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 p otential to serve as a kind of 'groundwater velocimeter'. The essentia l task is to determine whether the variation in heat output along the cylinder perimeter is sufficiently large to permit measurement for typ ical groundwater velocities. Using finite elements, the governing equa tions of advective thermal transport in saturated porous media are sol ved to obtain the variation in heat output along the circumference of the heated cylinder. An annular region of different hydraulic conducti vity is assumed to separate the cylinder from the surrounding formatio n. The creation of such a region during placement of a cylinder is ine vitable. A parametric study led to the following conclusions: (1) A sm aller cylinder radius is preferable since the time to achieve a partic ular degree of asymmetry in heat output is then greatly reduced, (2) A n annular region of lower hydraulic conductivity, relative to formatio n, reduces output asymmetry by no more than 25%, but if hydraulic cond uctivity 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 lea st groundwater speed which may be accurately measured by such a device will depend heavily upon instrumentation but is tentatively placed at about 5.0 x 10(-5) cm/s. Theoretical results are approximately confir med by preliminary experiments with a prototype device which has been constructed so as to directly measure the expected variation in therma l output. Partial construction details are provided.