Approximate discharge for constant head test with recharging boundary
1Centre for Hydrogeology, University of Neuchâtel, 11 rue Emile Argand, Neuchâtel, CH 2000 Switzerland. philippe.renard@unine.ch
Ground Water
|May 11, 2005
Summary
A new approximate solution simplifies calculating groundwater discharge to wells and tunnels near constant head boundaries. This method offers a 2% maximum error, improving upon complex Laplace transform solutions for aquifer analysis.
Area of Science:
- Hydrogeology
- Groundwater modeling
- Aquifer hydraulics
Background:
- Calculating groundwater discharge to wells or tunnels with constant head boundaries typically uses complex Laplace transform solutions.
- These solutions are crucial for interpreting well tests and estimating groundwater inflow into tunnels.
Purpose of the Study:
- To develop a simple approximate solution for groundwater discharge calculations.
- To provide a more accessible alternative to numerical inversion of Laplace transforms.
Main Methods:
- The proposed solution is an approximation derived from an exact analytical solution.
- It involves a weighted mean of early-time and late-time asymptotic behaviors.
Main Results:
- The approximate solution achieves a maximum relative error of approximately 2% compared to the exact analytical solution.
- This demonstrates its accuracy and reliability for practical applications.
Conclusions:
- The developed approximate solution offers a significant simplification for analyzing groundwater flow to wells and tunnels.
- It provides a valuable tool for hydrogeologists and engineers, enhancing the interpretation of field data and the estimation of groundwater resources.
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