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三维压裂缝网不稳定压力半解析求解方法

王志凯 程林松 曹仁义 王进 贾品 王选茹

王志凯, 程林松, 曹仁义, 王进, 贾品, 王选茹. 三维压裂缝网不稳定压力半解析求解方法. 力学学报, 2021, 53(8): 1-11 doi: 10.6052/0459-1879-21-183
引用本文: 王志凯, 程林松, 曹仁义, 王进, 贾品, 王选茹. 三维压裂缝网不稳定压力半解析求解方法. 力学学报, 2021, 53(8): 1-11 doi: 10.6052/0459-1879-21-183
Wang Zhikai, Cheng Linsong, Cao Renyi, Wang Jin, Jia Pin, Wang Xuanru. Semi-analytical method for unstable pressure of 3D fracture network. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(8): 1-11 doi: 10.6052/0459-1879-21-183
Citation: Wang Zhikai, Cheng Linsong, Cao Renyi, Wang Jin, Jia Pin, Wang Xuanru. Semi-analytical method for unstable pressure of 3D fracture network. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(8): 1-11 doi: 10.6052/0459-1879-21-183

三维压裂缝网不稳定压力半解析求解方法

doi: 10.6052/0459-1879-21-183
基金项目: 国家自然科学基金资助项目(U1762210)和(ZY19-XA411-FW1128)资助项目
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

    曹仁义, 副教授, 主要研究方向: 油气渗流理论与应用. E-mail: caorenyi@126.com

  • 中图分类号: TE33

SEMI-ANALYTICAL METHOD FOR UNSTABLE PRESSURE OF 3D FRACTURE NETWORK

  • 摘要: 受地应力及压裂工艺影响, 大斜度井水力压裂缝网展布复杂, 缝网中存在不同倾斜方向、不同展布形态及不同贯穿程度的压裂缝. 本文通过将裂缝面离散为若干矩形微元实现裂缝形态有效表征, 将渗流过程划分为基质向裂缝流动及裂缝向井筒流动两阶段, 采用有限差分方法构建离散裂缝面内不稳定渗流数值解, 结合封闭边界面源函数及叠加原理构建基质内不稳定渗流解析解, 耦合裂缝内流动数值解与基质内流动解析解, 求解了三维压裂缝网不稳定压力. 基于积分中值定理提出了点源、特殊线源代替面源求解基质内渗流的求解方法, 分析了该方法的可行性及适用条件, 在保证模型精度的同时提升了计算效率. 研究表明, 在基质内采用点源函数面积分求解面源的方法可准确求解三维压裂缝网井底压力动态但计算效率极低, 基于积分中值定理的点源、特殊线源近似面源求解方法可大大提升计算效率, 且在裂缝微元划分较为精细(微元无因次边长小于0.15)时可取得较高精度, 基于该模型分析了裂缝导流能力、裂缝倾角、裂缝高度及裂缝段间距对压裂大斜度井典型试井曲线的影响.

     

  • 图  1  多段压裂井三维缝物理模型

    Figure  1.  Physical model of multi-fractured well with 3D fractures

    图  2  椭圆缝离散表征

    Figure  2.  Discrete characterization of elliptical fracture

    图  3  裂缝微元局部坐标系示意图

    Figure  3.  Schematic diagram of local coordinate system of fracture elements

    图  4  坐标轴转换示意图

    Figure  4.  Schematic diagram of coordinate axis transformation

    图  5  本文模型与Teng模型结果对比

    Figure  5.  Comparison of the result of our model with Teng model

    图  6  本文模型与Al Rbeawi模型结果对比

    Figure  6.  Comparison of the result of our model with Al Rbeawi model

    图  7  网格划分对线源求解效果影响

    Figure  7.  Effect of meshing on line source solution

    图  8  回流段流动示意图

    Figure  8.  Diagram of flow in flowback period

    图  9  简化模型求解效果示意图

    Figure  9.  Diagram of simplified model

    图  10  单一倾斜缝流动阶段划分

    Figure  10.  Identification of the flow regimes of incline fracture

    图  11  多段压裂倾斜缝流动阶段

    Figure  11.  Flow regimes of multi-stage incline fractures

    图  12  裂缝导流能力敏感性分析

    Figure  12.  Sensitivity analysis of well storage coefficient

    图  13  裂缝倾角敏感性分析

    Figure  13.  Sensitivity analysis of well storage coefficient

    图  14  裂缝高度敏感性分析

    Figure  14.  Sensitivity analysis of fracture height

    图  15  段间距敏感性分析

    Figure  15.  Sensitivity analysis of fracturing interval

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  • 收稿日期:  2021-04-28
  • 录用日期:  2021-06-25
  • 网络出版日期:  2021-07-07

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