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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2016, Vol. 33 ›› Issue (3): 221-233.doi: 10.3969/j.issn.1005-3085.2016.03.001

• •    下一篇

非均质表皮层径向双层承压井流数学模型的半解析解

王玉林1,  谢康和2,  黄大中3,  李传勋4   

  1. 1- 武夷学院土木工程与建筑学院，福建 武夷山 354300
    2- 浙江大学软弱土与环境土工教育部重点实验室，杭州 310027
    3- 铁道第三勘察设计院集团有限公司，天津 300251
    4- 江苏大学土木工程与力学学院，镇江 212013
  • 收稿日期:2014-03-25 接受日期:2015-11-23 出版日期:2016-06-15 发布日期:2016-08-15
  • 基金资助:
    浙江省自然科学基金重点项目 (Z5080175)；福建省自然科学基金 (2012J05096)；福建省教育厅科技项目 (JA13322).

A Mathematical Model and its Semi-analytical Solution for the Flow of Anisotropic Confined Aquifer with Two Radial Layers Considering Heterogeneity of Well Skin

WANG Yu-lin1,  XIE Kang-he2,  HUANG Da-zhong3,  LI Chuan-xun4   

  1. 1- College of Civil Engineering and Architecture, Wuyi University, Wuyishan, Fujian 354300
    2- MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou 310027
    3- Third Railway Survey and Design Institute Group Corporation, Tianjin 300251
    4- Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013
  • Received:2014-03-25 Accepted:2015-11-23 Online:2016-06-15 Published:2016-08-15
  • Supported by:
    The Natural Science Foundation of Zhejiang Province (Z5080175); the Natural Science Foundation of Fujian Province (2012J05096); the Natural Science Foundation Sponsored by the Educational Department of Fujian Province (JA13322).

PDF (PC)

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摘要：

考虑表皮层和未扰动承压层的非均质性、各向异性以及竖向越流补给作用，建立了径向双层承压三维井流的数学模型，采用Laplace变换和矩阵理论求得表皮层和未扰动承压层的水头降以及井壁流量的半解析解．应用所求解编制计算程序，分析了表皮层沿竖向随机变化的渗透性对承压层井流的影响，结果表明：表皮层非均质变化形态决定了表皮层内和其附近处的水头降以及井壁流量的竖向分布规律，表皮层对承压层渗流产生的影响范围与承压层的竖向渗透系数大小有关；改善井周岩土介质渗透性或增大“负表皮层”厚度可提高抽水井产量；表皮层径向渗透系数较小时，承压层的水头降幅度主要取决于承压层径向渗透系数的大小，而当表皮层径向渗透系数较大时，承压层径向渗透系数和竖向渗透系数均对承压层水头降有较大影响．

关键词: 各向异性, 非均质, 表皮效应, 矩阵微分方程, Laplace变换, 承压含水层

Abstract:

Considering the properties of heterogeneity and anisotropy of wellbore skin, a mathematical model for the unsteady 3D flow in an anisotropic confined aquifer with two radial layers is developed. Using the Laplace transform technique and matrix theory, the solutions of drawdown for skin zone and formation zone, as well as the distribution of flux along well screen, are derived. Basing on the derived solutions, a numerical program is developed, and the flow subjected to stochastic change of permeability of layered skin zone is analyzed. The results indicate that: the vertical distribution of drawdown within skin zone and its vicinity, as well as the flux along well screen depend on the vertical heterogeneity of skin zone. While the influence range of skin zone is closely related with the vertical permeability of confined aquifer. Improvement of permeability or increasing thickness of negative skin can effectively raise well production. The magnitude of drawdown is mainly decided by the vertical permeability of formation zone and less influenced by the radial permeability of formation zone when radial permeability in skin zone is low, while the drawdown is obviously affected by not only the vertical permeability but also the radial permeability of formation zone when radial permeability in skin zone is comparatively large.

Key words: anisotropy, heterogeneity, skin effect, matrix differential equation, Laplace transformation, confined aquifer

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