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Effects of source cavity shape on steady, three‐dimensional flow of soil gases
Author(s) -
Warrick A. W.,
Rojano A.
Publication year - 1999
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/1999wr900045
Subject(s) - line source , mechanics , radius , point source , flow (mathematics) , porous medium , line (geometry) , thermal conduction , spherical geometry , physics , steady state (chemistry) , geometry , spherical model , materials science , optics , thermodynamics , porosity , chemistry , mathematics , computer security , computer science , condensed matter physics , composite material
For a point or a spherical source in infinite space the steady state potential is simply a constant over the distance from the source. Flow of soil gases was studied by comparing results for other cavity shapes for sources (or sinks) to the spherical solution. Cavity shapes included a vertical line source of finite length, a prolate spheroid with a vertical axis of rotation, and a vertical well also of finite length and radius. Questions addressed include the distance over which the differences between a sphere and the alternatives become negligible and what radius of spherical source at a given pressure results in the same flow rate as from the other shapes. For a vertical line source the pressure is within 5% of the pressure for the spherical source at a distance of 2.5 times the vertical line and within 1% beyond 6 times the vertical line. Similar results were expressed for the other shapes relative to a spherical source. Travel times are presented in a generalized relationship illustrated for spherical and finite line sources. The results are relevant to other potential problems as well, for example, steady water flow in saturated porous media, steady water flow in unsaturated porous media without gravity, heat conduction, diffusion, and electrostatics.