Citation: | JIA Xinxin, WANG Lei, ZHANG Hao, SUN Xiaoling, DUAN Liya, WANG Xin. A Low-Order Model Method for 2-Phase Oil Reservoir Simulation[J]. Applied Mathematics and Mechanics, 2021, 42(9): 891-899. doi: 10.21656/1000-0887.410235 |
[2]李淑霞, 谷建伟. 油藏数值模拟基础[M]. 东营: 中国石油大学出版社, 2009.(LI Shuxia, GU Jianwei. The Fundamental of Petroleum Reservoir Simulation[M]. Dongying: China University of Petroleum Press, 2009.(in Chinese))
|
ZIENKIEWICZ O C, TAYLOR R L. The Finite Element Method for Fluid Dynamics[M]. 6th ed. Barcelona: Butterworth-Heinemann, 2000.
|
[3]AZIZ K, SETTARI A. Petroleum Reservoir Simulation[M]. London: Applied Science Publishers,1979.
|
[4]VINSOME P K W. Orthomin: an iterative method for solving sparse banded sets of simultaneous linear equations[C]//Proceedings Fourth Symposium on Reservoir Simulation, Society of Petroleum Engineers of AIME. 1976: 149-159.
|
[5]许建红, 程林松, 周颖, 等. 一种求解低渗透油藏启动压力梯度的新方法[J]. 石油勘探与开发, 2007,34(5): 594-597.(XU Jianhong, CHENG Linsong, ZHOU Ying, et al. A new method for calculating kickoff pressure gradient in low permeability reservoirs[J]. Petroleum Exploration and Development,2007,34(5): 594-597.(in Chinese))
|
[6]BEHIE A, VINSOME P K W. Block iterative methods for fully implicit reservoir simulation[J]. Society of Petroleum Engineers Journal,1982, 22(5): 658-668.
|
[7]BHOGESWARA R, KILLOUGH J E. Parallel linear solvers for reservoir simulation: a generic approach for existing and emerging computer architectures[J]. SPE Computer Applications,1994,6(1): 5-11.
|
[8]CAO H, TCHELEPI H, WALLIS J, et al. Parallel scalable unstructured CPR-type linear solver for reservoir simulation[C]//SPE Annual Technical Conference and Exhibition. 2005.
|
[9]SIROVICH L. Turbulence and dynamics of coherent structures, part 1: coherent structures[J]. Quarterly of Applied Mathematics,1987, 45(3): 561-571.
|
[10]SIROVICH L. Turbulence and dynamics of coherent structures, part 2: symmetries and transformations[J]. Quarterly of Applied Mathematics,1987, 45(3): 573-582.
|
[11]SIROVICH L. Turbulence and dynamics of coherent structures, part 3: dynamics and scaling[J]. Quarterly of Applied Mathematics,1987, 45(3): 583-590.
|
[12]SIROVICH L. Analysis of turbulent flows by means of the empirical eigenfunctions[J]. Fluid Dynamics Research,1991,8(1/4): 85-100.
|
[13]GHARBI R B, QASEM F, SMAOUI N. Characterizing miscible displacements in heterogeneous reservoirs using the Karhunen-Loéve decomposition[J]. Petroleum Science and Technology,2003, 21(5/6): 747-776.
|
[14]VERMEULEN P T M, HEEMINK A W, TE STROET C B M. Reduced models for linear groundwater flow models using empirical orthogonal functions[J]. Advances in Water Resources,2004,27(1): 57-69.
|
[15]WU Z, LAURENCE D, UTYUZHNIKOV S, et al. Proper orthogonal decomposition and dynamic mode decomposition of jet in channel crossflow[J]. Nuclear Engineering and Design,2019, 344: 54-68.
|
[16]丁鹏, 陶文铨. 一种预测流动和传热问题的快速算法[J]. 西安交通大学学报, 2007, 41(3): 271-273.(DING Peng, TAO Wenquan. Fast algorithm for prediction of fluid flow and heat transfer[J]. Journal of Xi’an Jiaotong University,2007,41(3): 271-273.(in Chinese))
|
[17]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 Wenquan. 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))
|
[18]吴学红, 陶文铨, 吕彦力, 等. 不可压缩流动问题快速计算的降阶模型[J]. 中国电机工程学报, 2010,30(26): 69-74.(WU Xuehong, TAO Wenquan, Lü Yanli, et al. Reduced order model for fast computation of incompressible fluid flow problem[J]. Proceedings of the CSEE,2010,30(26): 69-74.(in Chinese))
|
[19]HEIJN T, MARKOVINOVI C R, JANSEN J D. Generation of low-order reservoir models using system-theoretical concepts[J]. SPE Journal,2004, 9(2): 202-218.
|
[20]LEASK S B, MCDONELL V G, SAMUELSEN S. On the use of dynamic mode decomposition for liquid injection[J]. Automization and Sprays,2019,29(11): 965-985.
|
[21]VAN DOREN J F M, MARKOVINOVI C R, JANSEN J D. Reduced-order optimal control of water flooding using proper orthogonal decomposition[J]. Computational Geosciences,2006, 10(1): 137-158.
|
[22]贾欣鑫, 王鑫, 王虎, 等. 两相水驱油低阶模型计算方法研究[J]. 科学技术与工程, 2017,17(6): 55-60.(JIA Xinxin, WANG Xin, WANG Hu, et al. The calculation method for reduced model of the water flooding[J]. Science Technology and Engineering,2017,17(6): 55-60.(in Chinese))
|
[23]孙宪航, 徐明海, 贾欣鑫, 等. 预测水驱油藏中油、水流动问题的快速方法[J]. 应用数学和力学, 2015,36(12): 1228-1237.(SUN Xianhang, XU Minghai, JIA Xinxin, et al. 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.(in Chinese))
|
[24]SUN X, XU M. Optimal control of water flooding reservoir using proper orthogonal decomposition[J]. Journal of Computational and Applied Mathematics,2017, 320: 120-137.
|