Energy consumption and product size distributions in choke-fed, high-compression roll mills

International Journal of Mineral Processing, 32 ( 1991 ) 59-79

59

Elsevier Science Publishers B.V., Amsterdam

Energy consumption and product size distributions in choke-fed, high-compression roll mills D.W. Fuerstenau a, A. Shuklab and P.C. Kapur b adept, of Materials Science and Mineral Engineering, University of California, Berkeley, CA 94720, USA bDept, of Metallurgical Engineering, Indian Institute of Technology, Kanpur, 208016, India (Received July 24, 1990; accepted after revision January 2, 1991 )

ABSTRACT Fuerstenau, D.W., Shukla, A. and Kapur, P.C., 1991. Energy consumption and product size distributions in choke-fed, high-compression roll mills. Int. J. Miner. Process., 32: 59-79. Four minerals, dolomite, limestone, quartz and hematite, were ground in a laboratory-size chokefed, high-compression roll mill, a newly invented energy-efficient comminution machine. The size distributions of the ground solids were analyzed for energy-size reduction relationships and for development of a model of grinding kinetics in terms of energy expended in the mill. The results show that the size distributions are self-similar, that log median size decreases linearly with the amount of fines generated, and that the inverse of the median size increases directly with energy input, which in turn can be controlled by adjusting the milling force on the rolls. The standard population balance model of grinding kinetics, used widely for tumbling mills, must be modified in order to account for increasing energy dissipation as the bed of particles gets packed progressively more tightly during its passage through the rolls. The resulting model simulates the product size distributions as a function of energy input quite accurately. A noteworthy observation is that, unlike in ball mill grinding, the breakage rate parameters in pressurized roll mills remain relatively insensitive to particle size, and consequently most coarse and medium size particles in the feed get broken in only one pass through the rolls. This characteristic feature is reflected in the superior performance of roll mills in energy terms.

INTRODUCTION

Optimal utilization of energy in the comminution of brittle solids, as measured for instance by the surface area produced per unit energy expended, is achieved when a single particle is broken slowly under pure compression (Schoenert, 1967). The next most efficient method is by the compressive loading of a bed of particles in a piston-die arrangement. In this mode, comminution occurs primarily by very high localized interparticle stresses gener0301-7516/91/$03.50

© 1991 - - Elsevier Science Publishers B.V.

60

i) V~ FIJERS~IEN.\~. E I ' A I .

ated within the particle bed. No separate ~carrier' is employed for the transport of energy to the solids, unlike in ball mills and similar media-type grinding equipment. For this reason, among others, the energy consumption for a comparable degree of size reduction in the compression loading route is only onehalf of that in ball milling (Schoenert, 1988 ). Comminution in a piston-die batch operation is hardly a practical proposition for bulk grinding tasks. For continuous operations on a large scale, a set of high-compression (that is pressurized) counter-rotating cylindrical rolls, shown in Fig. 1., can duplicate the piston loading of particulate bed with only a marginal loss of efficiency. Consequently, the choke-fed, pressurized roll mill invented by Schoenert (1985) is perceived as a major breakthrough in improving the productivity and energy efficiency of the size reduction process from coarse (several millimeters) size feeds down to trans- and sub-sieve size products. In view of the large capital already invested in industrial ball mill installations, in many instances it may not be economical to replace these mills completely by the pressurized roll mills. It turns out, however, that the roll mill can be employed advantageously in an existing grinding circuit in a pregrinding mode, where it acts as a 'booster' for the ball mill, resulting in significantly enhanced throughput and reduced energy consumption (Schwechten and Milburn, 1990 ). Grinding media mills in general and ball mills in particular have been studied and analyzed extensively, especially in the last three decades or so. Detailed and quite realistic mathematical models based on particle population balances are now available for scale-up, simulation and control of grinding mills and the associated circuits (Herbst and Fuerstenau, 1980; Austin et al., 1984; Prasher, 1987 ). Moreover, the classical energy 'laws' of comminution of solids have been successfully integrated with the phenomenological description of grinding kinetics under well defined and unambiguous stipulations for deriving general relationships between the specific energy consumption and the size spectra of ground particles and its fineness indices, such as

~

-----Choke

feed

Fig. 1. Schematicdrawingof a choke-fed,high-compressionroll mill.

ENERGY CONSUMPTION AND PRODUCT SIZE

61

median size or some other percentile (Kapur and Fuerstenau, 1987 ). On the other hand, because it has been put to commercial use only recently, very little information is available on the energetic-kinetic aspects of grinding in high-compression roll mills. Understandably, most of the research thus far has been directed towards establishing empirical or semi-empirical engineering correlations for the design and scale-up of the industrial-size mills. (Schoenert, 1988; Brachth~iuser and KeUerwessel, 1988). In an allied area, Fuerstenau et al. (1990a) have recently presented extensive data for energy consumption when mineral particles are broken singly in a pair of rigidly mounted rolls. It was shown that on a uniform basis of comparison, the grinding efficiency was up to five times greater than in ball milling. In a follow-up work, Kapur et al. (1990), presented a torque model which related the energy expended in turning the rolls to feed size and roll gap, two of the most important process variables. Some of these results are pertinent to the analysis of choke-fed, pressurized rolls presented in this paper. The objective of this communication is to examine the size distributions of a number of minerals ground dry in a laboratory-scale choke-fed, high-compression roll mill and relate the product to specific energy consumption. This relationship is attempted at two levels: ( 1 ) an empirical energy-size reduction 'law' which provides a rational and consistent basis for comparing the efficiency of pressurized rolls with single-particle breakage at one ideal extreme and grinding in media mills at the other end; and (2) a population-balance-based phenomenological model of grinding kinetics in terms of energy expended in turning the rolls which could be useful for obtaining a deeper insight into the operational characteristics of this machine, as well as for simulation of roll mill circuits. EXPERIMENTAL The experiments reported here were carried out with a laboratory-scale pressurized roll mill located at the Technical University of Clausthal. The device is comprised of two counter-rotating rolls of 200 m m diameter each, mounted on a strong frame. The bearings of one roll are fixed, while the other roll can slide laterally for adjustment of the gap. The milling force is applied by spring-press loading of the movable rolls. The rolls can run with a circumferential speed in range 0.1-3 m s- 1, with the roll torque being measured by a transducer attached to the drive shaft and coupled to a recorder. The gross cumulative energy input is computed by integrating power draft over the time of the experimental run. Details of the mill and its operation have been given by Schwechten (1987). The feeds were 8 × 10-mesh size fractions of crushed dolomite, limestone, quartz, and hematite minerals. These are the same materials that were used in previous investigations (Fuerstenau et al., 1990a). As the feed size was

62

I).t,~ tlfERSI|N \{ I:l .\1

"[ABLE 1 Experimental conditions for grinding in the choke-fed high-compression laborator.~ size roll mill Feed (8× 10 mesh)

Roll gap (mm)

Roll force (kN)

Energy inpul (kWh t- ~)

Dolomite

3.0 3.3 2.5 2.8 2.6

9 14 33 45 54

1.46 !.64 3. 1.7 3.22 4.36

Limestone

3.4 3.6 2.9 3.2 2.8

10 18 32.5 43 52.5

1.31 1.67 2.77 2.97 3.11

Quartz

3.2 3.1 2.8

13 29.5 43

1.17 2.19 3.11

Hematite

2.7 2.2

18 40.5

1.25 2.36

quite coarse and exhibited relatively high friction against the roll surface, it was fed by gravity only from a hopper funnel mounted above the roll gap, without taking recourse to a force feeding arrangement such as a screw-type feeder. The ground product was deagglomerated to break up any briquettes formed, and subjected to standard wet-dry sieve analysis at Berkeley in the usual manner. Table 1 provides the experimental details including the nature of the feed, roll gap, milling force and energy consumption. In order to broaden the coverage, an additional set of data for Rammelsberg ore ground in pressurized rolls reported by Schoenert ( 1984 ) was also examined. TEST RESULTS

Size distributions Figures 2, 3 and 4 show on log-log scale the experimental size distributions of ground dolomite, limestone and quartz, respectively, at different levels of energy expenditure. A few size distributions have been excluded (for example, in the case of dolomite ) in order to avoid excessive crowding of the data points. Hematite showed similar size distribution curves, but these are not exhibited here as data for only two energy levels were available. A characteristic feature of the size distribution curves is that these are in-

63

ENERGY CONSUMPTION AND PRODUCT SIZE

100 90 60

Dolomite (Sx10mesh feed)

70

6G 50

C .E ~.o LI...

"6 30

E D Simulated 20

--

- Functionol form

- -

Fine t u n e d

Expt'l

Energy (kWht -1',

A [] O

4.36 3.22 1.64 8 mesh

10

i

12

I

I

11 10

I

I

I

I

I

9

8

7

6

5

Size Index,

I 4

I 3

I 2

I~ 1

0

i

Fig. 2. Experimentaland simulatedsize distributionsof dolomite groundin a roll mill. variably convex in curvature in the coarse size range when observed from above. In other words, hardly any coarse size particles are left after only one pass through the pressurized rolls. In contrast, the distribution curves generated in a ball mill are initially concave in shape, implying that large amounts of unbroken feed particles and partially broken near feed-size coarse particles are present. These curves subsequently straighten out and finally acquire a convex shape only after prolonged grinding periods. The shape of the size distribution curves is in fact an index of the comminution efficiency of the mill. As demonstrated later in this paper, the breakage of coarse and medium size solids in a roll mill is an almost deterministic event and relatively insensitive to particle size, whereas in a ball mill the selection for breakages has a large stochastic, hit-and-miss component which, moreover, is strongly dependent on size. As shown in Figs. 5, 6 and 7 (for dolomite, limestone and quartz, respectively) the size distributions generated by high-compression roll mills are selfsimilar, when the data are replotted as a function of a dimensionless size, that is, size rescaled by a characteristic length such as the median size. This self-

64

I) V~ FUERS FEN ;~.1r E-I 41

100

Limestone

90 I

(8x10

mesh

feed)

i

7@

~

so

0

30

-5 E U Simulated

---

20

Functional Fine tuned

form

Expt'l Energy (kWht -1) A 3.11

15

O

2.77

E]

1.67

o I

I

I

1"2 11 10

I

9

I

8

I

7

I

6

1.31 I

5

I

4

"N

8 mesh I

3

I

2

I

1

0

Size Index, i Fig. 3. Experimental and simulated size distribution of limestone ground in a roll mill.

preserving behavior was also observed in the breakage of single particles in rigidly mounted rolls (Fuerstenau et al., 1990a), and is invariably encountered in ball mill products obtained under highly diverse operating conditions (Kapur, 1972; Venkataraman, 1988; Fuerstenau et al., 1990b ). An important property of self-similar distributions is that as grinding proceeds, the size spectra of comminuted particles are driven exclusively by reduction in its characteristic length. Consequently, the median size becomes a valid and consistent measure of the degree of fineness of the ground product. It is therefore a natural choice for an energy-size reduction relationship for roll mills.

Energy-size reduction relationship These relationships are useful for comparing the grinding efficiencies of various mill-material systems operating in different comminution modes. It was shown (Fuerstenau et al., 1990a; Kapur et al., 1990) that in the case of single-particle breakage, a measure of the size reduction was achieved, called the reduction ratio, Xf/Xso, where Xfis the feed size (or mean feed size) and

65

ENERGY CONSUMPTION AND PRODUCT SIZE

'°I 8O

Quartz

70

(Sx 10 mesh feed)

60 5C 4C e-

30

L2 O~ > 20

-5 E Simulated

U 10 . 9 ?8

.

.

.

Functional Fine tuned

-Expt'l

6

12 11

t0

9

8

7

6

Energy (k Wht ~

3.11

A

5

0

2.19

0

1.17

5

form

4

3

8 rnesh

2

1

0

Size Index, i Fig. 4. Experimental and simulated size distributions o f quartz ground in a roll mill.

100

ooz~ 5' 8O 0

C 60 14.

o

-

.>

4~

,~

-~ ~o

z~

Dolomite

~o. ForceI E.ergy tSi=e,Xso (kN)

E

AO'~'

0O

I ( k W h t " ) I (IJm)

9 14

_

20

-0° ~ ~ ' ~ l

0.1

i

zx C] ~7 i

i

I

0.5

l

i ill

33

I

45 54

i

1.0

Dimensionless Size, X / Xso

Fig. 5. Self-similar size distributions of dolomite.

1.46 1.~

J 445 I 410

317

12s°

3.22 & 36

i

i

225 210

i

5.0

i

i ii

10

0(3

I)W

FUERSI[Nk[:EI

k[

100 Aft

8o~-


® >

o 3

Limestone

-

Roll Force (kN)

40-

E U

20-

O

10.0

O

18.0 32.5 43.0 52.5

0

I

0.1

t

I I 1 I 11

I

0.5

I

1

1

1.0

Dimensionless

Energy

Isize, x5ol

(k Wht-~) I (pm) 1.31 I 490 1,67 I 360 2.77

I 245

2.97 3.11 I

5

I

200 95

I III

10

20

X/X5o

Size~

Fig. 6. Self-similarsize distributionsof limestone. []

lO0 I Quartz

I

O

Roll Force

Energy

(kN) 130 O 29,5 A 43.0

80

Size, XS0

A

(pro)

I (kWht-~) [ 1.17 2.19 3.11

[]

[]

/~)

665 460

[]

3~0

.~ 60 ul ® >

4O ¸

E u 20

[] I

0.05

o ~ t

L l I I

0.1

I

I

Dimensionless Fig. 7. S e l f - s i m i l a r

size distributions

I

I

0.5

I

Size,

I I I I

1

1

L

I

5

X/Xso

of quartz.

Sso is the median product size, increases linearly with the specific energy input. Figures 8, 9, 10 and 11 for 8 X 10-mesh feeds of dolomite, limestone, quartz and hematite, respectively, show that this energy-size reduction relationship holds equally well for choke-fed, hi,h-compression roll mills. For comparison, we have included in these figures the data for single-particle

67

ENERGY CONSUMPTION AND PRODUCT SIZE

o= ,

o-

Dolomite

10

x

d

'~O 6

2.3

IZ

.o_ :~ -o r~-

,-i/" ~

- - /

lm.h

~ 1

/~ 19x10

I

01

0

.ode

v 18~ 9 si.g,e

~

I 0.5

1 1.0

I 1.5

I 2.0

Grinding Energy,

.

Po~ti.,e

,,

,,

O 18x10

Choke Fed

I 2.5

I 3.0

I 3.5

k W h ~ "1

Fig. 8. Reduction ratio as a function of energy when dolomite particles are broken singly and in a choke-fed roll mill. 12

Li mestone

C~

mo 10 )<

O

8

o" "6 n,

3.4 6

o u "o

Feeds Breakage 4 6

J

V

8x ,

I Single Particle

2

0

i 0.5

I 1.0

I 1.5

I 2.0

I 2.5

I 3.0

3.5

Grinding Energy, kWht -I Fig. 9. Reduction ratio as a function of energy when limestone particles are broken singly and in a choke-fed roll mill.

breakage of 8 × 9 and 9 × 10 mesh feeds. It may be inferred from the slopes that the process efficiency in choke-fed roll mills is always less than that for single-particle breakage. The ratios of the two efficiencies are: dolomite 38%, limestone 57%, quartz 46%, and hematite 65%. On average, the pressurized roll mill efficiency is roughly one-half of the efficiency for the single-particle breakage results.

g _ z

n"

~ ( Z / ./4-= j y /

/

/ ~ 1

I

I

0.5

1.0

Feed, mesh ~7 8x 9 A 9x10

Breakage Mode Single Particle ....

O 8x10

Choke Fed

I

i

~.~

2.0

I

2.s

I

3.0

G r i n d i n g Energy~ k W h t -1 Fig. 10. Reduction ratio as a function of energy when quartz panicles are broken singly and in a choke-fed roll mill.

6

o s

Hematite

2

n., 3.1

g~ 3 '10

Feed,

/I" 2

1

j /

Breakage

y lSx 9 I Single Panicle

1

0.5

I

1.0

I

1.5

I

2.0

2.5

Grinding E n e r g y , kWht -1 Fig. ] ]. Reduction ratio as a function of energy when hematite panicles are broken singly and in a choke-fed roll mill.

ENERGY CONSUMPTIONAND PRODUCT SIZE

69

It was stated in the introduction that the grinding efficiency in a ball mill is again about one-half of what it is in high-compression roll mills (Schoenert, 1988). In other words, breakage of single particles under compressive load is about four times more energy-efficient than is breakage in a ball mill. This conclusion is in general agreement with the results ofFuerstenau et al. (1990a) who found that the slopes of the initial straight line segments of Xf/Xso versus energy curves for ball mill data were as low as one-fifth of the slopes for singleparticle breakage results. GRINDING MODEL AND SIMULATION

Unlike in tumbling mills, there is no explicit running grinding time in highcompression roll mills, only a fixed-time duration for one pass of solids through the rolls. On the other hand, size distribution curves of the ground product shift towards the finer size in a regular manner as specific energy input to the mill is increased by enhancing the milling force on the rolls. In ball mill grinding also, the size distributions shift in a similar manner with increasing expenditure of energy, that is with longer grinding time. This apparently holds even when the power draw (that is, rate of energy input) is not constant but undergoes considerable variations with time, as shown recently by Fuerstenau et al. (1990b). Furthermore, the size distributions produced in roll mills and ball mills are self-similar. These observations suggest that it should be possible to model roll mills by employing, with suitable modifications, the equations of grinding kinetics for ball and similar tumbling mills, provided the process is formulated in terms of cumulative input energy, rather than in terms of grinding time. This can be accomplished by starting with the standard integrodifferential equation of grinding kinetics (Kapur, 1987):

dF(x,t) ~ ,~ -~ k(v)B(v,x)M(v,t) dv

(1)

where F(x,t) and M(x,t) are, respectively, the mass-related distribution function and density function in particle size x at grinding time t; k(v) is the specific breakage rate function and B (v,x) is the cumulative breakage distribution function of progeny particle of size x when v size particles are broken. Herbst and Fuerstenau ( 1973 ) made an important observation that within its normal operating range the breakage rate functions in a tumbling mill are related to the specific power draft, P, by:

k(v)=k°(v)P

(2)

where k ° (v) is the breakage constant normalized with respect to energy input rate and it is a characteristic of material size and its grindability. Combining eqs. 1 and 2 and noting that the increment in specific energy input d E = P dt yields:

7()

D.V,' } UERS'II~N,~II [:1 ~|

dF(x,E) dE

['J~'k ° (v)B(v,x)M(v,E) ~

dr,

/3)

In the case of pressurized rolls the direct proportionality between k and P is unlikely to hold for the simple reason that as it passes through the rolls, the column of material becomes increasingly compressed, resulting in disproportionately greater dissipation of energy by interparticle friction. Consequently, the energy component that actually goes into stressing the particles to breakage is progressively reduced. As a working hypothesis, we assume that the retardation implicit in breakage rate as energy input increases can be incorporated by modifying eq. 2 as:

k(v)=k °(v)P/E';

0
(4)

Substitution into eq. 1 yields:

dF(x,E' ) dE'

~ k ° ( v)B(v,x )M( v,E' ) dv ~-

(5)

Here the rescaled energy term E' is: E' =

1

1-y

E 1-"

(6)

Equation 5 in density function form becomes:

dM(x,E')dE, -

k°(x)M(x'E')+~°k°(v)dB-~ x)M(v'E')dv

(7)

Under fairly broad stipulations, namely, the size dependence of the specific breakage rate is of power function type:

k°(x)=A°x a

(8)

and the breakage distribution function is normalizable, that is:

B(v,x) =B(x/v)

(9)

Equation 5 has a similarity solution (Kapur, 1972 ) as follows:

F(x,E' )-Z(x/Xso)

(10)

in which the median size Xs0 is a function of the energy expended and, moreover, is related to the a m o u n t of material finer than a given size (say, Xi of ith mesh) by (Fuerstenau et al., 1990b): In )(5o =

-c~Fi +c2

( 11 )

where c~ and c2 are constants for a size. We have already shown in Figs. 5, 6 and 7 that the distributions are indeed self-similar. From Fig. 12, we conclude

71

ENERGY CONSUMPTION AND PRODUCT SIZE

0,7 0.5

0.3 0.2 -400 -200 0.1

I

-100

-48

I

-20

[

-14

[

[

E E

0.7 6 0.5

~- 0.a

._N tO "~

IE

0.2

-400-200 I

0.1

-100

-48

I

-28

I

-14mesh

I

I

0.9

0.3 -400 -200

02i' 0

-I00

~ 20

l 40 Fines

-48

-28

-14mesh

~

1

60

ao

i 1oo

in G r o u n d P r o d u c t , %

Fig. 12. Relationship between median size and fines generated when 8 × 10 mesh feeds are ground in a choke-fed roll mill.

that the relationship in eq. 11 between an index of fineness and the fines produced holds quite well for different mesh openings ranging from 14 to 400 mesh. We mention in passing that this relationship is also valid for size distributions generated by the breakage of single particles, as shown in Fig. 13. In light of the foregoing results, it would seem that the grinding model in eq. 5 or 7 with the rescaled energy term is perhaps appropriate for choke-fed, high-compression roll mills. If so, then the estimates of associated grinding rates, k ° (x), and progeny distributions, B(x/v), are required for simulation studies and for obtaining insight into the comminution mode of roll mills. For this purpose we first discretize the size in eq. 7 in the usual manner (Kapur, 1987): dl~ i(E, )

dE'

i-1

- - k ° M ' ( E ' ) + ~' k~b,_jMj(E')

(12)

j=l

where k7 is energy-normalized breakage rate parameter for mass (or mass fraction ) of particles Mj (E') in the jth size interval, Xj _ l < X_< Xj), and bi_j

72

l>.X~ F U E R S - I E N A t l E'i - \ L

0.4 ~_~270_ -100 k_

-35 mesh

1

i

---

I m

I

2.0

Quartz

E E 8

,g

1.0 0.8

Feed

0.6

~7 8x9 mesh A 9 x 10 mesh

_-270 -100

-35 mesh

0.4 I

I

2.0

[

I

Dolomite

N

1.0 r-

0.8

0.6

5r

-270

0.4

-100

-35mesh

I

I

I

I

2.0

Limestone 10 08 06 04

-100

-270

0

-35mesh

1

I

I

1

10

20

30

40

Fines

in Ground

50

Product,'/.

Fig. 13. Relationship between median size and fines generated when 8 x 9 and 9 X 10 mesh particles are broken singly in a pair of rigidly mounted rolls.

is the difference-similar breakage distribution parameter. Reid's solution ( 1965 ) to this set of first-order coupled equations is: i

Mi(E) = Y, hijexp [ - ~ E ~-y]

(13)

j=l

where the pre-exponential term h o is a function of k}', bi_j and Mj(o) and:

F.)O - k jO/ ( l - y )

(14) Next we assume a reasonably flexible four-parameter functional form for ~', namely:

1~']=A °X;I ( 1 + QX q)

( 15 )

ENERGY CONSUMPTIONAND PRODUCT SIZE

73

For bi_j we employ a widely quoted function whose cumulative form is: Bij=fb

~

+ (l--f))

=Bi_ j

(16)

and: b o = B i _ lj - B~j = bi_j

( 17 )

The grinding parameters were estimated from the experimental data in two stages. In the first stage, eight exponents and constants (that is y, A °, a, Q, q, 0, c and d) were determined by minimizing the squares of the errors between experimental M's and model values summed over all sizes and energy levels. A quasi-Newton method was employed for the search. The back-calculated size distributions, based on functional forms ofk-j and bo are shown as broken lines along with experimental data in Figs. 2, 3 and 4. The agreement between the simulated and actual distributions was further improved in the second stage by fine tuning the individual k-j values, along with the energy exponent y as well as the q~, c and d parameters of the B o function. This time the search was repeated over a narrow range centered on the best estimates obtained in the first stage. The back-calculated distributions based on the fine-tuned grinding parameters are also included as solid lines in Figs. 2, 3 and 4. As anticipated, the agreement is improved somewhat. The main point to note, however, is that whether one uses functional forms for the grinding parameTABLE2 Comparison of experimental and simulated limestone size distributions in cumulative percent passing Mesh passing

Grinding energy ( k W h t - L)

1.31

-8 - 10 - 14 -20 -28 -35 -48 -65 - 100 - 150 -200 -270 -400

1.67

2.77

2.97

3.11

exp.

sml.

exp.

sml.

exp.

sml.

exp.

sml.

exp.

sml.

100 86.7 74.8 63.6 55.1 46.7 39.6 35.2 29.9 24.0 18.8 15.3 12.6

100 86.1 74.3 63.7 55.0 47.2 39.9 33.9 28.4 23.1 18.6 15.3 12.5

i00 87.9 78.1 68.8 60.6 53.6 45.1 38.8 32.3 26.5 21.8 18.1 14.7

100 89 78.4 68.3 59.8 52.0 44.5 38.2 32.4 26.6 21.6 17.9 14.9

100 93.8 85.1 76.0 68.4 60.4 53.5 46.4 40.5 33.9 27.6 23.3 20.0

100 93.8 86.1 77.5 70.0 62.5 54.9 48.4 42.1 35.4 29.4 24.9 21.1

100 94.4 87.3 79.4 72.1 65.6 57.3 50.9 43.6 37.0 31.4 26.4 21.8

100 94.4 87.0 78.7 71.3 64.0 56.5 50.0 43.6 36.7 30.6 26.0 22.1

I00 95.5 88.5 80.1 72.5 64.5 57.8 50.7 45.0 38.2 31.9 27.5 24.1

100 94.7 87.6 79.5 72.2 64.9 57.5 51.0 44.5 37.7 31.4 26.7 22.8

exp. = experimental; sml. = simulated.

74

i).~A }'i [ERSI'EN ",,I ; E ] .\1

Size Interval Index, i o._ I'."

1.5

12

11 [

10 I

9

8

,

T

1.0

7

1---

6 I

5

A

"~ o.s 0.6

4

3

qF" -~---~-----t

.~-"z:~-J

2

"~

' ' ' / 7 1.0

'T-'

/ ' dO.6

~-"

o8 ,~-

~

13.

0.4

0,4

rr

Dolomite

~ 0.2

m

..~"

(Sx1Omesh feed)

2

/"

dO.2

0.1

'r-

g 2, 11

I

,

i

L

~

,

10

9

8

7

6

5

~,

L

J

,

3

2

t

~o.o2 0

Size Range Index~i-j Fig. 14. Energy-normalized breakage rate parameters and breakage distribution parameters of dolomite.

Size Interval Index, i °.i,~ '~ ~ 0

0. ~

1.5

12

11

10

9

8

7

6

5

4

3

2

I

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f

~1

8 x 10 mesh 1.0 0.8

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0.4

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0.8

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n." e~

0.2 .2 3n

O~ 0,2

o.1 .~_

I~1 0.1

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0.04 an

11

I, 10

I

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I

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I

I

I

I

9

8

?

6

5

4

3

2

1

0.02 0

Size Range Index, i-j Fig. 15. Energy-normalized breakage rate parameters and breakage distribution parameters of limestone.

75

ENERGY CONSUMPTION AND PRODUCT SIZE

Size Interval Index, i

1.6~, 12

=%_

®

11

10

9

6

'7

6

--"

5

4

3

.......

2

1

'7" =-

~.

1.0

- 1.0

o8,i

10.8

E

-

2 0.6

0.6

¢~

E

2 n

0.4

0.4

I:z:

Quartz 0.2

.~

( 8 x lOmesh f e e d )

O1 .xO

....

n°

0.2

Functional form

o.1

.Q 'E

o., g 0.08 0.06 0 t,. m

0.0~

0.02

~ 11

10

0 9

8

. ?

6

0 5

4

1 3

Z

1

0

Size Range Index,i-j

Fig. 16. Energy-normalized breakage rate parameters and breakage distribution parameters of quartz.

ters or fine-tuned individual rate constants, the overall quality of fit in the case of high-compression roll mills is quite comparable with what is generally achieved in modelling of ball mills. The closeness of fit can be appreciated by inspection of Table 2 which compares the experimental and computed size distribution values of limestone at five energy input levels. Similar close agreements were also obtained for dolomite and quartz minerals. The estimated grinding parameters, both in functional form and after fine tuning as plotted in Figs. 14, 15 and 16 for dolomite, limestone and quartz, respectively. Interestingly enough, the breakage rate parameters conform approximately to a power function form, as required in eq. 8 for realization of self-similar distributions. The erratic fluctuations of individual E ° values in a narrow band could be due to experimental errors in the data, among other reasons. In any case, it seems that limited deviation from the power function law for the breakage rate parameters does not affect the self-similar behavior in an appreciable way. The most significant observation is that in all three cases, the E ° values remain relatively high unlike in a ball mill where the spe-

70

D.V¢. F! IERS'I'ENAI~

80}-

Rammelsberger

~

Erz

60F 50!

~/~/_~

J

///

~

i~

,'F.e0

I/11t/I/I " i/"

ii 10~9~"

/

8p

/

/

//

O

1.49

0 ~r

/"

1.15 0.93

ZX

/t

0.70 SimulOted Fine tuned

L /-t~

I,

Expt't Energy(kWht- ) El 2.26

//

~I 5

/ /

/

30

~>

/,

~

:

i

ET AI

I

I

0.02

i

I i i II I

0.05

I

I

I

I I I III

0.1 0.2 0.5 Porticle Size, mm

I 2.0

1.0

i

I 5.0

Fig. 17. Experimental and simulated size distributions of Rammelsberg ore ground in a roll mill.

100 Rommelsberger Erz Roll

o 80 >( vx N

~

60

E (kWht -I) 0.70 0.93 1.15 1.49 1.62 2.26

Force

(RN) 9.5 15.5 20.0 28.0 31.0 48.0

O [] 0 /~ V 0

[]<> z-v~ X50 (rnm) 0?63 0.623 0.569 0.489 0.440 0.456

{-i~ A~0 O OF] [~7 O

.-~ 40 E u

*'

20 0 t

I

i

0.05

I

I

t

II

0.1

i

[

I

I

I

i

0.5 X / X6o

Fig. 18. Self-similar size distributions of Rammelsberg ore.

i

I 1

1.0

I

[

I

|

5

I

I

1 1

10

ENERGY CONSUMPTION AND PRODUCT SIZE

77

Rornmelsberger Erz

4 "t3

,o

3 x

~2 o

x

1

I

0

I

0.5

I

I

I

1.0 1.5 2.0 Energy, kwht -1

2.5

Fig. 19. Reduction ratio of Rammelsberg ore as a function of energy expended. o._

2.G

IX:

~' 0,5 8.

& 0.2 0.1

,,o,i

,

0.02

,/L

....

0.05

~

0.1

~

0.2 Porticle

~

,

I ....

0.5 Size~

I

1.0 rnrn

i

2.0

,

,/0.001 5.0

Fig. 20. Energy-normalized breakage rate parameters and breakage distribution parameters of Rammelsberg ore. cific rate constants drop sharply with decreasing particle size, especially in the m e d i u m and fine size range. This apparently is the crucial difference between the two kinds o f grinding mills. As a consequence, the pressurized roll mill can perform size reduction tasks much more efficiently energy-wise than the ball mill.

7~

I ) ; ~, i : i l E R S I E N \ I

E l \1

The analysis of the experimental data described above was repeated tbr data on the grinding of Rammelsberg ore (Schoenert, 1984). Figure l 7 includes the feed and ground size distributions at five energy levels. Figure 18 shows that the distributions are self-similar. From Fig. 19 it is concluded that not only the linear relationships between the inverse of Xso and energy expended is obeyed, but significantly, pressurized rolls tend to become more or less ineffective beyond a threshold energy input level. Figure 20 includes the estimates of the fine-tuned grinding parameters which, in turn, lead to reasonably accurate simulation as seen in Fig. 17. DISCUSSION AND CONCLUSIONS

We have attempted here an analysis of choke-fed, high-compression roll mills. It seeks to relate the energy consumption with an index of fineness and the size distribution of the ground mass in an explicit manner. Schoenert ( 1988 ) has already presented semi-empirical correlations for the power draft of a roll mill per unit solids mass ground as a function of roll gap, speeding and milling force. These scale-up and design aids may be coupled with the energy-size distribution model presented in this paper for an integrated analysis of pressurized roll mills. In summary, we conclude: (1) The product-size distribution curves produced in choke-fed, highcompression roll mills are similar in shape to those generated in ball mills after prolonged grinding times. A single pass through the rolls is sufficient to break nearly all coarse particles. (2) The distributions are self-similar and log median size decreases linearly with increasing production of fines. This characteristic is seen in both ball mill products as well as in the breakage of single particles. (3) The inverse of the median size increases linearly with the energy expended in turning the rolls (the energy input can be controlled by changing the milling force). The slopes of the plots of Xso-1 versus E are consistent measures of the grinding efficiency and can be used to compare with the efficiencies in the single-particle breakage mode and in ball milling. Single-particle breakage is about twice as efficient as choke-fed pressurized rolls, which in turn is roughly two times better than the ball mill. (4) A satisfactory model of grinding in roll mills can be developed by incorporating a modification for energy dissipation in the standard population balance-based grinding equation. This model could be quite useful for simulation and control of closed-loop roll mill circuits or without the ball mill in series or in tandem. (5) An important observation is that unlike in the ball mill, the back-calculated energy-normalized specific breakage rate parameters remain relatively high irrespective of the particle size which apparently is the main reason for improved efficiency of pressurized roll mills.

ENERGY CONSUMPTION AND PRODUCT SIZE

79

ACKNOWLEDGMENTS

The authors wish to express appreciation to the United States Bureau of Mines for support of this research under the Generic Mineral Technology Center Program in Comminution (Grant Nos. G1175149 and G1125149), and the Alexander von Humboldt Foundation for partial support of this research. Particular thanks are due Dr. D. Schwechten who performed the grinding experiments on the Clausthal laboratory roll mill during the time that one of us (D.W. Fuerstenau) was there.

REFERENCES Austin, L.G., Klimpel, R.R. and Luckie, P.T., 1984. Process Engineering of Size Reduction: Ball Milling. Society of Mining Engrs., New York, NY. Brachth~iuser, M. and Kellerwessel, J., 1988. High pressure comminution with roller presses in mineral processing. In: E. Forssberg (Editor), Proc. XVIth Int. Miner. Process. Congres, Stockholm, Sweden, 5-10 June, 1988. Dev. Miner. Process., 10A: 209-219. Fuerstenau, D.W., Kapur, P.C., Schoenert, K. and Marktscheffel, M., 1990a. Comparison of energy consumption in the breakage of single particles in a rigidly mounted roll mill with ball mill grinding. Int. J. Miner. Process., 28: 109-126. Fuerstenau, D.W., Kapur, P.C. and Velamakanni, B., 1990b. A multi-torque model for the effects of dispersants and slurry viscosity on ball milling. Int. J. Miner. Process., 28:81-98. Herbst, J. and Fuerstenau, D.W., 1973. Mathematical simulation of dry ball milling using specific power information. Trans. AIME, 254: 343-348. Herbst, J. and Fuerstenau, D.W., 1980. Scale-up procedures for continuous grinding mill design using population balance models. Int. J. Miner. Process., 7:1-31. Kapur, P.C., 1972. Self preserving size spectra of comminuted particles. Chem. Eng. Sci., 27: 425-431. Kapur, P.C., 1987. Modeling of tumbling mill batch processes. In: C.L. Prasher (Editor), Crushing and Grinding Process Handbook. Wiley, New York, NY, pp. 323-363. Kapur, P.C. and Fuerstenau, D.W., 1987. Energy-size reduction 'laws' revisited. Int. J. Miner. Process., 20: 45-57. Kapur, P.C., Schoenert, K. and Fuerstenau, D.W., 1990. Energy-size relationship for breakage of single particles in a rigidly-mounted roll mill. Int. J. Miner. Process., 29:221-233. Prasher, C.L., 1987. Crushing and Grinding Handbook. Wiley, New York, NY. Reid, K.J., 1965. A solution to the batch grinding equation. Chem. Eng. Sci., 20: 953-963. Schoenert, K., 1967. Modellrechnungen zur Druckzerkleinerung. Aufbereit. Tech., 8:1-11. Schoenert, K., 1984. Voruntersuchung zur Feinmahlung yon Rammelsberger Erz. Research Report. Schoenert, K., 1985. Zur Auslegung yon Gutbett-WalzenmiJhlen. Zero. Kalk Gibs, 38: 728-730. Schoenert, K., 1988. A first survey of grinding with high-compression roller mills. Int. J. Miner. Process., 22: 401-412. Schwechten, D., 1987. Trocken- und Nassmahlung spr/Sder Materialien in der Gutbett-WalzenmiJhle. Ph.D. Dissertation, Technische Universit~it Clausthal, Clausthal Zellerfeld. Schwechten, D. and Milburn, G.H., 1990. Experiences in dry grinding with high compression roller mills for end product quality below 20 microns. Miner. Eng., 3: 23-34. Venkataraman, K.S., 1988. Predicting the size distributions of fine powders during comminution. Adv. Ceram. Mater., 3: 498-502.