Exact solution for two-dimensional flow to a well in an anisotropic domain

Area of Science:

• Hydrogeology
• Computational Fluid Dynamics
• Geosciences

Background:

• Analytic element method (AEM) is widely used for groundwater flow modeling.
• Current AEM applications often assume isotropic hydraulic conductivity.
• Modeling anisotropic domains with AEM typically uses coordinate transformations, which can lead to inaccuracies near wells.

Purpose of the Study:

• To develop a novel analytic solution for steady-state groundwater flow to a well in an anisotropic domain.
• To address the shortcomings of existing coordinate transformation methods in meeting the constant head boundary condition at the well.
• To provide a more accurate model for flow fields close to pumping wells in anisotropic aquifers.

Main Methods:

• The study employs a conformal mapping technique.
• A new analytic solution is derived for two-dimensional steady flow.
• The solution is specifically designed to satisfy governing equations and boundary conditions.

Main Results:

• The presented solution accurately models steady flow to a well in anisotropic media.
• It precisely satisfies the constant head boundary condition at the well radius.
• This overcomes the limitations of standard coordinate transformation methods in near-well regions.

Conclusions:

• The new analytic solution offers a significant improvement for modeling groundwater flow in anisotropic domains using the analytic element method.
• It provides accurate results for both far-field and near-well flow conditions.
• This method enhances the reliability of estimating head at pumping wells in complex hydrogeological settings.