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

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  • Ali Mahdavi

    (Arak University)

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.

Suggested Citation

  • Ali Mahdavi, 2019. "Transient-state Analytical Solution for Arbitrarily-Located Multiwells in Triangular-Shaped Unconfined Aquifer," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(10), pages 3615-3631, August.
    • Handle: RePEc:spr:waterr:v:33:y:2019:i:10:d:10.1007_s11269-019-02324-6
    DOI: 10.1007/s11269-019-02324-6
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    References listed on IDEAS

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    1. Ali Mahdavi & Hamid Seyyedian, 2013. "Transient-State Analytical Solution for Groundwater Recharge in Triangular-Shaped Aquifers Using the Concept of Expanded Domain," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(8), pages 2785-2806, June.
    2. Ali Mahdavi, 2019. "Response of Triangular-Shaped Leaky Aquifers to Rainfall-Induced Groundwater Recharge: an Analytical Study," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(6), pages 2153-2173, April.
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