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Numerical simulation of Forchheimer flow to a partially penetrating well with a mixed-type boundary condition.

Mathias, S.A. and Wen, Z. (2015) 'Numerical simulation of Forchheimer flow to a partially penetrating well with a mixed-type boundary condition.', Journal of hydrology., 524 . pp. 53-61.


This article presents a numerical study to investigate the combined role of partial well penetration (PWP) and non-Darcy effects concerning the performance of groundwater production wells. A finite difference model is developed in MATLAB to solve the two-dimensional mixed-type boundary value problem associated with flow to a partially penetrating well within a cylindrical confined aquifer. Non-Darcy effects are incorporated using the Forchheimer equation. The model is verified by comparison to results from existing semi-analytical solutions concerning the same problem but assuming Darcy’s law. A sensitivity analysis is presented to explore the problem of concern. For constant pressure production, Non-Darcy effects lead to a reduction in production rate, as compared to an equivalent problem solved using Darcy’s law. For fully penetrating wells, this reduction in production rate becomes less significant with time. However, for partially penetrating wells, the reduction in production rate persists for much larger times. For constant production rate scenarios, the combined effect of PWP and non-Darcy flow takes the form of a constant additional drawdown term. An approximate solution for this loss term is obtained by performing linear regression on the modeling results.

Item Type:Article
Keywords:Forchheimer equation, Partially penetrating well, Non-Darcy flow.
Full text:(AM) Accepted Manuscript
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Publisher statement:NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Hydrology. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Hydrology, 524, May 2015, 10.1016/j.jhydrol.2015.02.015.
Record Created:02 Mar 2015 15:50
Last Modified:04 May 2015 16:19

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