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A technique for measuring the ash content of coal in a tailings stream
Int. J. 4ppI. Radiat. I.~m. Vol. 34. No. 1. pp. 45 54. 1983
0020-708X,83,1111)045-10503.0~) 0 Pergamon Press Ltd
Printed in Great Britain
A Technique for Measuring the Ash Content'of Coal in a Tailings Stream I. S. B O Y C E Applied Nuclear Geophysics Group, Atomic Energy Research Establishment, Harwell, Didcot, Oxon., U.K.
A technique is described for developing an on-line instrument measuring the ash content of coal in a coal washery tailings stream. The method employs two radioisotope-detector systems, a 137Cs density transmission gauge and a Compton backscatter x-ray gauge with 1°9Cd. TO evaluate the technique under typical plant conditions, a full-scale slurry measuring loop was constructed. The accuracy of the "'dry basis" ash measurement, in a measurement time of 500 s was ___4~o ash (95~o confidence level) for an ash range from 48 to 66~ ash with the solids content varying from 18 to 35~o. A calibration procedure is described which requires no knowledged of the values of the solids contents of the slurries used for calibration.
I. Introduction
substance, aluminium as the mineral content and water. A diagram of the relevant radiation attenuation and scattering considerations is given in Fig. 1. If, p' = mass attenuation coefficient at the energy of the incident radiation; ~ " = mass attenuation coefficient at the energy of the backscattered radiation (/z" = / a ' for coherent scattering); a = scattering coefficient for either C o m p t o n or coherent scattering; and /~ = ~ ' + if', then for an infinitely thick sample the saturation backscattered intensity n for i components in concentrations r~ (by weight) is,
THERE is a requirement to control the efficiency of froth flotation cells at coal washery plants. Continuously monitoring on-line the ash content of coal in the tailings slurry out-put stream will provide necessary information for this control. On-line equipment already exists for measuring the ash content of particulate coal. This paper describes an extension to one of those methods (low energy x-ray backscatter) to establish a technique on which to base the development of an on-line instrument measuring the ash content of coal in a concentrated tailings stream.
E ¢Tiri
n = k i
(1) #iri'
i
2. Method of Measurement
If suffixes, c, a and w refer to carbon, aluminium and water respectively, r is the weight fraction of ash in the coal and s is the weight fractions of solids in the slurry, equation (1) then becomes,
The solids content of the tailings output stream from froth flotation cells is typically 5~o. Preliminary calculations indicated that a more acceptable sensitivity is achieved if the ash measurement is made on a more concentrated slurry of about 20°J0 solids content. With a slurry of this concentration, the chosen method of measurement comprises two radioisotope gauges. An x-ray backscatter gauge primarily measures the ash content of the slurry whilst a 7-ray transmission gauge primarily measures the solids content of the slurry. By suitably combining the outputs of the two gauges• the "'dry basis" ash content of coal in the slurry can be determined.
n = k aars + ac(1 - r)s + aw(1 - s) #ars +/1,(1 - r)s +/~w(1 - s)"
(2)
•The choice of a suitable radiation energy is a compromise between two conflicting requirements. O n the one hand the energy must be high enough so that the incident and backscattered x-rays are not severely attenuated when they pass through the wall of the slurry containment vessel. On the other hand a relatively low energy is required to achieve a high sensitivity of ash measurement, the sensitivity S, being defined as the relative change in backscattered x-ray intensity for a given relative change in ash content,
2.1. x-ray backscatter gauge
For an understanding of the problem and the factors affecting the choice of x-ray energy, it is convenient to consider the coal slurry as a threecomponent system consisting of carbon as the coal
~n/n dn r S . . . . . . 8r/r dr n 45
(3)
I. S. Boyce
46
use/l~ -----lq, = /l which gives. z = z0 exp - [_pc(l _ s) + s "
16)
As pc is not constant but varies with the ash content of the coal*, it is seen that solids content is not measured uniquely by a ``'-ray transmission gauge, The manner in which ash content interferes with the solids content determination is developed empirically in Section 8.1. 'INFINITELY'
THICK
COAL
SLURRY
3. Re-circulating Slurry Loop p.'
--
moss attenuation coefficient incident radiation.
for
~ " --
mass a t t e n u a t i o n coefficient for b a c k scattered radiation (2 lr b o c k s c o t t e r i n g assumed )
o" =
Cornpton scattering cross-section
Suffixes c , a and w refer to cool ash and water respectively
substance,
FiG. 1. Simple three-component model for ash-in-tailings.
Differentiating equation (2) with respect to r and combining with equation (3), an expression for S(r,s) can be derived. Following a series of such calculations it was concluded that a measurement based on Campton backscattering of 22keV x-rays from [°9Cd offered the best compromise between the factors mentioned above. 2.2 ;'-Ray transmission .qauge An accurate knowledge of the solids content must be available to convert the ash content of the slurry into ash content of the solids. A convenient method of doing this is to use a radioisotope transmission gauge based on a ~3VCs source. The theoretical model in this case has two components; coal (c) and water(w). If the linear path of the 7-rays through the slurry is considered to be formed of two parts, xc and x~, each component having density Pc and P d = 1), then the transmitted 7-ray intensity z is given by, z = z0 exp - [#cPg% + #~,Cw]
(41
where Zo is the incident radiation intensity and/~¢ and /t,~ are the mass attenuation coefficients for ~3VCs ",,-rays in coal and water respectively. Using the solids content wt/wt fraction s to relate x~ and x , and putting the total path length through the slurry (x~ + x,,,) equal to x, equation (4) becomes,
- = -oexp
/
In order to establish a realistic accuracy to which the ash content (corrected for variations in solids content) could be measured, a fullscale re-circulating slurry loop was constructed so that the work would be based on slurries flowing under envisaged conditions at a coal-washery plant. A schematic diagram of the slurry loop is shown in Fig. 2. Slurry from a sump tank (capacity 180 LI is pumped around a primary flow loop. At a "T" junction located below the maximum rise of the primary flow loop, some of the slurry is taken through a valve V I and discharges freely into the vertically mounted flow-cell. Another valve V2 controls the flow rate t h r o u g h ' t h e flow-cell from which the slurry then passes back into the sump tank. With V2 set to give a suitable flow rate, V1 is adjusted so that the flow-cell is just on the point of overflowing. 3.1 Source-detector systems and flow-cell A schematic diagram of the arrangement of the two sources and detectors on the flow-cell is shown in Fig. 3. The density transmission gauge comprised a 4 mCi
/
gouge x_ioy
vI
gouge
Density V2
p,(l ~ s ) + s
(5)
For simplified feasibility calculations it is sufficient to
* It was conlirmed experimentally, with the coals being used. that coat particle density could be represented by, p = 0.95 + 0.017 1'!i, ash).
FiG. 2. Schematic diagram of the re-circulating slurry loop.
Measuring the ash content of coal
47
T - r a y scintillation detector in lead collimator
4 mCi 137Cs source in lead collimator
Horizontal axes of the two detector systems separated by 150 mm
Polypropylene f l o w - cell
/
\
\
\
N ~
\
~ ~11 --
0 . 2 5 mCi ~°gCd the centre [ of a heavy alloy
__---1-sourcein
I1~=.--"'--
1 , I \
\
x - r a y scintillation detector
FIG. 3. Schematic diagram of the two source-detector systems.
source of 13~Cs and a scintillation counter with a 25 mm dia. x 25 m m thick NaI(T1) crystal. The x-ray backscatter gauge comprises a scintillation counter with a 75 mm dia. x 1 mm thick NaI(T1) crystal and mounted on the crystal window was a 0.25mCi source of 1°9Cd let into an annular disc of heavy alloy. This whole assembly was firmly mounted in contact with a wall of the flow-cell. The heavy alloy disc serves the very important function of preventing a large fraction of x-rays backscattered by the flowcell wall from reaching the detector. Ideally only x-rays scattered from within the slurry should be recorded. The horizontal axis of the two detector systems were separated vertically by about 150 mm. This was necessary so as to reduce to a minimum the interference from 13:Cs ;'-rays with the x-ray detector. The flow-cell was constructed from polypropylene, a material chosen because of its low attenuation for 20keV x-rays combined with a high resistance to abrasion from coal slurries. The rectangular crosssectional size was 150 x 75 mm. A slurry path length of 150mm was chosen for the ;'-ray transmission gauge as this can be shown to provide near optimum sensitivity for the density gauge. The 75 mm dimension is simply a convenient size greater than the saturation backscatter depth labour 4 0 m m ) for ]°gCd 22 keV x-rays.
3.2 Electronic system Basically this provided for the print-out of counts recorded in a chosen measurement time. For the density gauge detector, a total energy count system was used, i.e. all events above a minimum energy threshold were recorded. However for the x-ray detector a pulse amplitude selector was incorporated. This enabled two energy windows to be set so that the required 20 keV x-rays could be recorded separately from the unwanted high energy ;,-ray component of 1°9Cd. Figure 4 shows an energy spectrum from the x-ray detector for water in the flow-cell with the chosen settings f o r t h e two energy windows W l and W2. The x-ray detector system also incorporated a gain stabilisation unit. This operated on the well defined 20 keV peak and automatically made changes to the gain of the detector to counteract any tendency for the energy spectrum to move relative to the settings of the two energy windows. A multi-channel analyser was also connected to the x-ray detector output to enable energy spectra to be recorded.
4. Interference Effects in the Backscatter Energy Window Two factors give rise to counts in the energy window W1 which are not associated with backscattering
48
I.S. Boyce 16000
~l-~W I
..A w
W2
14000
>=
12000
to 0
I0000
(5 tit
o o 1
8000 6000
co
4000
2000
0
I0 20
30 40 x-roy
50 60
energy,
70 80 90 keV
100
FIG. 4. Water backscatter spectrum from the flow-cell.
of 22keV x-rays. One of these contributions arises from 88 keV y-rays which form a small fraction (3%) of the output from t°9Cd. These backscatter at 65 keV and are not totally resolved within the energy window W2. The number appearing in W1 was determined by placing a 0.5 mm copper disc over the 1°9Cd source. This attenuates 22keV x-rays by a factor of 2 x 10- 5 whereas 88 keV is only attenuated by a factor of 0.8. Figure 5 shows the backscattered spectrum obtained from water in the flow-cell with the copper disc over the source. The fraction of counts appearing in energy window W l was 0.10 of the number appearing in window W2. The other cause of counts appearing in W l (and also appearing in W2) arises from scattering of ~37Cs '/-rays. With water in the flow-cell and the ,09 Cd source removed,
2000
".~-- W I
-'-
1800
I
1600
I
W2
---
1400 1200
(5 w
o o ~. o
I000
aoo 600 4OO 200 ~0
20
30
40 50 6o 70 80 x - r a y energy, keV
90
100
FIG. 5. Water backscatter spectrum from the flow-cell with 0.5 mm copper disc covering the t°'~Cd s o u r c e .
Fig. 6 shows the energy spectrum for scattered 13-Cs ":-rays appearing in W1 and W2. With the axes of the two detectors separated by 150 ram, this interference is quite small, being only 18 cps and 240cps in W1 and W2 respectively. Due allowance was made for these contributions when deriving the net backscattered countrate in window Wl.
5. Coal Slurry S a m p l e s Slurries of five different ash values were used. They covered an ash range (dry basis} from 48 to 66°0 and had been made by combining froth cell feed and tailings in various proportions. Details of the ash values. as later determined from samples taken during the experimental work, are given in Table 1.
6. Experimental Procedure with the Slurry Loop Each of the five slurry samples (initially having a solids content of about 30%) was, in turn, transferred into the sump tank of the slurry loop. When countrat6 conditions appeared steady, as continuously monitored by a chart recorder, a set of measurements were taken. This comprised recording the counts from the density gauge and backscatter gauge (windows WI and W2) for a total period of 500 s separated into 5 periods of 100s each. At the end of each 100s period a small sample of slurry was taken from the outlet of the flow-cell. The total volume of sample removed was about 2 L. This was later weighed and carefully oven dried (at a temperature of I10~C) so that the solids content could be determined. After a set of countrate measurements had been recorded, a quantity of water added to the sump tank so as to
Measuring the ash content o{ coal
49
40-
35-
I 30-
~ 2s ¢5 ~
20
0
_o g 15 o
I0
5
0
I II
tO
I
20
I
30
I
40
I
,50
x - r o y energy,
I
60
I
70
I
80
I 90
I00
keV
FIG. 6. Spectrum of 1arCs interference in the x-ray detector with water in the flow-cell.
reduce the solids content by about 3~o. This measurement and sampling procedure was repeated until the solids content was reduced to ~/bout 20~o. The slurry was then removed from the sump tank. Each of the other four slurry samples, of differing ash, was then handled in a similar manner. A total of 24 oven dried samples were collected and these were then analysed for ash content.
7. Results All the relevant ash values, solids contents and countrates are tabulated in Table 1. As the decay of ~°gCd was significant during the course of these measurements, the countrates have been corrected to a common reference date before entering them into •the table. Figures 7 and 8 have been drawn from the data in Table 1 to show the relationship between density gauge countrate and x-ray backscatter gauge countrate each against °o solids. As solids contents were not accurately known until after representative samples had been taken and dried, it was not possible to produce slurries having exactly the same ~o solids for each of the five ash values. A series of curves therefore cannot be drawn directly of x-ray backscatter gauge countrate against °o ash for a range of solids contents. However. such curves can be derived from Fig. 8. Using this figure, relevant countrates, for each of the five ash values, can be read off for a number of
chosen solid contents. This has been done to produce Fig. 9 where the straight lines represent the best "least squares fit" with the added constraint that the slopes of the lines are all equal. The relevant importance of solids content, when trying to measure ash, can now be seen from this figure. A change of 5~o solids content, for a constant ash value, produces approximately the same change in x-ray backscatter gauge countrate as does a change of 10~o ash for a constant solids content. This is further illustrated from Figs 10 and 11 which show two pairs of typical spectra from three different slurries. Figure 10 is for slurries having the same solids contents but differing in ash, whereas Fig. 11 is for the same ash sample but at different solids contents. By comparing these two figures it is seen that a change of 18~o ash produces about the same change in the x-ray spectrum as does a 9~o change in solids content. So as before, a I~o change in solids is equivalent to a 2 ~ change in ash. Another point worth noting from these two figures in conjunction also with Fig. 4, is the complete lack of sensitivity of the 88 keV 7-ray (backscattered at 65 keV) to changes in composition. Whilst the peak intensity in Wt changes by nearly a factor of four between water (Fig. 4) and the dotted spectrum of either Figs 10 or 11, there is virtually no change in the peak intensity in W2. These results have shown that to obtain an accuracy of 2°,,0ash, the solids content has to be known to at least 1°,o solids. However. the density gauge does
I.S. Boyce
50
TABLE 1. Experimental data relevant to the full-scale slurry loop Cps Sample ref. no.
Backscatter gauge
Residual errors*
°o Solids
Den. gauge
WI
W2
Nett Wl
30.5 27.5 24~ 20.8
998 1023 1048 1080
2503 2825 3309 3678
3545 3577 3607 3628
2148 2467 2948 3315
2.4 0.6 -4.9 0.4
0.0 0.2 1.7 -0.3
Mean
66.2 66.4 66.3 65.9 66.2
31.9 28.5 25.7 22.9 20.0
1004 1033 1052 1073 1090
2827 3154 3409 3677 3988
3596 3617 3624 3634 3648
2467 2792 3046 3314 3623
-2.4 - 1.7 - 1.2 0.6 -0.9
0.5 -0.3 -0.1 -0.6 0.3
Mean
6t.2 61.2 60.9 61.1 61.0 6l.t
35.2 32.2 29.0 25.2 21.6
984 1010 1038 1059 1083
2639 2967 3238 3581 3915
3592 3614 3629 3639 3653
2280 2606 2920 3216 3550
0.9 - 1.9 -0.7 -1.l 0.6
0.1 0.3 -0.8 0.1 0.0
Mean
57.4 57.5 57.5 57.7 57.6 57.5
34.4 30.1 26.2 22.4 18.5
1000 1031 1055 1083 1111
2880 3223 3544 3967 4488
3602 3616 3634 3650 3670
2519 2862 3180 3602 4121
0.4 1.2 1.5 1.5 - 1.2
-0.1 -0.5 -0.1 -0.2 0.3
Mean
54.2 54.1 54.1 54.1 53.6 54.0
29.1 26.5 24.3 21.5 19.7
1045 1069 1078 1097 1113
3522 3783 4046 4377 4593
3632 3656 3657 3663 3676
3159 3417 3680 4011 4225
2.0 5.8 -0.1 - 2.4 0.7
0.1 - 2.0 0.5 0.9 -0.4
Mean
47.8 48.2 47.4 47.6 47.4 47.7
1230
8765
3830
8382
°o Ash
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Water re~rence
°o Ash
r.m.s 2.0
° o Solids
r.m.s. 0.7
* Residual errors (a) ');, Ash: the differences between the values predicted by equation (181 and the true values (column 2). (bl °~ Solids: the differences between the values predicted by equation (10) and the true values (column 3). However, the values of r used in equation (101 were those derived from equation (18). not measure solids content uniquely. Equation (6) Section 2.2, predicted, and Fig. 7 confirmed, that a prior knowledge of ash content is required before solids content can be evaluated. The next section deals with the interdependence of these two countrate measurements and methods for correcting for solids content variations.
8. Data Handling and Accuracy A number of regression equations were calculated relating selected parameters from ash content, solids content, density gauge countrate and backscatter gauge countrate (net countrate in window WI). The constants of the equations were calculated by the usual method of "qeast sum of squares" for the residual errors, and the root mean square (r.m.s.) of residual errors gives a measure of the "goodness of fit" of the data to the proposed equation.
In the results that follow, the following notation is used along with the data from Table I. r = °Jo ash constant: s = o~ solids content (wt/wt); n = backscatter gauge, net W1. cps; - = density gauge cps; al, a2, etc = constants; b:, b2, etc = constants. The first set of equations calculated for solids content and then ash content each require a prior knowledge of the other parameter (i.e. ash content has to be known when evaluating solids content and vice versa). These equations were then combined to produce two methods that could be used with an on-line instrument to measure ash content directly. Further consideration was given to developing a single calibration procedure that did not necessitate this intermediate stage of having to first produce two calibration equations based on known solids contents. Such a procedure was developed, semi-theoretical and semi-empirical, and is described in the last part of this section.
Measuring the ash content ol coal
%
Ash
"o
--o-477 ---x--54.0 --&--575
1120
I ~ x
o
--a--
51
g u
66.2
~o ~
4000
o
o
e-
t-
g Q
1040
g
g
,ooo
D ,,D
\\,\ I
--
15
I
i
P
25 % Solids
2500
I x
~Xl&
Solids
35
FIG. 7. Density gauge countrate against °,o solids.
I 50
I
I 60
-
_ J
J 70
% Ash
8.1 Calculating solids content, knowing ash content If Fig. 7 is redrawn to extend the absissa to 0~o solids, it is seen that all five lines converge to pass through the countrate value for water (0Vo solids). They have the form, (7)
z = bl + b2"s
with a common intercept b~ and a gradient b: varying as a function of ash content. It was tested, and found to be a good approximation, that b2 could be expressed as a linear function of ash, i.e.
FIG. 9. x-Ray backscatter gauge countrate against ash content (derived from Fig. 81.
(8)
b2 = b3 + b='r
Combining equations (7) and (8), and renumbering the constants, gives, (9)
z = bl + b2"s + b 3 " s ' r or
z b~ s = b2 + b~'r" -
(lOt
A "'least squares fit" of the relevant 24 sets of data to 4500
\
~a
__-: ....
% Ash 47'.7
tx,\ ~ \ " ~ = ~ ~ \ \
----o----
54.0
7000
61.t 66.2
6000
57.5
~ ~,
I.~--W I
~'~
W2
5000
~ 3500
~
~
c~
\N
% Ash 4000
---
48 s6
% Solld$ 26
26
--.3000
2500
(.3 I000
15
25 % Solids
35
FIG. 8. x-Ray backscatter gauge countrate against solids content,
0
I0
2LO SO 40 50 60 70 x - r o y energy,
80 90 I00 keY
FIG. 10. Comparison of spectra from hvo slurries with the same solids content but differing in ash content.
52
I.S. Boyce 7000
L-~--W I
W2
~,~-
tably valid. The values of the constants are given in Table 2.
! ]
6000
>
8.3 Accuracy jor the direct nzeas,o'ement c~lash content based on separate calibration" equations/br solids and ash contents that require a prior knowledye o f solids content
! 5000 %Ash 48 ----- 48
(,O
O~
4000
% Solids 26
i i
35
-
o o
~.
1 3ooo
I
,3 ~ooo
'
,ooo
',I
;
"
1
",,
Ii
'~
Two methods were devised for using equations (10) a n d (13) to produce a means whereby an on-line gauge could evaluate the ash content corrected for variations in solids content. 8.3.1 Quadratic method. Equations (101 and (13) can be c o m b i n e d to eliminate solids content, s. giving.
I l
I,
r o
IO
20
30
40
.50
x-roy
60
energy,
70
80
90
keY
FIG. 11. Comparison of spectra from two slurries with the same ash content but differing in solids content.
equation (9) gave r.m.s, error in z of 3 c p m which is equivalent to a r.m.s, error in s of 0.47% solids. The values of the constants are given in Table 2. 8.2 Calculating ash content, knowing solids content It was shown in Fig. 9 that the relationship between backscatter gauge nett countrate a n d % ash was represented by, n = al + a2"r
(11)
where a2 is c o n s t a n t (over the range of solids content being considered) a n d aa varies with solids content. This variation was found to be approximately linear, i.e. a t = a 3 + a4"s
(12)
C o m b i n i n g equations (11) a n d (12) a n d r e n u m b e r i n g the constants gives, r = a t -- a 2 'n -+- a 3 "s
(13)
A "least squares fit" to this equation for the 24 data points gave a r.m.s, error in r of 1.5% ash, confirming that the assumptions a n d a p p r o x i m a t i o n s were accep-
TAIILE 2.
+ a2"n + a 3 \(~ - ~z-bl -h~.; 1
a~
O n expanding, this produces a quadratic expression in r based on the 6 constants, whose values have already been evaluated, a n d the countrates of the two detectors. It was established that the larger root of this quadratic gives the required ash value. The accuracy of this m e t h o d was checked b3; calculating the differences between the true known values of ash content a n d the values of r calculated from this quadratic expression for each of the 24 pairs of data for n a n d -. The r.m.s, error of the differences was 3.2°0 ash. One sample, n u m b e r 10 in Table 1, gave an exceptionally large error of 8.2% ash. If this was omitted, the r.m.s. error was reduced to 2.8°0 ash. 8.3.2. lterative method. Equations (10) and (13) were again used. Considering each pair of data values of n and z in turn. an initial value of solids content of 30°, was assumed. This assumed value was used in equation (13) to give the first estimate for r. This estimate was then used in e q u a t i o n (10) to give an improved value for s. E q u a t i o n (13) was used a second time with this improved value of s to give the second estimate for r, a n d so on. It was found that after a b o u t 5 - I 0 such iterations no significant further changes were taking place in the recalculated values of s a n d r. Table 3 shows values of s a n d r for 10 iterations for sample n u m b e r 19. This particular sample has been illustrated as it represents the worst case with the true solids content being only 18.5°o c o m p a r e d to the in-
Constants and r.m.s, errors for the various least squares regression equations
Equation constant al or hi a2 or b2 a3 or h3 u4 us u~, Residual r.m.s, error
(14)
I00
Equation number in text (I 0) 1.2392 x 10s -3.3371 -6.6686 × lO - 2
3 cps )0.5% solids
( l 3)
(I 8)
1.8103 x 10: -2.1718 x 10 2 -2.1337
-7.5001 x 102 -4.6323 x 10 -t 2.3944 5.2420 x 10 "~ --1.6069 x I0 "~ -2.1521 x 10 s _.0 , ash
.5% ash
53
Measurino the ash content ofcoal
TABLE 3. An example of the iteration method for evaluating ash content Sample number 19
then renumbering the constants, the final expression is obtained, r = a I 4- il2"n 4- a3"z
°
%
Iteration
Solids
Ash
+ a4"n'z+
1 2 3 4 5 6 7 8 9 10 True value Error
30.00 24.80 21.70 20.19 19.53 19.25 19.14 19.09 19.07 19.07 18.50 0.57
27.47 38.57 45.19 48.41 49.82 50.41 50.65 50.75 50.79 50.81 53.60 - 2.79
A "least squares fit" to this equation for the 24 data points gave a r.m.s, error of 2.0% ash; the individual residual errors are shown in Table 1. This represents a significant improvement over the previous methods. The values of the constants are given in Table 2. Sample numbers 3 and 21 gave errors of - 4 . 9 and 5.8% ash respectively. If these were omitted from the calculations, then the r.m.s, error for the remaining 22 data points was reduced to 1.4% ash. A check was made to ensure that this "least squares fit" was not specific solely to the data on which it was based. To do this a "least squares fit" was again calculated, this time omitting sample numbers 2, 5, 10, 19 and 22. These samples represented a range of solids contents, one from each of the five main ash values. This r.m.s, error of the equation based on the remaining 19 data points was 2.1% ash. Using this latest equation, the ash contents of the five omitted samples were calculated and compared with their known true ash values. The r.m.s, error of these five differences was 2.0% ash. This confirmed that equation (18) was valid for general use.
itial assumed value of 30%. The r.m.s, error, based on the differences between the true ash contents and the calculated values after ten iterations, for all 24 samples was 3.0% ash. 8.4 Accuracy f o r the direct measurement o f ash content based on a calibration procedure that requires no knowledge o f solids content The two methods described above in Section 8.3 each have two c o m m o n disadvantages. One is the requirement to have to measure the solids contents of all the slurry samples used in the calibration work before the two calibration equations can be evaluated. The second disadvantage is that the overall error in estimating the ash content will be a combination of errors from each of the two separate calibration equations. The method now to be described, semi-theoretical and semi-empirical, eliminates those disadvantages. It uses a direct single calibration procedure which requires no knowledge of solids contents. Equation (10) can be written,
Expanding this for a limited number of terms and renumbering the constants gives, s = bl + b2"z + b a ' z ' r + b4"r
(15)
A squared tel'm in 'n' is added to equation (13), as experience in backscatter measurements has shown that. in general, the variation with countrate is a quadratic, i.e. r = as + a2"n + a 3 • n 2 + a4"s
Part of the overall 2.0% r.m.s, error in ash, mentioned in the above section, will be due to counting statistics from the countrate measurements of the two detectors. It can be shown, from the propagation of errors, that when measurements in n and z are combined in a formula to give an overall figure r, where r = f(n,z), then the standard deviatatibn in r is given by,
I(£V.
far',::
+ t-~-~z) "o':
(19)
where tr, and tr, are the individual standard deviations for n and z respectively. It can further be shown that for a measurement time of t (s)
7,
6. =
and
a~ =
,/:
cps
which reduces equation (19) to
(16)
Eliminating s between Equations (15) and (16) and renumbering the constants gives,
°"
,,/7 ~/\a,)
+
Differentiating equation (18) gives,
r = (as 4- a2"n 4- a3'n 2 + a 4 " z l ' ( a s + a6"z) - i
(18)
9. Equivalent Error in Ash Due to Counting S t a t i s t i c s
a, = ~/\On.]
s = b4(z - b l ) ' ( t + bs"r) - I
a s ' z 2 + a6"n 2
(17)
On expanding, to include up to squared terms, and
0r ~n
-
a2 + a 4 " z + 2'o6"11
(20)
54
I.S. Boyce
10. Conclusion
and ?r
- as + a ~ ' n
?z
+ 2"asz.
For a coal of high ash, at a high solids content, typical values of n and z (from Table 3) are about 2200 and 1000 cps respectively. Substituting all relevant data into equation (20) gives,
1
a~,, \
11 -"~+ 116 = ~Jot°/ash.
(21)
\
So for a measurement time of 500 s, as used in this work, or, = 0.5~ ash. The results of these calculations are only relevant to the strengths of the two particular radioisotope sources used in this work. Also it will be noted, from equation (21), that the main contribution to or, came from the second term under the square root. This is the density gauge contribution. The strength of the 137Cs source could, with advantage, be increased by a factor of four. This would reduce a, to ~r, =
_55
+ 29 = - ~ ~o ash
which for the same 500 s measurement period as before, would reduce a, to 0.20/0 ash.
This study has shown that it is possible to produce an on-l'ine instrument to monitor continuously the ash content of a concentrated tailings slurry and to calculate the ash content, corrected for solids content." of the solid material. The method employs two radiosotope-detector systems. One is a I3~Cs density transmission gauge and the other a C o m p m n backscatter x-ray gauge with tO9Cd ' A data handling procedure has been developed which will enable a instrument to be calibrated over a wide range of slurry solids contents without requiring a knowledge of the values of the solids contents. Only "dry basis" ash values are needed for calibration. An ash range from 48 to 66°; ash was tested with solids content from 18 to 35°,,. The accuracy for the "dry basis" ash measurement, in a 500 s measurement time, was + 4°~oash at the 95°;0 confidence level.
Acknowledgements--The work described above was totally
supported by the Mining Research and. Development Establishment of the National Coal Board and we wish to thank the Director of that establishment for permission to publish this paper.
0020-708X,83,1111)045-10503.0~) 0 Pergamon Press Ltd
Printed in Great Britain
A Technique for Measuring the Ash Content'of Coal in a Tailings Stream I. S. B O Y C E Applied Nuclear Geophysics Group, Atomic Energy Research Establishment, Harwell, Didcot, Oxon., U.K.
A technique is described for developing an on-line instrument measuring the ash content of coal in a coal washery tailings stream. The method employs two radioisotope-detector systems, a 137Cs density transmission gauge and a Compton backscatter x-ray gauge with 1°9Cd. TO evaluate the technique under typical plant conditions, a full-scale slurry measuring loop was constructed. The accuracy of the "'dry basis" ash measurement, in a measurement time of 500 s was ___4~o ash (95~o confidence level) for an ash range from 48 to 66~ ash with the solids content varying from 18 to 35~o. A calibration procedure is described which requires no knowledged of the values of the solids contents of the slurries used for calibration.
I. Introduction
substance, aluminium as the mineral content and water. A diagram of the relevant radiation attenuation and scattering considerations is given in Fig. 1. If, p' = mass attenuation coefficient at the energy of the incident radiation; ~ " = mass attenuation coefficient at the energy of the backscattered radiation (/z" = / a ' for coherent scattering); a = scattering coefficient for either C o m p t o n or coherent scattering; and /~ = ~ ' + if', then for an infinitely thick sample the saturation backscattered intensity n for i components in concentrations r~ (by weight) is,
THERE is a requirement to control the efficiency of froth flotation cells at coal washery plants. Continuously monitoring on-line the ash content of coal in the tailings slurry out-put stream will provide necessary information for this control. On-line equipment already exists for measuring the ash content of particulate coal. This paper describes an extension to one of those methods (low energy x-ray backscatter) to establish a technique on which to base the development of an on-line instrument measuring the ash content of coal in a concentrated tailings stream.
E ¢Tiri
n = k i
(1) #iri'
i
2. Method of Measurement
If suffixes, c, a and w refer to carbon, aluminium and water respectively, r is the weight fraction of ash in the coal and s is the weight fractions of solids in the slurry, equation (1) then becomes,
The solids content of the tailings output stream from froth flotation cells is typically 5~o. Preliminary calculations indicated that a more acceptable sensitivity is achieved if the ash measurement is made on a more concentrated slurry of about 20°J0 solids content. With a slurry of this concentration, the chosen method of measurement comprises two radioisotope gauges. An x-ray backscatter gauge primarily measures the ash content of the slurry whilst a 7-ray transmission gauge primarily measures the solids content of the slurry. By suitably combining the outputs of the two gauges• the "'dry basis" ash content of coal in the slurry can be determined.
n = k aars + ac(1 - r)s + aw(1 - s) #ars +/1,(1 - r)s +/~w(1 - s)"
(2)
•The choice of a suitable radiation energy is a compromise between two conflicting requirements. O n the one hand the energy must be high enough so that the incident and backscattered x-rays are not severely attenuated when they pass through the wall of the slurry containment vessel. On the other hand a relatively low energy is required to achieve a high sensitivity of ash measurement, the sensitivity S, being defined as the relative change in backscattered x-ray intensity for a given relative change in ash content,
2.1. x-ray backscatter gauge
For an understanding of the problem and the factors affecting the choice of x-ray energy, it is convenient to consider the coal slurry as a threecomponent system consisting of carbon as the coal
~n/n dn r S . . . . . . 8r/r dr n 45
(3)
I. S. Boyce
46
use/l~ -----lq, = /l which gives. z = z0 exp - [_pc(l _ s) + s "
16)
As pc is not constant but varies with the ash content of the coal*, it is seen that solids content is not measured uniquely by a ``'-ray transmission gauge, The manner in which ash content interferes with the solids content determination is developed empirically in Section 8.1. 'INFINITELY'
THICK
COAL
SLURRY
3. Re-circulating Slurry Loop p.'
--
moss attenuation coefficient incident radiation.
for
~ " --
mass a t t e n u a t i o n coefficient for b a c k scattered radiation (2 lr b o c k s c o t t e r i n g assumed )
o" =
Cornpton scattering cross-section
Suffixes c , a and w refer to cool ash and water respectively
substance,
FiG. 1. Simple three-component model for ash-in-tailings.
Differentiating equation (2) with respect to r and combining with equation (3), an expression for S(r,s) can be derived. Following a series of such calculations it was concluded that a measurement based on Campton backscattering of 22keV x-rays from [°9Cd offered the best compromise between the factors mentioned above. 2.2 ;'-Ray transmission .qauge An accurate knowledge of the solids content must be available to convert the ash content of the slurry into ash content of the solids. A convenient method of doing this is to use a radioisotope transmission gauge based on a ~3VCs source. The theoretical model in this case has two components; coal (c) and water(w). If the linear path of the 7-rays through the slurry is considered to be formed of two parts, xc and x~, each component having density Pc and P d = 1), then the transmitted 7-ray intensity z is given by, z = z0 exp - [#cPg% + #~,Cw]
(41
where Zo is the incident radiation intensity and/~¢ and /t,~ are the mass attenuation coefficients for ~3VCs ",,-rays in coal and water respectively. Using the solids content wt/wt fraction s to relate x~ and x , and putting the total path length through the slurry (x~ + x,,,) equal to x, equation (4) becomes,
- = -oexp
/
In order to establish a realistic accuracy to which the ash content (corrected for variations in solids content) could be measured, a fullscale re-circulating slurry loop was constructed so that the work would be based on slurries flowing under envisaged conditions at a coal-washery plant. A schematic diagram of the slurry loop is shown in Fig. 2. Slurry from a sump tank (capacity 180 LI is pumped around a primary flow loop. At a "T" junction located below the maximum rise of the primary flow loop, some of the slurry is taken through a valve V I and discharges freely into the vertically mounted flow-cell. Another valve V2 controls the flow rate t h r o u g h ' t h e flow-cell from which the slurry then passes back into the sump tank. With V2 set to give a suitable flow rate, V1 is adjusted so that the flow-cell is just on the point of overflowing. 3.1 Source-detector systems and flow-cell A schematic diagram of the arrangement of the two sources and detectors on the flow-cell is shown in Fig. 3. The density transmission gauge comprised a 4 mCi
/
gouge x_ioy
vI
gouge
Density V2
p,(l ~ s ) + s
(5)
For simplified feasibility calculations it is sufficient to
* It was conlirmed experimentally, with the coals being used. that coat particle density could be represented by, p = 0.95 + 0.017 1'!i, ash).
FiG. 2. Schematic diagram of the re-circulating slurry loop.
Measuring the ash content of coal
47
T - r a y scintillation detector in lead collimator
4 mCi 137Cs source in lead collimator
Horizontal axes of the two detector systems separated by 150 mm
Polypropylene f l o w - cell
/
\
\
\
N ~
\
~ ~11 --
0 . 2 5 mCi ~°gCd the centre [ of a heavy alloy
__---1-sourcein
I1~=.--"'--
1 , I \
\
x - r a y scintillation detector
FIG. 3. Schematic diagram of the two source-detector systems.
source of 13~Cs and a scintillation counter with a 25 mm dia. x 25 m m thick NaI(T1) crystal. The x-ray backscatter gauge comprises a scintillation counter with a 75 mm dia. x 1 mm thick NaI(T1) crystal and mounted on the crystal window was a 0.25mCi source of 1°9Cd let into an annular disc of heavy alloy. This whole assembly was firmly mounted in contact with a wall of the flow-cell. The heavy alloy disc serves the very important function of preventing a large fraction of x-rays backscattered by the flowcell wall from reaching the detector. Ideally only x-rays scattered from within the slurry should be recorded. The horizontal axis of the two detector systems were separated vertically by about 150 mm. This was necessary so as to reduce to a minimum the interference from 13:Cs ;'-rays with the x-ray detector. The flow-cell was constructed from polypropylene, a material chosen because of its low attenuation for 20keV x-rays combined with a high resistance to abrasion from coal slurries. The rectangular crosssectional size was 150 x 75 mm. A slurry path length of 150mm was chosen for the ;'-ray transmission gauge as this can be shown to provide near optimum sensitivity for the density gauge. The 75 mm dimension is simply a convenient size greater than the saturation backscatter depth labour 4 0 m m ) for ]°gCd 22 keV x-rays.
3.2 Electronic system Basically this provided for the print-out of counts recorded in a chosen measurement time. For the density gauge detector, a total energy count system was used, i.e. all events above a minimum energy threshold were recorded. However for the x-ray detector a pulse amplitude selector was incorporated. This enabled two energy windows to be set so that the required 20 keV x-rays could be recorded separately from the unwanted high energy ;,-ray component of 1°9Cd. Figure 4 shows an energy spectrum from the x-ray detector for water in the flow-cell with the chosen settings f o r t h e two energy windows W l and W2. The x-ray detector system also incorporated a gain stabilisation unit. This operated on the well defined 20 keV peak and automatically made changes to the gain of the detector to counteract any tendency for the energy spectrum to move relative to the settings of the two energy windows. A multi-channel analyser was also connected to the x-ray detector output to enable energy spectra to be recorded.
4. Interference Effects in the Backscatter Energy Window Two factors give rise to counts in the energy window W1 which are not associated with backscattering
48
I.S. Boyce 16000
~l-~W I
..A w
W2
14000
>=
12000
to 0
I0000
(5 tit
o o 1
8000 6000
co
4000
2000
0
I0 20
30 40 x-roy
50 60
energy,
70 80 90 keV
100
FIG. 4. Water backscatter spectrum from the flow-cell.
of 22keV x-rays. One of these contributions arises from 88 keV y-rays which form a small fraction (3%) of the output from t°9Cd. These backscatter at 65 keV and are not totally resolved within the energy window W2. The number appearing in W1 was determined by placing a 0.5 mm copper disc over the 1°9Cd source. This attenuates 22keV x-rays by a factor of 2 x 10- 5 whereas 88 keV is only attenuated by a factor of 0.8. Figure 5 shows the backscattered spectrum obtained from water in the flow-cell with the copper disc over the source. The fraction of counts appearing in energy window W l was 0.10 of the number appearing in window W2. The other cause of counts appearing in W l (and also appearing in W2) arises from scattering of ~37Cs '/-rays. With water in the flow-cell and the ,09 Cd source removed,
2000
".~-- W I
-'-
1800
I
1600
I
W2
---
1400 1200
(5 w
o o ~. o
I000
aoo 600 4OO 200 ~0
20
30
40 50 6o 70 80 x - r a y energy, keV
90
100
FIG. 5. Water backscatter spectrum from the flow-cell with 0.5 mm copper disc covering the t°'~Cd s o u r c e .
Fig. 6 shows the energy spectrum for scattered 13-Cs ":-rays appearing in W1 and W2. With the axes of the two detectors separated by 150 ram, this interference is quite small, being only 18 cps and 240cps in W1 and W2 respectively. Due allowance was made for these contributions when deriving the net backscattered countrate in window Wl.
5. Coal Slurry S a m p l e s Slurries of five different ash values were used. They covered an ash range (dry basis} from 48 to 66°0 and had been made by combining froth cell feed and tailings in various proportions. Details of the ash values. as later determined from samples taken during the experimental work, are given in Table 1.
6. Experimental Procedure with the Slurry Loop Each of the five slurry samples (initially having a solids content of about 30%) was, in turn, transferred into the sump tank of the slurry loop. When countrat6 conditions appeared steady, as continuously monitored by a chart recorder, a set of measurements were taken. This comprised recording the counts from the density gauge and backscatter gauge (windows WI and W2) for a total period of 500 s separated into 5 periods of 100s each. At the end of each 100s period a small sample of slurry was taken from the outlet of the flow-cell. The total volume of sample removed was about 2 L. This was later weighed and carefully oven dried (at a temperature of I10~C) so that the solids content could be determined. After a set of countrate measurements had been recorded, a quantity of water added to the sump tank so as to
Measuring the ash content o{ coal
49
40-
35-
I 30-
~ 2s ¢5 ~
20
0
_o g 15 o
I0
5
0
I II
tO
I
20
I
30
I
40
I
,50
x - r o y energy,
I
60
I
70
I
80
I 90
I00
keV
FIG. 6. Spectrum of 1arCs interference in the x-ray detector with water in the flow-cell.
reduce the solids content by about 3~o. This measurement and sampling procedure was repeated until the solids content was reduced to ~/bout 20~o. The slurry was then removed from the sump tank. Each of the other four slurry samples, of differing ash, was then handled in a similar manner. A total of 24 oven dried samples were collected and these were then analysed for ash content.
7. Results All the relevant ash values, solids contents and countrates are tabulated in Table 1. As the decay of ~°gCd was significant during the course of these measurements, the countrates have been corrected to a common reference date before entering them into •the table. Figures 7 and 8 have been drawn from the data in Table 1 to show the relationship between density gauge countrate and x-ray backscatter gauge countrate each against °o solids. As solids contents were not accurately known until after representative samples had been taken and dried, it was not possible to produce slurries having exactly the same ~o solids for each of the five ash values. A series of curves therefore cannot be drawn directly of x-ray backscatter gauge countrate against °o ash for a range of solids contents. However. such curves can be derived from Fig. 8. Using this figure, relevant countrates, for each of the five ash values, can be read off for a number of
chosen solid contents. This has been done to produce Fig. 9 where the straight lines represent the best "least squares fit" with the added constraint that the slopes of the lines are all equal. The relevant importance of solids content, when trying to measure ash, can now be seen from this figure. A change of 5~o solids content, for a constant ash value, produces approximately the same change in x-ray backscatter gauge countrate as does a change of 10~o ash for a constant solids content. This is further illustrated from Figs 10 and 11 which show two pairs of typical spectra from three different slurries. Figure 10 is for slurries having the same solids contents but differing in ash, whereas Fig. 11 is for the same ash sample but at different solids contents. By comparing these two figures it is seen that a change of 18~o ash produces about the same change in the x-ray spectrum as does a 9~o change in solids content. So as before, a I~o change in solids is equivalent to a 2 ~ change in ash. Another point worth noting from these two figures in conjunction also with Fig. 4, is the complete lack of sensitivity of the 88 keV 7-ray (backscattered at 65 keV) to changes in composition. Whilst the peak intensity in Wt changes by nearly a factor of four between water (Fig. 4) and the dotted spectrum of either Figs 10 or 11, there is virtually no change in the peak intensity in W2. These results have shown that to obtain an accuracy of 2°,,0ash, the solids content has to be known to at least 1°,o solids. However. the density gauge does
I.S. Boyce
50
TABLE 1. Experimental data relevant to the full-scale slurry loop Cps Sample ref. no.
Backscatter gauge
Residual errors*
°o Solids
Den. gauge
WI
W2
Nett Wl
30.5 27.5 24~ 20.8
998 1023 1048 1080
2503 2825 3309 3678
3545 3577 3607 3628
2148 2467 2948 3315
2.4 0.6 -4.9 0.4
0.0 0.2 1.7 -0.3
Mean
66.2 66.4 66.3 65.9 66.2
31.9 28.5 25.7 22.9 20.0
1004 1033 1052 1073 1090
2827 3154 3409 3677 3988
3596 3617 3624 3634 3648
2467 2792 3046 3314 3623
-2.4 - 1.7 - 1.2 0.6 -0.9
0.5 -0.3 -0.1 -0.6 0.3
Mean
6t.2 61.2 60.9 61.1 61.0 6l.t
35.2 32.2 29.0 25.2 21.6
984 1010 1038 1059 1083
2639 2967 3238 3581 3915
3592 3614 3629 3639 3653
2280 2606 2920 3216 3550
0.9 - 1.9 -0.7 -1.l 0.6
0.1 0.3 -0.8 0.1 0.0
Mean
57.4 57.5 57.5 57.7 57.6 57.5
34.4 30.1 26.2 22.4 18.5
1000 1031 1055 1083 1111
2880 3223 3544 3967 4488
3602 3616 3634 3650 3670
2519 2862 3180 3602 4121
0.4 1.2 1.5 1.5 - 1.2
-0.1 -0.5 -0.1 -0.2 0.3
Mean
54.2 54.1 54.1 54.1 53.6 54.0
29.1 26.5 24.3 21.5 19.7
1045 1069 1078 1097 1113
3522 3783 4046 4377 4593
3632 3656 3657 3663 3676
3159 3417 3680 4011 4225
2.0 5.8 -0.1 - 2.4 0.7
0.1 - 2.0 0.5 0.9 -0.4
Mean
47.8 48.2 47.4 47.6 47.4 47.7
1230
8765
3830
8382
°o Ash
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Water re~rence
°o Ash
r.m.s 2.0
° o Solids
r.m.s. 0.7
* Residual errors (a) ');, Ash: the differences between the values predicted by equation (181 and the true values (column 2). (bl °~ Solids: the differences between the values predicted by equation (10) and the true values (column 3). However, the values of r used in equation (101 were those derived from equation (18). not measure solids content uniquely. Equation (6) Section 2.2, predicted, and Fig. 7 confirmed, that a prior knowledge of ash content is required before solids content can be evaluated. The next section deals with the interdependence of these two countrate measurements and methods for correcting for solids content variations.
8. Data Handling and Accuracy A number of regression equations were calculated relating selected parameters from ash content, solids content, density gauge countrate and backscatter gauge countrate (net countrate in window WI). The constants of the equations were calculated by the usual method of "qeast sum of squares" for the residual errors, and the root mean square (r.m.s.) of residual errors gives a measure of the "goodness of fit" of the data to the proposed equation.
In the results that follow, the following notation is used along with the data from Table I. r = °Jo ash constant: s = o~ solids content (wt/wt); n = backscatter gauge, net W1. cps; - = density gauge cps; al, a2, etc = constants; b:, b2, etc = constants. The first set of equations calculated for solids content and then ash content each require a prior knowledge of the other parameter (i.e. ash content has to be known when evaluating solids content and vice versa). These equations were then combined to produce two methods that could be used with an on-line instrument to measure ash content directly. Further consideration was given to developing a single calibration procedure that did not necessitate this intermediate stage of having to first produce two calibration equations based on known solids contents. Such a procedure was developed, semi-theoretical and semi-empirical, and is described in the last part of this section.
Measuring the ash content ol coal
%
Ash
"o
--o-477 ---x--54.0 --&--575
1120
I ~ x
o
--a--
51
g u
66.2
~o ~
4000
o
o
e-
t-
g Q
1040
g
g
,ooo
D ,,D
\\,\ I
--
15
I
i
P
25 % Solids
2500
I x
~Xl&
Solids
35
FIG. 7. Density gauge countrate against °,o solids.
I 50
I
I 60
-
_ J
J 70
% Ash
8.1 Calculating solids content, knowing ash content If Fig. 7 is redrawn to extend the absissa to 0~o solids, it is seen that all five lines converge to pass through the countrate value for water (0Vo solids). They have the form, (7)
z = bl + b2"s
with a common intercept b~ and a gradient b: varying as a function of ash content. It was tested, and found to be a good approximation, that b2 could be expressed as a linear function of ash, i.e.
FIG. 9. x-Ray backscatter gauge countrate against ash content (derived from Fig. 81.
(8)
b2 = b3 + b='r
Combining equations (7) and (8), and renumbering the constants, gives, (9)
z = bl + b2"s + b 3 " s ' r or
z b~ s = b2 + b~'r" -
(lOt
A "'least squares fit" of the relevant 24 sets of data to 4500
\
~a
__-: ....
% Ash 47'.7
tx,\ ~ \ " ~ = ~ ~ \ \
----o----
54.0
7000
61.t 66.2
6000
57.5
~ ~,
I.~--W I
~'~
W2
5000
~ 3500
~
~
c~
\N
% Ash 4000
---
48 s6
% Solld$ 26
26
--.3000
2500
(.3 I000
15
25 % Solids
35
FIG. 8. x-Ray backscatter gauge countrate against solids content,
0
I0
2LO SO 40 50 60 70 x - r o y energy,
80 90 I00 keY
FIG. 10. Comparison of spectra from hvo slurries with the same solids content but differing in ash content.
52
I.S. Boyce 7000
L-~--W I
W2
~,~-
tably valid. The values of the constants are given in Table 2.
! ]
6000
>
8.3 Accuracy jor the direct nzeas,o'ement c~lash content based on separate calibration" equations/br solids and ash contents that require a prior knowledye o f solids content
! 5000 %Ash 48 ----- 48
(,O
O~
4000
% Solids 26
i i
35
-
o o
~.
1 3ooo
I
,3 ~ooo
'
,ooo
',I
;
"
1
",,
Ii
'~
Two methods were devised for using equations (10) a n d (13) to produce a means whereby an on-line gauge could evaluate the ash content corrected for variations in solids content. 8.3.1 Quadratic method. Equations (101 and (13) can be c o m b i n e d to eliminate solids content, s. giving.
I l
I,
r o
IO
20
30
40
.50
x-roy
60
energy,
70
80
90
keY
FIG. 11. Comparison of spectra from two slurries with the same ash content but differing in solids content.
equation (9) gave r.m.s, error in z of 3 c p m which is equivalent to a r.m.s, error in s of 0.47% solids. The values of the constants are given in Table 2. 8.2 Calculating ash content, knowing solids content It was shown in Fig. 9 that the relationship between backscatter gauge nett countrate a n d % ash was represented by, n = al + a2"r
(11)
where a2 is c o n s t a n t (over the range of solids content being considered) a n d aa varies with solids content. This variation was found to be approximately linear, i.e. a t = a 3 + a4"s
(12)
C o m b i n i n g equations (11) a n d (12) a n d r e n u m b e r i n g the constants gives, r = a t -- a 2 'n -+- a 3 "s
(13)
A "least squares fit" to this equation for the 24 data points gave a r.m.s, error in r of 1.5% ash, confirming that the assumptions a n d a p p r o x i m a t i o n s were accep-
TAIILE 2.
+ a2"n + a 3 \(~ - ~z-bl -h~.; 1
a~
O n expanding, this produces a quadratic expression in r based on the 6 constants, whose values have already been evaluated, a n d the countrates of the two detectors. It was established that the larger root of this quadratic gives the required ash value. The accuracy of this m e t h o d was checked b3; calculating the differences between the true known values of ash content a n d the values of r calculated from this quadratic expression for each of the 24 pairs of data for n a n d -. The r.m.s, error of the differences was 3.2°0 ash. One sample, n u m b e r 10 in Table 1, gave an exceptionally large error of 8.2% ash. If this was omitted, the r.m.s. error was reduced to 2.8°0 ash. 8.3.2. lterative method. Equations (10) and (13) were again used. Considering each pair of data values of n and z in turn. an initial value of solids content of 30°, was assumed. This assumed value was used in equation (13) to give the first estimate for r. This estimate was then used in e q u a t i o n (10) to give an improved value for s. E q u a t i o n (13) was used a second time with this improved value of s to give the second estimate for r, a n d so on. It was found that after a b o u t 5 - I 0 such iterations no significant further changes were taking place in the recalculated values of s a n d r. Table 3 shows values of s a n d r for 10 iterations for sample n u m b e r 19. This particular sample has been illustrated as it represents the worst case with the true solids content being only 18.5°o c o m p a r e d to the in-
Constants and r.m.s, errors for the various least squares regression equations
Equation constant al or hi a2 or b2 a3 or h3 u4 us u~, Residual r.m.s, error
(14)
I00
Equation number in text (I 0) 1.2392 x 10s -3.3371 -6.6686 × lO - 2
3 cps )0.5% solids
( l 3)
(I 8)
1.8103 x 10: -2.1718 x 10 2 -2.1337
-7.5001 x 102 -4.6323 x 10 -t 2.3944 5.2420 x 10 "~ --1.6069 x I0 "~ -2.1521 x 10 s _.0 , ash
.5% ash
53
Measurino the ash content ofcoal
TABLE 3. An example of the iteration method for evaluating ash content Sample number 19
then renumbering the constants, the final expression is obtained, r = a I 4- il2"n 4- a3"z
°
%
Iteration
Solids
Ash
+ a4"n'z+
1 2 3 4 5 6 7 8 9 10 True value Error
30.00 24.80 21.70 20.19 19.53 19.25 19.14 19.09 19.07 19.07 18.50 0.57
27.47 38.57 45.19 48.41 49.82 50.41 50.65 50.75 50.79 50.81 53.60 - 2.79
A "least squares fit" to this equation for the 24 data points gave a r.m.s, error of 2.0% ash; the individual residual errors are shown in Table 1. This represents a significant improvement over the previous methods. The values of the constants are given in Table 2. Sample numbers 3 and 21 gave errors of - 4 . 9 and 5.8% ash respectively. If these were omitted from the calculations, then the r.m.s, error for the remaining 22 data points was reduced to 1.4% ash. A check was made to ensure that this "least squares fit" was not specific solely to the data on which it was based. To do this a "least squares fit" was again calculated, this time omitting sample numbers 2, 5, 10, 19 and 22. These samples represented a range of solids contents, one from each of the five main ash values. This r.m.s, error of the equation based on the remaining 19 data points was 2.1% ash. Using this latest equation, the ash contents of the five omitted samples were calculated and compared with their known true ash values. The r.m.s, error of these five differences was 2.0% ash. This confirmed that equation (18) was valid for general use.
itial assumed value of 30%. The r.m.s, error, based on the differences between the true ash contents and the calculated values after ten iterations, for all 24 samples was 3.0% ash. 8.4 Accuracy f o r the direct measurement o f ash content based on a calibration procedure that requires no knowledge o f solids content The two methods described above in Section 8.3 each have two c o m m o n disadvantages. One is the requirement to have to measure the solids contents of all the slurry samples used in the calibration work before the two calibration equations can be evaluated. The second disadvantage is that the overall error in estimating the ash content will be a combination of errors from each of the two separate calibration equations. The method now to be described, semi-theoretical and semi-empirical, eliminates those disadvantages. It uses a direct single calibration procedure which requires no knowledge of solids contents. Equation (10) can be written,
Expanding this for a limited number of terms and renumbering the constants gives, s = bl + b2"z + b a ' z ' r + b4"r
(15)
A squared tel'm in 'n' is added to equation (13), as experience in backscatter measurements has shown that. in general, the variation with countrate is a quadratic, i.e. r = as + a2"n + a 3 • n 2 + a4"s
Part of the overall 2.0% r.m.s, error in ash, mentioned in the above section, will be due to counting statistics from the countrate measurements of the two detectors. It can be shown, from the propagation of errors, that when measurements in n and z are combined in a formula to give an overall figure r, where r = f(n,z), then the standard deviatatibn in r is given by,
I(£V.
far',::
+ t-~-~z) "o':
(19)
where tr, and tr, are the individual standard deviations for n and z respectively. It can further be shown that for a measurement time of t (s)
7,
6. =
and
a~ =
,/:
cps
which reduces equation (19) to
(16)
Eliminating s between Equations (15) and (16) and renumbering the constants gives,
°"
,,/7 ~/\a,)
+
Differentiating equation (18) gives,
r = (as 4- a2"n 4- a3'n 2 + a 4 " z l ' ( a s + a6"z) - i
(18)
9. Equivalent Error in Ash Due to Counting S t a t i s t i c s
a, = ~/\On.]
s = b4(z - b l ) ' ( t + bs"r) - I
a s ' z 2 + a6"n 2
(17)
On expanding, to include up to squared terms, and
0r ~n
-
a2 + a 4 " z + 2'o6"11
(20)
54
I.S. Boyce
10. Conclusion
and ?r
- as + a ~ ' n
?z
+ 2"asz.
For a coal of high ash, at a high solids content, typical values of n and z (from Table 3) are about 2200 and 1000 cps respectively. Substituting all relevant data into equation (20) gives,
1
a~,, \
11 -"~+ 116 = ~Jot°/ash.
(21)
\
So for a measurement time of 500 s, as used in this work, or, = 0.5~ ash. The results of these calculations are only relevant to the strengths of the two particular radioisotope sources used in this work. Also it will be noted, from equation (21), that the main contribution to or, came from the second term under the square root. This is the density gauge contribution. The strength of the 137Cs source could, with advantage, be increased by a factor of four. This would reduce a, to ~r, =
_55
+ 29 = - ~ ~o ash
which for the same 500 s measurement period as before, would reduce a, to 0.20/0 ash.
This study has shown that it is possible to produce an on-l'ine instrument to monitor continuously the ash content of a concentrated tailings slurry and to calculate the ash content, corrected for solids content." of the solid material. The method employs two radiosotope-detector systems. One is a I3~Cs density transmission gauge and the other a C o m p m n backscatter x-ray gauge with tO9Cd ' A data handling procedure has been developed which will enable a instrument to be calibrated over a wide range of slurry solids contents without requiring a knowledge of the values of the solids contents. Only "dry basis" ash values are needed for calibration. An ash range from 48 to 66°; ash was tested with solids content from 18 to 35°,,. The accuracy for the "dry basis" ash measurement, in a 500 s measurement time, was + 4°~oash at the 95°;0 confidence level.
Acknowledgements--The work described above was totally
supported by the Mining Research and. Development Establishment of the National Coal Board and we wish to thank the Director of that establishment for permission to publish this paper.