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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。
Considering the heterogeneity, anisotropy, and overburden of the overlying aquitard in the surface layer of the pumping well, a radial bilayer anisotropic unsteady confined well flow model was established. The finite difference method for vertical space variables is used to transform the initial boundary value problem of three-dimensional seepage partial differential equations into the initial boundary value problem of matrix partial differential equations. The semi-analytical solution of the head drop of the radial perturbation layer (skin layer) and the non-perturbation layer is obtained by applying the Laplace transform and matrix theory. The calculation and analysis of the radial permeability coefficient of the epidermis along the linear and random changes of the pumping well were carried out by the application. The results showed that the negative skin effect caused the increase of the head drop of the confined aquifer to be larger, resulting in the head drop curve. At the radial boundary, a top fold occurs; the positive skin effect causes the head of the confined aquifer to decrease in amplitude, resulting in a drop in the head drop curve at the radial junction; the head of the confined aquifer at a certain level drops. It is affected not only by the permeability coefficient of the skin layer in the same horizontal layer but also by the permeability coefficient of the skin layer in the adjacent upper and lower layers.