考虑非均匀表皮效应的承压稳态井流差分解  

Finite Difference Solution for Steady Well Flow in Confined Aquifer with Consideration of Non-Uniform Skin Effect

作　　者：王玉林[1] 谢康和[2] 李传勋[3] 黄大中 钟瑜隆 

机构地区：[1]武夷学院土木工程与建筑学院,福建武夷山354300 [2]浙江大学海滨和城市岩土工程研究中心,杭州310027 [3]江苏大学土木工程系,江苏镇江212013 [4]铁道第三勘察设计集团有限公司,天津300142

出　　处：《地下空间与工程学报》2016年第1期20-24,54,共6页Chinese Journal of Underground Space and Engineering

基　　金：福建省自然科学基金(2012J05096);南平市科技项目(N2010Z10(8));浙江省自然科学基金重点项目(Z5080175);福建教育厅A类项目(JA13322)

摘　　要：鉴于现有的井流模型理论通常将竖井井周的表皮层视为各向同性、厚度竖向均匀分布,与工程实际不符合,其对承压层水头降和竖井产能的计算和分析产生较大误差,笔者考虑了井周表皮层非均匀分布、竖向越流作用和承压层各向异性,建立了相应的承压含水层地下水稳态井流模型,采用有限差分方法,将三维渗流偏微分方程转化为矩阵微分方程,通过矩阵理论求得承压层渗流数学模型的半解析解。应用数学软件编制程序,将得到问题解应用于实例分析,结果表明:承压层表皮层扰动区半径、渗透系数及其竖向分布形态对承压层水头降及竖井产能都有明显的影响。In the existing model theory for the radial flow in an aquifer,the assumption has frequently been made that the skin region around penetrating well is uniform and isotropic,which distinctly differs from the real situation and brings a great error in evaluating the drawdown of hydraulic head and the production of vertical well. For improving the accuracy in engineering evaluation,the new model for radial flow under constant head drawdown is presented,in which the non-uniform distribution of skin effect and anisotropy of confined aquifer is considered. By the method of finite difference,the differential equation for 3D flow is transferred into matrix differential equation,and then the corresponding solution is attained by matrix theory. Using the mathematical software in compiling a program,the formulas for the flow are applied to some examples,and the result shows that the skin thickness,permeability of skin and their distribution pattern obviously influence both the hydraulic drowdown and prodution of vertical well.

关 键 词：差分法 表皮效应 矩阵微分方程 各向异性 定降深 稳态流 

分 类 号：TV12[水利工程—水文学及水资源] TU46[建筑科学—结构工程]