大规模油藏数值模拟的块压缩存储及求解
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摘要
针对三相黑油模型模拟时大规模对角稀疏线性方程组存储占用大量内存、求解耗时的问题,研究大规模稀疏系数矩阵的压缩存储及求解方法。提出了有效节点压缩和块压缩存储结合的压缩存储方法,以油藏节点为单元,利用3个实数组分别存储稀疏矩阵块主对角元素、下三角及上三角的非零块元素;由于模拟中形成的系数矩阵具有位置对称性,利用3个整型数组存储下三角非零块元素的地址信息,减少了内存损耗及运算中非零元素的搜索次数。在此基础上,采用Krylov子空间块广义极小余量GMRES迭代法结合块不完全LU预处理方法求解上述线性方程组。结果表明,解法收敛速度快、稳定性好,可以提高大型稀疏线性方程组的求解速度。经过黑油模型标准考题的测试证实,该方法能够有效求解大规模油藏数值模拟问题。
The block compressed storage and solving methods in reservoir simulation are explored to resolve large sparse linear equations emerging in three-phase black oil model.In this paper,the active nodes are compressed firstly,and then the block main diagonal elements,nonzero block elements in lower triangular and upper triangular are separately stored into three real arrays.Owing to the coefficient matrix arising in the reservoir simulation being symmetrical,the addresses of block elements in lower triangular are deposited in three integer arrays.This block compressed storage method can save lots of memory and reduce the search frequencies of non-zero elements.On the basis of such compression storage,the block incomplete LU preconditioned generalized minimal residual method(GMRES) is adopted to solve the equations,showing that it is an effective method possessing fast convergence and good stability.Testing of black oil model example reveals that the block compressed storage and solving methods are effective in solving the large-scale reservoir simulation.
The block compressed storage and solving methods in reservoir simulation are explored to resolve large sparse linear equations emerging in three-phase black oil model.In this paper,the active nodes are compressed firstly,and then the block main diagonal elements,nonzero block elements in lower triangular and upper triangular are separately stored into three real arrays.Owing to the coefficient matrix arising in the reservoir simulation being symmetrical,the addresses of block elements in lower triangular are deposited in three integer arrays.This block compressed storage method can save lots of memory and reduce the search frequencies of non-zero elements.On the basis of such compression storage,the block incomplete LU preconditioned generalized minimal residual method(GMRES) is adopted to solve the equations,showing that it is an effective method possessing fast convergence and good stability.Testing of black oil model example reveals that the block compressed storage and solving methods are effective in solving the large-scale reservoir simulation.
引文
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[14]林小兵.二维多相油藏数值模拟的BILUCG算法[J].石油勘探与开发,1987,14(1):76-84.Lin Xiaobing.BILUCG algorithm for 2-D multiphase reservoirsimulation[J].Petroleum Exploration and Development,1987,14(1):76-84.
[2]Chen Zhangxin,Huan Guanren,Ma Yuanle.Computational methodsfor multiphase flows in porous media[M].Philadelphia:Society forIndustrial and Applied Mathematics,2006:1-2.
[3]Kazemi A,Stephen K D.油藏数值模拟自动历史拟合方法:以Nelson油田为例[J].石油勘探与开发,2012,39(3):326-337.Kazemi A,Stephen K D.Schemes for automatic history matching ofreservoir modeling:A case of Nelson oilfield in the UK[J].Petroleum Exploration and Development,2012,39(3):326-337.
[4]Li Xiaobo,Wu Shuhong,Song Jie,et al.Numerical simulation ofpore-scale flow in chemical flooding process[J].Theor.Appl.Mech.Lett.,2011,1(2):022008.
[5]Wang Baohua,LüShujuan,Lu Qishao,et al.Long time behavior offinite difference solution for a semilinear parabolic equation[J].DCDIS-A,2007,14(S2):141-147.
[6]纪淑红,田昌炳,石成方,等.高含水阶段重新认识水驱油效率[J].石油勘探与开发,2012,39(3):338-345.Ji Shuhong,Tian Changbing,Shi Chengfang,et al.Newunderstanding on water-oil displacement efficiency in a highwater-cut stage[J].Petroleum Exploration and Development,2012,39(3):338-345.
[7]李巧云,张吉群,邓宝荣,等.高含水油田层系重组方案的灰色决策优选法[J].石油勘探与开发,2011,38(4):463-468.Li Qiaoyun,Zhang Jiqun,Deng Baorong,et al.Greydecision-making theory in the optimization of strata seriesrecombination programs of high water-cut oilfields[J].PetroleumExploration and Development,2011,38(4):463-468.
[8]Wu Shuhong,Han Min,Ma Desheng,et al.Streamflooding toenhance recovery of a waterflooded light-oil reservoir[J].JPT,2012(1):64-66.
[9]韩大匡.关于高含水油田二次开发理念、对策和技术路线的探讨[J].石油勘探与开发,2010,37(5):583-591.Han Dakuang.Discussions on concepts,countermeasures andtechnical routes for the redevelopment of high water-cut oilfields[J].Petroleum Exploration and Development,2010,37(5):583-591.
[10]邹存友,常毓文,王国辉,等.水驱开发油田合理油水井数比的计算[J].石油勘探与开发,2011,38(2):211-215.Zou Cunyou,Chang Yuwen,Wang Guohui,et al.Calculation on areasonable production-injection well ratio in waterflooding oilfields[J].Petroleum Exploration and Development,2011,38(2):211-215.
[11]成谷,张宝金.反射地震走时层析成像中的大型稀疏系数矩阵压缩存储和求解[J].地球物理学进展,2008,23(3):674-680.Cheng Gu,Zhang Baojin.Compression storage and solution of largesparse matrix in traveltime tomography of reflection seismic data[J].Progress in Geophysics,2008,23(3):674-680.
[12]Saad Y,Gmres M S.A generalized minimal residual algorithm forsolving nonsymmetric linear systems[J].Siam J.Sci.Stat.Comput.,1986,7(3):856-869.
[13]Li Wenjun,Chen Zhangxi,Richard E E,et al.Comparision of theGMRES and ORTHOMIN for the black oil model in porous media[J].Int.J.Numer.Meth.Fluids.,2005,48(5):501-519.
[14]林小兵.二维多相油藏数值模拟的BILUCG算法[J].石油勘探与开发,1987,14(1):76-84.Lin Xiaobing.BILUCG algorithm for 2-D multiphase reservoirsimulation[J].Petroleum Exploration and Development,1987,14(1):76-84.
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