Spatial distribution studies of milling particles, milling charge and grist

Interntaiomd Journal of Applied Radiation lind Isotopes. Vol 3L pp. 179 to 185 © Pergamon Press Lid 1980. Printed in Great Britain

0020-708X/80/0301-0179502.00/0

Spatial Distribution Studies of Milling Particles, Milling Charge and Grist* JIl~i THYN and JAN POKORN~'f Institute for Research, Production and Application of Radioisotopes, Pfistavni 24 Prague 7, Czechoslovakia (Received 30 May 1979)

Applications of the narrow-beam y-ray method for dry grinding powder technology are discussed. In a model of a vertically agitated ball-mill, the spatial distribution of model milling charge with and without model grist and the spatial distribution of the grist were investigated. The model volume was 101. Polystyrene balls (diameter 4.5 mm) were used as a model of the milling charge and limestone--CaCO3 of diameter 0.04-0.1 mm as a model of the grist. A system of mixing discs (10 rev s- 1) on a coaxial shaft kept the mill-charge in vibrational motion. The results are presented in the form of graphs of the bulk density of the mill balls or the bulk density of the grist plotted against the height or distance from the stirred axis. The radionuclides 24tAm and 137Cs w e r e used as radiation sources.

I. Introduction

of the radiation field (induced by a suitable radiation source). These changes are caused by variation in the properties and parameters of the medium under investigation. Radiation methods can be divided into two methods, one utilizing a narrow and the other a broad beam of radiation. The narrow-beam geometry presumes that only those photons impinge on the detector which traverse the distance between the source and the detector without interaction, while the photons, undergoing any interaction process on this path, are eliminated from the beam. Under these conditions, the following relation is valid for the detected radiation flux density, I, and the thickness of the homogeneous medium layer, x, penetrated by the beam:

THE use of radionuclides yields information important for the control and automation of chemical plants. Besides the use of the so-called "open sources" as radiotracers for investigation of the dynamic characteristics of devices or whole plants, ~1-3~ sealed sources are commonly used in industry, e.g. for the radiometric determination of the thickness of fiat materials, t*-7) level gauging in storage tanks ~7-9> or for density measurements/~°-12~ fl-Emitters are used for the study of solid materials in thin layers (of the order of millimetres). ~,-Radiations and sources of neutron radiation are suitable for studies in centimetre layers. The great advantage of 7-sources is the fact that the quantities required may be obtained by measurement through the wall of the device. This paper reports on applications of ~-sources (1) For spatial distribution studies of milling particles (milling charge) in a model device of a vertically agitated ball mill (VABM) in conditions of dry grinding without grist and (2) for spatial .distribution studies of milling charge and grist in the above-mentioned model under the same conditions of dry grinding. In both cases the above-mentioned radiation method is used. In this method information is obtained from the changes of the physical parameters * This paper is taken from a report entitled "Radiometric measurement of bulk density and flow of solid particles", which was presented at the International Symposium on In-stream Measurements of Particulate Solid Properties, Bergen, Norway (August 22-23, 1978). $ Research Institute.of Macromolecular Chemistry, Brno l, Tkalcovsk~ 2, Czechoslovakia.

I = Io exp(-p.x)

(1)

where /~ = linear attenuation coefficient, characteristic for the energy of the gamma radiation and for the material of the attenuating layer and I0 = radiation flux density for x = 0. Realization of narrow-beam conditions is achieved by collimation of both the radiation source and the detector. With sufficient collimation of the beam a good agreement of the actual dependence with the theory as given by equation (1) can be achieved.

2. Bulk Density Measurement-Spatial Distribution of Milling Charge 2.1 Backoround information

On a model device of a vertically agitated ball mill (further details are reported in Section 2.3), the spatial

179

180

J. Thf:n and J. Pokorn~:

that the individual linear attenuation coefficients of the arbitrary phase do not depend on spatial location in the system. This presumption is fulfilled if a narrow beam of monoenergetic radiation is used. As the linear attenuation coefficient, I~, for a medium of a given chemical composition is directly proportional to the density of the medium, the so called mass-coefficient of attenuation may be introduced with advantage:

/

I~

(cm-' g l)

P

3

where p = density of the environment. Presuming that the measured volume consists of a layer of air, x,, in front of and behind the wall of the device, having a thickness Xw, and a layer of a heterogeneous system (e.g. gas-liquid system (g s) with layers xo and x~) situated inside the device, then for the attenuation of the radiation intensity on the ith pass according to equation (2) and after introducing x one can obtain: li/lo = e x p [ - ( ~ p , x , + ct~,.p,.2xw

FIG. 1. Method of measurement. (1) Radiation source: (2) detector: {3,4) screening device: (5) device wall: (6) device. distribution of model milling charge without grist was investigated under dry grinding conditions. The volume of the cylindrical vessel of the full-scale plant VABM is about 1001; steel balls of diameter 6-8 mm are used as the milling charge. The system of mixing discs on the coaxial shaft "'kept" the charge of the mill in a vibrating movement. (The disc peripheral velocity was 6-12 ms-1.) The volume of the model was 8 l; polystyrene balls of diameter 4.5 mm were used as a model of the milling charge. The time average value of the "local" bulk density of the milling charge, ~ , expressed the mass of the polystyrene balls which were kept in the volume unit by the mixing discs. The space distribution of the milling charge which can be evaluated from these values is an important parameter for the optimization of milling technology. 2.2 Theoretical The method of measurement is apparent in Fig. l. The radiation source (1) is attached to one side of the model (5, 6) and the detector (2) is placed on the opposite side. The rays emitted from the source are collimated by the aperture of the screening device (3) exactly to the conmator aperture of the detector (4). From Fig. 1 it is evident that the radiation passes through different materials. In analogy to equation (l) for the passage of radiation through a number of homogeneous materials situated in succession along the pass, i, equation (2) can be written

Elimination of the effect of the walls and the environment can be performed by measuring the radiation intensity through the empty device (i.e. when x, = 0). For this measurement we have, according to equation (2): l~i'/lo = exp[-(c%p,x. + ~,,,pw2Xw + ~opgxi)]

(4)

where xi = the section intercepted in the device by the radiation beam in the ith position. If solid particles are presented in the device, then (5)

xi = x~i + x~i

The volume intercepted inside the device by the collimated beam in the ith position is Vii = ~zd{ xi/4 (cm 3)

(6)

where d~ is the diameter of the collimator aperture. If this volume Viicontains Gi = p~Ttd~ xsi/4 (g)

(7)

solid particles, then for their bulk density fi~ in this volume V~the following relation holds: 79~ = G~/V~ = psxsi/x~

(8)

If we introduce equations (5) and (8) into the relation obtained by dividing equation (4) by equation (3), we obtain for the intensity ratio l}'/li = exp[pixigq(1 - ~opo/otsp~)]

(9)

and hence for the investigated bulk density it follows that Pi = I n ( l ° / l ) i / x i ~ ( 1 -- ocoPo/°:~P~)

This equation may be used under the presumption

(3)

4- O~sDsXsi 4- o~tpox~i)]

(10)

As we can presume that (~gpo/ot, p,) .~ 1, equation

Spatial distribution ~?["millin~ char,qe and orist

181

When computing the volumes V~ and VI, we shall consider them, for simplification, as being cylindrical rather than cylinder jacket sectors. As is evident from Fig. 2, we choose, for example, the value of L2 so as to make the hatched areas a and b approximately equal. By means of equations (12) and (13) it is possible to determine approximately the variation of bulk density with cross section. It is obvious that this computation is not exact; the values of the bulk densities for certain locations are averaged over unequal volumes ( V 1 : ~ V 2 5~ V n ) . The great advantage of this method is the relatively small number of measurements and simple computation. 2.3 Experimental The VABM model is shown schematically in Fig. 3~ the parameters of the device being listed in Table 1. The shaft was situated on the vertical axis of the glass vessel of the ball mill, with perpendicularly attached mixing discs. The discs were at an angle of 120°C to each other, as is shown in Fig. 4. The shaft rotation can then be equal ( + ) or opposite ( - ) to the turning of the upper mixing disc to the next beneath. A series

FIG. 2. Fictitious volume evaluations. (10) is simplified to

8

Pl = ln(l°/l)i/xi~s

(11)

As VABM can be considered as an axis symmetrical system (i.e. Pi is a function of the distance from the axis and the bottom of the mill only), estimation of the local values of the bulk density can be done very easily. If we perform the measurement mentioned while deriving equation (11), i.e. if we determine I~ and li, we then may write for the individual sections according to Fig. 2:

Pie = Pl = In(l°/lh/(~qLlc)

(12a)

P2c = In (l°/l)2/(;qL2c)

(12b)

~,~ = In (I°/I),/(~L,c)

(12c)

The concentric circles divide section (2) into three parts, for which (from the material balance) may easily be obtained: p2c V2c = p2V2 + 2p1V'l

i

i..

I- ~ - ¢"d;:'~r ' " i I

7--71

.

7 •~ ! lll, i

I ul

~

i

tl

A-A

(13a)

For the nth section, equation (13a) can be written by analogy: n

1

~.cV.c = ~.V. + 2 ~ ~,Vl

(13b)

i

V~c is the total volume intercepted by the collimated beam within the device. Because measurements are always performed with d~/D ~< 1 (where D is the inner diameter of the device), we can suppose that V~c is in fact the volume of a cylinder with a base ~d.Z,/4 and height Lu which is the mean path length of the beam as well.

£

FIG. 3. VABM model. (1) VABM model; (2) asynchronous motor; (3) radiation source and screening device; (4) detector with screening device; (5) shaft with mixing disc; (6) scaler; (7) track; (8) speed indicator.

J. Th~,n and J. Pokorn);

182

TABLE 1. Parameters of the VABM model

Dimensions vessel diameter vessel height

D = 1.6 x 10-1 H = 5.0 × 10-1

m m

Millin9 charge (polystyrene balls) diameter of the balls density weight of the charge ball layer in the mill

~b = 4.5 × 10 ~ m Ps = 987 kg m 3 4.3 kg 4.1 × 10 ' m

I""

M ixinq elements, excentric discs (see Fi9. 4) disc diameter disc thickness disc number disc spacing i = 6 rotations applied radionuclide activity diameter of the collimator apperture

8.8 X 1 0 2 m 8 × 10 3 m i = 6 t,, = 5.6 × 10 2 m 10s 241Am 3.7 GBq d~ = 10 2 m

I"-"

o f e x p e r i m e n t s w a s c a r r i e d o u t to find t h e vertical d i s t r i b u t i o n o f t h e b u l k d e n s i t y of milling c h a r g e for different n u m b e r s a n d s h a p e s o f the discs at 10 rev s - ' in p o s i t i o n s A, B a n d C as s h o w n in Fig. 5, for b o t h positive a n d n e g a t i v e r o t a t i o n . Examples of measured relations PA = JA(H) resp. PB = f B ( n ) a n d Pc = Jc(H) w h e r e H is a d i m e n s i o n l e s s height, are p r e s e n t e d in Fig. 6. F r o m the figures it follows t h a t t h e b u l k d e n s i t y of t h e m i l l i n g c h a r g e i n c r e a s e s t o w a r d s the b o t t o m o f the vessel a n d t h a t it d e p e n d s o n t h e d i s t a n c e b e t w e e n t h e m i x i n g discs. T h e h o r i z o n t a l d i s t r i b u t i o n o f the m i l l i n g c h a r g e

FIG. 4. Mixing discs.

F-

FIG. 5. Positions in RA = 2.7 × 10 RR = 5.2 x 10 R c = 7.8 × 10

vertical measurements: 2m L A = 15.1 × 10 2 m 2m LB = 12.1 x 10 2 m 2m Lc = 4.5 × 10 2 m

Spatial distribution c f' milling charge and grist

183

was determined in the positions shown in Fig. 7, for the regions closely under and above the stirrer. The relation

+

o

o

~,

I

I

Q I0

I

I

I

]

05

"

'

O

/

k~ ~°6

I

I

1

I

0

A

Q

B

0

C

I

I

for six mixing discs and two directions of rotation is shown in Fig. 8. The ordinates, i.e. the local bulk densities, are in fact average values computed for fictitious volumes formed by the intersection of the beam with part of the apparatus as indicated by the dotted area on the figure. F r o m this figure the effect of an aperture in the mixing discs on the milling charge distribution is clearly evident. A more detailed description of experiments and analysis of measurement errors has been published previously; (14~ technological utilization of the results has been presented at the CHISA Congress 78.(~5)

/ /

//A

'

'

= fn,(R)

O

I B

02 i

I

I

I

I

I

.--i---I---. I

'

"

I

1

I

3. Bulk Density Measurement-Spatial Distribution of Milling Charge and Grist

1

,--I---~c,

3.1 Background information

'

The spatial distributions of milling charge and grist were investigated in the V A B M model mentioned above (see Section 2), under dry grinding conditions.

'

L~

FIG. 6. Bulk density vertical measurements.

/

•

7J

¢'

Y,

/

/ 6

2

I I

\ m

t

FIG. 7. Positions in horizontal measurements: R~ = 7.8 × 10 -2 m LI = 4.5 x 10 -2 m R2 =6.8 x 10 - 2 m L2 = 8.7 x 10 - 2 m R3 =5.8 x 10-2m L3 = 11.2 x 10-2m R4 = 5.2 x 10-2m L4 = 12.1 x 10-2m R5 =4.2 x 10-2m L5 = 13.5 x 10-2m R6 = 3.2 × 10 -2 m L6 = 14.6 x 10 -2 m R7 =2.7 x 10-2m L7 = 15.1 x 10-2m

J. Th.¢n and J. Pokorn.¢

184

(~ 1031O[

,~ I

+

kg m-305I

^~

when the bulk densities Psi and ~p~ are to be evaluated. As the mass coefficient of attenuation 0¢ depends on the energy of the radiation used, we obtain a system of two linear independent equations when we rewrite equation 1171 for two levels of energy E' and E":

_

:~H2

HI

Xi([)si~s 4- f)pi~p) = A I

(18a)

xi(fi~i~' + PviO(/,)= AI'

(18b)

where A = ln(l/1)i and ' or " denotes the values corresponding to radiation energy E' and E" respectively. Solving equations (18a) and (18b) for the bulk density of milling charge i)s~ we have:

Subsequent considerations (for example the horizontal distribution of the bulk density) are analogous to those mentioned in Section 2. 3.2 Experimental

ISvo[urne

Iqo. 8. Bulk density measurements (milling charge).

The time average values of local bulk density of milling charge or grist (represented by polystyrene balls) which is kept in the volume unit by means of mixing discs, were evaluated experimentally.

From equation (19) it follows that the experimental conditions must satisfy the following inequality:

The ratios of the mass attenuation coefficients of the model milling charge (polystyrene balls) and the model grist (easily obtainable powder) for different radionuclides are presented in Table 2. The optimal combination is for CaCO3 and radionuclides 241Am and ~37Cs. One alternation which would give better results is utilizing BaCI2, although higher activity of the low energy nuclide is needed in this case. For equal operating conditions tsee Section 2.2) several experiments have been performed in order to assess the bulk density of the milling charge and the grist in the vertical and horizontal direction, respectively (i.e. P,R =,/sB(H) and pp, =.I~,R(H) and

3.2 Theoretical The same principle of measurement was used as mentioned in the preceding Section. The derivation of the basic relation for the intensity ratio I~/I~ is analogous as well. If milling charge and grist are present in the device, the following relation holds: X i ~ Xsi + Xpi @ X~i

(14)

The bulk density relation (15) is analogous to equation (8):

Pis = p~x~i/xiresp. T)ip = ppXpl/Xl

Na2CO3 CaCO3 BaC12

I'SAu

137Cs

6OCo

160 keV)

2O3Hg

(280 keV)

(411 keV)

1661 keV)

(1250 keV)

0.975 0.530 0.038

1.09 1.04 0.648

1.07 1.05 0.917

1.12 1.07 1.15

1.12 1.09 1.09

TABLE 3. Experimental conditions, parameters of the VABM model and quality of the milling charge (polystyrene balls: see Table 1)

(16)

Quality of the grist ICaC03 powder) grain size 4) = density p = total weight of milling charge = total weight of grist = Radionuclides used 241Am 137Cs

then equation (17), giving bulk density of both the milling charge and the grist, can be written as: [)siO~s -~ PpiO~p = ln(l'i / l ) / x i

2alAm

(15)

If we can presume again that

(c%pa,,'~p~) ,~ 1 resp. (o:gpd2cppp) ,~ 1

TABLE2. Mass attenuation coefficients ratios ~t,/Ctpfor polystyrene and powder according to Ref. 116"1

(17)

Equation (17) is similar to equation (11). One more linear independent equation is needed

40-100 × 10-~'m 2.72g cm 3 4 kg 2 kg 3.7 GBq 130 MBq

185

Spatial distribution t)f milling charge and grist (2 I03 ~o / kg rrr30 8I

o~ol[

+

051~

.-.. :-:"

06 04 f 02

Ii

I II

i

I

2

i

1~]~1 + ~-I i

R

IHI

]

?l-;,

r-r. 2-c 0 gr+st • milling chorge

risl rolling chorge

o+ ° I

]~ tm~ c o o

•

•

•

flChOUS volume

,o=o o L

L

t

J

t

t

0.5

i

'-U --I- ____

1_ I

" I

O~"r~q"~

-

~

- R

A

,--

I 'i.--.--1 v

FIG. 9. Milling charge and grist bulk density measurements.

fl llf If ~-~om FIG. 10. Milling charge and grist local bulk density measurements.

~ , =.Lu(R) and Ppu = Jpu(R) respectively), for different types of mixing discs and for both positive and negative rotation. The conditions of the experiment are summarized in Table 3. The values of the mass attenuation coefficients (polystyrene balls with 24SAm and ~3VCs) and (limestone powder with 24~Am and ~3VCs) were found experimentally. Examples of measured relations are presented in Figs 9 and 10. Further information will be reported in the near futureJ TM

References I. ROTKIRCH E., KOMMONEN F. and CASTRI~N J. Radioisotope Tracers in Industry and Geophysics. IAEA, Vienna (1967). 2. KUBiN M., TH~'N J., HOVORKA J., ~VARC Z. and gT~PAN O. (in Czech) Radioisotopy 18, 249-272 (1977). 3. TnC¢~ J., gVARC Z., HOVORKA J., ~.ITN~¢ R. and NOVOTNi' P. (in Czech). Radioisotopy 18, 625~568 (1977).

4. KOHL J., ZENTER R. and LUKENS D. Radioisotope Applications Engineering, pp. 467 472. Nostrand, New York (1961). 5. ZUMWALT L. R. Nucleonics 12, 55 (1954). 6. LEIGHTON G. J. Electronics 25, 112 ([952). 7. Kerntechnische Praxis, 1955-1975, VEBRFT Messelektronik "Otto Sch6n", Dresden (1975). 8. GLASHEEN R. W. Chem. Engng Prog. 48, 489 (1954). 9. SMITH E. E. and WHIFFIN A. C. Engineer 194, 278 (1952). 10. BARTHOLOMEW R. N. and CASAGRANDE R. M. Ind.

Engng Chem. 49, 428 (1957). q l . GROSHE E. W. A.I.Ch.E.JI 1,358 (1955). 12. HUNT R. H., BILES W. R. and REED C. O. Petroleum Rafiner 36, 179-182 (1957). 13. GARDNER R. P. and ELY R. L. Radioisotope Measurement Applications in Engineering. Reinhold, New York (1967). 14. T H ~ J., POKORN? J. and CABRNOCH J. (in Czech) Radioisotopy 18, 1 35 (1977). 15. POKORN~"J., TH~N J. and ~ALOUDfK P. 6th Int. CHISA Congress, Prague, August (1978). 16. STIEGBAHN K. Alpha-, Beta-, Gamma-Spectroscopy. North-Holland, Amsterdam (1965). 17. DRYAK P. (in Czech) Internal Report UVVVR (1978). 18. TH'2"N J., POKORN~" J. and BUBAK O. Radioisotopy. To be published.