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

Mathias, S.A.; Wen, Z.

doi:10.1016/j.jhydrol.2015.02.015

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

Authors

Professor Simon Mathias s.a.mathias@durham.ac.uk
Professor

Z. Wen

Abstract

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.

Citation

Mathias, S., & Wen, Z. (2015). Numerical simulation of Forchheimer flow to a partially penetrating well with a mixed-type boundary condition. Journal of Hydrology, 524, 53-61. https://doi.org/10.1016/j.jhydrol.2015.02.015

Journal Article Type	Article
Acceptance Date	Feb 7, 2015
Publication Date	May 14, 2015
Deposit Date	Feb 27, 2015
Publicly Available Date	Mar 3, 2015
Journal	Journal of Hydrology
Print ISSN	0022-1694
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	524
Pages	53-61
DOI	https://doi.org/10.1016/j.jhydrol.2015.02.015
Keywords	Forchheimer equation, Partially penetrating well, Non-Darcy flow.

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Copyright 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.