Note: Descriptions are shown in the official language in which they were submitted.
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~ lthouyh this invention is directed principally
to the measurement of direction and/or rate of groundwater
flow in order to determi.ne the environmental effect, for
example, of septic leachate upon natural water systems,
the basic principles of this invention are applicable to
a wide range of problems in which the velocity and/or
direction of fluid flow is in question.
At present, many systems and techniques have
been developed to provide information about the direction
and/or rate of a fluid flow, including systems which rely
on steady state heating a tube through which a liquid flows
and measuring temperatures of the moving li~uid at upstream
and downstream locations relative to the heat source, to
obtain a hyperbolic measurement of flow rate. However, none
has to my knowledge been developed which involves measurement
of the distortion of a thermal field established by locally
heating a permeable mass through which the f].uid flows, to
obtain a linear measurement of fluid flow rate.
rrhis invent.ion relates to the discovery that the
distortion of a thermal field established in a porous
medium through which a very slowly flowing groundwater
system moves, can be used to provide a linear measurement
of the rate of such groundwater flow. ~ore specifically,
it was found that if temperature measurements are made at
different regions of the distorted field, so as in effect
to "map" it, not only can the flow azimuth be determined,
but also the rate of flow can be determined.
In a basic arrangement, the thermal field is
established by transferring a predetermined quantity of
heat energy to a highly localized region of a porous heat
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conductive medium through which the groundwater flows.
The localized region is at -the center o~ a surrounding
array of ternperature sensors. By not.ing the temperature
change differential between diametrically opposed pairs
of sensors, the pair indicating the greatest such differ-
ential provides information concerning the direction of
flow whereas the amplitude o~ the differential provides
a linear indication of the rate of flow.
In such system, the heat source was "pulsed"
whereafter the maximum temperature differentials between
the pairs of the sensors were recorded. It was discovered
that over a wide ran~e of groundwater flow velocities, the
temperature differentials peaked after the same elapsed
time subsequent to cessation of the heat "pulse", and that
the variation in maximum temperature differential in the
direction of flow, was essentially linearly related to
groundwater flow rate of velocity.
Figure 1 is a schematic diagram illustrating
certain basic features of the invention,
Figure 2 is a graph illustrating the li~earity
between maximum temperature differential
and fluid flow rate,
Figure 3 is a schematic illustrating one
embodiment of the invention,
Figure 4 is a schematic view illustrating one
embodiment of a proble assembly and
associated measuring circuitry,
Figure 5 is a graph illustrating certain
properties of the invention, and
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Figure 6 is a circuit diagram showing a
modified form of the control
assembly
Referring more particularly to Figure 1, certair.
principles of the present invention will be apparent
therefrom. As illustrated, a pair of temperature sensing
means 10 and 12 and which in the specific construction
illustrated take the form of termistors, are arrayed on
opposite sides of a heating element indicated generally
by the reference character 14. It will be understood
that the sensing means 10 and 12 as well as the heater
14 are to be disposed within a porous heat conductive
medium M through which the fluid whose flow character-
istics are being measured, flows. In the groundwater
system, the porous medium can be the soil itself, in
which case the naked heater and sensor may be inserted
thereinto. However, the sensing means and the heater
are preferably embedded in a porous or permeable mass
to provide a probe element to assure uniform and accurate
heat conductivity. When such an arrangement is used,
the porous mass should be formed of substantially uni-
formly sized spherical particles having heat conductivity
substantially greater than that of the fluid whose flow
is being measured, the particle size being not greater
than about 1.0 mm in diameter and sufficiently large
as will not impede, distort or adversely affect the
normal groundwater flow.
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In any even, with the arrangement as shown, a
timer indicated generally by the reference character 16
is actuated by suitable means not illustrated to energize
the heater 14 from the power source 18 for a predeter-
mined period of time In this way, a predetermined
quantity of thermal energy is introduced, the ammeter
20 being illustrated in the line connection to the heater
14 to illustrate this fact, i.e~, that the arrangement is
such as to provide a control power input to the heater 14
such that the heater dissipates a predetermined quantity
of heat conductive medium during a predetermined period
of time controlled by the timer 16.
In this fashion, the heater 14 is "pulsed" to
heat the porous mass M and establish a thermal field
within the flow path of the fluid whose flow character-
istics are being measured. In the absence of fluid flow
or movement, the field is centered about the location of
the heater 14 and is symmetrical or of predetermined shape
with respect thereto.
The two thermistors 10 and 12 are connected to
a suitable source 22 and the two branches of the circuitry
to the individual sensors 10 and 12 include, in addition
to the variable resistance displayed by the sensors, the
resistors 2~ and 26 respectively and a common variable
resistance element 28 suitably grounded as shown to
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connect the opposite side of the supply 22. The two
resistors 24 and 26 are o~ equal value and the resistor
28 is variable to establish a calibrated set point or
zero at the volt meter 30 at some predetermined temper-
ature of the two thermistors 10 and 12
The aforementioned thermal field, in the
presence of fluid movement or flow, will be distorted
and the deviation represented thereby will, dependent
upon the direction of flow, differentially affect -the
two thermistors 10 and 12. For example, i:E the flow of
the fluid is horizontally to the right in Figure 1, the
temperature experienced at and measured by the thermistor
12 will be higher than the temperature sensed at 10 and
this temperature differential is measured by the volt
meter 30 as will be readily apparent. Thus, in effect,
the distortion of the thermal field established by the
heater 14 is mapped by the sensing means 10 and 12,
with the amplitude o the voltage reading at the meter
30 being indicative of the degree of deviation or dis-
tortion of the thermal field. We have found that thedifferential reading measured at 30 between sensing
means diametrically located with respsect to each other
on opposite sides of the location of the heater 14 -Erom
which the thermal field emanates and wherein this
diametrical orientation is aligned with the direction of
fluid flow, is substantially linearly related to the flow
velocity of the fluid. This is illustrated in Figure 2,
the ordinate representing the temperature differential
between paired thermistors oriented along the direction
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of flow for various calculated rates of 1uid flow through
a porous, permeable medium.
Figure 5, appearing on the sheet of drawing
containing Figures 1 and 2, illustrates another rela-tionship
which obtains at the low groundwater velocities noted in
Figure 2, namely, that the peak temperature differential
and, hence, voltage differential between thermistors
aligned along the airection of ~low as aforesaid occurs
approximately three minutes subsequent to initiation of
the heat pulse at the heater 14, irrespecti~e of the flow
rate within the range depicted.
Figure 3 illustrates a practical embodiment
of the present invention and shows a somewhat more
detailed electrical circuit arrangement following the
principles illustrated in Figure 1. In Figure 3, a suitable
source of external voltage is indicated at 32, 34 with the
positive side 32 being connected through a manually operated
power on/offswitch 36 to the main input line 38. The
negative side 3~ o~ the source is connected throuyh a manual
pushbutton 38 as an input to the standard 555 type timer
indicated generally by the reference 40 so that when the
switch 38 is depressed, the timer actuates the constant power
circuit for a set period of 30 seconds. In the embodiment
of Figure 3, operation of the timer 40 causes the relay
coil 42 to be energized correspondingly to actuate the
two switches 44 and 46 thereof, the circuit through the
solenoid or relay coil 42 being completed through the NPN
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device indicated generally by the reference character 48.
The Device 48 is normally non-conductin.g but when -the
timer 555 is energized by depression of the pushbutton 38,
the output at pin number 3 thereof, as indicated by the
reference character 50,biases the transistor 48 on to
allow the relay coil 42 to be energi2ed for the period
of time taken before the timer 40 times out. Since the
type 555 timer is so well known, only the pin connections
thereof are illustrated and the necessary external component
connections thereto for providing a thirty second duration
energization of the relay coil 42.
When the coil 42 is energized, the switch 44
completes the circuit through the heater 14, which may
be provided with a suitable constant power source indicated
by the battery 52. The constant power circuit supplies an
electrica]. resistance heater 14 which corresponds to the
similarly reference heater in Figure 1, although shown for
convenience in a separate position in Figure 3, but which
is actually disposed centrally wi.th respect to the planar,
circular array 54 of thermistor elements 56. After the
heater has been energized for the period of time determined
by the timer 40, the relay coil 42 is deenergized and the :
switches 44 and 46 return to the full line position shown
in Figure 3. In this position, the heater 14 is no longer
energized and the switch 46 connects the main power line 38
to the appropriate source voltage input pin of the
liquid crystal display device indicated generally by the
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reference character 58. The device 58 illustrated is a
DATEL DIGITAL PANE~ METER (1.999V Model DS-3100U2I) with
external span adjust capability provided by a lOK variable
potentiometer
The rotary.switch 64 is employed to measure
difference between the analog high and analog low inputs
from diametrically opposed pairs of the thermistors 56 of
the array 54, such being indicated by reference characters
60 and 62. The array 54 of sensors comprises a circular
arrangement thereof about the common center whereat the
heater 14 is located as previously mentioned, so that the
diametrically opposed pairs of sensors provide, through the
rotary switch 64, the respective high and low inputs at
60 and 62 as illustrated. The potentiometer 68 is provided
so that its top 66 may be adjusted to provide the proper
reference voltage input to the device 58.
Figure 6 illustrates a solid state version of
that portion of the electrical system of Fi.gure 3 which
eliminates the relay 42, 44, 46 and provide.s a constant
power source to replace the battery 52. As shown, a
transistor 48 of the type used in Figure 3 is retained
and is used in conjunction with the diode 100 to eliminate
the need for mechanical switching. ~he operational ampli-
fier 102, diode 103, transistors 104 and 106 of types
lN1711 and MJ3001 respectively and connected as shown in
Darlington array, and the multiplier 108 form a constant
power source for the heater 14 when the timing circuit is
actuated. The DC-DC converter 110 is provided to supp].y
the voltages necessary for the devices :L02 and 108.
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As noted, the circuit portion shown in Figure 6 is illus-
trated merely to show that an all solid state arrangement
may be preferable.
Figure 4 illustrates another form of the invention
for measuriny groundwater flow. A probe assembly which is
indicated generally by the reference character 70 comprises
a porous mass of particulate material indicated by the
reference character 72, having a heat conductivity of at
least 10 times that of water and, imbedded therein, are a
heater element 74 and a surrounding array of sensors 76,
78, 80, 82, 84 and 86. The sensors 76, 80, 82 and 86 lie
in a common plane and are disposed in diametrically opposed
pairs whereas the sensors 76, 78, 82 and 84 lie in a second
plane orthogonal ~to the first-mentioned plane and, again,
arranged in diametrically opposed pairs and, lastly, the
sensors 78, 80, 84 and 86 lie in a third, orthogonal plane
whereby the heater element 74 lies at the center of the
spherical surface upon which the various sensors lie. IE,
now, the line through the sensors 76 and 82 is oriented in
the North direction as indicated, and the outputs of the
various sensors are connected as inputs to an X, Y, Z
comparator and computer 88, the precise direction o~
groundwater flow through the permeable structure 72 may
be recorded by the mechanism 90 in accordance with well-
known X, Y, Z resolution techniques. At the same time,
the flow rate is computed by determination of the temper-
ature differential between diametrically opposed points,
in the horizontal plane containing the sensors 76, 80,
82 and 86, which are aligned with the flow dlrection
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The pu~pose o~ the porous structure 72 is not
only accurately to position the sensors and heater and to
provide the proper heat conductivity -to produce the afore-
said thermal field but also to provide a probe which is
useful in a variety of soils. For example, although the
heaters and sensors may be arrayed directly in rather
small grained soils to obtain accurate measurements of
direction and flow velocity, large grain size soils may
give inaccurate readings because of distortions to the
thermal field caused by the soil particles themselves.
Thus, the porous structure 72 consists of an agglomeration
of similarly sized small particles through which the
groundwater flows so as uniformly to affect the various
sensors with respect to the thermal field generated by
the heater 74~
The heater and sensor array can be inserted
directly into the water saturated zone of fine gravel to
fine sand soil to measure the rate and direction of ground-
water flow or may be enclosed or encased in an end cap
o~ porous spherical material of suitable permeability.
Water moving through the irregular soil pores courses
through the permeahle substrate into which the sensing
elements and heater are situated. The flow is laminar
and continuous under normal groundwater flow conditions
(V = 30 ft. per day or less) flow through the porous end
cap continues to be laminar without the formation of any
boundary layers between probe and the water saturated
natural soil into which the probe is immersed. No
stagnation points exist, as in the case of fluid flow
around nonporous probes To sense the direction and rate
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of -flow, the probe is first oriented towards magne-tic North,
Each opposing pair of sensors is nulled to zero or a stable
difference recorded, As portraye~l in Figure 1, a heat pulse
is released into the porous substrate and moves symmetric-
ally outwards in all directions, The natural laminar flow
of groundwater influences the thermal field in the porous
solid, retarding the outward flow of heat at a maximum in
the direction in which laminar flow directly opposes heat
flow and augmenting the outward flow at a maximum in the
direction of the laminar flow, Sensors lying perpendicular
to the axis of flow would show no variation due to laminar
flow, since the distortion of the thermal field moving
through the solid matrix would remain equivalent for each.
The probe can be used in naturally porous soils
from fine gravel to fine silty sand. As the particle size
approaches that of medium gravel, the pathways of inter-
stitial -flow become too irreyular to measure direction
accurately. Similarly, variations in heat conductance
through larye particles (intra-particle conductance)
dominate heat transfer between particles (inter-particle
conductance), which leads to high variability in estimating
flow rate, ~hus, for measuring flow rates in gravel, it
is essential that the array be embedded in the porous mass
72 as shown in Figure 4, the mass 72 being composed of uni-
form spherical particles within the range of 1-.1 mm diameter
as long as the flow velocity through the gravel is not so
high as to be excessively impeded by the permeability of
the porous mass,
The vec-tor field indica-ted by the amplitude of
opposing pairs of heat sensors can provide additional
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in~ormation on the characteristics of yroundwater flow
apart from direction and rate of fLow. For the first
example, uniform horizontal flow occurs, all vectors will
correspond to the cosine of the vector solution ~or primary
direction of flow). However, if the column of water is
unstable vertically, the vectors will deviate from the
cosine of the direction of principal flow.
Described mathematically by the function:
y - acos~
where: y = the rate of flow in a direction (x)
a = the rate of 10w i~ the principle
direction of flow
x = the angle of deviation from the
direction of main flow.
For a second example, if the water mass has an
oscillating nature, moving back.and forth with a period
less than that for a reading, the heat flux field will
describe the main components of that motion,
If the water mass has an oscillating nature with
a period substantially greater than that of the time required
for measurement, such as groundwater in coastal areas sub-
jected to tidal action, successive recordings at appropriate
intervals can be employed to describe the harmonics of the
oscillatory motion
Lastly, if an array of three probe units are
inserted into shallow surface groundwater in a triangular
arrangement, the units can be used to detect the position
and approximate volume of displacement of a transient dis-
charge of water or liquid occurring between or nearby the
array Continual recordi.ng of the independent probes can
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establish the background flow conditions of rate and direc-
tion. Any sudden addition of volume to groundwater surface
creates an outwards rush of shallow groundwater displacing
the recorded principal direction of flow at the independent
units in a direction emanating from that of the source of
the displacement and proportional to the volume added.
Detection is quite rapid, as the introduced mass of liquid
need not reach the sensors, only the head differential due
to the propagated displacement.
In addition to detecting a discharge, a triangular
array can also be used surrounding a wi-thdrawal well to a
sure movement within the boundary property. With either
treatment of the withdrawn water or evaporation of the
pumped water, the monitoring system can be used to isolate
the local groundwater movement to form a flow cell so that
no groundwater flow will leave the property.
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