油大学出版社, 2008: 178-179.（LI Shu-xia, GU Jian-wei.Basis of Numerical Reservoir Simulation [M]. Shandong: China University of Petroleum Press, 2008: 178-179.(in Chinese))

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