Unified Analytical Solution for Radial Flow to a Well in a Confined Aquifer

TL;DR

This paper introduces a comprehensive analytical solution for modeling drawdown in anisotropic confined aquifers caused by well pumping, incorporating wellbore storage and partial penetration effects, and compares it with existing models.

Contribution

It provides a unified analytical solution that generalizes previous models by including wellbore storage, partial penetration, and anisotropy effects in aquifer drawdown analysis.

Findings

Solution reduces to classical models under specific conditions.

Graphical analysis shows effects of partial penetration, storage, and anisotropy.

Numerical inversion enables practical application of the solution.

Abstract

Drawdowns generated by extracting water from a large diameter (e.g. water supply) well are affected by wellbore storage. We present an analytical solution in Laplace transformed space for drawdown in a uniform anisotropic aquifer caused by withdrawing water at a constant rate from a partially penetrating well with storage. The solution is back transformed into the time domain numerically. When the pumping well is fully penetrating our solution reduces to that of Papadopulos and Cooper [1967]; Hantush [1964] when the pumping well has no wellbore storage; Theis [1935] when both conditions are fulfilled and Yang et.al. [2006] when the pumping well is partially penetrating, has finite radius but lacks storage. We use our solution to explore graphically the effects of partial penetration, wellbore storage and anisotropy on time evolutions of drawdown in the pumping well and in observation wells.