摘要
考虑了抽水井表皮层的非均质、各向异性和上覆弱透水层的越流作用,建立径向双层各向异性非稳定承压井流模型。对竖向空间变量采用有限差分法将三维渗流偏微分方程初边值问题转化为矩阵偏微分方程初边值问题。应用拉普拉斯变换和矩阵理论求得径向扰动层(表皮层)和非扰动层各自水头降的半解析解。应用所求解对表皮层径向渗透系数沿抽水井线性变化和随机变化两种情形进行实例计算和分析,结果表明,负表皮效应使承压含水层的水头降增幅变大,导致水头降曲线在径向交界处出现上折;而正表皮效应使承压含水层的水头降增幅变小,导致水头降曲线在径向交界处出现下折;某一层位处的承压含水层水头降,既受同水平层的表皮层渗透系数影响,又受到相邻上下层的表皮层渗透系数的影响。
A mathematical model for unsteady well flow in anisotropic confined aquifer with finite thickness of skin is presented considering the heterogeneity and anisotropy of wellbore skin. By the method of finite difference,initial boundary value problem of 3D flow differential equations is transformed into the initial boundary value problem of matrix differential equation. The Laplace transform technique and matrix theory are both adopted,and semianalytical solutions of drawdown for skin zone and formation zone are derived. Two cases that linear distribution and stochastic distribution of permeability of skin zone are taken as numerical examples. The results show that： negative skin effect leads to the increase of drawdown and the curve of drawdown-distance appears upturned tendency on the interface between skin zone and formation zone; while the positive skin leads to decrease of drawdown and curves of drawdown-distance bend down on the interface; Drawdown of hydraulic head in a certain sublayer of aquifer is affected not only by the skin with the identical depth but also by adjacently horizontal skins.
出处
《地下空间与工程学报》
CSCD
北大核心
2016年第6期1497-1503,共7页
Chinese Journal of Underground Space and Engineering
基金
浙江省自然科学基金重点项目(Z5080175)
福建省自然科学基金(2012J05096)
南平市科技项目(N2010Z10(9))
关键词
表皮层
半解析解
矩阵微分方程
径向双层
承压含水层
skin zone
seepage
matrix differential equation
radial double layers
confined aquifer
