Water Resources Management

, Volume 33, Issue 10, pp 3615–3631

# Transient-state Analytical Solution for Arbitrarily-Located Multiwells in Triangular-Shaped Unconfined Aquifer

• Ali Mahdavi
Article

## Abstract

This work presents an analytical solution for the linearized Boussinesq equation describing the nature of well hydraulics in equilateral triangular-shaped unconfined aquifer. This homogeneous, isotropic, fully-saturated porous media is hydraulically connected to three surrounding streams of constant-head. The solution enables modeling aquifer response to a system of arbitrarily-located, fully-penetrating multiwells (injection, extraction or combination of both), each characterized by stepwise time-varying rate. First, a fundamental solution is provided for multiwell-induced head distribution in an infinite aquifer domain. Image well theory is then efficiently implemented to create an equivalent flow field for the intended domain. Spatiotemporal head distribution is obtained in the form of fivefold series involving exponential integrals. Expressions are also derived to quantify stream depletion rates caused by a single pumping well, under both transient and steady-state conditions. As a hypothetical example, an aquifer remediation scheme is planned by combining two extraction wells with an injection one. The computed head profiles reveal strictly close agreement with numerical results obtained by finite element method. Sensitivity map for stream depletion rate is also discussed. The present results are found to exactly reproduce those available for the wedge-shaped domain, under certain geometric constraint. Finally, the solution is extended to the case of hemi-equilateral triangular-shaped aquifer with or without an impervious boundary line.

## Keywords

Multiwell hydraulics Analytical solution Triangular aquifer Image wells Stream depletion rate Linearized Boussinesq equation

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