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<p>This study investigates non-Darcian flow to a well in confined aquifers, considering radial hydraulic conductivity variations. A stratified computational model based on the Izbash equation is developed and then solved by using the transformed differential quadrature method (TDQM). Initially, a linearization approximation approach is used to handle the continuity equation of groundwater flow based on Izbash's law. The Laplace transform is then applied, and the radial direction is discretized according to the discretization rules of the TDQM. After introducing the boundary and interlayer continuity conditions, an overall solution matrix is constructed. By solving the matrix equation and applying the inverse integral transform, the non-Darcian drawdown solution for the confined aquifer with variable hydraulic conductivity is derived. After several validations, case studies are designed to analyze the effects of various parameters on drawdown, including comparisons between stratified and equivalent models, sensitivity analysis of hydraulic conductivity and the non-Darcian coefficient across different radial zones, and the influence of wellbore skin.</p>

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An exact solution for non-Darcian flow to a well in confined aquifers with variable permeability

  • 期刊论文

  • 发表日期：

    2026年3月20日

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  • Qing Wang,
  • Zhenming Shi,
  • Yongzhi Zhao

摘要

This study investigates non-Darcian flow to a well in confined aquifers, considering radial hydraulic conductivity variations. A stratified computational model based on the Izbash equation is developed and then solved by using the transformed differential quadrature method (TDQM). Initially, a linearization approximation approach is used to handle the continuity equation of groundwater flow based on Izbash's law. The Laplace transform is then applied, and the radial direction is discretized according to the discretization rules of the TDQM. After introducing the boundary and interlayer continuity conditions, an overall solution matrix is constructed. By solving the matrix equation and applying the inverse integral transform, the non-Darcian drawdown solution for the confined aquifer with variable hydraulic conductivity is derived. After several validations, case studies are designed to analyze the effects of various parameters on drawdown, including comparisons between stratified and equivalent models, sensitivity analysis of hydraulic conductivity and the non-Darcian coefficient across different radial zones, and the influence of wellbore skin.