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两套节点格林元嵌入式离散裂缝模型数值模拟方法

程林松 杜旭林 饶翔 曹仁义 贾品

程林松, 杜旭林, 饶翔, 曹仁义, 贾品. 两套节点格林元嵌入式离散裂缝模型数值模拟方法. 力学学报, 2022, 54(10): 2892-2903 doi: 10.6052/0459-1879-22-250
引用本文: 程林松, 杜旭林, 饶翔, 曹仁义, 贾品. 两套节点格林元嵌入式离散裂缝模型数值模拟方法. 力学学报, 2022, 54(10): 2892-2903 doi: 10.6052/0459-1879-22-250
Cheng Linsong, Du Xulin, Rao Xiang, Cao Renyi, Jia Pin. A numerical simulation approach for embedded discrete fracture model coupled Green element method based on two sets of nodes. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 2892-2903 doi: 10.6052/0459-1879-22-250
Citation: Cheng Linsong, Du Xulin, Rao Xiang, Cao Renyi, Jia Pin. A numerical simulation approach for embedded discrete fracture model coupled Green element method based on two sets of nodes. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(10): 2892-2903 doi: 10.6052/0459-1879-22-250

两套节点格林元嵌入式离散裂缝模型数值模拟方法

doi: 10.6052/0459-1879-22-250
基金项目: 国家自然科学基金(52174038)和中国石油科技重大项目(ZLZX2020-02-04)资助
详细信息
    作者简介:

    程林松, 教授, 主要研究方向: 油气渗流理论与应用. E-mail: lscheng@cup.edu.cn

    杜旭林, 博士, 主要研究方向: 多孔介质渗流力学及数值模拟方法. E-mail: duxulin_cup@foxmail.com

  • 中图分类号: TE319

A NUMERICAL SIMULATION APPROACH FOR EMBEDDED DISCRETE FRACTURE MODEL COUPLED GREEN ELEMENT METHOD BASED ON TWO SETS OF NODES

  • 摘要: 对于原始嵌入式离散裂缝模型(EDFM), 在计算包含裂缝单元的基质网格内的压力分布时采用了线性分布假设, 这导致了油藏开发早期对非稳态窜流量的计算精度不足. 因此, 本文提出了一种两套节点格林元法的EDFM数值模拟方法. 两套节点格林元法的核心思想是将压力节点与流量节点区分开, 一套压力节点设置在单元顶点, 另一套流量节点设置在网格边的中点, 满足局部物质守恒、具有二阶精度的同时, 可适用于任意网格类型. 本文将两套节点格林元法与EDFM耦合, 采用了非稳态渗流控制方程的边界积分形式推导了基质网格与裂缝网格之间传质量的新格式, 代替了线性分布假设以提高模拟精度; 此外, 修正后的EDFM能适应任意形态的基质网格剖分, 拓展了原始EDFM仅适用于矩形基质网格、难以考虑复杂油藏边界的局限性. 研究表明: 通过对比商业模拟软件tNavigator® LGR模块与原始EDFM, 验证了本文模型具有较高的早期计算精度; 以复杂油藏边界−缝网−SRV分区模型为例, 通过对比SFEM-COMSOL商业模拟软件, 验证了本文模型处理复杂问题的适应性. 本文研究可用于裂缝性油藏开发动态的精确模拟.

     

  • 图  1  压力和流量两套节点三角形单元示意图

    Figure  1.  Sketch of pressure and flux two sets of nodes in triangle cell

    图  2  基于改进格林元法的二维EDFM

    Figure  2.  Two-dimensional EDFM based on the modified GEM

    图  3  两套节点格林元方法中相邻单元方程组耦合示意图

    Figure  3.  Sketch of coupling adjacent element equations in two sets of nodes-based GEM

    图  4  裂缝交汇的星三角变换原理图

    Figure  4.  Schematics of star-delta transformation for fracture segments intersecting

    图  5  压裂水平井示意图

    Figure  5.  Sketch of fractured horizontal well

    图  6  三种不同模型压力分布对比图(1000 d)

    Figure  6.  Comparison of pressure distribution maps for three various simulators (1000 d)

    6  三种不同模型压力分布对比图(1000 d)(续)

    6.  Comparison of pressure distribution maps for three various simulators (1000 d) (continued)

    图  7  三种不同模型产油速度的对比图(1000 d)

    Figure  7.  Comparison of oil rate for three various simulators (1000 d)

    图  8  三种不同模型压力分布对比图(10 d)

    Figure  8.  Comparison of pressure distribution maps for three various simulators (10 d)

    图  9  井筒流量早期结果对比

    Figure  9.  Comparison of early-time results for wellbore flow rate

    图  10  原始EDFM和修正EDFM之间的误差比较

    Figure  10.  Error comparison between the original EDFM and the modified EDFM

    11  储层域示意图

    11.  Sketch of reservoir domain

    图  12  不同模型的网格剖分对比图

    Figure  12.  Comparison diagram of mesh division for different simulators

    12  不同模型的网格剖分对比图(续)

    12.  Comparison diagram of mesh division for different simulators (continued)

    图  13  修正EDFM与COMSOL产油速度的对比图(1000 d)

    Figure  13.  Comparison of oil rate between modified EDFM and COMSOL (1000 d)

    图  14  基础模型压力分布场图

    Figure  14.  Diagram of pressure distribution field for basic model

    图  15  不同SRV分区模型的压力分布对比(100 d)

    Figure  15.  Comparison of pressure distribution of different SRV zoning models (100 d)

    图  16  不同SRV对应的产量动态特征对比

    Figure  16.  Comparison of dynamic production characteristics corresponding to different SRV

    表  1  数值算例的输入参数

    Table  1.   Input parameters of numerical case

    PropertiesValuePropertiesValue
    reservoir thickness/m10initial reservoir pressure/MPa20
    matrix porosity0.15matrix permeability/mD1
    rock compressibility coefficient/MPa−11.08 × 10−4fracture aperture/m0.005
    fracture porosity0.45fracture permeability/mD70000
    oil viscosity/(mPa·s)2oil compressibility coefficient/MPa−13 × 10−3
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-06-05
  • 录用日期:  2022-08-24
  • 网络出版日期:  2022-08-25
  • 刊出日期:  2022-10-18

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