balance de energia de un jig

International Journal of Mineral Processing, 37 ( 1993 ) 189-207 189 Elsevier Science Publishers B.V., Amsterdam

A new energy dissipation theory of jig bed stratification. Part 2: a key energy parameter

determining bed stratification

R.X. Rong and G.J. Lyman Julius Kruttschnitt Mineral Research Centre, University of Queensland, Isled Road, Indooroopilly,

Qld. 4068, Australia

(Received 3 September 1991; accepted after revision 30 June 1992 )

ABSTRACT

Rong, R.X. and Lyman, G.J., 1993. A new energy dissipation theory of jig bed stratification. Part 2: a key energy parameter determining bed stratification. Int. J. Miner. Process., 37:189-207.

Based on a detailed dynamic energy dissipation analysis for a large experimental data base developed in a highly instrumented and controlled pilot Baum jig, the effects of operating parameters on some important energies in the jigging process have been analyzed. Changes in the frequency of pulsation and air pressure in the accumulator result in a large change of these energies.

According to regression analyses of the energy dissipation data, a new energy hypothesis is proposed, which indicates that the total energy dissipated in the jig bed within a cycle is the vital parameter determining the bed stratification. This energy is the difference between the energy input to the jig bed and the energy recovery on bed collapse. It is a combined product of the operating parameters, bed material characteristics, and jig structure. It can be suggested that for each type of bed material, a certain level of energy input is required to efficiently stratify the bed. This energy hypothesis remedies the defects of the previous jig theories, because the functions of the operating parameters and the air- water phase behaviour parameters are fully considered and analyzed.

I N T R O D U C T I O N

Jigging is one of the oldest and widely used preparation processes for coal and ore. The mechanism of jigging process has interested researchers for more than one hundred years. A great deal of effort has been expended by many researchers to explain the jig process. Five jig theories have been developed historically to explain jig bed stratification.

The classical theory denotes the earliest jig theory in which consideration is given to the motion of a single particle in the jig bed at first and then related to movement of masses of particles. This theory includes the principle of equal- settling particles, principle of interstitial currents, principle of acceleration, and principle of suction.

0301-7516/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.

190 R.X. RONG AND G.J. LYMAN

The earliest investigator of the principle of equal-settling particles was Rit- tinger (1870) who proposed a formula for terminal settling velocity of a single particle in a liquid. It was supposed that the stratification of particles starts with free spaces existing in the jig bed, and that the difference of the maximum upward stroke of water and the settling velocity of particles determines the state of particles in the bed. This principle was then modified by a number of researchers (Munroe, 1889; Chapman and Mott, 1928; Lunnon, 1928/ 1929; Kirkup, 1931; Spee, 1936; Hancock, 1937; Hirst, 1937; Kuhn, 1950).

The principle proposed by Munroe ( 1889 ) assumed that a particle moving in an interstitial space between other particles was like one moving freely in a confined channel. This concept was an attempt to explain why the large ratios of size can be treated in practice, but the assumption was fallacious, and the experimental results could not be proven by other workers (Richards, 1894; Javis, 1908; Hirst, 1933).

The principle of acceleration was also initially derived from the investigation of a single particle motion in a fluid under free-settling conditions by Rittinger (1870), and then developed by other researchers (Javis, 1908; Chapman and Mott, 1928; Hirst, 1933; Ushio, 1951; Charbonnier, 1959). This principle attempted to consider all the forces acting on the particles and assumed that the separation of a particle in jigging process depends on the specific gravity of the particle only, and the influence of the shape and size of the particle can be ignored.

Richards ( 1894, 1908 ) considered that pulsion and suction are two active phases of jigging and indicated the necessity of a suction phase, in particular for mixed sizes.

Gaudin (1939) listed three major effects contributing to the stratification in jigs: hindered-settling classification, differential acceleration at beginning of fall and consolidation trickling at end of full, of which the consolidation trickling is significant in jigging fine particles.

The classical theory outlined above has been used extensively in the first half of the century although the jigging process could not be truly explained by these principles.

A heavy medium theory has considered the jig bed as a heavy medium with alterable density in various conditions. The separation of particles in the jig is just the same as that in heavy medium according to the density of particles, i.e. largely determined by the difference of the density of particles in supposed medium (Hirst, 1933; Schaefer, 1950; Hoffmann, 1958; Spetl et al., 1968, 1973).

Mayer ( 1950, 1964) proposed a potential energy theory and indicated that between the unstratified and stratified state of the jig bed there exists a difference in potential energy, and that the undressed bed is a labile mechanical system under a gravity potential which strives toward the more stable (stratified) state having lower potential energy. It was emphasized that only energy

NEW ENERGY DISSIPATION THEORY OF JIG BED STRATIFICATION. PART 2 1 91

reduction is the physical cause of stratification of the jig bed. Mayer disagreed with the assumption that the jig stroke supplies the flow energy which causes stratification of the jig bed and argued that the supplied energies have only the effect of releasing the potential energy stored in the granular mixture and therefore are not directly responsible for the stratification.

The statistical theory (Rafales-Lamarka, 1962; Vinogradov et al., 1968) analyzed kinetics of the jigging process using a special method - - statistical law and supposed that the motion of particles in the bed obeys a statistical regularity.

The modem dispersion theory (Siwiec and Tumidajski, 1985 ) treated the jigging process as a quasi-diffusion with convection superimposed because of gravity and uplift forces. This theory assumes that a feed can be divided into two fractions, i.e. light fraction having the density lower than a separation density and heavy fraction having the density higher than the separation density, and that the particle of heavy fraction makes a jump of some length in the course of each water pulsation, and the jump length is a random variable following a gamma distribution.

The above jig theories describe the source or results of bed stratification. In particular, the potential energy and statistical theories can be used to explain some phenomena of the bed stratification. However, all the theories either fail to explain, or neglect to make explicit, the function of jig operating parameters which are so important in the jigging process.

Moreover, the comprehensive effect of all the operating parameters rather than individual ones on bed stratification is still obscure. In the jigging process, there should exist a parameter which is determined by the operating parameters, coal feed characteristics, and the jig structure, which has a key influence on the bed stratification.

Energy dissipation analysis in a pilot scale Baum jig has been described in part 1 of this paper (Rong and Lyman, 1993 ). From statistical analysis of the detailed energy dissipation data, a very significant point has been found, namely, that the energy dissipated in the jig bed within a cycle plays a vital role in determining the bed stratification. Using this hypothesis, together with a consideration of turbulence in the water flow in the jig, many phenomena of bed stratification can be explained.

In this paper, the arguments focus on dynamic energy dissipation and in- tegral values of dissipation within a cycle. The bed stratification is explained using concept of the energy dissipation and fluid turbulence in the jig.

The symbols used in part 2 can be found in the nomenclature of part 1 of this paper (Rong and Lyman, 1993 ).

ENERGY DISSIPATION WITHIN A CYCLE IN THE PILOT JIG

Part 1 of this paper (Rong and Lyman, 1993) described a compensation method for the energy balance in the pilot scale Baum jig, that is, the water


level signal in air chamber (WLAC) was shifted forward for two time slices which is one sixteenth of the period of a cycle. The energy dissipation of the jig within a cycle for all the experiments has been calculated using a typical test data corresponding to the nominal settings of the jig operating parameters (Table 1 ). The duration of the opening ramp of the inlet valve shown in Table 1 denotes the time interval from the commencement of opening to full opening of the inlet valve. The energy dissipation per time slice ( TI= 1/32 of a cycle) within a jigging cycle can be seen in a typical group of curves (Fig. 1 ). The two vertical lines A and B in the figure represent the settings of end of the inlet period (or commencement of the expansion period) and end of expansion period (or commencement of the exhaust period) respectively. Waveforms in the figure indicate the energies per time slice calculated from modified signal data (Rong and Lyman, 1991a) using the equations described in part 1 of this paper (Rong and Lyman, 1993 ).

The major energy input to the jig is the energy input from the compressed air E~a(t) (Fig. la). At the beginning of a cycle (commencement of inlet valve opening) a relatively constant recovery of energy from the water to the gas takes place as the water level in the air chamber rises against a relatively low gas pressure. This energy loss from the water decelerates the water to the point where the water changes direction and the pulsion stroke begins and Eca (t) becomes positive. The gas supplies energy to the water for a significant por- tion of the cycle (until after the exhaust valve opens) whereupon energy recovery (Eta (t), negative ) from water to gas begins again.

The work done by the atmosphere on the water at the surface in the jigging chamber corresponds to that water motion (Fig. 1 a, Eap (t) ).

The hutch water of the jig is fed from a head tank, and the supply pressure is constant. The energy input from the hutch water supply Ehw (t), depends on the flow variation. Notwithstanding the constant head feed, the hutch water flow varies in response to the changing pressure inside the jig body, which is determined by the water acceleration and water level in the jig (Fig. l b ). The energy input from this source is negligible.

TABLEI

Nominal settings of the jig operating parameters

The duration of the opening ramp of inlet valve ( ° ) 40

Air cycle ( ° )

Frequency of pulsations (pulses / min ) Air pressure in the accumulator (kPa) Hutch water flowrate (m3/sec) Bed thickness (mm)

Inlet Expansion Exhaust

199 38

123 57 10.35 0.0023

300

(a) For energies Eca(t). Eap(t) a n d Ebs(t) (b) For energy Ehw(t)

0.6 0.190

0.4

-0.4

0.2

=o 0.0

-0.2

-0.6

0.4

A B

Eca(t) ~I -~ Eap(t) -m- Ebsttl

i |

, , , , l , I , ,

20 40 60 80 100

I

~ 0.186

&

~ 0.182 O

~ 0.178

0.174

0.170

m

13

Ehw(t)

m I i m

20 40 60 80 100

%Cycle %Cycle

(c) For energy Ewo(t) (d) For energies Els(t) a n d Epc(t)

2 0 4 0 6 0 8 0

§ o.3

~ 0.2

0.1

0.0

NEW ENERGY DISSIPATION THEORY OF JIG BED STRATIFICATION. PART 2 19 3

i . - =

00

0.02

0.01

0.00 O

oo

-0.01

-0.02

-0.03

/ t X.=

-~- Els(t) Er~t)

! . I . !

40 60 8 0

!

20 100

%Cycle %Cycle

Fig. 1. A typical energy dissipation versus time slice within a jigging cycle.

In batch operation, the water overflow from the weir of the jigging chamber is intermittent. Thus energy loss due to the water overflow Ewo(t) is zero at the beginning and end o f a cycle when the water level in the jigging chamber is lower than the weir lip (Fig. l c ) . The m a x i m u m value o f the energy ap-


proximately occurs at the beginning of the exhaust period when the minimum value of the energy Ehw (t) occurs. Since the energy Ewo (t) is so small, the energy loss from the jigging system is also negligible.

Based on the assumed bed motion model (part 1; Rong and Lyman, 1993 ), the potential energy change Epc (t) rises when the bed material is lifted in the jigging chamber and falls as the bed collapses (Fig. 1 d). The variation of this energy is dependent on the particle and water motion in the jigging chamber.

The energy loss Els(t) due to the screen plate is mainly dependent on the pressure drop across the plate and the water velocity in the jigging chamber. The measured pressure difference between points above and below the screen plate depends on the static head difference between the two points, the actual pressure drop across the plate and the acceleration of the water in the jigging chamber. The pressure drop across the screen plate can be extracted from such measured pressure difference by correcting for the static head and acceleration effects (part 1; Rong and Lyman, 1993 ). Figure ld shows that energy loss across the plate is low during most of the cycle but rises rapidly during the suction phase.

The energy dissipated in the jig bed Ebs(t) is found by an overall energy balance in the jig. A positive energy value represents energy input to the jig bed within a cycle, and a negative value represents energy recovery on bed collapse (Fig. la) . The shape of the waveform is dependent on the jig operating parameters.

THE EFFECTS OF OPERATING PARAMETERS ON THE ENERGY INPUT FROM

COMPRESSED AIR AND THE ENERGY DISSIPATED IN THE JIG BED

The discussion about the effect of the operating parameters on the energy dissipation in the jig will focus attention on the energies input from compressed air (Eca( t ) and E¢ai ) and the energies dissipated in the jig bed ( Ebs ( t ) and Ejb) (part 1, Rong and Lyman, 1993), because these energy terms are important in the stratification process. During the experiments, one operating parameter was varied while the other operating parameters were kept constant.

Figures 2 to 9 demonstrate the influences of some operating parameters on the critical energy terms using the calculated data of the energy dissipation in the case that the signal WLAC was shifted forward for one sixteenth of the period of a cycle (part 1, Rong and Lyman, 1993 ). From these figures it can be seen that i. With the increase of the inlet period of the air cycle (Figs. 2 and 3 ), the

variations of the energies E~ (t) and Ebs (t) decrease considerably. The net energy input from compressed air reaches a maximum value at about 180 °, but the energy dissipated in the bed increases almost continuously with increasing the inlet period duration.

NEW ENERGY DISSIPATION THEORY OF JIG BED STRATIFICATION. PART 2 195

(a) F o r e n e r g y Eca( t ) (b) F o r e n e r g y Eca I

0.5

0.4

i 0.3 0.2

0.1

o.o o

-O. 1

~ -0.2

~ -0.3 a.1

-0.4 0

220 degree

0.30

i 0.25

0.20

o 0.15

0.IO

0.05

z 0.00

, I , I ~ ' ' -0.05 , I ' • ' , ' ' 20 40 60 80 I00 120 140 160 180 200 220 240

% Cycle Inlet period of the air cycle (degrees)

Fig. 2. The effect of the inlet period of the air cycle on the energies Eca(t) and Ecai.

(a) F o r e n e r g y Ebs( t ) (b) F o r e n e r g y Ejb

1.0 0.30 [-

0.6 0.25

iiii I -0.6 0.00

- 1.0 -0.05 ' " 0 20 40 60 80 100 120 140 160 180 200 220 240

% Cycle Inlet period of the air cycle (degrees)

Fig. 3. T h e effect o f the inlet per iod o f the air cycle o n the energies Ebs(t ) and Ejb.

ii. Figures 4 and 5 illustrate that as the frequency of pulsations increases, the fluctuations o f the energies Eta (t) and Ebs (t) decrease. The variations of these energy terms are absolutely changed when the frequency is 71 pulsations/min. With the increase of the frequency of pulsations from 43 to 71 pulsations/min, the energies Ecai and Ejb decrease sharply. When

196 g.X. RONG AND G.J, LYMAN

(a) For e n e r g y Eca(t) (13) For e n e r g y Eca i

0.5

~'~ 0.4

0.3

0.2

t 8 o.1

0.0

~ -0.1

~ -0.2

-0.3

-0.4

j • ~ 43 ppm 4 - 50 ppm

57 ppm • -e- 6 4 p p m

i ! a i !

20 40 60 80 I00

0.30

0.15

4O 50 60 70 80

% Cyde Frequency of pulsations (pul/min)

Fig. 4. The effect of frequency of pulsat ions on the energies E ~ ( t ) and Ecai.

(a) Fo r e n e r g y Ebs(t) (b) For e n e r g y Ejb

1.0

0.6 ,o

~ 0.2

-0.2

~ --0.6

! | i

50 60 7O

-~- 64 puks/min ~/" 71 puls/min

a l l !

20 40 60 80 100

0.30 A

0.25 .o

0.20

0.15

0 . i 0

0.05

~ o.oo z

-0.05 40

-1.0 0 80

% Cycle Frequency of pulsations (pul/rnin)

Fig. 5. The effect of frequency of pulsat ions on the energies Ebs(t) and Ejb.

the frequency setting is 64 pulsations/min, at which the pilot jig may be in resonance state, the energy Eta (t) shows a normal variation with time, but the energy Ebs(t) fluctuates significantly. The fact that the energy Ejb is negative at this frequency may be attributed to the unsuitable time phase shift for the particular case.


(a) F o r e n e r g y Eca( t ) (13) F o r e n e r g y E c a I

0.5 = 0.30

0.20 0.2 ~

E o.15 i o.1 ~o o.o ~ °"° F ~ , ~

-0.1

F z o.oo

-0.3 -0.05 -0.4 . , , i . , , , , , .

0 20 40 60 80 100 6 7 8 9 10 11 12

% Cycle Air pressure In the accumula tor (kPa)

Fig. 6. T h e effect o f t he a i r p r e s s u r e in the a c c u m u l a t o r on the ene rg ies E~a(t) a n d Ec~,.

(a) F o r e n e r g y Ebs( t ) (b) F o r e n e r g y Ejb

_= e,

0.6

0.2 ,-q 0.20 I

=~ o.15r

-0.2 ~ 0 . I0

-0.6 ~ o

~ 0.00

- - - -v -N.n-~ " " ' ' 1. 0 0 20 40 60 80 100 6 7 8 9

J

! , ! ,

10 II 12

% Cycle Air pressure in the accumula tor (kPa)

Fig. 7. T h e effect o f t he a i r p r e s s u r e in t he a c c u m u l a t o r on t he ene rg ies Ebs( t ) a n d Ej~.

iii. Figures 6 and 7 show that the variation of energy terms E~a (t) and Ebs (t), and the net energies Eca i and Ejb all increase with increase of the air pressure in the accumulator. As the air pressure nearly doubles (from 6.3 to 11.5 kPa), the energies Ejb and Ecai approximately double and triple, respectively.


(a) F o r e n e r g y Eca(t) (b) F o r e n e r g y E c a i

0.5

0.4

• o 0.3

0.2

~o 0.I

0.0

"O'I i

t -0.2

-0.3

-0.4 0

"~- 0.00205 m3/s -4- 0.00237 m3/s -B- 0.00267 m3/s

I I I !

20 40 60 80 100

0.30

0.25

e~ E 0.20 8 ~ 0.15

~ 0.10

~ 0 . 0 5 I

0.00 t

-0 .05" 0.10

a I n I n I I

0.15 0.20 0.25 0.30

% Cycle Hutch water flowrate (m3/s)*100

Fig. 8. T h e effect o f the hutch water f lowrate o n the energies Eta(t) and Eca i.

(a) F o r e n e r g y Ebs(t) (b) F o r e n e r g y Ejb

1.0

o.6 ..Q

0.2

-0.2;

-0.6 0.00237 m3/s -w- 0.00267 m3/s

I n i !

20 40 60 80 IO0

0.30

0.25

0.20

~O 0.15

0. I0

~ 0 . 0 5

~ 0.00 Z

-0.05 0.I0

-1.0 i I , I a I i 0 0.15 0.20 0.25 0.30

% Cycle Hutch water flowrate |m3/sl* I00

Fig. 9. T h e effect o f the hutch water f lowrate o n the energies Ebs( t ) and Ejb.

iv. Figures 8 and 9 show that hutch water flowrate generally has little effect on both the energy terms. However, at the maximum hutch water flow both the energy terms increase substantially. This may be due to the fact that the mass of water in the jig increases with the increase of the hutch water flowrate. The frequency of pulsations at the resonant point of the


jig system is then reduced. At 57 pulsations/min of the frequency and 0.00267 m3/s hutch water flowrate, the jig resonates, therefore, the energies Ecai and Ejb increase significantly.

The above analysis indicates that two operating parameters (the frequency of pulsations and air pressure in the accumulator) give strong influences on the energy input from the compressed air and the energy dissipated in the jig bed.

If comparing with the modelling investigation results of bed stratification in the pilot scale Baum jig (Rong and Lyman, 1991 b ), it is of interest to note that the importance of these two operating parameters (frequency and air pressure) to both the energy dissipated in the jig bed and extent of bed stratification are exactly the same.

T U R B U L E N C E I N T H E J I G G I N G C H A M B E R

The Reynolds number Re is usually used to characterize the flow pattern. In general, pipe flow turbulence is fully established when Re> 4000. At the other extreme, eddies around protrusions and solid bodies in a fluid form at much lower local Reynolds numbers. For spheres, for example, in a stream of fluid, true turbulence (with a spectrum of eddy sizes and chaotic motion) sets in only if Re> 1000 (Davis, 1972).

For the pilot jig, the absolute value (ABS) of Reynolds number is calculated using the following equation.

Re(t ) =ABS[ pw WVj/t (t)D 1 (1)

where Re( t ) =- Reynolds number at time t, pw=water density (kg/m3), (t) = water velocity inside the jigging chamber at time t, D= equivalent

diameter of the jigging chamber (m), and p = viscosity of water (kg/m- sec). The equivalent diameter of the jigging chamber was used here to characterize the largest scale of flow in the jig under conditions where the bed is dilated and therefore mobile. This is particularly true in a continuous jig where the horizontal flow in the jig is substantial with sufficient turbulence to suspend the fine solids on the surface of the particle bed. No matter what direction of the water flow (pulsion or suction), the Reynolds number must always be positive.

Calculation results show that the average Reynolds number, which is based on the equivalent diameter of the jigging chamber size and the average absolute water velocity in this chamber, within a cycle is in the range of 2.3 × 104 to 1.3 × 105 for all the experimental data in which the energy dissipation was calculated. Obviously, the water flow in the jigging chamber would appear to be a very strong turbulent flow pattern.


In jigging process, the turbulence may be process-determining. With so high a Reynolds number, there is a wide turbulence spectrum of superimposing eddy element, which can be seen obviously from the particle motion in the jigging chamber, in particular near the water surface. This must effect on the fluid-particle energy transfer and motion trajectory of panicles.

It may be true that the turbulence is necessary to transfer the energy from

~ (a) F o r ' easy to w a s h ' mate r ia l (35-3 mm)

g

t ~

2.8

2.7

2.6

2.5

2.4

2.3

2.2

2.1 2.0

Q

D

m

I t

[ ]

f f ! i i

4.0 6.0 8.0 I0.0 12.0

Reynolds number • 10 -4

14.0

0a) F o r ' i n t e rmed ia t e ' ma te r i a l (35-3 ram)

o

o

2.8

2.7

2.6

2.5

2.4

2.3

2.2

2.1 2.O

! ! i |

4.0 6.0 8.0 10.0 Reynolds number • 10 .4

! |

12.0 14.0

Fig. 10. The scattergram of the relationship between the concentration profile index and the average Reynolds number in the jigging chamber within a cycle.

TABLE 2

Average Reynolds number for the experiments with the best bed stratification

For the easy to wash bed material 61983 For the intermediate (washability) bed material 60456


water fluid to particles and create the stratification condition in jigging process. But, it should exist on an appropriate scale. If the scale is too small, particles can not get enough energy to be moved and stratified in terms of their density. On the other hand, if the turbulence is too wide, it will lead to a remixing of the stratified particles and reduce the stratification accuracy of the bed.

Two series of experimental data representing bed stratification of easy and intermediate washability bed materials have been analyzed. The size and density distributions of these bed materials can be found elsewhere (Rong and Lyman, 1992 ). As described in part 1 of the paper, a special index m concentration profile index (CPI) - - is a more accurate one to evaluate extent of bed stratification than generally used probable eITor (Ep). Using this index, the relationship between the CPI and the average Reynolds number within a cycle for 35-3 mm size fraction is illustrated in Fig. 10. Increasing of the CPI value represents improvement of the bed stratification. The average Rey- nolds numbers for the experiments which have the best bed stratification in each series test are given in Table 2. It can be seen that the better bed stratification for this batch jig happens in the condition that the Reynolds number is around 6 × 104. However, there exist a certain ranges of the Reynolds number, in response to a number of tests with different CPI values (Fig. l 0 ). That fact indicates that the Reynolds number may give a influence, to some extent, on the bed stratification, but it is not a key parameter in determining it.

Although considerable information has been published on the turbulence subject theoretically, the knowledge about the fluid dynamics of a mixture of particles of arbitrary density, size, and concentration with a fluid where both are in turbulent motion is not sufficient. Nor was the investigation of the influence of turbulence on bed stratification described above sufficient, therefore, this subject needs to be further investigated and developed.

THE E N E R G Y DISSIPATED IN THE JIG BED AS THE KEY P A R A M E T E R

D E T E R M I N I N G THE BED STRATIFICATION

An attempt was made to investigate the relationship between the bed stratification and the energies involved in the jigging system. To exclude the strong influence of the jigging time, as noted elsewhere (Rong and Lyman, 199 lb) , only data sets for which jigging time was strictly controlled were used in regression analysis. Initially, all the energies calculated in the energy dissipation analysis (part 1; Rong and Lyman, 1993) were involved in a multiple regression analysis, from which the following energy parameters within a jigging cycle and average Reynolds numbers in different cases were extracted for further step-wise regression analysis (Table 3). The power parameters (EA (g), EA (h) and EA (i)) in this table were net values per cycle and can be


TABLE 3

Definition of the energy parameters used in the step-wise regression analysis

Energy parameters ( E A ( ) )

Definition Units

C d e f g h i j k 1

gross energy input to the jigging system from compressed air (EcAIN) kJ gross energy recovery to compressed air from the jigging system kJ ( ECAOUT ) net energy input per cycle from the compressed air (EcAx) kJ gross energy input to the jig bed (EjBIN) kJ gross energy recovery from the jig bed collapse (EjI3OUT) kJ net energy dissipated in the jig bed per cycle (EjB) kJ the power used for lifting the jig bed kW the power used for settling the jig bed down kW total power acting on the jig bed kW average Reynolds number within a cycle average Reynolds number when the jig bed is lifted average Reynolds number when the jig bed settles down

TABLE 4

A summary of the step-wise regression results of the energy dissipation data (the energy parameters refer to Table 3 ). Phase case 3 for WLAC

Washability Size Statistical analysis of bed mat. (mm)

Variables Parameter F-test Correlation R R 2 entered

Easy to wash

Intermediate

35-16 1 f 18.305 0.730 0.534 16-8 1 f 14.874 0.694 0.482 8-3 1 f 25.072 0.781 0.610

35-3 1 f 37.763 0.838 0.702

35-16 1 f 12.608 0.550 0.303 16-8 1 h 15.715 0.593 0.351 8-3 1 f 22.547 0.661 0.437

35-3 1 f 16.417 0.601 0.361

calculated by the energy parameters (EA (d), EA (e) and EA (f)) divided by the time interval of per time slice.

The bed stratification index is based on the CPI and the above twelve parameters are the variables in the step-wise regression for phase shift correc- tion case 3. Table 4 gives a summary of the statistical analysis results on size- by-size basis. This analysis shows the most significant energy parameter in relation to the bed stratification, and the corresponding F-test and R-squared values.


It is of interest to find that only one parameter is included in the regression equation for two series of tests with different particle sizes. The most significant energy parameter is clearly the EA (f), i.e. the total energy dissipated in the jig bed within a cycle (Ejb). This energy is the difference between the energy input to the jig bed and the energy recovery on bed collapse. The statistical analysis results are acceptable for the tests using easy to wash material, but worse for the tests using another bed material. The Reynolds Number has been extracted from the regression equation finally, so it is proved again that the Reynolds number is not the key parameter to determine bed stratification.

The energy required for the bed stratification is transferred by air-water phase. The significant energy, i.e. the energy dissipated in the jig bed within a cycle (Ejb), is mainly determined by the gross energy input from the compressed air (Ecai). And the energy Ecai is strongly influenced by the operating parameters used in the jigging process. Therefore, the energy EjbiS closely related to the jig operating parameters.

Scattergrams of the concentration profile index against net energy dissipated in the jig bed per cycle for two different types of bed material (total size distribution) are presented as Fig. 11.

It is evident that i. When the energy dissipated in the jig bed is too small, the bed stratifi-

cation is less good (in small CPI value). ii. As the energy acting on the jig bed increases, the bed stratification is

generally improved. iii. The optimal bed stratification may occur at the energy dissipated in the

jig bed within a cycle of higher than 0.20 kJ for easy to wash bed material, and around 0.20 kJ for the intermediate to wash bed material.

Since the values of the correlation coefficient for the regressions are of an intermediate value (0.84 and 0.60), one does not expect the diagrams to show a precise correlation. However, the tendency for bed stratification to improve with increased energy dissipation is evident. The trend for the "easy to wash" material is clearer than that for another bed composition.

The concept of energy dissipation being a unifying factor for control of stratification leads naturally to the hypothesis that there should be an optimal energy dissipation for a granular bed material. An optimal value (a maximum stratification index value ) is not evident in the plots as jigging conditions did not extent to high enough energy dissipation levels to show a decrease in stratification index.

The real value of the above two analyses is that (it is suggested that) stratification can be correlated with a single parameter that integrates the effects of all operating parameters. Even though the correlation is less strong than one might desire, the results suggest that an avenue for further endeavour with improved experimental techniques and measurement. For each type of bed material, a certain energy may be required to efficiently stratify the bed.

204 R.X. R O N G AND G.J. LYMAN

(a) For 'easy to wash ' material (35-3 m m )

• 2.8

2 .7

2.6 Dam m u

"~ 2 .5 m m

2 .4 [] o o~ 2 .3

o 2 .2

2.1 J i l - 0 . 0 5 0 . 0 0 0 . 0 5 0 . I 0 0 . 1 5

o 0 Net energy d iss ipat ion in the Jig bed (IcJ)

0.20

(b) For ' intermediate' material (35-3 mm)

k 2 .8 1

.~ 2 .7

2.6 • •

,~ 2 .5 * • • •

• •@ 2 .4 • @@ •

2 .3 • ~ •

2 .2 • •

2.1 J I i ,

- 0 . 05 0 . 0 0 0 . 0 5 0. I 0 0 . 1 5 O O Net energy d iss ipat ion in the Jig bed tic, J)

0 . 2 0

Fig. 11. The scattergram of the relationship between the concentration profile index and the net energy dissipated in the jig bed within a cycle.

The main object of adjusting the jigging operating parameters is to generate a suitable net energy dissipation in the jig bed.

It has been noted in the past that a variety of combination of settings of operating parameters on a jig will provide similar extents of stratification in the bed. The batch jigging test work conducted has demonstrated that different sets of operating parameters can produces different behaviour of the water in the jig (Rong and Lyman, 1991 a). In other words, different values of the jig settings do not produce unique types of jig behaviour. If it is true that the energy dissipation in the bed is an adequate unifying parameter for stratification, then any settings of the jigging parameters that produce the same energy dissipation in the bed will achieve similar stratification results.

The phenomena that in each compartment of industrial jigs and any type of pilot jig, the jigging process has a preferred frequency of pulsations, or the

NEW ENERGY DISSIPATION THEORY OF JIG BED STRATIFICATION. PART 2 2 0 5

inlet period setting of the air cycle, or the air pressure, or the other operating parameters, can also be elucidated by this viewpoint. The significance of this outcome is that it remedies the defects of previous jig theories or hypothesis, because the function of the operating parameters, and the air-water behaviour in the jigging process are fully considered for investigating the bed stratification mechanism.

Mayer (1964) stated that in jigging process, the energy supplied by stirring or by the jig stroke have only a releasing effect on the potential energy stored in the stratified granular mixture. Obviously, Mayer's above viewpoint can not be supported by the statistical analysis results of substantial experimental data. The potential energy theory (Mayer, 1964) may be used to explain the internal cause of the bed stratification, and the new energy hypothesis described above may be used to expound the external cause of the bed stratification. Thus, the mechanism of jig bed stratification can be further understood.

C O N C L U S I O N S

The operating parameters which appear to strongly influence the energy input from the compressed air and the energy dissipated in the jig bed are the frequency of pulsation and operating air pressure.

Based on the equivalent diameter of the jigging chamber size and the average absolute water velocity in this chamber, the calculated Reynolds number in the jigging chamber is very high, therefore, the water flow appears to be a strong turbulent flow pattern. The wide turbulence spectrum of superimposing eddy element must effect the fluid-particle energy transfer and trajectory of particles. The turbulence may be necessary to transfer the energy from the water flow to particles, but it should exist on an appropriate scale. Too high or low a turbulence level would lead to worse bed stratification. A good bed stratification may require a suitable range of Reynolds number, but it is not the key parameter in determining the bed stratification.

According to regression analyses using the energy dissipation data which were calculated on the basis of the assumed model of the bed motion, a new energy hypothesis is proposed. This hypothesis indicates that the net energy dissipated in the jig bed within a cycle is a vital parameter determining the bed stratification. This energy is the difference of the energy input to the jig bed and the energy recovery on bed collapse. It is a combined product of the operating parameters, bed material characteristics, and jig structure. For each type of bed material, a certain energy may be required to efficiently stratify the bed material. Using such a hypothesis, many phenomena of the jigging process can be elucidated.


REFERENCES

Chapman, W.R. and Mott, R.A., 1928. The Cleaning of Coal. Chapman and Hall Ltd., London, 680 pp.

Charbonnier, R.P., 1959. A study of a simplified theory of gravity concentration in coal jigs. Can. Min. Bull., 52: 385-388.

Davis, J.T., 1972. Turbulence Phenomena - - Introduction to the Eddy Transfer of Momentum, Mass and Heat, Particularly at Interfaces. Academic Press, New York and London, 412 pp.

Gaudin, A.M., 1939. Principles of Mineral Dressing. McGraw-Hill, New York and London, 554 PP.

Hancock, R.T., 1937. The law of motion of particles in a fluid. Inst. Min. Eng. Trans., 94:114- 121.

Hirst, A.A., 1933. The fundamental principles involved in the separation of particles by virtue of density difference. Inst. Min. Eng. Trans., 85: 236-268.

Hirst, A.A., 1937. Co-ordination of theories of gravity separation. Inst. Min. Eng. Trans., 94: 93-110.

Hoffmann, E., 1958. Experience with single bed jigs for the production of two or more products. Proccedings, 3rd Int. Coal Prep. Conf., Liege, D3, pp. 387-399.

Javis, R.P., 1908. Investigation on jigging. Trans. Am. Inst. Min. Eng., 39:451-521. Kirkup, R.H., 1931. The laws of movement of bodies in a fluid. Fuel, 10: 196-205. Kuhn, C., 1950. New Observations on the hydraulic cleaning process and their use for calcula-

tion of jigs characteristics. Proceedings, 1st Int. Coal Prep. Conf., Paris, D9, pp. 323-335. Lunnon, R.G., 1928/1929. The laws of motion of particles in a fluid. Inst. Min. Metall. Trans.,

38:402-413. Mayer, F.W., 1950. A new theory concerning the mechanism of settling with its consequences

for the rational shape of the diagram of the washing stroke and development of the corresponding regulator of a non-plunger jig. Proceedings, First Intern. Coal Prep. Conf., Paris, A7, pp. 316-322.

Mayer, F.W., 1964. Fundamentals of potential theory of the jigging process. Proceedings, 7th Intern. Miner. Processing Cong., New York, Part 2, pp. 75-86.

Munroe, H.S., 1889. The English versus the continental system of jigging - - is close sizing ad- vantageous? Trans. Am. Inst. Min. Eng., 22: 637-659.

Rafales-Lamarka, E.E., 1962. The jigging theory. Gorn. Zh., 10:17 l - 177 (in Russian ). Richards, R.H., 1894. Close sizing before jigging. Trans. Am. Inst. Min. Eng., 24: 409-486. Richards, R.H., 1908. Ore Dressing. McGraw-Hill, New York, Vol. I, 2nd. ed., 643 pp. Rittinger, P.R., 1870. Movable sieve jigs. Fixed sieve jigs with side plungers and under plungers.

Aufbereitungskunde, 165-270 (in German). Rong, R.X. and Lyman, G.J., 199 l a. The mechanical behaviour of water and gas phases in a

pilot scale Baum jig. Coal Prep., 9: 85-106. Rong, R.X. and Lyman, G.J., 199 lb. Modelling jig bed stratification in a pilot scale Baum jig.

Miner. Eng., 4:611-623. Rong, R.X. and Lyman, G.J., 1992. The effect of jig operating parameters on bed stratification

in a pilot scale Baum jig. Fuel, 71: 115-123. Rong, R.X. and Lyman, G.J., 1993. A new energy dissipation theory of jig bed stratification.

Part 1: Energy dissipation analysis in a pilot scale baum jig. Int. J. Miner. Process., 37:165- 188.

Schaefer, O.. 1950. A contribution to the elucidation of the principles of washing in plunger jigs. First Int. Coal Prep. Conf., Paris, D6, pp. 308-315.

Siwiec, A. and Tumidajski, T., 1985. Mathematical model of ore processing in a jig based on the analysis of grain movements. Arch. Gorn., 30:311-318.

Spee, V., 1936. Concerning the theory of coal washing. Trans. Chem. Eng. Cong., World Power Conference, London, 2, pp. 1-29.


Spetl, F., Puncmanova, J. and Prochazka, V., 1968. Gravity separation of fine coals. Proceed- ings, 8th Int. Miner. Processing Cong., Leningrad, G-6.

Spetl, F., Puncmanova, J. and Prochazka, V., 1973. Development and results of a new jig. Pro- ceedings, 6th Intern. Coal Prep. Conf., Paris, 19E, 12 pp.

Ushio, H., 1951. The capacity of Baum-type jig regarded from the motion of particles in wash- box. J. Fuel Soc., Jpn., 30:324-332 (in Japanese).

Vinogradov, N.N., Rafales-Lamarka, E.E. and Kollody, K.K., Egorov, N.S., Melik-Stepanova, A.G. and Gurvich, G.M., 1968. New trends in theory and technology of jigging the minerals. Proceedings, 8th Int. Miner. Processing Cong., Leningrad, C-2, 8 pp.

balance de energia de un jig

Documents