Approximate solution for solute transport during spherical-flow push-pull tests

Area of Science:

• Hydrogeology
• Environmental Engineering
• Geochemistry

Background:

• Accurate modeling of solute transport is crucial for understanding groundwater contamination and remediation.
• Single-well push-pull tests are valuable tools for in-situ aquifer characterization.
• Existing models often assume radial or linear flow, which may not fully represent complex field conditions.

Purpose of the Study:

• To derive an approximate analytical solution for the advection-dispersion equation under spherical-flow conditions.
• To evaluate the applicability of the spherical-flow solution to single-well push-pull tests, particularly in packed intervals or partially penetrating wells.
• To compare the performance of the spherical-flow solution against its cylindrical-flow counterpart using numerical simulations.

Main Methods:

• Derivation of an approximate analytical solution for solute transport under spherical flow.
• Conducting two-dimensional numerical simulations of solute transport in single-well push-pull tests.
• Comparing simulated extraction-phase breakthrough curves with the derived spherical-flow solution and a cylindrical-flow model.

Main Results:

• The derived spherical-flow solution demonstrated good agreement with simulated breakthrough curves when the injection/extraction region length was small relative to aquifer thickness and solute frontal position.
• Discrepancies between the spherical-flow solution and simulations increased with greater anisotropy in hydraulic conductivities.
• The spherical-flow solution provides a valuable approximation for specific single-well test scenarios, especially where radial assumptions are less appropriate.

Conclusions:

• The developed analytical solution offers a practical approach for analyzing solute transport in spherical flow during single-well push-pull tests.
• The solution's applicability is contingent on aquifer geometry and hydraulic properties, with limitations noted for highly anisotropic conditions.
• Users should exercise caution and consider the inherent assumptions of isotropy and homogeneity when applying this spherical-flow solution.