THEORETICAL ANALYSIS OF AN IMPERVIOUS,HEATED-CYLINDER ‘GROUNDWATER VELOCIMETER’

An isothermally heated, impervious cylinder, which is placed normal to the path of flowing groundwater, is theoretically evaluated for its potential to serve as a kind of ‘groundwater velocimeter’. The essential task is to determine whether the variation in heat output along the cylinder perimeter is sufficiently large to permit measurement for typical groundwater velocities. Using finite elements, the governing equations of advective thermal transport in saturated porous media are solved to obtain the variation in heat output along the circumference of the heated cylinder. An annular region of different hydraulic conductivity is assumed to separate the cylinder from the surrounding formation. The creation of such a region during placement of a cylinder is inevitable. A parametric study led to the following conclusions: (1) A smaller cylinder radius is preferable since the time to achieve a particular degree of asymmetry in heat output is then greatly reduced. (2) An annular region of lower hydraulic conductivity, relative to formation, reduces output asymmetry by no more than 25%, but if hydraulic conductivity is increased, output asymmetry can increase several times. (3) For annular regions having a higher hydraulic conductivity than the surrounding formation, annular thickness is not important. (4) The least groundwater speed which may be accurately measured by such a device will depend heavily upon instrumentation but is tentatively placed at about 5⋅0×10⁻⁵ cm/s. Theoretical results are approximately confirmed by preliminary experiments with a prototype device which has been constructed so as to directly measure the expected variation in thermal output. Partial construction details are provided.