An accurate solute transport model is critical to the interpretation of single-well push-pull (SWPP) test. Previous studies of SWPP test generally consider solitary aquifer that is confined by impermeable layers. Also, existing solutions for solute transport in aquifer-aquitard systems only consider the injection phase and over-simplify the flow field by assuming uniformly distributed velocity in the aquitard. In this study, we developed a numerical model with Dirichlet boundary condition for SWPP test affected by leakage described by a low-permeability non-Darcian expression involving a threshold pressure gradient (I₀). Our SWPP test model considered transient flow in multi-phases, which include injection, chase, rest and extraction phases. Finite-difference scheme was adopted to solve the models of flow and solute transport. The results indicate that an increasing hydraulic diffusivity leads to a greater peak value of breakthrough curve (BTC) while a medium with larger grain size results in less estimation error when using steady-state flow model to interpret the transient SWPP test. Additionally, A greater I₀ makes the solute stored in aquitard more difficult to be extracted out due to dispersion dominance, which results in higher BTC values. For the purpose of application, a lumped dimensionless index called the non-Darcian index (NDI) was proposed to quantify the overestimation degree by neglecting leakage, and the underestimation degree by accounting for Darcian leakage, when interpreting the SWPP test with low-permeability non-Darcian leakage. The long-term slope of breakthrough curve coupled with the NDI can be employed to determine the cases in which the low-permeability non-Darcian leakage should be considered.

准确的溶质传输模型对于解释单井推挽（SWPP）测试至关重要。先前对SWPP测试的研究通常考虑由不可渗透层限制的孤立含水层。同样，在含水层－阿奎塔尔系统中用于溶质运移的现有解决方案仅考虑注入阶段，并通过假设在阿奎塔尔中均匀分布的速度来过分简化流场。在这项研究中，我们开发了一种具有Dirichlet边界条件的数值模型，用于SWPP测试受泄漏影响，该泄漏由低渗透性非Darcian表达式所描述，涉及阈值压力梯度（I ₀）。我们的SWPP测试模型考虑了多阶段的瞬态流动，包括注入，追逐，静止和提取阶段。采用有限差分法求解流动和溶质运移的模型。结果表明，当使用稳态流模型解释瞬态SWPP测试时，增大的水力扩散系数会导致更大的突破曲线（BTC）峰值，而具有较大晶粒尺寸的介质会导致较小的估计误差。另外，我更大₀由于分散度优势，使存储在无水芒草中的溶质更难以提取出来，从而导致更高的BTC值。出于应用的目的，在解释低渗透率非SWPP测试时，提出了一种称为非达西指数（NDI）的集总无量纲指数，以通过忽略泄漏来量化高估程度，并通过考虑Darcian泄漏来量化低估程度。 -达西泄漏。突破曲线的长期斜率与NDI结合可用于确定应考虑低渗透性非达西漏的情况。