Note: Descriptions are shown in the official language in which they were submitted.
NS-380
CALIBRATION OF NUCLEAR DENSITY METERS
Field of the Invention
[0001] This invention relates to systems and methods of calibrating nuclear
density meters.
Background
[0002] Nuclear density meters or gauges are used in the bitumen processing
industry to
measure the density of process fluids. Such gauges are well known and are
known to be
efficient, non-intrusive and safe instruments. Their basic principle of
operation is based on
attenuation of a narrow beam of gamma photons emitted by a radioactive nuclide
through a
process pipeline. The degree of attenuation is measured by a detector, and is
correlated to the
density and composition of the process fluid they pass through, and the
distance travelled.
Assuming a pipeline inside diameter is constant, measurement of the
transmitted radiation
intensity is inversely proportional to the absorber density, and is dependent
on the absorption
coefficient of the process fluid.
[0003] Accurate readings depend on accurate calibration of the gauges.
Calibration requires
the use of standard samples having known properties, however, representative
and repeatable
samples are difficult to obtain with large slurry pipelines which transport
large particles and/or
non-homogenous materials.
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[0004] Therefore, there remains a need in the art for methods and systems of
more accurately
calibrating nuclear density gauges used in large-scale mining operations.
Summary of the Invention
[0005] The invention comprises a calibration method that may be used to
calibrate nuclear
density meters without the need for sample verification. The method may be
performed
online and is based on first principles, eliminating the need to use
representative stream
contents as the calibration standard.
[0006] In any nuclear density meter, the amount of gamma radiation that
reaches a detector
can be predicted as it follows the Lambert/Beers absorption law. However,
there are negative
factors that will skew the prediction. In embodiments of this invention, the
extent of those
negative factors are determined and then the calibration curve is compensated
to reduce,
eliminate or mitigate them. The two main negative factors are changing
absorption
coefficients and gamma buildup.
[0007] Absorption coefficients must be representative of the stream makeup.
This calculation
may be made using known coefficients and must be used to compensate for the
changing
hydrogen component of an aqueous based slurry with varying solids content.
[0008] The gamma buildup issue presents a much more difficult problem. The
problem arises
because not all gamma photon-matter interactions result in a complete
absorption. Many will
scatter or deflect into the detector face and do so at a lower energy. These
lower energy
photons are detected by non-energy discriminate detectors and result in a
detected intensity
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that is many times higher than is predicted by the fundamental absorption
laws. As a
consequence, the calibration curves of any nuclear density meter that has not
been
compensated for this extra measured radiation intensity will be in error.
[0009] In one embodiment, the method comprises the step of compensating for
the gamma
scatter by inserting a gamma buildup correction factor into the calibration
curve. Gamma
buildup and consequently buildup factors are very much dependent on the
geometry of the
installation. Pipe diameters and wall thickness for example greatly influence
photon scatter.
These correction factors may be empirically derived and take into account the
negative
geometric influences.
[0010] Therefore, in one aspect, the invention may comprise a method of
calibrating a
nuclear density meter used in the measurement of density of a sand/water/oil
slurry, without
sampling the slurry, comprising the steps of:
(a) determining a net attenuation coefficient for the slurry being measured;
and
(b) mitigating radiation buildup by taking one or more of the following
steps:
i. physically preventing scattered radiation from reaching a detector;
ii. providing an energy sensitive detector and measuring only higher energy
non-
scattered photons; or
iii. modifying a calibration curve by applying a correction factor to a basic
attenuation equation to account for the increase in radiation reaching the
detector,
wherein the correction factor is determined empirically.
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Brief Description of the Drawings
[0011] The following drawings form part of the specification and are included
to further
demonstrate certain embodiments or various aspects of the invention. In some
instances,
embodiments of the invention can be best understood by referring to the
accompanying
drawings in combination with the detailed description presented herein. The
description and
accompanying drawings may highlight a certain specific example, or a certain
aspect of the
invention. However, one skilled in the art will understand that portions of
the example or
aspect may be used in combination with other examples or aspects of the
invention.
[0012] Figure 1 shows a graph illustrating errors with conventional on-line
density
measurements.
[0013] Figure 2 shows a schematic nuclear density sensor arrangement.
[0014] Figure 3A shows a schematic representation of gamma rays not originally
directed at
the detector can be scattered and directed into the detector where they will
be detected. These
rays are not accounted for by the fundamental attenuation equation. Figure 3B
shows a
schematic representation of rays which are scattered out of the beam directed
to the detector
can be re-scattered back into the detector. Rays of this type lead to "build-
up" of the gamma
energy detected.
[0015] Figure 4 shows a graph demonstrating that the gamma attenuation
coefficient varies
both with energy and element.
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[0016] Figure 5 shows a graph showing that the attenuation coefficient is a
function of the
slurry composition, particularly the solids fraction.
[0017] Figure 6 is a schematic representation of potential pathways gamma
photons can take
between the source and detector.
[0018] Figure 7 is a schematic representation of collimators inserted to
prevent scattered off-
axis photons from reaching the detector.
[0019] Figure 8 shows output from a multi-channel analyzer/ sodium iodide
scintillation
crystal.
[0020] Figure 9 is a graph showing effect of changing attenuation coefficient
GO and buildup
factor (6).
[0021] Figure 10 is a graph showing the error incurred if calibration is
attempted from first
principles and buildup in the system is not included in the model.
[0022] Figure 11 is a schematic representation of a test apparatus setup.
[0023] Figure 12 is a graph showing relative gamma intensity can be derived
from MCA
histogram.
[0024] Figure 13 is a graph showing density estimates (from measured
intensities and eqn. 4)
plotted against the true measured densities for the three solutions.
[0025] Figure 14 is a graph showing density estimates using the total counts
from the MCA
plotted against the true measured densities.
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[0026] Figure 15 is a graph showing MCA energy spectra of a 29 cm barrel of
salt solution
showing the effect of simulating 1" (2.5 cm) pipe walls using steel plate.
[0027] Figure 16 is a graph showing the same data used in Figure 15 but the
count rates have
been normalized at the photopeak.
[0028] Figure 17 is a graph showing the value of In (1w/Is) plotted for the
1.5 s.g. salt solution
with and without pipe walls.
[0029] Figure 18 shows the required buildup correction varies as the wall
thickness changes.
[0030] Figure 19 shows the build-up correction for three different detection
techniques:
photopeak counts, total counts and a commercial (Berthold) system that counts
some smaller
set of total counts.
[0031] Figure 20 shows the build up correction (cm) using Equation 4(A), and
the build up
factor (.4)) using Equation 4(B), as a funciton of pipe diameter
[0032] Figure 21 shows two graphs which demonstrate a non-collimated detector
allows
considerably more radiation to fall on the detector.
[0033] Figure 22 shows a graph, similar to Figure 17, where the value of In
(1w/Is) is plotted
for the 1.5 SG salt solution, this time, with and without collimation on the
detector.
[0034] Figure 22 is a graph comparing 1" collimation and 2" collimation.
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Detailed Description
[0035] In this description, certain terms have the meanings provided. All
other terms and
phrases used in this specification have their ordinary meanings as one of
skilled in the art
would understand. Such ordinary meanings may be obtained by reference to
technical
dictionaries, well-known to those skilled in the art.
[0036] Measuring fluid density in a process pipe by nuclear absorption is a
well-known
process. A beam of energetic gamma photons from a radioactive isotope source
is directed
through a cross-section of the pipe (either along the diameter or a chord) and
the energy of the
beam exiting the other side is measured, as is shown schematically in Figure
2. The amount
of detected energy is a function of the mass between the source and detector,
so, as the process
stream changes, its density can be determined from a gamma energy measurement.
[0037] Gamma photons passing through the material are occasionally scattered
out of the
beam by interaction with the tightly bound electrons of the material's atoms
and the beam is
gradually attenuated as it passes through the fluid. The scattering is related
to the number and
size of the atoms and thus is related to both the density of the material and
its atomic
composition. The attenuation is characterized by the "mass attenuation
coefficient" which is
different for each material and varies with the energy of the gamma photons.
[0038] The intensity of the exiting beam is given by the following:
= Iroe-ppr
(1)
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Where /0 is the intensity measured at the detector when the pipe is empty, I
is the intensity
after the pipe is filled with fluid, 1.1 is the mass absorption (attenuation)
coefficient (cm2/g) for
the fluid, p is the slurry density (g/cm3), and t is the distance across the
slurry (usually the
pipe ID) (cm).
10039] In a density measurement application, it can be assumed that the value
/, accounts for
attenuation of the beam caused by pipe walls, source holder, insulation, or
any material other
than the process flow, through which the radiation beam passes.
[0040] In practice, the measurement of /0 is always relative to a reference;
usually a pipe filled
with water. When water is measured, the equation is:
It) e-11-Pwris
(2)
The value of In, is stored and the water replaced by slurry; the measurement
is repeated to
give:
jr = I e¨ 11,P,',
(3)
where 'Is, ps, and Is now refer to the slurry. The attenuation coefficient for
slurry, ps, will
vary with its composition.
[0041] To determine the value of ps , the slurry density, the ratio of
equations (2) and (2a)
provides:
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Hp. tõ e-1.1 w
=
w 0-
¨
I s I e¨p,pst,
Taking the natural logarithm and re-arranging results in:
ln(Jõ) In(is) = ¨/õ, põ, t,,, psi), ts
and
p. ________ 1'4' 1
p ( (1k,) ______________________ ))
11 5 t S t5
Since the pipe diameter is the same, tw = ts, this may be rearranged as:
p5 = PI, + 1 (1n(/)¨ In(i, ))
IA.,is
(3A)
and the density can be determined. This equation is often written in the form:
Ps = B pH, C (In ( /w) - in ( /8))
(3B)
[0042] When representative samples of the stream are available, the constants
B and C can
empirically be determined by comparing the detector signal (I) with the
density of the
samples. It is not necessary to know the precise values for it/ or t. In many
industrial
applications, samples of the fluid can be taken and the above constants easily
adjusted in order
to calibrate the measurement system. However, it is not feasible to obtain
representative
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sample of a stream of a sand slurry flowing in a large diameter pipe.
Therefore, the
calibration methods of the present invention may be required.
[0043] When samples are not available, the attenuation equation can still be
applied, but there
are some additional factors need to be taken into consideration. Values of the
attenuation
coefficients, px, must be known. The attenuation coefficient varies with both
the energy of the
gamma radiation employed and the atomic weight of the slurry constituents. The
values are
well known and tabulated and, though they change with the makeup or solids
content of the
slurry, the net coefficient for mixtures can be readily calculated.
[0044] The proportions of water, sand, clay, and bitumen all vary with the
solids content of a
slurry. Since each of these components has a different attenuation, the
average attenuation
coefficient of the mixture will also vary. The overall absorbance coefficient,
,u, can readily be
calculated if the composition of the slurry is known.
iti =E wilif
where rvi is the fraction by weight of the ith atomic constituent and the pi
are the coefficients
for each element. The coefficients are calculated to high precision and tables
of values are
readily available. The mass attenuation coefficient is referred to as p. The
/../ values for the
predominant elements in a clay-and slurry are given in the table below.
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Element p (cm2/g)
(for gammas with energy of
0.662 MeV)
Hydrogen 0.1544
Oxygen 0.0774
Silicon __________________ 0.0775
Aluminum 0.0748 ______
Potassium 0/0759
Iron 0.0737
Magnesium 0.0766
Water 0.0859
[0045] At the gamma energy of 0.662 MeV, most elements have about the same
coefficient.
Hydrogen is anomalous, with an attenuation coefficient about two times the
others (see Figure
4). At the energy of cesium 137, the coefficient for most elements is about
the same. A
notable exception is hydrogen, which is about 2 times as great. Since water is
the main
constituent of bitumen slurries, the overall coefficient varies with the
slurry composition.
Since water contains llwt% hydrogen, it has a higher effective attenuation; a
fact that is very
important in aqueous slurries since the proportion of water changes with
density.
[0046] The effective p for aqueous sand/clay slurries is shown in Figure 5.
These values were
obtained by calculating the effect of various elements at various
concentrations as density is
varied. The attenuation coefficient is a function of the slurry composition,
particularity the
fraction solids. This is because the elements making up the solids have a
coefficient, which is
quite different from water. Since the coefficient varies with solids, it will
then be a function of
density. With no solids, the slurry will have the same density as water and
the same
coefficient. As solids increase the slurry coefficient will decrease as the
graph in Figure 5
shows.
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[0047] Equation (1) describes only the attenuation of the gamma beam as it
passes through the
liquid. In addition to the radiation of the unattenuated portion of the beam,
additional
radiation also falls on the detector. A phenomenon called radiation "build-up"
can greatly
increase the radiation reaching the detector. Build-up occurs when gamma rays
that are not
originally directed at the detector, are scattered and redirected into the
detector, as shown
schematically in Figure 3a. Also, when gamma radiation is scattered out of the
original well-
directed beam, it can interact again with the fluid and be re-scattered. It
loses some energy in
scattering and if the absorber is large enough, the deflected gamma will be
scattered again,
and again until all its energy is absorbed. However, some of these gamma
photons leave the
absorber after one or more scatterings and depending on the geometry can reach
the detector,
as shown in Figure 3b. The total amount of energy falling on the detector can
be several times
greater than that of the unattenuated beam strength predicted by equation (1).
Since only the
unattenuated portion of the beam can be accurately described by equation (1),
it is desirable to
prevent the scattered radiation from reaching the detector or otherwise
accounting for the
scattered radiation. Then the known values for absorption coefficients can be
used with
confidence and no sampling will he required.
[0048] There are three main ways of accounting for this build-up:
1. Prevent the scattered radiation from reaching the detector. This is
accomplished by
using collimation on the source and detector to limit the beam to what is
called the "narrow
beam geometry". The collimation prevents the scattered and re-scattered
radiation from
reaching the detector.
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2. Use an energy sensitive detector. Since scattered gamma photons have lost
some of
their energy, the use of an energy sensitive detector, such as a sodium iodide
(NaI)
scintillation crystal coupled with a multi-channel analyzer (MCA), allows the
unattenuated
gamma photons, those predicted by equation (1), to be distinguished from the
lower-energy
scattered photons. Only the high-energy photons that have not been scattered
are counted; the
rest are ignored.
3. Account for the extra radiation. Various attempts have applied different
empirical
corrections to the basic attenuation equation to account for the increase in
radiation reaching
the detector.
[0049] Figure 6 shows schematically how radiation from the source interacting
with any
material in the region can be scattered at an angle, which will deflect it
into the detector. Only
the unscattered radiation can be accurately described mathematically; that
which takes the red
dashed path. A large number of off-axis photons which have been scattered by
the slurry and
pipes can also reach the detector. In practice, the number of scattered gamma
photons reaching
the detector will outnumber the photons in the main beam by a factor of 5 to
10. These
scattered photons are difficult to describe in a model.
[0050] In Figure 7, a collimator of high-density material is shown to
attenuate scattered
radiation while allowing the non-scattered radiation beam to reach the
detector. Collimation
will substantially reduce the number of scattered photons reaching the
detector. A collimator
may be provide at both the source and detector sides, however, in practice
often only the
collimator at the detector side is needed.
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[0051] Gamma photons which have interacted with atoms of the fluid and been
scattered out
of the main beam can subsequently interact with other atoms and be scattered
in the direction
of the detector. These scattered photons will have lost some energy because of
the interactions
and will arrive at the detector with a lower energy than photons that have
passed through the
fluid without interacting.
[0052] In an alternative embodiment, a detection system capable of measuring
the energy of
individual photons can be used to distinguish between the scattered photons
and those of the
main beam. A sodium iodide (NaI) scintillation crystal coupled to a compact
multi-channel
analyzer (MCA) was used for this investigation. Figure 8 shows an example of
the output
from this system. The output of the MCA is a histogram of the number photons
received as a
function of the energy of each photon detected. The peak on the right is
produced by high
energy gamma photons which enter the crystal from the source without having
undergone any
scattering interactions. The count rates at lower energies are from photons
from the same
source (same initial energy) but now have less energy from having been
scattered.
[0053] This combination measures the number of gamma photons at each energy
and presents
the information as a histogram. In this example, gamma photons from a
radioactive Cesium
137 source are being detected. Photons which have lost energy via scattering
show as lower
energy. Cesium 137 (a common source for density measurement applications)
produces a
gamma photon with energy of 0.662 MeV (million electron volts). These photons
are
responsible for the photopeak on the right in Figure 8. If only those photons
received with the
photopeak energy are counted and the rest ignored, then the conditions to
accurately use
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equations (1) and (3) along with known attenuation coefficients are satisfied
to estimate the
density.
[0054] In an alternative embodiment, the extra energy may be accounted for by
simply
including a multiplying "buildup factor" in the basic equation:
/ = Bf e-uP
The buildup factor Bf is greater than 1 and can be as high as 10. The factor
is related to the
material of the absorber and may be expressed in different ways [4,5,6]. In
one example, it
may be expressed as:
Bf =e "P 6
Buildup will increase with ,u and p. In this form, the effect of buildup can
be thought of as
modifying the path length. That is, we will artificially reduce the path
length t by an amount 6
the equation may be written as:
I = I e-"P' 6)
[0055] This gives an "effective path length" which is less than the actual
path length. Extra
radiation from buildup effects will lead to greater signal intensity at the
detector, thus
simulating the effect of a shorter path length. Equipped with this expression
of the attenuation
equation, density can be estimated directly from a measurement of I, provided
6 is known.
Equation 3 (above) may be modified, including l to get:
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1-1 w P.
s + _________ in (/õ. ) In(/5))
(4)
or
plc //õ,
c = + , __ , In __
1,t ¨
(4A)
Ps = Pie 11. 1
In(/'
1.1, CD ps t
\'s
(413)
In arriving at this equation, we assume that the buildup correction, 6, is the
same for water and
slurry. If is small compared to t, its inclusion will have a small effect. If
it is significant but
can be estimated reasonably well, its effect, and the measurement error due to
buildup, will be
minimized (see Figure 9).
[00561 In a conventional nuclear density gauge installation, the instrument
should be
calibrated with at least two materials of known density. In slurry
applications, these are
usually water and a slurry of accurately known (by sampling) density. Often
several slurry
samples are taken and averages used. Alternatively, the manufacturer will
calibrate the
instrument based on some model of how the instrument will respond. The
accuracy of this
calibration depends on the accuracy of the manufacturer's model.
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[0057] In one embodiment of the present invention, the sampling requirement is
eliminated by
using a model based on equation (4), which is taken to describe the response
of the instrument
with sufficient accuracy.
[0058] If it is assumed that all materials have the same absorption
coefficient and there is no
buildup phenomenon, a form of equation (1) would be used, however, the
resulting calibration
would result in the instrument reading low, as shown in Figure 9 (no
correction line ¨ an error
of about 10% at an specific gravity of 1.5.). If the equation we use to
calibrate the instrument
includes a correction for the changing p value, the calibration would result
in readings that are
better, but still low (middle line ¨ an error of about 5 %). If both the
correct p and the effect
of buildup, 6, are accounted in the equation, the instrument reading will
approach the true
density value (top line).
[0059] Unlike i, the buildup coefficient cannot be readily calculated.
However, since it is
expected to be strongly influenced by geometry and the detection system, it
was felt that it
could be measured for various geometries and its value approximated for real
applications
with similar geometries to those tested.
[0060] Figure 10 shows the error, which could be made by using a model, which
does not
include a buildup factor. The error is greater if the buildup for a particular
system is larger. If
there is no buildup, as in a narrow beam geometry, the meter reading will be
accurate even if
the model does not include buildup effects. If the buildup effect is as great
as 20, then the
meter error will be quite large when the effect of buildup is ignored in the
model. For
example if the true specific gravity is 1.4 and the buildup in the system has
a value of 10, then
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meter will read 1.34 if this buildup number has been ignored. If the
measurement geometry
can be modified so that the buildup is small, then the error incurred will be
much smaller even
if only an approximate estimate of ô delta is used in the model. For example;
if the buildup
can be reduced to 3, then the error in specific gravity will be less than 0.02
even if the buildup
is ignored.
Examples
Examples are provided which demonstrate the feasibility of using a simple
model for gamma
attenuation (as expressed by equation 4) to relate a gamma measurement to the
specific
gravity of a slurry without the need for empirical calibration. The effect of
variable
attenuation coefficients, discussed above can be calculated and readily
included in the model.
Examples aimed at exploring the extent of radiation buildup and the
feasibility of specifying
values for buildup factors to be included in the model.
Experimental Set-up
[0061] The test equipment is shown schematically in Figure 11. The equipment
had the
following features:
1. Slurry was simulated using water and salt solutions (specific gravities of
1, 1.37, 1.5
and 1.7).
2. Steel plates were used to simulate the pipe walls.
3. A 180 millicurie Cesium 137 source was used.
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4. A 2"x2" NaI scintillation crystal was used in conjunction with a compact
1028 channel
multichannel analyzer.
5. Various absorption plates of tungsten and steel were available.
6. Steel collimators of various diameters from 0.25 to 2".
[0062] The tests were determined using salt solutions which is believed to
accurately simulate
the results expected from slurries. Several samples of each salt solution were
taken and
specific gravity determined. The attenuation factor for each solution was
calculated using the
known elemental composition and the salt concentration.
Solution Specific gravity Specific gravity Attenuation
(as specified by (as measured) coefficient
supplier) (cm2/g)
water 1.0 0.0859
38 wt % CaCI 1.37 1.354 0.0821
42 wt % CaBr2 1.5 1.485 1 0.0804
52 wt % CaBr2 1.7 1.712 0.0791
The source size of about 180 millicuries was about 5 to 10% of the size
normally used for
large slurry line applications. Because of the smaller source size, longer
radiation count times
were required to provide an accurate measure of the radiation signal. The
counting time for
each test was typically 300 seconds. Personnel were shielded from the source
by sand bags
and a specific area flagged off for entry by authorized personnel only.
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[0063] The detector was a 2"x2" Nal scintillation crystal. The photomultiplier
was directly
coupled to a miniature multichannel analyzer (MCA) which in turn was connected
via a USB
connection to a computer. The detector was shielded with steel plates from
background
radiation; this shielding reduced the background to a negligible level. A
detector of the type
used with commercial density measurement system (Berthold Technologies) was
also used in
some tests.
[0064] A series of test was performed using 29.2 cm (11.5") barrels with water
and three salt
solutions with specific gravities of 1.35, 1.5 and 1.7. Measurements were
performed with and
without collimation. The collimator was a 1" diameter hole in heavy steel
plate three inches
thick and was placed next to the detector. Readings were also taken with the
collimator
placed next to the source. The signal from the MCA detector is treated in
three ways (Figure
12).
a) The total count at all energies. This reports all the gamma photons
detected at any
energy; this includes the photons which pass through the fluid and pipe
without interacting
(those described by equation 1) as well as those scattered within the fluid
and pipe walls
but still reaching the detector (those photons responsible for the buildup).
The total count
will simulate the behaviour of a detector without energy discrimination
ability and mimics
the response of the detectors in most commercial density instruments. This is
the simplest
measurement for an instrument manufacturer to supply; all the gamma pulses are
counted
regardless of energy.
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b) The gross counts within the photopeak. This reports all the photons within
the energy of
the photo peak (the photons which have passed through without interaction) as
well as
photons from the natural background radiation. As far as the instrument is
concerned, only
pulses above a certain energy need to be counted; this is also relatively
simple to achieve.
c) The net counts in the photo peak. The value for net counts is derived from
the gross
counts by subtracting the baseline interpolated through the photopeak. This is
intended to
eliminate any background effects. To measure the net counts in the photopeak,
a full
multichannel analyzer is required to provide the entire spectrum.
Figure 12 shows the relative gamma intensity can be derived from MCA histogram
signal in
several ways. a) the area under the full peak histogram b) the area under the
photopeak or c)
the area under the photopeak with the extrapolated baseline removed (cross-
hatched area)
[0065] For each set of measurements, the collimators and shields were put in
place and a
barrel of room temperature water was positioned in the path of the beam. The
shutter was
opened and the MCA allowed to collect information for 300 seconds; the total
count was
stored and used as the water reference measurement.
[0066] This barrel of water was replaced with a barrel of salt solution and
the measurement
repeated. Each of the salt mixtures was measured in the same manner. A typical
test result
would be as follows: Conditions
= Simulated slurry pipe ID 29.21 cm (11.5")
= Simulated pipe walls 1" steel
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= Collimation diameter 1" (detector side only)
Atten. Coeff. Total counts Gross Peak Net
Peak Counts
Pipe contents Counts
(calculated) (300)sec (300)sec
(300)sec
1.0 SG water 0.0859 ein2µ0 195234 46368 32874
1.35 SG. sari 0.0821 118980 25422 17895
1.5 SG. so1'n 0.0804 97591 19932 13341
1.7 SG sol'n 0.0791 72920 14247 9096
Recalling Equation 4, developed earlier, and the detector outputs, I, for
water and the salt
solutions, the density estimated from the modeled response of the system is
calculated:
w P11,
s in ____________________________
s s (i
s
[0067] The values estimated above were then compared to the actual density of
the salt
solution as determined gravimetrically. The value of c") which gives use the
best match is then
assumed to be the correct buildup correction for the particular geometry used.
Figure 13
shows the density estimates (from measured intensities and eqn. 4) plotted
against the true
measured densities for the three solutions. With buildup correction applied,
the error is
estimated to be about 0.5 g/cm3 at 1.5. The correction parameter 6 is adjusted
to minimize the
error. In this case, 6 3.5 cm. (The dotted line
depicts a best match).
[0068] Total count rates from the detector (rather than just the photopeak
counts) were used in
the calculation, and the results shown in Figure 14. In this case, a much
larger buildup factor
is required in the model. This is much as expected, since from the total gamma
count includes
22
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more scattered radiation than does the peak count. With no buildup accounted
for, the error is
about 0.15 at a value of 1.5. If the same correction as the previous case is
used, there is still a
large error. In order to minimize the error, a buildup of 6 9.5 cm is
required.
Effect ofpipe walls
The wall of the pipe has a large influence on the transmission of gamma energy
through the
measurement system. Figure 15 shows the MCA output for a 29 cm diameter thin
walled
barrel along with the same barrel with 1" thick steel walls (simulated with
plates). The steel
pipe wall reduces the transmitted energy by about 95%. This is the main reason
frequent
standardization of a density meter is very important; if the pipe wall wears
by 1 millimeter, the
radiation at the detector in this example will increase by 10% and the
estimate of slurry
density will change by 3 %. Frequent standardization (referencing the system
with water) will
largely eliminate this error. Figure 15 shows the MCA energy spectra of a 29
cm barrel of salt
solution showing the effect of simulating 1" (2.5 cm) pipe walls using steel
plate. Thick pipe
walls reduce the energy reaching the detector by about 90%.
[0069] The wall will also have an effect on the scattered gamma energy. The
wall will scatter
many more photons than the slurry; some of these will reach the detector at
lower energy than
the photopeak. The effect of the wall next to the detector will have the
greater effect, merely
because of geometry. As long as the proportion of this extra scattered energy
stays the same
for the water reference and the slurry measurement, there will be no error
because of it.
However, this proportion does not remain constant, requiring a buildup
correction that
depends on wall thickness.
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[0070] Figure 16 uses the same data used in Figure 15 but the count rates have
been
normalized at the photopeak. The proportion of lower-energy, scattered
radiation (relative
to the photopeak energy) is much higher for the 1" pipe wall case.
Again looking at the basic equation,
(
in \ ,
In/7- = ty p ¨pWpW )(t
/ s s 1
s i
it is noted that in a given situation with values for pm, is, pw, ps, and 6,
that the value of in
(Iw / Is) should be fixed. However, scattered gammas have a slightly different
path lengths
and lower energy (leading to different values for pt, as in Figure 4), and the
term In (Iw / Is)
should reflect this.
[0071] In Figure 17, the measured values of In (1w/Is) are plotted as a
function of energy.
Three observations can be made:
1. the value of ln (Iw / Is) varies with energy, as expected,
2. the variation is different depending on the wall thickness of the pipe ( 0"
or 1-), and
3. at the photopeak, the value is about the same. At lower values there is
significant
difference.
Accordingly, if only the information at the photopeak energy is used, a wide
range of
conditions can be described with the same model. If information from lower
energies is
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included as well, then the model must be tailored for different conditions (in
the example, for
different pipe wall thicknesses).
[0072] In practice, using an MCA gives the option of using only the counts
within the
photopcak. Figure 18 shows that this would allow the two cases here (different
wall
thicknesses) to be treated in exactly the same way. If total counts were used,
then the two
cases would need to be treated differently, for example by ascribing a
different buildup factor
which would be a function of wall thickness. Figure 18 shows that the required
buildup
correction varies as the wall thickness changes. This would be expected since
more
attenuation in the path increases the opportunity for scattered rays finding a
path to the
detector. It is difficult to avoid measuring all the scattered radiation, but
by limiting the
detection to the photopeak net counts alone (blue points) the buildup
correction is about 3 cm,
independent of wall thickness, If the total signal is used, the correction is
larger and more
variable.
[0073] Comparing this figure with Figure 10 which shows the error due to
improperly
selecting the buildup correction, we see that the use of the photopeak signal
can significantly
reduce the potential for error. A similar series of measurements was carried
out using a 55 cm
drum to simulate a larger line. For these tests, a gamma detection system from
a manufacturer
(Berthold) of commercial density gauges was available. While this instrument
also used a NaI
scintillation detector, it was not possible to ascertain the signal analysis
method used, but it
was not an MCA. The intensities measured were over a range of energies but the
limits of the
range are not known.
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100741 Figure 19 shows the results. Several pipe wall thickness were again
simulated and the
buildup correction which best match the true density of the test solutions was
determined.
The results are similar to those for the 29 cm drum. The buildup correction
when the count
rate in the net photopeak was used is again reasonably constant and only a
small error would
be incurred by using the same value for all conditions; a value of about 3 cm
would be
appropriate for both drum diameter and any of the wall thickness measured.
[0075] The buildup correction was considerably higher (compared to the 29 cm
drum) for the
total count rate measure. This could be expected with a larger diameter. The
results for the
Berthold detector were intermediate between the net peak and the total peak
results. This
suggests that the Berthold ignores some of the lower energy pulse when taking
the count rate
measurement. (This is commonly done in pulse counting electronics).
Effect of pipe diameter
The above data was plotted to show the effect of pipe diameter and shown in
Figure 20.
Although we have results for only 29 cm and 55 cm pipe diameters, these show a
large effect.
If total counts are used, the buildup correction must be varied from 7 cm for
the smaller
diameter to 13 for the larger. If only photopeak counts are used, a factor of
about 3 cm will
suffice for both diameters. Only 55 cm data was available for the commercial
detector.
[0076] The results show a definite advantage in using only the photopeak. With
the
photopeak, the buildup factor is almost the same even though the diameter is
doubled. If total
counts are used, a separate factor for each case must be determined. (Here a
linear variation of
the correction factor with diameter is shown, but no data was collected to
support this.)
26
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[0077] The commercial detector appears to respond midway between a total count
device and
a photopeak counting device.
Effect of collimation
[0078] From the previous discussions, the collimation of the gamma beam should
have a large
influence on the findings. Figure 20 shows data for a case where there was no
collimation of
the NaI detector ( 2" x 2"x 2" cube) and where a collimator, 1" diameter and
3" in length, was
placed in front of the detector. These measurements were taken with the 1.5 SG
solution in 29
cm drum.
[0079] The most obvious effect of collimation is the reduction of the signal.
The total count
rate (total area) is reduced by a factor of almost five. The photopeak count
rate is reduced by a
factor of three. The immediate consequence of this is that if a collimator is
used, a larger
source size is required to provide the same count rate as an non-collimated
detector. As
shown in Figure 21, a non-collimated detector allows considerably more
radiation to fall on
the detector. This reduces the source size for a given count rate, but
significantly increases the
amount of scattered radiation hitting the detector. On the right, the two
spectra have been
normalized to show how much this proportion between the photopeak and total
counts has
changed. When we examine the scattered gamma radiation, we see that the
collimator does,
as expected, reduce the amount of scattered radiation considerably. Figure 21
compares the
two cases (after normalization) and we see that the scattered radiation is
almost completely
eliminated. Most of the remaining low energy counted is the result of
scattering within the NaI
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crystal itself and is the result of 662 keV gammas which have reached the
crystal without
being scattered.
100801 The term ln (Iw / Is) was calculated and its value compared across the
energy spectrum
(Figure 22) this time, with and without collimation on the detector. In this
case the term takes
on the same value for each case at any energy. So, while the build-up
correction will be
different depending on the range of energy used in the calculation, it will be
the same for both
the collimated and non-collimated cases. This result is a little different. We
see that the value
changes with energy as a result of buildup, but the ratio at any energy is the
same for both
cases. The average value for the total counts will be different than for the
peak counts, but it
will be the same for both the collimated and non-collimated cases. This means
a larger
buildup correction will be required if the average total counts are used, but
the correction
factor will not be too sensitive to whether or not the detector is collimated.
[0081] 1" and 2" collimation were compared with the same results: for thick
walls the buildup
factor needed to be increased significantly when using total counts, but the
collimation used
made no difference. When using the photopeak counts, the factor was not a
function of wall
thickness and remained small; collimation had only a small effect (Figure 23).
The buildup
correction needs a slight increase from 3 cm to 4 cm. For the total count
measurement, even
though the buildup correction required was much higher, there was no
noticeable difference
between the 1" collimation and 2" collimation cases. The pipe walls were
simulated with
combinations of 0.5" steel and 1" steel plates with the total thickness shown
here.
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Conclusions from Testing
[0082] Improved performance of nuclear density gauges is possible. This
improvement can
be achieved at the same time as eliminating sampling for calibration.
Preferably collimation
is not used alone to eliminate buildup effects on thick-walled pipes.
Preferably, frequent
standardization (measuring output with water) is desirable to maintain
accuracy under any
system of calibration. Preferably, superior performance may be achieved with
an energy
discriminating sensor such as a NaI scintillation crystal in combination with
a MCA. This
will, however, reduce the count rate considerably and to maintain a
sufficiently large signal-
to-noise, a larger radiation source may be required. An alternative to a
larger source may be to
accept a slower response time.
Definitions and Interpretation
[0083] The description of the present invention has been presented for
purposes of illustration
and description, but it is not intended to be exhaustive or limited to the
invention in the form
disclosed. Many modifications and variations will be apparent to those of
ordinary skill in the
art without departing from the scope and spirit of the invention. Embodiments
were chosen
and described in order to best explain the principles of the invention and the
practical
application, and to enable others of ordinary skill in the art to understand
the invention for
various embodiments with various modifications as are suited to the particular
use
contemplated.
[0084] The corresponding structures, materials, acts, and equivalents of all
means or steps
plus function elements in the claims appended to this specification are
intended to include any
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structure, material, or act for performing the function in combination with
other claimed
elements as specifically claimed.
[0085] References in the specification to "one embodiment'', "an embodiment",
etc., indicate
that the embodiment described may include a particular aspect, feature,
structure, or
characteristic, but not every embodiment necessarily includes that aspect,
feature, structure, or
characteristic. Moreover, such phrases may, but do not necessarily, refer to
the same
embodiment referred to in other portions of the specification. Further, when a
particular
aspect, feature, structure, or characteristic is described in connection with
an embodiment, it is
within the knowledge of one skilled in the art to affect or connect such
aspect, feature,
structure, or characteristic with other embodiments, whether or not explicitly
described. In
other words, any element or feature may be combined with any other element or
feature in
different embodiments, unless there is an obvious or inherent incompatibility
between the
two, or it is specifically excluded.
[00861 It is further noted that the claims may be drafted to exclude any
optional element. As
such, this statement is intended to serve as antecedent basis for the use of
exclusive
terminology, such as "solely," "only," and the like, in connection with the
recitation of claim
elements or use of a "negative" limitation. The terms "preferably,"
"preferred," "prefer,"
"optionally," "may," and similar terms are used to indicate that an item,
condition or step
being referred to is an optional (not required) feature of the invention.
[0087] The singular forms "a," "an," and "the" include the plural reference
unless the context
clearly dictates otherwise. The term "and/or" means any one of the items, any
combination of
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the items, or all of the items with which this term is associated. The phrase
"one or more" is
readily understood by one of skill in the art, particularly when read in
context of its usage.
[0088] As will also be understood by one skilled in the art, all language such
as "up to", "at
least", "greater than", "less than", "more than", "or more", and the like,
include the number
recited and such terms refer to ranges that can be subsequently broken down
into sub-ranges
as discussed above. In the same manner, all ratios recited herein also include
all sub-ratios
falling within the broader ratio.
[0089] The term "about" can refer to a variation of 5%, + 10%, 20%, or
25% of the
value specified. For example, "about 50" percent can in some embodiments carry
a variation
from 45 to 55 percent. For integer ranges, the term "about" can include one or
two integers
greater than and/or less than a recited integer at each end of the range.
Unless indicated
otherwise herein, the term "about" is intended to include values and ranges
proximate to the
recited range that are equivalent in terms of the functionality of the
composition, or the
embodiment.
[0090] As will be appreciated by one skilled in the art, aspects of the
present invention may be
embodied as a system, method or computer program product. Accordingly, aspects
of the
present invention may take the form of an entirely hardware embodiment, an
entirely software
embodiment (including firmware, resident software, micro-code, etc.) or an
embodiment
combining software and hardware aspects that may all generally be referred to
herein as a
"circuit," "module" or "system." Furthermore, aspects of the present invention
may take the
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form of a computer program product embodied in one or more computer readable
medium(s)
having computer readable program code embodied thereon.
[0091] Any combination of one or more computer readable medium(s) may be
utilized. The
computer readable medium may be a computer readable signal medium or a
computer
readable storage medium. A computer readable storage medium may be, for
example, but not
limited to, an electronic, magnetic, optical, electromagnetic, infrared, or
semiconductor
system, apparatus, or device, or any suitable combination of the foregoing.
More specific
examples (a non-exhaustive list) of the computer readable storage medium would
include the
following: an electrical connection having one or more wires, a portable
computer diskette, a
hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable
programmable read-only memory (EPROM or Flash memory), an optical fiber, a
portable
compact disc read-only memory (CD-ROM), an optical storage device, a magnetic
storage
device, or any suitable combination of the foregoing. In the context of this
document, a
computer readable storage medium may be any tangible medium that can contain,
or store a
program for use by or in connection with an instruction execution system,
apparatus, or
device.
[0092] A computer readable signal medium may include a propagated data signal
with
computer readable program code embodied therein, for example, in baseband or
as part of a
carrier wave. Such a propagated signal may take any of a variety of forms,
including, but not
limited to, electro-magnetic, optical, or any suitable combination thereof. A
computer
readable signal medium may be any computer readable medium that is not a
computer
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readable storage medium and that can communicate, propagate, or transport a
program for use
by or in connection with an instruction execution system, apparatus, or
device.
[0093] Program code embodied on a computer readable medium may be transmitted
using
any appropriate medium, including but not limited to wireless, wireline,
optical fiber cable,
RF, etc., or any suitable combination of the foregoing.
[0094] Computer program code for carrying out operations for aspects of the
present
invention may be written in any combination of one or more programming
languages,
including an object oriented programming language such as Java, Smalltalk, C++
or the like
and conventional procedural programming languages, such as the "C" programming
language
or similar programming languages. The program code may execute entirely on the
user's
computer, partly on the user's computer, as a stand-alone software package,
partly on the
user's computer and partly on a remote computer or entirely on the remote
computer or server.
In the latter scenario, the remote computer may be connected to the user's
computer through
any type of network, including a local area network (LAN) or a wide area
network (WAN), or
the connection may be made to an external computer (for example, through the
Internet using
an Internet Service Provider).
[0095] Aspects of the present invention are described below with reference to
flowchart
illustrations and/or block diagrams of methods, apparatus (systems) and
computer program
products according to embodiments of the invention. It will be understood that
each block of
the flowchart illustrations and/or block diagrams, and combinations of blocks
in the flowchart
illustrations and/or block diagrams, can be implemented by computer program
instructions.
33
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These computer program instructions may be provided to a processor of a
general purpose
computer, special purpose computer, or other programmable data processing
apparatus to
produce a machine, such that the instructions, which execute via the processor
of the
computer or other programmable data processing apparatus, create means for
implementing
the functions/acts specified in the flowchart and/or block diagram block or
blocks.
[0096] These computer program instructions may also be stored in a computer
readable
medium that can direct a computer, other programmable data processing
apparatus, or other
devices to function in a particular manner, such that the instructions stored
in the computer
readable medium produce an article of manufacture including instructions which
implement
the function/act specified in the flowchart and/or block diagram block or
blocks.
[0097] The computer program instructions may also be loaded onto a computer,
other
programmable data processing apparatus, or other devices to cause a series of
operational
steps to be performed on the computer, other programmable apparatus or other
devices to
produce a computer implemented process such that the instructions which
execute on the
computer or other programmable apparatus provide processes for implementing
the
functions/acts specified in the flowchart and/or block diagram block or
blocks.
[0098] The flowchart and block diagrams in the Figures illustrate the
architecture,
functionality, and operation of possible implementations of systems, methods
and computer
program products according to various embodiments of the present invention. In
this regard,
each block in the flowchart or block diagrams may represent a module, segment,
or portion of
code, which comprises one or more executable instructions for implementing the
specified
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logical function(s). It should also be noted that, in some alternative
implementations, the
functions noted in the block may occur out of the order noted in the figures.
For example, two
blocks shown in succession may, in fact, be executed substantially
concurrently, or the blocks
may sometimes be executed in the reverse order, depending upon the
functionality involved. It
will also be noted that each block of the block diagrams and/or flowchart
illustration, and
combinations of blocks in the block diagrams and/or flowchart illustration,
can be
implemented by special purpose hardware-based systems that perform the
specified functions
or acts, or combinations of special purpose hardware and computer
instructions.
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