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.

参考文献

[1] 韩大匡,陈钦雷,闫存章.油藏数值模拟基础[M].北京:石油工业出版社,1999:241-242.
Han Dakuang,Chen Qinlei,Yan Cunzhang.The basis of reservoir simulation[M].Beijing:Petroleum Industry Press,1999:241-242.
[2] Chen Zhangxin,Huan Guanren,Ma Yuanle.Computational methods for multiphase flows in porous media[M].Philadelphia:Society for Industrial and Applied Mathematics,2006:1-2.
[3] Li Xiaobo,Wu Shuhong,Song Jie,et al.Numerical simulation of pore-scale flow in chemical flooding process[J].Theor.Appl.Mech.Lett., 2011,1(2):68-72.
[4] Wu Shuhong,Han Min,Ma Desheng,et al.Streamflooding to enhance recovery of a waterflooded light-oil reservoir[J]. JPT,2012,64(1):64-66.
[5] 关文龙,吴淑红,蒋有伟,等.高含水油藏转注蒸汽三维物理模拟研究[J].石油学报,2009,30(3):404-408.
Guan Wenlong,Wu Shuhong,Jiang Youwei,et al.3D physical model of steam injection in high water-cut reservoir[J].Acta Petrolei Sinica,2009,30(3):404-408.
[6] 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.Grey decision-making theory in the optimization of strata series recombination programs of high water-cut oilfields[J].Petroleum Exploration and Development,2011,38(4):463-468.
[7] Wang Baohua,Lü Shujuan,Lu Qishao,et al.Long time behavior of finite difference solution for a semilinear parabolic equation[J].DCDIS A Supplement,Advances in Dynamical Systems,2007,14(S2):141-147.
[8] 杨仁锋,姜瑞忠,刘世华,等.特低渗透油藏非线性渗流数值模拟[J].石油学报,2011,32(2):299-306.
Yang Renfeng,Jiang Ruizhong,Liu Shihua,et al.Numerical simulation of nonlinear seepage in ultra-low permeability reservoirs[J].Acta Petrolei Sinica,2011,32(2):299-306.
[9] 姚军,张娜,黄朝琴,等.非均质油藏多尺度混合有限元数值模拟方法[J].石油学报,2012,33(3):442-447.
Yao Jun,Zhang Na,Huang Zhaoqin,et al.Multiscale mixed finite element numerical simulation for heterogeneous reservoirs[J].Acta Petrolei Sinica,2012,33(3):442-447.
[10] 于洪敏,任韶然,左景栾.空气泡沫驱数学模型与数值模拟方法[J].石油学报,2012,33(4):653-657.
Yu Hongmin,Ren Shaoran,Zuo jingluan.A mathematical model and numerical simulation method for air-foam flooding[J].Acta Petrolei Sinica,2012,33(4):653-657.
[11] Saad Y.Iterative methods for sparse linear systems[M].New York:PWS Publishing,2000:269-278.
[12] Cai Mingchao,Mu Mo,Xu Jinchao.Preconditioning techniques for a mixed Stokes/Darcy model in porous media applications[J].J.Comput.Appl.Math.,2009,233(2):346-355.
[13] Saad Y,Schultz M H.GMRES:a generalized minimal residual algorithm for solving nonsymmetric linear systems[J].Siamj.Sci.Stat.Comput,1986,7(3):856-869.
[14] Li W J,Chen Z X,Huan G R,et al.Comparison of the GMRES and ORTHOMIN for the black oil model on unstructured grids[J].Int.J.Numer.Meth.Fluids,2006,52(9):941-962.

[1]	余义常, 郭睿, 林敏捷, 沈毅, 沈博珩, 朱光亚, 李峰峰, 王一帆, 颜元. 中东地区碳酸盐岩储层孔喉结构特征及开发对策 ——以伊拉克X油田M组为例[J]. 石油学报, 2023, 44(2): 369-384.
[2]	孙亮, 李勇, 李保柱. 中东地区碳酸盐岩油藏分类评价方法与注水开发对策[J]. 石油学报, 2022, 43(2): 270-280.
[3]	王付勇, 曾繁超, 赵久玉. 低渗透/致密油藏驱替-渗吸数学模型及其应用[J]. 石油学报, 2020, 41(11): 1396-1405.
[4]	王建民, 张三. 特低渗透砂岩油层钻井液侵入程度及影响[J]. 石油学报, 2019, 40(9): 1095-1103.
[5]	苏皓, 雷征东, 李俊超, 龚斌, 赵文琪, 鞠斌山, 张荻萩, 秦鹤. 储集层多尺度裂缝高效数值模拟模型[J]. 石油学报, 2019, 40(5): 587-593,634.
[6]	陈汶滨, 赵明, 蔡明俊, 潘红, 倪天禄, 罗波. 基于指标特征模型的油藏注水开发效果定量化评价[J]. 石油学报, 2016, 37(S2): 80-86,111.
[7]	姚　军　张　娜　黄朝琴　王月英. 非均质油藏多尺度混合有限元数值模拟方法[J]. 石油学报, 2012, 33(3): 442-447.
[8]	蒋友兰　田世澄　唐湘明. 气顶底水油藏注水开发影响因素——以韦8断块为例[J]. 石油学报, 2012, 33(2): 284-287.
[9]	姜瑞忠杨仁锋刘世华张晓亮. 油藏数值模拟模型转化过程中非平衡现象[J]. 石油学报, 2010, 31(4): 617-622.
[10]	李少华张昌民 Clayton V.Deutsch. 基于储层静态地质参数的一种随机建模结果排序方法[J]. 石油学报, 2010, 31(3): 445-448.
[11]	任岚赵金洲胡永全罗伟. 压裂井生产动态模拟的天然差分法[J]. 石油学报, 2010, 31(3): 501-505.
[12]	白振强, 王清华, 杜庆龙, 郝兰英, 张善严, 朱伟, 于德水, 王贺军. 曲流河砂体三维构型地质建模及数值模拟研究[J]. 石油学报, 2009, 30(6): 898-902,907.
[13]	吴忠宝, 胡文瑞, 宋新民, 冉启全, 甘俊奇. 天然微裂缝发育的低渗透油藏数值模拟[J]. 石油学报, 2009, 30(5): 727-730,734.
[14]	左景栾, 樊泽霞, 任韶然, 闫方平, 丁岗, 徐亮, 胡开明, 王希强. 纯梁油田樊41块油井挤注防垢技术[J]. 石油学报, 2008, 29(4): 615-618,624.
[15]	侯健, 郭兰磊, 元福卿, 杜庆军, 于波. 胜利油田不同类型油藏聚合物驱生产动态的定量表征[J]. 石油学报, 2008, 29(4): 577-581.

油藏数值模拟中BILU0-GMRES方法的应用

Applications of BILU0-GMRES in reservoir numerical simulation

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价