Solutions for Groundwater Flow to a Pumping Well with an Exponentially Decreasing Variable-Rate in a Sloping Aquifer

Area of Science:

• Hydrogeology
• Groundwater Hydrology
• Environmental Engineering

Background:

• Aquifer pumping tests often involve decreasing rates and sloping terrains, factors often studied independently.
• The combined effects of variable pumping rates and aquifer slope on groundwater flow lack sufficient academic investigation.

Purpose of the Study:

• To develop a two-dimensional groundwater flow model for a sloping aquifer with an exponentially decreasing variable pumping rate.
• To provide a more accurate analytical solution for analyzing pumping test data in complex aquifer conditions.

Main Methods:

• Developed a semi-analytical solution using Laplace transform and finite Fourier cosine transform, incorporating a linearized free-surface boundary.
• Created a numerical model to precisely depict the linearized boundary and account for water table decline.

Main Results:

• The time-drawdown curve shows a downward trend at intermediate times under variable pumping rates.
• Linearization errors are acceptable for slopes less than π/6, validating the analytical model's applicability.
• The new solution effectively interprets field pumping test data and laboratory results, outperforming previous models for constant rates.

Conclusions:

• The developed semi-analytical solution accurately models groundwater flow in sloping aquifers with variable pumping rates.
• This model enhances the accuracy of hydraulic parameter inversion, especially when compared to methods using average pumping rates.
• The findings are crucial for understanding and managing groundwater resources in heterogeneous and dynamic aquifer systems.