A Lagging Model for Describing Drawdown Induced by a Constant-Rate Pumping in a Leaky Confined Aquifer

What changes when flux and gradient need not respond at the same instant?

Can a pumping-test model represent a delayed relation between radial water flux and the drawdown gradient while retaining finite-well effects?

A finite pumping well in a leaky confined aquifer

A leaky confined aquifer pumped at a constant rate through a finite-radius well, with wellbore storage and skin included at the pumping well.

Separate response times in the radial constitutive relation

The formulation assigns one macroscopic response time to radial flux and another to the drawdown gradient, then embeds that relation in a finite-well pumping-test solution.

Equal response times cancel in the constitutive relation. Setting both to zero gives the Classical Darcy limit.

Early-time agreement improved in the field comparison

For the Rapid City field case, the lagging formulation improved the early-time fit across five observation wells relative to the Classical Darcy response used for comparison.

Animated research summary

The animation explains the paper's physical and mathematical logic. Conceptual curves are not presented as new field observations.