摘要
考虑表皮效应竖向非均匀分布,建立各向异性承压层3D稳态井流数学模型,为求得问题的解,首先将表皮效应系数视为分段连续函数,再根据该分段函数将承压层划分成N层,然后通过差分法将问题转化为求解矩阵微分方程边界值问题,最后通过矩阵理论求得相应问题的解。应用数学软件对所求得解进行编程,并应用于实例计算和分析中。结果表明,在距竖井较近处,承压层水头降和流量沿竖向分布均与表皮效应系数函数变化趋势相反,即承压层某深度处的表皮效应系数越大(小),则相应位置的水头降和流量越小(大);而距竖井较远处,仅当竖向渗透系数相对于水平渗透系数较小时,才仍具有前述变化规律;承压层不同深度处的水头降沿径向的分布曲线的幅度值,不仅取决于该处的表皮效应系数大小,而且取决于竖向渗透系数与水平渗透系数相对值大小。
With consideration of nonuniform skin effect factor, the mathematical model for 3D radial flow for anisotropic confined aquifer is presented. To attain solution for the corresponding problem, the skin effect factor is deemed as piecewise continuous functions, according to which the confined aquifer is divided into N layers. Then the method of finite difference is used to transfer the original problem into matrix differential equation with boundary conditions; and finally, by matrix theory, the solution is attained. With mathematical software, the solution is applied to numerical examples. Results show that： In the region close to vertical well, the variation of drawdown and flux component is inversely related to the skin effect factor; that is, larger skin effect factor leads to smaller drawdown and flux, vice versa, while in the region far from vertical well, the same tendency of variation keeps only for the situation that vertical permeability is far smaller than radial permeability. Therefore, the amplitude value of the curves s＊- r＊ for different layers of confined aquifer depends on both the value of skin effect factor and the ratio of vertical permeability to radial permeability.
出处
《岩土力学》
EI
CAS
CSCD
北大核心
2011年第7期2133-2138,共6页
Rock and Soil Mechanics
基金
浙江省自然科学基金重点项目(No.Z5080175)
教育部高校博士点专项基金项目(No.20070335179)
关键词
表皮效应系数
数学模型
矩阵微分方程
有限差分法
承压含水层
skin effect factor
mathematical model
matrix differential equation
finite difference method
confined aquifer
