While the effect of small-scale skin has been extensively investigated, numerical models incorporating the effect require expensive computational cost due to fine spatial discretization of the skin and have not been widely available. This study develops a new model for slug tests at a partially-penetrating well in a two-zone confined aquifer of skin and formation zones. A new basic formulation defines transient flow in the skin with an additional skin factor reflecting the skin storage effect. The formulation assumes horizontal flow in the skin with excluding the vertical skin hydraulic conductivity. The analytical solution and finite element solution of the model are developed. The analytical expression relating the skin factor to the skin specific storage is derived. Results suggest the formulation is a useful alternative to conventional flow equation for the skin in achieving coarse spatial discretization and low computational cost. The present solution agrees well with the field head data obtained from Butler (2019). To conclude, this study presents theoretical advance and efficient simulation in modeling of well hydraulics.

虽然小尺度皮肤的影响已被广泛研究，但由于皮肤的精细空间离散化，包含该影响的数值模型需要昂贵的计算成本，并且尚未广泛使用。本研究开发了一种新模型，用于在表层和地层区域的两层承压含水层中的部分穿透井中进行段塞测试。一种新的基本配方定义了皮肤中的瞬态流动，并带有反映皮肤储存效应的额外皮肤因子。该公式假定皮肤中的水平流动，不包括垂直皮肤水力传导率。建立了模型的解析解和有限元解。导出了将皮肤因子与皮肤特定存储相关联的解析表达式。结果表明，在实现粗略的空间离散化和低计算成本方面，该公式是皮肤常规流动方程的有用替代方案。目前的解决方案与从 Butler (2019) 获得的现场头部数据非常吻合。总之，本研究提出了井水力学建模的理论进步和有效模拟。