A Tool and a Method for Obtaining Hydrologic Flow Velocity Measurements in Geothermal Reservoirs Page: 4 of 9
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PROCEEDINGS, Eleventh Workshop on Geothermal Reservoir Engineering
Stanford University, Stanford, California, January :21-23, 1986
A TOOL AND A METHOD FOR OBTAINING HYDROLOGIC
FLOW VELOCITY MEASUREMENTS IN GEOTHERMAL RESERVOIRS
C. R. Carriganl, J. C. Dunn2 and H. C. Hardeel
(2) Exploratory Energy
Downhole instruments based on a
thermal perturbation principle are
being developed to measure heat flow
in permeable formations where
convective transport of heat is
important. To make heat flow
measurements in these regions, the
ground water velocity vector must be
determined. A downhole probe has
been designed to measure the local
ground water velocity vector. 'The
probe is a cylindrical heat source
operated at a constant heat flux.
In a convecting environment, surface
temperatures on the probe are
perturbed from those values of a
purely conductive environment. With
the aid of analytical and numerical
models, these temperature
differences can be related to the
local velocity vector.
Hot wire or hot film anemometry is
commonly used in engineering
applications to determine flow
velocities of gases in pipes,
channels and other configurations.
A simple hot wire anemometer
measures the velocity of a gas
indirectly by relating the power
supplied to the sensor to the
velocity of the fluid in a direction
normal to the sensor (Dally et al,
1984). Heat produced by ohmic
dissipation within the sensor
element is removed by the flow of
cooler gas past the element. The
resultant cooling of the element
causes a change in its electrical
resistance that can be related to
the fluid velocity. We describe
here a tool based on a similar
approach that can be used to
estimate flow velocity in a
permeable medium. It is found that
application of the hot wire approach
is relatively uncomplicated if the
tool is placed in a permeable
formation so that the porous matrix
surrounding it is left more or less
undisturbed. This circumstance
could be achieved for a shallow well
drilled into a sandy zone with
backfilling of the hole.
Calculations indicate that the tool
can also be used in the wire-line
mode in an uncased hole if the
effects of the well pressure
distribution on the pressure field
in the porous medium are considered.
ANALYSIS OF OPERATION
A three dimensional analytical model
for flow in a permeable medium past
a heated prolate spheroidal body has
been developed by Romero (1983a).
The geometry of the problem solved
by Romero is illustrated in Figure
1. Here a slender body of radius,
a, and length, 21, is aligned
parallel to the vertical axis, z.
The azimuthal coordinate of the
Darcy velocity is given by $ while
its angle to the vertical is given
by 80. The dimensionless
quantity n,. which defines the
axial location on the probe, is
scaled by the half length, 1.
In a saturated porous medium,
Darcy's law and the Boussinesq
approximation are assumed to apply.
For a given velocity Um , which
characterizes Darcy flow in the far
field of the tool, a solution for
the pressure and temperature fields
in the vicinity of the heated tool
was obtained. In particular, the
solution for the temperature
distribution on the tool surface as
a function of both the far field
velocity and prescribed heat flux
across the tool surface is
required. There are two
significantly different length
scales that characterize the
problem. One is the characteristic
dimension of the tool while the
other is the thermal diffusion
length, a/U., where a is the
thermal diffusivity. The ratio of
the two lengths is given by the
Peclet number Pe. The typical
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Carrigan, C.R.; Dunn, J.C. & Hardee, H.C. A Tool and a Method for Obtaining Hydrologic Flow Velocity Measurements in Geothermal Reservoirs, article, January 21, 1986; United States. (digital.library.unt.edu/ark:/67531/metadc886194/m1/4/: accessed January 16, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.