Jr. Feldkamp, THEORETICAL-ANALYSIS OF AN IMPERVIOUS, HEATED-CYLINDER GROUNDWATER VELOCIMETER, International journal for numerical and analytical methods in geomechanics, 20(11), 1996, pp. 815-830
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.