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Journal of Engineering Mathematics

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01-02-2022

Fluid injection through a line source into a wet porous medium

Authors: Catherine A. Browne, Lawrence K. Forbes

Published in: Journal of Engineering Mathematics | Issue 1/2022

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Abstract

We consider a fluid solution that is injected through a horizontal line sink into an already saturated porous medium. The injected fluid is denser than the ambient fluid, and so it develops into a vertical plume as time progresses. Boussinesq theory is used to approximate this two-fluid system, and we develop a semi-analytical spectral technique to solve the resulting system of equations numerically. Accurate plume shapes are obtained, and their dependence on the injection rate and the density ratio of the two fluids is illustrated. A large-time asymptotic solution is also presented, and it is shown to agree very closely with the numerical results after sufficient time.

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Title: Fluid injection through a line source into a wet porous medium
Authors: Catherine A. Browne
Lawrence K. Forbes
Publication date: 01-02-2022
Publisher: Springer Netherlands
Published in: Journal of Engineering Mathematics / Issue 1/2022
Print ISSN: 0022-0833
Electronic ISSN: 1573-2703
DOI: https://doi.org/10.1007/s10665-021-10200-9

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