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A radiotracer technique for the measurement of the residence time distribution of the grinding mills
mixed with the already crushed material and its behaviour thereafter was not sensitive to its original form.
International Jo,rnul o/ Applied Rudiation & Isotopes. Vol 31. pp. 187 to 188 © Pergamon Press Ltd 1980. Printed in Great Britain 0020-708X/80,'0301-0187502.00/0
Procedure Instrumentation
A Radiotracer Technique for the Measurement of the Residence Time Distribution of Grinding Mills
The radioactivity at the output of the mill was recorded in a continuous manner. The requirements for the detecting device were: (a) The penetration of the collimation was to be minimal, i.e. less than 1°/o of the signal. (b) The resolution of the collimator was to be as sharp as possible with minimal edge effect. (c) Since the average residence time was found to be of the order of 2.5 sec, the response and time constants of all mechanical and electronic modules of the setup should not be greater than 0.3 sec.
H. A. K O S T A L A S and C. GOTSIS* Department of Chemical Engineering, University of Toronto, Toronto, Ontario M5S 1A4, Canada
(Received 16 August 1979)
The individual modules which made up the detecting device are listed below in the same order of sequence as in the experimental setup.
Introduction AN IMPORTANT characteristic of grinding mills is the residence time of the particles being ground. In the past, nuclear techniques have been used (t-3~ in the form of either activation techniques or tracer methods. However all the techniques examined so far involve sampling at the output of the mill, which after processing lead to a histogram of the a m o u n t discharged vs time. This sampling procedure becomes especially difficult in the case where the residence time is very short as in our situation where it was found to be of the order of 10 sec or less.tS~ Furthermore the technique now described gives a continuous recording instead of an histogram. In the case of the mill under investigation it was assumed that the milling system could be approximated analytically by the log probability distribution function.
P(t) = 5011 + erf[ln(t/to.5)/v/2ln(cr)]]
(1)
where
P(t) = the percentage of tracer discharged after time t t0.5 = the time required for half of the a m o u n t of the tracer to be discharged a2 = the variance of the mean residence time a = deviation = to.84/to5 eft(x) = the error function of x This analytical approach is described in detail in Ref. (4). It was recognized that the tracer had to be in a solid form with physical characteristics identical to those of the sample particles. For example, this could be achieved either by radioactivating a few grains of the sample or by making a pellet out of a quantity of radioactive powder. Two factors of local character, namely the power level of the experimental reactor and health physics considerations, made it necessary to apply the following procedure. Instead of solid radioactive materials use was made of an aqueous solution of 99mTcO4. with specific activity of 700 /zc/ml. Its short half-life, its low 7-ray energy and the absence of fl-emission made 99mTc the radioisotope of choice. The radioactive liquid was poured onto the top of the coal feed. It was just sufficient to wet the surface of only two or three pieces of the coal. It was assumed that as soon as the tagged material entered the mill and started to be crushed, it became well * Department of Chemical Engineering, Pennsylvania State University, PA 16801, U.S.A. 187
(a) (b) (c) (d) (e) (f)
A 2 × 1.5 inch NaI(TI) scintillation detector. An 805 Canbera preamplifier. A 410 O R T E C spectroscopy amplifier. A 1431 Canbera single channel analyzer. A 1481 Canbera linear rate meter. A 212 Linear Instruments chart recorder.
The requirements which were mentioned above were all met by using a 2 in. thick cylindical lead collimator where the front surface of the NaI detector was distant 4 in. from the front surface of the collimator. The low energy photons emitted from 99"Tc, 140keV, allows for an excellent signal-to-noise ratio and an almost perfect resolution response curve. Penetration and penu m b r a effects were also negligible.
Radiotracer experiment A total of 700/~c of 99mTcO4 in the form of aqueous solution was kept in a glass vial shielded in a lead container. After the milling system had achieved steady conditions the contents of the vial were emptied instantaneously onto the coal grains which were at the edge of the hopper pan. The time of this action was considered as time zero. It was assumed that the time interval necessary for the coal to travel from the pan edge to the input of the mill was insignificant compared to the residence time. In order to eliminate radiation hazards due to inhalation o f radioactive dust, the emergent material was collected in a sealed container. The exposure dose rate from the mill or the collected ground material was found to be well below the m a x i m u m permissible level. Due to the short half-life of the isotope (6 h) there was no radioactive disposal problem either.
Results Two typical recordings are presented in Fig. 1, where counts per minute at the outlet of the mill vs time are plotted. Each curve is for different feed rate of the mill. The areas under the curves have not been normalized since neither the a m o u n t of the radiotracer used nor the a m o u n t of the radiotracer trapped in the mill was exactly known. The percentage of tracer which was discharged after time t, and which is denoted as P(t), now can be obtained by integrating the results of Fig. 1 and is expressed as percen tage of the area under the whole curve. If the a s s u m p t i o n ' that we have made at the beginning is correct, that equa-
188
Technical Note
3
2
I
©
,
,
,
,
,
,
E
2
5
4
5
6
,
,A
.I . . . . . .
.
-
-- Ynme (SJ
15
FIG. I. Recordings of discharge profiles at the output of the mill for two different feed rates+
I00
o
214
kg/min
x
295
kg / m i n
50
~5 I0
J
d~ Ox 0 x 0 0
0
x X
x
- %
Pit) I0
50
90
99
FIG. 2. A log probability plot of the time, t, vs the percentage of tracer, P(t), which has been discharged at the output of the mill.
tion (1) expresses analytically the milling system, then if we plot time vs P(t) on log probability graph paper we should obtain a straight line. This plot is given in Fig. 2. The experimental results, as it can be seen, are in very good agreement with those theoretically expected.
Conclusion A new technique has been established for the measurement of very short residence times of grinding mills. This technique gives a continuous recording of the discharge profile at the outlet of the mill and is much faster and simpler than the other techniques, mentioned in the introduction. The technique also seems to be particularly useful in cases where sampling at the output is not possible. The radiation hazards are minimal and there is no waste disposal problem. The information about the residence time is obtained with an accuracy of better than 10% which is considered to be acceptable for practical purposes. Further improvements can be made to assure better accuracy,
better quantification and to extract more information from each experimental run.
- Acknowledgements--We would like to thank Professor O. Trass of the University of Toronto for giving us the opportunity to fulfill this work.
References l. GARDNER R. P., SUKANINAJ TEE K. Powder Technol. 7, 169 0973). 2. MORERIA R. M., DE CASTRO J. O. N. M. and GARDNER R. P. Powder Technol. 6, 75 (1972). 3. GARDNER R. P , RODGERS R. S. and VERGEHESE K. Int. J. appl. Radiat. Isotopes 28, 861 (1977). 4. IRANI R. R. J. phys. Chem. 63, 1603 (1959). 5. GoTms C. M.Sc. Thesis, University of Toronto (1976).
International Jo,rnul o/ Applied Rudiation & Isotopes. Vol 31. pp. 187 to 188 © Pergamon Press Ltd 1980. Printed in Great Britain 0020-708X/80,'0301-0187502.00/0
Procedure Instrumentation
A Radiotracer Technique for the Measurement of the Residence Time Distribution of Grinding Mills
The radioactivity at the output of the mill was recorded in a continuous manner. The requirements for the detecting device were: (a) The penetration of the collimation was to be minimal, i.e. less than 1°/o of the signal. (b) The resolution of the collimator was to be as sharp as possible with minimal edge effect. (c) Since the average residence time was found to be of the order of 2.5 sec, the response and time constants of all mechanical and electronic modules of the setup should not be greater than 0.3 sec.
H. A. K O S T A L A S and C. GOTSIS* Department of Chemical Engineering, University of Toronto, Toronto, Ontario M5S 1A4, Canada
(Received 16 August 1979)
The individual modules which made up the detecting device are listed below in the same order of sequence as in the experimental setup.
Introduction AN IMPORTANT characteristic of grinding mills is the residence time of the particles being ground. In the past, nuclear techniques have been used (t-3~ in the form of either activation techniques or tracer methods. However all the techniques examined so far involve sampling at the output of the mill, which after processing lead to a histogram of the a m o u n t discharged vs time. This sampling procedure becomes especially difficult in the case where the residence time is very short as in our situation where it was found to be of the order of 10 sec or less.tS~ Furthermore the technique now described gives a continuous recording instead of an histogram. In the case of the mill under investigation it was assumed that the milling system could be approximated analytically by the log probability distribution function.
P(t) = 5011 + erf[ln(t/to.5)/v/2ln(cr)]]
(1)
where
P(t) = the percentage of tracer discharged after time t t0.5 = the time required for half of the a m o u n t of the tracer to be discharged a2 = the variance of the mean residence time a = deviation = to.84/to5 eft(x) = the error function of x This analytical approach is described in detail in Ref. (4). It was recognized that the tracer had to be in a solid form with physical characteristics identical to those of the sample particles. For example, this could be achieved either by radioactivating a few grains of the sample or by making a pellet out of a quantity of radioactive powder. Two factors of local character, namely the power level of the experimental reactor and health physics considerations, made it necessary to apply the following procedure. Instead of solid radioactive materials use was made of an aqueous solution of 99mTcO4. with specific activity of 700 /zc/ml. Its short half-life, its low 7-ray energy and the absence of fl-emission made 99mTc the radioisotope of choice. The radioactive liquid was poured onto the top of the coal feed. It was just sufficient to wet the surface of only two or three pieces of the coal. It was assumed that as soon as the tagged material entered the mill and started to be crushed, it became well * Department of Chemical Engineering, Pennsylvania State University, PA 16801, U.S.A. 187
(a) (b) (c) (d) (e) (f)
A 2 × 1.5 inch NaI(TI) scintillation detector. An 805 Canbera preamplifier. A 410 O R T E C spectroscopy amplifier. A 1431 Canbera single channel analyzer. A 1481 Canbera linear rate meter. A 212 Linear Instruments chart recorder.
The requirements which were mentioned above were all met by using a 2 in. thick cylindical lead collimator where the front surface of the NaI detector was distant 4 in. from the front surface of the collimator. The low energy photons emitted from 99"Tc, 140keV, allows for an excellent signal-to-noise ratio and an almost perfect resolution response curve. Penetration and penu m b r a effects were also negligible.
Radiotracer experiment A total of 700/~c of 99mTcO4 in the form of aqueous solution was kept in a glass vial shielded in a lead container. After the milling system had achieved steady conditions the contents of the vial were emptied instantaneously onto the coal grains which were at the edge of the hopper pan. The time of this action was considered as time zero. It was assumed that the time interval necessary for the coal to travel from the pan edge to the input of the mill was insignificant compared to the residence time. In order to eliminate radiation hazards due to inhalation o f radioactive dust, the emergent material was collected in a sealed container. The exposure dose rate from the mill or the collected ground material was found to be well below the m a x i m u m permissible level. Due to the short half-life of the isotope (6 h) there was no radioactive disposal problem either.
Results Two typical recordings are presented in Fig. 1, where counts per minute at the outlet of the mill vs time are plotted. Each curve is for different feed rate of the mill. The areas under the curves have not been normalized since neither the a m o u n t of the radiotracer used nor the a m o u n t of the radiotracer trapped in the mill was exactly known. The percentage of tracer which was discharged after time t, and which is denoted as P(t), now can be obtained by integrating the results of Fig. 1 and is expressed as percen tage of the area under the whole curve. If the a s s u m p t i o n ' that we have made at the beginning is correct, that equa-
188
Technical Note
3
2
I
©
,
,
,
,
,
,
E
2
5
4
5
6
,
,A
.I . . . . . .
.
-
-- Ynme (SJ
15
FIG. I. Recordings of discharge profiles at the output of the mill for two different feed rates+
I00
o
214
kg/min
x
295
kg / m i n
50
~5 I0
J
d~ Ox 0 x 0 0
0
x X
x
- %
Pit) I0
50
90
99
FIG. 2. A log probability plot of the time, t, vs the percentage of tracer, P(t), which has been discharged at the output of the mill.
tion (1) expresses analytically the milling system, then if we plot time vs P(t) on log probability graph paper we should obtain a straight line. This plot is given in Fig. 2. The experimental results, as it can be seen, are in very good agreement with those theoretically expected.
Conclusion A new technique has been established for the measurement of very short residence times of grinding mills. This technique gives a continuous recording of the discharge profile at the outlet of the mill and is much faster and simpler than the other techniques, mentioned in the introduction. The technique also seems to be particularly useful in cases where sampling at the output is not possible. The radiation hazards are minimal and there is no waste disposal problem. The information about the residence time is obtained with an accuracy of better than 10% which is considered to be acceptable for practical purposes. Further improvements can be made to assure better accuracy,
better quantification and to extract more information from each experimental run.
- Acknowledgements--We would like to thank Professor O. Trass of the University of Toronto for giving us the opportunity to fulfill this work.
References l. GARDNER R. P., SUKANINAJ TEE K. Powder Technol. 7, 169 0973). 2. MORERIA R. M., DE CASTRO J. O. N. M. and GARDNER R. P. Powder Technol. 6, 75 (1972). 3. GARDNER R. P , RODGERS R. S. and VERGEHESE K. Int. J. appl. Radiat. Isotopes 28, 861 (1977). 4. IRANI R. R. J. phys. Chem. 63, 1603 (1959). 5. GoTms C. M.Sc. Thesis, University of Toronto (1976).