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Electrodynamic conductance separation with use of alternating fields
Journal of Electrostatics, 14 ( 1 9 8 3 ) 1 7 5 - - 1 8 6
175
Elsevier Science P u b l i s h e r s B.V., A m s t e r d a m - - P r i n t e d in T h e N e t h e r l a n d s
ELECTRODYNAMIC CONDUCTANCE SEPARATION WITH USE OF A L T E R N A T I N G FIELDS
MAREK SZCZERBINSKI
Institute of Electrical Power Engineering, Stanisfaw Staszic University o f Mining and Metallurgy, Krakdw (Poland) ( R e c e i v e d O c t o b e r 6, 1 9 8 2 ; a c c e p t e d in revised f o r m M a r c h 7, 1 9 8 3 )
Summary T h e l i m i t a t i o n s o f e l e c t r o d y n a m i c d r u m s e p a r a t o r s are a n a l y s e d a n d a n e w a l t e r n a t i v e c o n d u c t a n c e m e t h o d is p r e s e n t e d . T h i s m e t h o d consists in t h e e l e c t r i f i c a t i o n o f feed grains b y a l t e r n a t i n g field f o l l o w e d b y t h e s e p a r a t i o n at a s t a t i o n a r y field. T h e t h e o r e t i c a l p r e - a s s u m p t i o n s are given a n d t h e e x p e r i m e n t a l results are p r e s e n t e d a n d discussed.
1. Limitations o f conductance drum separators The electrodynamic separation of minerals has a limited industrial usefulness. There are only some special areas where electrodynamic separation is successful where more conventional methods are not. This dry m e t h o d is attractive, for instance, in desert regions, or in regions where the handling of water is complicated by low temperatures. Most electrodynamic separators are based on the electrical conductivity differences of mixed granular solids. Such separators m a y be divided into those using a pure static field and those having a " c o r o n a " field [1]. The m o s t widely used corona separator is illustrated in Fig. 1. Mineral grains pass 1
°o°
o~, ;,,
•
•
J
o~e
Fig. 1. C o r o n a c o n d u c t a n c e s e p a r a t o r : 1 - feed h o p p e r , 2 - r o t a t i n g e l e c t r o d e , 3 - c o u n t e r electrode, 4 - receiver, 5 - c o r o n a e l e c t r o d e , 6 - b r u s h .
0304-3886/83/$03.00
© 1 9 8 3 Elsevier S c i e n c e P u b l i s h e r s B.V.
176
through the corona discharge and assume some charges. Next, the feed falls on a rotating drum. Grains having small relaxation times (i.e. " c o n d u c t o r s " ) allow the charges to conduct away rapidly. Subsequently, they take up some charges o f opposite sign and are repelled b y field forces into Bin I. However, grains having large relaxation times (i.e. "non-conductors") lose little or no charge: they are " p i n n e d " to the rotating drum by means of image forces. Eventually, these grains are removed with the aid of a brush into the receiver Bin II. In order to determine the limitations of conductance drum separators one must find the criteria to define the limit between the " c o n d u c t o r s " and "non-conductors". Consider Fig. 2, for which the equation of the grain free charge is formulated as follows Q(t) = U Ca + Cg
lle E Rg(C~' + Cg)
-- Q0 exp
g(
,
(1)
where U is the voltage between the separator electrodes, Ca the capacitance between the grain and the counter electrode, Cg the capacitance o f the grain, Rg the resistance of the grain, Q0 the charge of the grain at t = 0 (i.e. the charge obtained at the corona discharge), and t is the time (t = 0 just as the grain comes into contact with the rotating electrode). 1
k
Qo
2
,-_///I "/
Z
1,'--
co
U
Rg
Rg (a)
Cg"
1
Qo
(b)
Fig. 2. F e e d grain o n t h e surface o f t h e r o t a t i n g e l e c t r o d e (a) and t h e equivalent electric diagram (b): 1 - grain, 2 - r o t a t i n g e l e c t r o d e , 3 - c o u n t e r e l e c t r o d e .
The characteristics of " c o n d u c t o r " charge Q I and " n o n - c o n d u c t o r " charge Q2 versus time of the rest on the rotating electrode are presented in Fig. 3. Analysis of this leads one to regard that the separation takes place when the time of contact between the grain and the rotating electrode te fulfills the following formula R g Cg, ,~ tc "~ Rg2Cg 2
,
(2)
where Rg, is the resistanceof the "conductor" grain,Rg~ the resistanceof the ,, non-conductor ,, grain,C~ the capacitance of the ¢, conductor ,, grain, and Cg~ is the capacitance of the "non-conductor" gram.
177
Q(t) U-Ca+Cg Co 2
/•(t)
I
J Rgl"Cg1 t
i~(t ) ; Rg2"Cg 2
Igt
Qo Fig. 3. Charges of " c o n d u c t o r " Q,(t) and " n o n - c o n d u c t o r " corona conductance drum separator.
Q2(t) versus time
for the
For mechanical reasons, the contact time tc cannot be shorter than 0.01 s. As a result, we find that the " c o n d u c t o r s " are all grains having relaxation times RgCg ~ 0.01 s. On the contrary, the "non-conductors" are all grains having relaxation times far longer than 0.01 s. Thus, the conductance drum separators have only a limited field of its usefulness. They cannot be used when the relaxation times o f both separated components are shorter than 0.01 s (as is usual in raw material separation). Now, let us consider what is meant by the relaxation time RgCg of the grain. Some authors interpret this as the p r o d u c t of grain resistivity and grain permittivity [ 2 ] . In fact, the relaxation time is, as a rule, longer than the above p r o d u c t because of contact resistance b e t w e e n the rotor and the grain. As follows from Schnitzler's calculations, the resistances of separated grains must fulfill the following conditions [3] : Rg, ~ < 2 × 10 n ~
,
(3)
Rg 2 /> 4 × I 0 '2 ~2 ,
(4)
and
(these inequalities have been established for the typical permittivities of minerals). Unfortunately, grains of many minerals have a value of Rg far below 2 X 1011 ~2. This is why, for many raw material mixtures, the use of conductance drum separators is impossible. 2. Principles o f a new m e t h o d [4] A m e t h o d proposed by the author m a y extend the conductance separation field for the cases defined b y the dependence Rg,, Rg ~< 2 X 10 ~1 ~ . The pictorial diagram of the separator is shown in Fig. 4. ~he feed (consisting o f " c o n d u c t o r " and " n o n , c o n d u c t o r " grains) falls from the feeder into the elec-
178
,4
o
oo
\
•
o
U-
-+q_
o •
o
o
m
•
•
• o
Fig. 4. Principle of the conductance separation with use of alternating field: 1 - feed hopper, 2 - electrificationelement, 3 - alternating voltage generator, 4 - stationary electric field, 5 - receiver.
trification element carrying an alternating voltage of angular frequency coo. The grains are sinusoidally charged: the charge amplitude IQI versus frequency co is expressed by the known formula, typical for R C elements: IQI
=
IQol . ~/I + c o 2 R g 2 C g 2
(5)
'
where Q0 is the charge amplitude for co -+ 0, co is the angular frequency of the alternating voltage (co = 2 +f), and f is the frequency. The attenuation diagrams of the "conductor" charge IQII and "non-conduc tor" charge IQ21 are presented in Fig. 5. For coo, the amplitude of the "con-
IQl IQol
Igw I Rg2"Cg
~0 2
I Rg I "Cg I
Fig. 5. Attenuation diagrams for the grain charges Q~(o~ ) and Q2(o~ ).
179 d u c t o r " grain charge IQ,I is close to IQ01 b u t the amplitude of the "nonc o n d u c t o r " grain charge IQ21 is close to zero. Next, the feed f , ll~ into the stationary electric field. The charged grains of the " c o n d u c t o r " are rejected by the field forces to the side receiver Bins I (left or right - depending on the instantaneous polarisation of the electrification element when the grain loses contact with it). On the other hand, the uncharged grains of the "non-conduct o r " fall into the middle Bin II. (Some grains of the " c o n d u c t o r " which lose contact with the electrification element just when the instantaneous voltage is close to zero fall into Bin II too.) The half-period of the alternating voltage is the analogue of tc from Section 1. The condition of the separation derived from the above discussion is as follows: 1/Rg~Cg I >=>fo/2 ~ 1/Rg Cg2 ,
(6)
where f0 = ¢o0/2~. Thus, the frequency of 50 Hz is the analogue of tc = 0.01 s. But in this case, as distinguished from the drum separators, one is able to set the value o f f0 some orders of magnitude greater than 50 Hz.
3. Experimental results The analysed separation m e t h o d has been tested by means of a device illustrated in Fig. 6. The mixture is transported to a cyclone where all dusts are rejected. Then the feed falls into the electrification element carrying an alternating voltage. The root-mean-square value of the alternating field intensity amounts to 5.0 kV/cm. Next, the mixture is subject to the stationary electric field of 3.5 kV/cm. The height of the separation chamber is 40 cm and its width is 17.5 cm. The receiver consists of 7 equal bins. When both the electric fields are absent the grain distribution in the receiver is symmetrical. Receiver distribution analyses of 7 hard coal components (see Table 1) have been studied. Every c o m p o n e n t has been studied alone. The frequencies used are as follows: 300 Hz, 1 000 Hz, 3 000 Hz, 10 000 Hz, 30 000 Hz. Besides, the distributions for the switch S~ open have been analysed. In this paper, a summary o f the most interesting findings is presented. Every distribution presented is an arithmetic mean of 3 tests. These tests are o f satisfactory reproducibility (for significance ~ = 0.05, the confidence intervals are always below 2.5%). The analysis o f the histograms in Fig. 7 suggests that the distributions of vitrain for all frequencies are close to its distribution for "S, open". In other words, the majority o f the grains ignore the alternating electric fields of the frequencies used. This fact leads to the conclusion that the majority of the studied vitrain grains meet the dependence 1/RgCg .~ 300 Hz. The asymmetry o f the distributions may be explained in terms of a contact potential phenomenon. Further studies have led to the conclusion that the other materials of similar resistivity (i.e. clarain
180
I> 2
transporting Q[P
U,~ $1
5
4
.---
i
6
I 112131415i~17 6
~./o
i 16o?.
Fig. 6. E x p e r i m e n t a l s e p a r a t i o n device : 1 - feed h o p p e r , 2 - b a t c h e r o f c o n c e n t r a t i o n , 3 c y c l o n e , 4 - e l e c t r i f i c a t i o n e l e m e n t , 5 - s e p a r a t i o n c h a m b e r , 7 - receiver, 8 - alternating voltage g e n e r a t o r , S l-switch. TABLE 1 Resistivities o f t h e hard coal c o m p o n e n t s s t u d i e d
No.
Hard coal components
Resistivity [~ cm]
1 2 3
vitrain vitrain-durain durain semi-shine durain bass mudstone pyrite
10s--101° 10s--101° 108--101° 108--101° 10'--108 106--10 s 102--106
4
5 6 7
1, 2, 3 and 4 - - p e t r o g r a f i c hard coal c o m p o n e n t s ; 5 and 6 - - a s h c o n t e n t s ; 7 - - n o n ~ r g a n i c sulphur compound.
181
['.J 40 f = 300 H z
30 20 10 0
1
,
I 2
l 3
4
5
6
7
bin
1
[./.] 4O 30 f = 30 000
20
Hz
10
1
2
3
4
5
6
7
bin
J
[./,] 4O 30 20 open
S1
10
I 1
2
3
4
5
6
7
bin
F i g . 7. H i s t o g r a m s o f t h e vitrain d i s t r i b u t i o n s .
similar distributions to the vitrain. However, the distributions of other materials investigated (i.e. bass, mudstone and pyrite) strongly depend on the frequency used (Fig. 8). This fact arises from the lower resistivities of these components (see Table 1) so many of their grains satisfy the dependence 300 Hz < 1]RgCg< 30 000 Hz. The greater the frequency, the distribution
182
[./o] 30 f = 300 Hz
20
[
10 0
2
3
4
5
6
7
bin
2r
[./.] 7O 60 50. 40' 30' 20
f_- 1000 Hz
10. 0
N
1
2
I
3
4
5
7
I
bin
T
E'/.] J 7060504030 S 1 open
20
10
o Fig. 8.
1
2
J
3
4
5
6
7
b
bin
Histograms o f the mudstone distributions.
is closer to the "$1 open situation". This fact is consistent with the theory presented above. The frequency characteristics o f the bin contents are presented in Figs. 9 and 10. The summary contents of bins "1", "2", "6" and "7" (indicated as
183
7i) are the analogue of the contents of bin I from Fig. 4. On the other hand, the summary contents o f bins "3", " 4 " and " 5 " (indicated as 7n) are the analogue of the contents of bin II. Figures 11 and 12 present the characteristics o f the arithmetic mean x(f) and standard deviation s(f) characterizing the distributions in the receiver. The characteristics presented are in agreement with the theoretical assumptions - with the exception o f bass. The bass grains have a characteristic "lamella" shape. This leads to a great influence o f contact potential and results in considerable asymmetries of the distributions. Nevertheless, the fact that s(f) is ever growing within the range o f 1 000--10 000 Hz is still inexplicable and requires some additional studies. The differences between the characteristics of the hard coal c o m p o n e n t s indicate the possibility of separation. To demonstrate this, the separation of raw coal (0.8--0.6 mm) with sulphur content of 5.3% has been carried out. 7i
Ira] 7O
® 60'
'0 ,@
® f[.z] 0 3oo
lOOO
3000
10000
30000
Fig. 9. Characteristics7i(f): ~/I presents the s u m m a r y contents of the flank bins "1 ", "2", "6" and "7 ". The designations of the characteristicsin Figs. 9--12 are the same as the numeration of the hard coal components in Table 1.
184
E!I, 90
60
@
'./-
5O
©,
, [Hz] 3O
300 1000 3000 I(~0"00 30000 Fig. 10. Characteristics ~II(f): ~ n presents the s u m m a r y contents of the middle bins "3", " 4 " and " 5 "
These experiments have led to coal desulphurisation but the results achieved are not fully satisfactory from a technological standpoint. For example, for f = 300 Hz, the sulphur contents in the concentrate have been lowered to 2.9%. In tailings (36% of the feed) the sulphur contents have amounted to 9.5%. 4. Conclusions The experimental results agree with theoretical expectation and demonstrate the possibility of the separation by the method discussed. Nevertheless, on the basis of the experiments performed the technological usefulness of the method discussed cannot be confirmed. Thus, further work must consider other useful minerals - for which conventional methods do not succeed. After that, experimental optimisation of the method is required.
185
S
[./.] I 35
3(
25
20
I
10
5
,[Hz] 0 300
1000
3000
10000
30000
Fig. II. Arithmetic means of the receiver distributions ~(f).
Acknowledgements The author gratefully acknowledges the help received from his collegues Kazimierz Chudyba and Antoni Ciesla from the Institute of New Conversions o f Energy at Stanis](aw Staszic University of Mining and Metallurgy, Krak6w. He also owes a great deal to his consultant, Professor Dr. Zbigniew Jasicki.
186
[°/o]' 60
f
4 ~_ 3o0
1000
3000
10000
EHzl
30000
Fig. 12. Standard deviations of the receiver distributions s(f).
References 1 0 . C . Ralston, Electrostatic Separation of Mixed Granular Solids, Elsevier, Amsterdam, London, N e w York, Princeton, 1961. 2 J.E. Lawyer, State of the art of Electrostatic Separation of Minerals, J. Electrochem. Soc., February 1969, p. 57 C. 3 H. Schnitzler, Untersuchung des Walzenscheiders sowie ein Verfahren zur Messung des elektrischen Widerstands yon Staub und zur Bestimmung der Korniibergangswiderstands, Bergbau Archiv, 1950, Bll/12. 4 Polish Patent No. 84 486.
175
Elsevier Science P u b l i s h e r s B.V., A m s t e r d a m - - P r i n t e d in T h e N e t h e r l a n d s
ELECTRODYNAMIC CONDUCTANCE SEPARATION WITH USE OF A L T E R N A T I N G FIELDS
MAREK SZCZERBINSKI
Institute of Electrical Power Engineering, Stanisfaw Staszic University o f Mining and Metallurgy, Krakdw (Poland) ( R e c e i v e d O c t o b e r 6, 1 9 8 2 ; a c c e p t e d in revised f o r m M a r c h 7, 1 9 8 3 )
Summary T h e l i m i t a t i o n s o f e l e c t r o d y n a m i c d r u m s e p a r a t o r s are a n a l y s e d a n d a n e w a l t e r n a t i v e c o n d u c t a n c e m e t h o d is p r e s e n t e d . T h i s m e t h o d consists in t h e e l e c t r i f i c a t i o n o f feed grains b y a l t e r n a t i n g field f o l l o w e d b y t h e s e p a r a t i o n at a s t a t i o n a r y field. T h e t h e o r e t i c a l p r e - a s s u m p t i o n s are given a n d t h e e x p e r i m e n t a l results are p r e s e n t e d a n d discussed.
1. Limitations o f conductance drum separators The electrodynamic separation of minerals has a limited industrial usefulness. There are only some special areas where electrodynamic separation is successful where more conventional methods are not. This dry m e t h o d is attractive, for instance, in desert regions, or in regions where the handling of water is complicated by low temperatures. Most electrodynamic separators are based on the electrical conductivity differences of mixed granular solids. Such separators m a y be divided into those using a pure static field and those having a " c o r o n a " field [1]. The m o s t widely used corona separator is illustrated in Fig. 1. Mineral grains pass 1
°o°
o~, ;,,
•
•
J
o~e
Fig. 1. C o r o n a c o n d u c t a n c e s e p a r a t o r : 1 - feed h o p p e r , 2 - r o t a t i n g e l e c t r o d e , 3 - c o u n t e r electrode, 4 - receiver, 5 - c o r o n a e l e c t r o d e , 6 - b r u s h .
0304-3886/83/$03.00
© 1 9 8 3 Elsevier S c i e n c e P u b l i s h e r s B.V.
176
through the corona discharge and assume some charges. Next, the feed falls on a rotating drum. Grains having small relaxation times (i.e. " c o n d u c t o r s " ) allow the charges to conduct away rapidly. Subsequently, they take up some charges o f opposite sign and are repelled b y field forces into Bin I. However, grains having large relaxation times (i.e. "non-conductors") lose little or no charge: they are " p i n n e d " to the rotating drum by means of image forces. Eventually, these grains are removed with the aid of a brush into the receiver Bin II. In order to determine the limitations of conductance drum separators one must find the criteria to define the limit between the " c o n d u c t o r s " and "non-conductors". Consider Fig. 2, for which the equation of the grain free charge is formulated as follows Q(t) = U Ca + Cg
lle E Rg(C~' + Cg)
-- Q0 exp
g(
,
(1)
where U is the voltage between the separator electrodes, Ca the capacitance between the grain and the counter electrode, Cg the capacitance o f the grain, Rg the resistance of the grain, Q0 the charge of the grain at t = 0 (i.e. the charge obtained at the corona discharge), and t is the time (t = 0 just as the grain comes into contact with the rotating electrode). 1
k
Qo
2
,-_///I "/
Z
1,'--
co
U
Rg
Rg (a)
Cg"
1
Qo
(b)
Fig. 2. F e e d grain o n t h e surface o f t h e r o t a t i n g e l e c t r o d e (a) and t h e equivalent electric diagram (b): 1 - grain, 2 - r o t a t i n g e l e c t r o d e , 3 - c o u n t e r e l e c t r o d e .
The characteristics of " c o n d u c t o r " charge Q I and " n o n - c o n d u c t o r " charge Q2 versus time of the rest on the rotating electrode are presented in Fig. 3. Analysis of this leads one to regard that the separation takes place when the time of contact between the grain and the rotating electrode te fulfills the following formula R g Cg, ,~ tc "~ Rg2Cg 2
,
(2)
where Rg, is the resistanceof the "conductor" grain,Rg~ the resistanceof the ,, non-conductor ,, grain,C~ the capacitance of the ¢, conductor ,, grain, and Cg~ is the capacitance of the "non-conductor" gram.
177
Q(t) U-Ca+Cg Co 2
/•(t)
I
J Rgl"Cg1 t
i~(t ) ; Rg2"Cg 2
Igt
Qo Fig. 3. Charges of " c o n d u c t o r " Q,(t) and " n o n - c o n d u c t o r " corona conductance drum separator.
Q2(t) versus time
for the
For mechanical reasons, the contact time tc cannot be shorter than 0.01 s. As a result, we find that the " c o n d u c t o r s " are all grains having relaxation times RgCg ~ 0.01 s. On the contrary, the "non-conductors" are all grains having relaxation times far longer than 0.01 s. Thus, the conductance drum separators have only a limited field of its usefulness. They cannot be used when the relaxation times o f both separated components are shorter than 0.01 s (as is usual in raw material separation). Now, let us consider what is meant by the relaxation time RgCg of the grain. Some authors interpret this as the p r o d u c t of grain resistivity and grain permittivity [ 2 ] . In fact, the relaxation time is, as a rule, longer than the above p r o d u c t because of contact resistance b e t w e e n the rotor and the grain. As follows from Schnitzler's calculations, the resistances of separated grains must fulfill the following conditions [3] : Rg, ~ < 2 × 10 n ~
,
(3)
Rg 2 /> 4 × I 0 '2 ~2 ,
(4)
and
(these inequalities have been established for the typical permittivities of minerals). Unfortunately, grains of many minerals have a value of Rg far below 2 X 1011 ~2. This is why, for many raw material mixtures, the use of conductance drum separators is impossible. 2. Principles o f a new m e t h o d [4] A m e t h o d proposed by the author m a y extend the conductance separation field for the cases defined b y the dependence Rg,, Rg ~< 2 X 10 ~1 ~ . The pictorial diagram of the separator is shown in Fig. 4. ~he feed (consisting o f " c o n d u c t o r " and " n o n , c o n d u c t o r " grains) falls from the feeder into the elec-
178
,4
o
oo
\
•
o
U-
-+q_
o •
o
o
m
•
•
• o
Fig. 4. Principle of the conductance separation with use of alternating field: 1 - feed hopper, 2 - electrificationelement, 3 - alternating voltage generator, 4 - stationary electric field, 5 - receiver.
trification element carrying an alternating voltage of angular frequency coo. The grains are sinusoidally charged: the charge amplitude IQI versus frequency co is expressed by the known formula, typical for R C elements: IQI
=
IQol . ~/I + c o 2 R g 2 C g 2
(5)
'
where Q0 is the charge amplitude for co -+ 0, co is the angular frequency of the alternating voltage (co = 2 +f), and f is the frequency. The attenuation diagrams of the "conductor" charge IQII and "non-conduc tor" charge IQ21 are presented in Fig. 5. For coo, the amplitude of the "con-
IQl IQol
Igw I Rg2"Cg
~0 2
I Rg I "Cg I
Fig. 5. Attenuation diagrams for the grain charges Q~(o~ ) and Q2(o~ ).
179 d u c t o r " grain charge IQ,I is close to IQ01 b u t the amplitude of the "nonc o n d u c t o r " grain charge IQ21 is close to zero. Next, the feed f , ll~ into the stationary electric field. The charged grains of the " c o n d u c t o r " are rejected by the field forces to the side receiver Bins I (left or right - depending on the instantaneous polarisation of the electrification element when the grain loses contact with it). On the other hand, the uncharged grains of the "non-conduct o r " fall into the middle Bin II. (Some grains of the " c o n d u c t o r " which lose contact with the electrification element just when the instantaneous voltage is close to zero fall into Bin II too.) The half-period of the alternating voltage is the analogue of tc from Section 1. The condition of the separation derived from the above discussion is as follows: 1/Rg~Cg I >=>fo/2 ~ 1/Rg Cg2 ,
(6)
where f0 = ¢o0/2~. Thus, the frequency of 50 Hz is the analogue of tc = 0.01 s. But in this case, as distinguished from the drum separators, one is able to set the value o f f0 some orders of magnitude greater than 50 Hz.
3. Experimental results The analysed separation m e t h o d has been tested by means of a device illustrated in Fig. 6. The mixture is transported to a cyclone where all dusts are rejected. Then the feed falls into the electrification element carrying an alternating voltage. The root-mean-square value of the alternating field intensity amounts to 5.0 kV/cm. Next, the mixture is subject to the stationary electric field of 3.5 kV/cm. The height of the separation chamber is 40 cm and its width is 17.5 cm. The receiver consists of 7 equal bins. When both the electric fields are absent the grain distribution in the receiver is symmetrical. Receiver distribution analyses of 7 hard coal components (see Table 1) have been studied. Every c o m p o n e n t has been studied alone. The frequencies used are as follows: 300 Hz, 1 000 Hz, 3 000 Hz, 10 000 Hz, 30 000 Hz. Besides, the distributions for the switch S~ open have been analysed. In this paper, a summary o f the most interesting findings is presented. Every distribution presented is an arithmetic mean of 3 tests. These tests are o f satisfactory reproducibility (for significance ~ = 0.05, the confidence intervals are always below 2.5%). The analysis o f the histograms in Fig. 7 suggests that the distributions of vitrain for all frequencies are close to its distribution for "S, open". In other words, the majority o f the grains ignore the alternating electric fields of the frequencies used. This fact leads to the conclusion that the majority of the studied vitrain grains meet the dependence 1/RgCg .~ 300 Hz. The asymmetry o f the distributions may be explained in terms of a contact potential phenomenon. Further studies have led to the conclusion that the other materials of similar resistivity (i.e. clarain
180
I> 2
transporting Q[P
U,~ $1
5
4
.---
i
6
I 112131415i~17 6
~./o
i 16o?.
Fig. 6. E x p e r i m e n t a l s e p a r a t i o n device : 1 - feed h o p p e r , 2 - b a t c h e r o f c o n c e n t r a t i o n , 3 c y c l o n e , 4 - e l e c t r i f i c a t i o n e l e m e n t , 5 - s e p a r a t i o n c h a m b e r , 7 - receiver, 8 - alternating voltage g e n e r a t o r , S l-switch. TABLE 1 Resistivities o f t h e hard coal c o m p o n e n t s s t u d i e d
No.
Hard coal components
Resistivity [~ cm]
1 2 3
vitrain vitrain-durain durain semi-shine durain bass mudstone pyrite
10s--101° 10s--101° 108--101° 108--101° 10'--108 106--10 s 102--106
4
5 6 7
1, 2, 3 and 4 - - p e t r o g r a f i c hard coal c o m p o n e n t s ; 5 and 6 - - a s h c o n t e n t s ; 7 - - n o n ~ r g a n i c sulphur compound.
181
['.J 40 f = 300 H z
30 20 10 0
1
,
I 2
l 3
4
5
6
7
bin
1
[./.] 4O 30 f = 30 000
20
Hz
10
1
2
3
4
5
6
7
bin
J
[./,] 4O 30 20 open
S1
10
I 1
2
3
4
5
6
7
bin
F i g . 7. H i s t o g r a m s o f t h e vitrain d i s t r i b u t i o n s .
similar distributions to the vitrain. However, the distributions of other materials investigated (i.e. bass, mudstone and pyrite) strongly depend on the frequency used (Fig. 8). This fact arises from the lower resistivities of these components (see Table 1) so many of their grains satisfy the dependence 300 Hz < 1]RgCg< 30 000 Hz. The greater the frequency, the distribution
182
[./o] 30 f = 300 Hz
20
[
10 0
2
3
4
5
6
7
bin
2r
[./.] 7O 60 50. 40' 30' 20
f_- 1000 Hz
10. 0
N
1
2
I
3
4
5
7
I
bin
T
E'/.] J 7060504030 S 1 open
20
10
o Fig. 8.
1
2
J
3
4
5
6
7
b
bin
Histograms o f the mudstone distributions.
is closer to the "$1 open situation". This fact is consistent with the theory presented above. The frequency characteristics o f the bin contents are presented in Figs. 9 and 10. The summary contents of bins "1", "2", "6" and "7" (indicated as
183
7i) are the analogue of the contents of bin I from Fig. 4. On the other hand, the summary contents o f bins "3", " 4 " and " 5 " (indicated as 7n) are the analogue of the contents of bin II. Figures 11 and 12 present the characteristics o f the arithmetic mean x(f) and standard deviation s(f) characterizing the distributions in the receiver. The characteristics presented are in agreement with the theoretical assumptions - with the exception o f bass. The bass grains have a characteristic "lamella" shape. This leads to a great influence o f contact potential and results in considerable asymmetries of the distributions. Nevertheless, the fact that s(f) is ever growing within the range o f 1 000--10 000 Hz is still inexplicable and requires some additional studies. The differences between the characteristics of the hard coal c o m p o n e n t s indicate the possibility of separation. To demonstrate this, the separation of raw coal (0.8--0.6 mm) with sulphur content of 5.3% has been carried out. 7i
Ira] 7O
® 60'
'0 ,@
® f[.z] 0 3oo
lOOO
3000
10000
30000
Fig. 9. Characteristics7i(f): ~/I presents the s u m m a r y contents of the flank bins "1 ", "2", "6" and "7 ". The designations of the characteristicsin Figs. 9--12 are the same as the numeration of the hard coal components in Table 1.
184
E!I, 90
60
@
'./-
5O
©,
, [Hz] 3O
300 1000 3000 I(~0"00 30000 Fig. 10. Characteristics ~II(f): ~ n presents the s u m m a r y contents of the middle bins "3", " 4 " and " 5 "
These experiments have led to coal desulphurisation but the results achieved are not fully satisfactory from a technological standpoint. For example, for f = 300 Hz, the sulphur contents in the concentrate have been lowered to 2.9%. In tailings (36% of the feed) the sulphur contents have amounted to 9.5%. 4. Conclusions The experimental results agree with theoretical expectation and demonstrate the possibility of the separation by the method discussed. Nevertheless, on the basis of the experiments performed the technological usefulness of the method discussed cannot be confirmed. Thus, further work must consider other useful minerals - for which conventional methods do not succeed. After that, experimental optimisation of the method is required.
185
S
[./.] I 35
3(
25
20
I
10
5
,[Hz] 0 300
1000
3000
10000
30000
Fig. II. Arithmetic means of the receiver distributions ~(f).
Acknowledgements The author gratefully acknowledges the help received from his collegues Kazimierz Chudyba and Antoni Ciesla from the Institute of New Conversions o f Energy at Stanis](aw Staszic University of Mining and Metallurgy, Krak6w. He also owes a great deal to his consultant, Professor Dr. Zbigniew Jasicki.
186
[°/o]' 60
f
4 ~_ 3o0
1000
3000
10000
EHzl
30000
Fig. 12. Standard deviations of the receiver distributions s(f).
References 1 0 . C . Ralston, Electrostatic Separation of Mixed Granular Solids, Elsevier, Amsterdam, London, N e w York, Princeton, 1961. 2 J.E. Lawyer, State of the art of Electrostatic Separation of Minerals, J. Electrochem. Soc., February 1969, p. 57 C. 3 H. Schnitzler, Untersuchung des Walzenscheiders sowie ein Verfahren zur Messung des elektrischen Widerstands yon Staub und zur Bestimmung der Korniibergangswiderstands, Bergbau Archiv, 1950, Bll/12. 4 Polish Patent No. 84 486.