一种快速求解交联聚合物驱数学模型的方法
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摘要
针对油藏数学模型求解效率低下的问题,研究了快速求解交联聚合物驱数学模型的方法。根据交联聚合物驱的调驱机理,建立了三维两相五组分(油、水、聚合物、交联剂和交联聚合物)的交联聚合物驱数学模型,模型的求解采用隐式压力、显式饱和度和显式浓度的求解方法。其中,压力的求解提出了计算效率更高、更稳定的Douglas差分格式,利用分步降维的思路求解。与商业化的油藏数值模拟软件CMG相比,采用Douglas差分格式并结合追赶法求解交联聚合物驱数学模型,可以大幅度提高模型的计算效率,为快速求解交联聚合物驱油藏数学模型提供了一种有效方法。
To solve the problem of the poor computational efficiency in solving reservoir mathematical model,we studied a fast solution. A three-dimension,two-phase(oleic,aqueous)and five-component(oil,water,polymer,cross-linked polymer,cross-linker)mathematical model was presented according to the profile control and flooding mechanism of cross-linked polymer flooding. Based on IMPES method,a more efficient and more stable Douglas difference scheme was proposed which uses the step-by-step reduced-order idea to solve a model. The simulation result shows that compared with commercial simulator CMG,the Douglas difference scheme in combination with chase method can greatly improve the solution efficiency,which provides an effective way to solve a reservoir mathematical model.
To solve the problem of the poor computational efficiency in solving reservoir mathematical model,we studied a fast solution. A three-dimension,two-phase(oleic,aqueous)and five-component(oil,water,polymer,cross-linked polymer,cross-linker)mathematical model was presented according to the profile control and flooding mechanism of cross-linked polymer flooding. Based on IMPES method,a more efficient and more stable Douglas difference scheme was proposed which uses the step-by-step reduced-order idea to solve a model. The simulation result shows that compared with commercial simulator CMG,the Douglas difference scheme in combination with chase method can greatly improve the solution efficiency,which provides an effective way to solve a reservoir mathematical model.
引文
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[16]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,2008.
[17]苏雪霞,王旭,周亚贤,等.国内提高采收率用交联聚合物驱油体系研究进展[J].精细石油化工进展,2007,8(4):22–25.Su Xuexia,Wang Xu,Zhou Yaxian,et al.Research progress on improving oil recovery by using crosslinked polymer oil-displacing system in China[J].Advances in Fine Petrochemicals,2007,8(4):22–25.
[18]Peaceman D W,Rachford H H.The numerical solution of parabolic and elliptic differential equations[J].Journal of the Society for Industrial and Applied Mathematics,1955,3(1):28–41.
[19]Douglas J,Rachford H H.On the numerical solution of heat condition problems in two and three space variables[J].Transactions of the American Mathematical Society,1956,82:421–439.
[2]周志齐,张毅.胜利油田交联聚合物调驱技术研究及应用[J].西安石油学院学报:自然科学版,2000,15(5):21–24.Zhou Zhiqi,Zhang Yi.Study on crosslinked polymer oil displacement and its application in Shengli Oil Field[J].Journal of Xi′an Petroleum Institure:Natural Science Edition,2000,15(5):21–24.
[3]Moradi-Araghi A.A review of thermally stable gels for fluid diversion in petroleum production[J].Journal of Petroleum Science and Engineering,2000,26(1–4):1–10.
[4]Alqam M H,Nasr-El-Din H A,Lynn J D.Treatment of super K-zones using gelling polymers[C].SPE 64989,2001.
[5]Reddy B R,Eoff L,Dalrymple E D,et al.A Natural polymer-based cross-linker system for conformance gel systems[J].SPE Journal,2003,8(2):99–106.
[6]孙志斌,郑延欣,李明远,等.交联聚合物溶液封堵多孔介质机理研究[J].高分子材料科学与工程,2005,21(2):225–228,232.Sun Zhibin,Zheng Yanxin,Li Mingyuan,et al.Study on mechanism of plugging porous media of linked polymer solution[J].Polymeric Materials Science and Engineering,2005,21(2):225–228,232.
[7]马艳,陈祖华,李超,等.交联聚合物驱技术的矿场应用效果及开采特征[J].西南石油学院学报,2006,28(6):78–80.Ma Yan,Chen Zuhua,Li Chao,et al.Field application and production behavior of cross-linking polymer flooding technology[J].Journal of Southwest Petroleum Institute,2006,28(6):78–80.
[8]王代流,肖建洪.交联聚合物微球深部调驱技术及其应用[J].油气地质与采收率,2008,15(2):86–88.Wang Dailiu,Xiao Jianhong.Application of deep-profile control and displacement technology of crosslinked polymer micro-ball system[J].Petroleum Geology and Recovery Efficiency,2008,15(2):86–88.
[9]李科星,钱志鸿,杜金阳,等.交联聚合物动态成胶及运移的室内模拟研究[J].西南石油大学学报:自然科学版,2012,34(4):115–121.Li Kexing,Qian Zhihong,Du Jinyang,et al.Laboratory study on dynamic gelation behavior and transfer process of corsslinked polymer[J].Journal of Southwest Petroleum University:Science&Technology Edition,2012,34(4):115–121.
[10]Yuan Shiyi,Han Dong,Wang Qiang,et al.Numerical simulation study on weak gel injection[C].SPE 64291,2000.
[11]Yuan Shiyi,Han Dong,Wang Qiang,et al.Numerical simulator for the combination process of profile control and polymer flooding[C].SPE 64792,2000.
[12]宋立新.交联聚合物驱数学模型研究[J].特种油气藏,2003,10(4):38–40.Song Lixin.Mathematical model of cross-linked polymer drive[J].Special Oil and Gas Reservoirs,2003,10(4):38–40.
[13]Xie C J,GUAN Z L,Blunt M,et al.Numerical simulation of oil recovery after cross-linked polymer flooding[J].Journal of Canadian Petroleum Technology,2009,48(4):37–41.
[14]廉培庆,同登科,李琳琳.高温高岩油藏交联聚合物驱研究进展[J].精细石油化工进展,2010,11(7):4–7.Lian Peiqing,Tong Dengke,Li Linlin.Development of crosslinked polymer flooding in high temperature and high salt reservoirs[J].Advances in Fine Petrochemicals,2010,11(7):4–7.
[15]莫则尧,刘兴平,彭力田,等.优化和并行一个油藏数值模拟软件中的解法器[J].石油学报,2000,21(2):56–61.Mo Zeyao,Liu Xingping,Peng Litian,et al.Optimizing and paralleling a sparse liner equations solver package for reservoir simulating software[J].Acta Petrolei Sinica,2000,21(2):56–61.
[16]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,2008.
[17]苏雪霞,王旭,周亚贤,等.国内提高采收率用交联聚合物驱油体系研究进展[J].精细石油化工进展,2007,8(4):22–25.Su Xuexia,Wang Xu,Zhou Yaxian,et al.Research progress on improving oil recovery by using crosslinked polymer oil-displacing system in China[J].Advances in Fine Petrochemicals,2007,8(4):22–25.
[18]Peaceman D W,Rachford H H.The numerical solution of parabolic and elliptic differential equations[J].Journal of the Society for Industrial and Applied Mathematics,1955,3(1):28–41.
[19]Douglas J,Rachford H H.On the numerical solution of heat condition problems in two and three space variables[J].Transactions of the American Mathematical Society,1956,82:421–439.