油藏数值模拟中BILU0-GMRES方法的应用

doi:10.7623/syxb201305017

石油学报 ›› 2013, Vol. 34 ›› Issue (5): 954-958.DOI: 10.7623/syxb201305017

油藏数值模拟中BILU0-GMRES方法的应用

王宝华, 吴淑红, 李巧云, 李小波, 李华

中国石油勘探开发研究院提高石油采收率国家重点实验室北京 100083

收稿日期:2013-02-24 修回日期:2013-05-10 出版日期:2013-09-25 发布日期:2013-08-01
通讯作者: 王宝华
作者简介:王宝华,女,1978年2月生,2000年毕业于黑龙江大学,2010年获北京航空航天大学博士学位,现为中国石油勘探开发研究院博士后,主要从事油藏数值模拟方面的研究。Email:baohuawang@petrochina.com.cn
基金资助:
中国石油天然气股份有限公司科技攻关项目(2011A-1010);中国石油勘探开发研究院院级课题项目(2011Y-012)及北京市科学技术委员会重大专项(Z121100004912001)资助。

Applications of BILU0-GMRES in reservoir numerical simulation

WANG Baohua, WU Shuhong, LI Qiaoyun, LI Xiaobo, LI Hua

PetroChina Research Institute of Petroleum Exploration & Development; State Key Laboratory of Enhanced Oil Recovery, Beijing 100083, China

Received:2013-02-24 Revised:2013-05-10 Online:2013-09-25 Published:2013-08-01

摘要/Abstract

摘要：

在油藏数值模拟中通常需要将数学模型转化为大规模线性方程组,求解这些方程组将耗费大量的时间。考虑到黑油模型的物理特性,将其在油藏节点上离散得到的子阵视为构成系数矩阵的基本元素,利用块不完全LU0(BILU0)预处理方法与块广义极小残量法(BGMRES)相结合,迭代求解方程组得到BILU0-GMRES方法。该方法具有更强的稳定性和收敛性,它能提高系数矩阵迭代的速度,减少迭代收敛的次数,并且矩阵规模越大,这种优势越明显。对严重非均质边底水油藏SPE9的测试结果表明,块预处理GMRES方法具有较高的精度,能够准确模拟油藏的开发过程并对生产动态作出预测。

关键词: 块ILU0预处理, 块广义极小残量法, 油藏数值模拟, 注水开发, 生产动态

Abstract:

Mathematical models in reservoir numerical simulation usually have to be translated into large-scale linear equations, and it takes lots of time to solve them. Taking physical characteristics of the black oil model into account, sub-matrices (block) can bedispersed from reservoir nodes as integral elements that constitute a coefficient matrix, herein the sub-matrix scale is determined by control equations and unknowns. The block incomplete LU0 (BILU0) preconditioning was combined with the block generalized minimal residual method (BGMRES) to iteratively solve the equations, and the comparison illustrated that the BILU0-GMRES method obtained is of greater stability and convergence, it can accelerate the iteration speed of a coefficient matrix and reduce the frequency of iterative convergence, moreover, the greater the scale of a matrix, the better the advantage of this approach. The testing performed on a reference example (SPE9) of a reservoir with severely heterogeneous edge and bottom water indicated that the block ILU0-GMRES method is of higher accuracy and it can well and truly simulate the development process of a reservoir and predict the production performance precisely.

Key words: block ILU0 preconditioning, block generalized minimal residual method, reservoir numerical simulation, water-flooding development, production performance

中图分类号:

TE319

王宝华, 吴淑红, 李巧云, 李小波, 李华. 油藏数值模拟中BILU0-GMRES方法的应用[J]. 石油学报, 2013, 34(5): 954-958.

WANG Baohua, WU Shuhong, LI Qiaoyun, LI Xiaobo, LI Hua. Applications of BILU0-GMRES in reservoir numerical simulation[J]. Editorial office of ACTA PETROLEI SINICA, 2013, 34(5): 954-958.

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油藏数值模拟中BILU0-GMRES方法的应用

Applications of BILU0-GMRES in reservoir numerical simulation

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