International Journal of Mineral Processing, 27 ( 1989} 125-132 125 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

A Procedure for Rapid Determinat ion of the Bond Work Index

N. MAGDALINOVIC

University of Belgrade, Technical Faculty at Bor, 19210 Bor (Yugoslavia)

(Received November 24, 1987; accepted after revision November 17, 1988)

ABSTRACT

Magdalinovid, N., 1989. A procedure for rapid determination of the Bond work index. Int. J. Miner. Process., 27: 125-132.

The grindability of an ore in the process of mineral dressing can be determined by use of the Bond work index (Wi). This index is determined on a laboratory-scale using a Bond ball-mill and by simulating dry grinding in a closed circuit until the 250% circulating load has been obtained. This happens only after 7-10 grinding cycles, which shows that the procedure is a lengthy and complex one and is therefore susceptible to procedural errors.

Starting from the first-order grinding kinetics defined by means of the Bond ball mill, this paper discusses a simplified procedure for a rapid determination of the work index by just two grinding tests. The applicability of the simplified procedure has been proved on samples of copper ore, andesite and limestone. The values obtained by this procedure do not differ by more than 7% from those obtained in the standard Bond test. A final appraisal of the reliability of the proposed pro- cedure can only be given after more testwork on other materials.

INTRODUCTION

According to the standard Bond test, the work index (Wi) is found by sim- ulating dry grinding in a closed circuit in a Bond ball mill until the 250% cir- culating load has been achieved (Bond, 1949, 1952, 1961 ). The feed is a minus 3.327 mm, 700 cm 3 sample. The first grinding test is started with an arbitrarily chosen number of mill revolutions. At the end of each grinding cycle, the entire

product is discharged from the mill and is screened on a test sieve. Fresh feed material is added to the over-size to bring the total weight back

to that of the original charge. This charge is then returned to the mill. The number of revolutions in the second grinding cycle is calculated so as to grad- ually produce the 250% circulating load. After the second cycle, the same pro- cedure of screening and grinding is continued until the test-sieve under-size

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produced per mill revolution becomes constant tbr the last three grinding cycles. This will give the 250~i circulating load. The Bond test takes 7 l0 cycles. The test-sieve under-size from the last grinding cycle is analyzed by screening.

To calculate the work index ( W~} in a laboratory-scale ball mill. Bond first derived the equation:

NIP' W,= 1.1 (~.~ i 100 (1)

and thereafter derived the revised formula that is currently in use:

44.5 14/,--1.1 (2)

p,,~:~GO.m(lO 10"~ \'F!

where: Wi=Bond work index (kWh t - l ) ; Pc=test-sieve mesh size (~m); G=weight of the test-sieve fresh under-size per mill revolution (g min-1); F--test-sieve mesh size passing 80% of the feed before grinding (pm); P= opening of the tested sieve size passing 80% of the last-cycle sieve under- size product (pm).

The Bond work index has been widely used in designing full-scale mills but the Bond test is rather complex, lengthy and susceptible to procedural errors and this is why attempts have been made to abbreviate and simplify Bond's test procedure.

Smith and Lee (1968) compared Bond grindability with straight batch-type grindability. Their results show that the two are empirically related; hence, it is possible to estimate Bond grindability from batch tests.

Ocepek (1969) simplified the Bond test by substituting an open cycle for a closed cycle of grinding and the work index was determined through three tests.

Kapur (1970) analyzed the batch-grinding cycles involved in Bond grinda- bility tests and then developed a mathematical algorithm for "stage-wise" sim- ulation of this test and an assessment of the Bond work index.

Magdalinovid and Cumpujerovid (1983) have shown that an approximate value of the work index can be determined by just one grinding test.

Bond's first formula (eq. 1 ) was used in the calculations. The differences between the values obtained from this new and the standard Bond test have a range of around 15% in all abovementioned abbreviated procedures.

GRINDING KINETICS IN THE BOND BALL MILL

Tests of grinding kinetics in the Bond ball mill (Figs. 1 and 2) have shown that over a shorter grinding period the process follows the law of first order kinetics, i.e.:

R = Roe -kt (3)

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N t I I I I I

to S 30

f i' 5 | I 1 I I i_

I 2 3 z 5 6 GRINDING TIMEominute5

Fig. 1. The kinetics of copper ore grinding.

~ ~oo ~80

~0 ~" 3o

~ 2o

~ so

~ 5 I 1 i I I I I I ! 2 3 L 5 6 ? 8

6RINDIN6 TildE. rm'nute5

Fig. 2. The kinetics of andesite grinding.

where: R = test-sieve over-size at the time (t); Ro=test-sieve over-size at the beginning of grinding (t = 0); k = grinding rate constant; t = grinding time.

The grinding rate constant (k) can be determined from just one grinding test. From eq. 3 it follows that:

k=lnRo - lnR t (4)

This makes it possible to achieve substantial time savings and simplifications in the procedure for determining the work index (Wi).

SIMULATION OF THE STANDARD BOND TEST FOR F INDING THE WORK INDEX

In the standard Bond test at a standard 250% circulating load (Fig. 3 ):

R - -=2.5 U

U+R=M

(5)

(6)

I2h

R -- -Mr---~

o I

Fig. 3. A simulation of closed-circuit grinding in the standard Bond test designed to find the work index.

where: R=weight of the test sieve over-size (g); U=weight of the new feed (g); M=weight of the mill feed (g).

From eqs. 5 and 6 it follows that:

R=2"5 M (7) 3.5

U= ~--~M, . (8)

In a standard grinding cycle at the 250% circulating load, the weight of the test sieve over-size at the beginning of grinding (Ro) is:

25 Ro =~M+ 1 ,~.5 Mro (9)

namely:

[2.5 1 ) Ro=~,~.5+~.5r,, M (10)

where ro=the proportion of test sieve over-size in the new feed (expressed in parts of unity).

From eq. 3 which gives the grinding kinetics in the Bond ball mill for the standard grinding cycle, the following expression can be derived for the 250% circulating load:

3.5 3~+ ~sro Me -~t' (11)

or:

2.5 2.5 1 3.5_ ~ ~5 + 3--~ro ) e -k'' (12)

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From eq. 12 it follows that:

In(1 +0.4ro) (13) t- k

where: t = grinding time in a standard grinding cycle after which the over-size (R) on the test sieve is { 2.5/3.5 )M, which corresponds to the 250% circulating load; k = grinding rate constant for coarser product, defined by eq. 4.

With the Bond ball mill, the total number of mill revolutions iN) is taken into account rather than the grind time it). Since:

N t=- - i14)

by substituting the expression of t from eq. 14 into 4 and 13, it follows that:

k_n(lnRo - lnR) (15) N

In ( 1 + 0.4ro) Nc =n k (16)

where: n= number of mill revolutions per minute; N=tota l number of mill revolutions; Nc = total number of mill revolutions giving the (2.5/3.5) M test sieve over-size, which corresponds to the 250% circulating load.

The derived eqs. 9, 15 and 16 make it possible to abbreviate the Bond test to only two grinding tests. The abbreviated procedure for finding the work index is as follows:

(1) The work index is determined from feed crushed to 100% minus 3.327 mm (the same as for the standard Bond test).

(2) The feed is screened to determine its size distribution which is then plotted on a graph.

(3) A 700 cm 3 sample is collected and weighed (M). (4) The value of R = (2.5/3.5)M is calculated. (5) From the original feed an adequate sample is taken and screened on a

test sieve. The under-size is discarded while the over-size is retained. At least R over-size has to be prepared for the two grinding tests.

(6) Two separate samples, weighing ( 1/3.5)M g each, necessary for the two grinding tests, are collected from the original feed.

(7) Two samples are formed for the two grinding tests by mixing test sieve over-size weighing { 2.5/3.5)M/item 5 ) with the sample weighing ( 1/3.5 )M (item 6).

(8) The proportion of the coarse size (Ro) in the samples is calculated. (9) The first sample is fed into the Bond mill and is ground for an arbitrarily

chosen number of mill revoluti6ns (N= 50, 100 or 150).

131)

(10) After grinding, the ev.tire sample is screened on a test sieve and the over-size is weighed (R).

(11) The over-size grinding rate constant (k) is calculated from eq. 15. ( 12 ) The total number of mill revolutions (N,.) ibr the second grinding test

is calculated from eq. 16. (13) The second sample is fed into the Bond mill and is ground for Nc mill

revolutions. ( 14 ) After grinding, the entire sample is screened on the test sieve. Both the

over-size and the under-size are weighed. The weight of the over-size should be equal or approximately equal to (2.5/3.5)M whereas the weight of the un- der-size (m) should be: m= ( 1/3.5)M.

(15) Size distribution of the under-size from the second test is determined by means of screen analysis and the value P is determined graphically.

(16) The weight (G) of the new under-size obtained per mill revolution in the second test is calculated from:

I rn-~-~M(1-ro)

G- Nr.

(17) The work index (Wi) is derived from the Bond formula (eq. 2). The above described abbreviated procedure for the determination of the work

index is based on the assumption that the grinding rate constant (k) for the coarse size product (Ro) grinding in the standard Bond test at the 250% cir- culating load is equal or approximately equal to the grinding rate constant (k') for the coarse size product (R~) grinding in the abbreviated test procedure (k = k' ) and that, at the same time, the size distributions of the test sieve un- der-size are nearly equal to each other (P=P'). Experiments with samples of copper ore, limestone and andesite at several different mesh sizes of test sieves have shown that the above assumptions were correct (k'/k= 1.005 to 1.012; P/P' = 1.007 to 1.014).

The work index (Wi) has been established for the samples of copper ore, andesite and limestone following both the standard Bond procedure and the abbreviated procedure as described in this paper. The results are given in Table I below.

By comparing the values of the work index obtained by means of the Bond and the abbreviated test procedures it can be seen that the differences never exceed 7%. This confirms that the abbreviated procedure can be employed for a rapid and simple determination of the work index. To make an adequate evaluation of the reliability of the abbreviated procedure however, more exten- sive testwork has to be conducted with other materials.

The proposed procedure can be very useful in routine monitoring of ore

131

TABLE I

Comparative presentation of the work index values obtained by means of the Bond and the ab- breviated test procedures

Sample Mesh of grind Work index (kWh/t) Difference (%) Pc(/~m ) A= Wi(B) - Wi(A)

Bond test, Abbreviated test, Wi (B) W~(B) W,(A)

100

Copper ore 500 15.40 14.57 + 5.4 315 13.79 12.83 + 7.0 160 11.84 11.46 + 3.2 80 12.90 13.07 - 1.3

Andesite 500 25.05 24.42 + 2.5 315 19.90 21.25 -6.8 160 22.70 21.31 +6.1 80 22.38 22.00 + 1.7

Limestone 500 14.26 13.33 +6.5 315 13.57 12.78 +5.8 160 11.04 10.48 + 5.1 80 11.70 11.41 + 2.5

grindability and for the control of grinding parameters in commercial operations.

The first grinding test in the abbreviated procedure can indicate the initial number of mill revolutions derived from eq. 16, with which the Bond test for the determination of the work index could be commenced. Thus, the number of grinding tests in the standard Bond procedure can be reduced.

CONCLUSION

Based on the defined first-order grinding kinetics in the Bond ball mill, a procedure has been developed for the rapid determination of the work index (Wi) by means of just two grinding tests.

The applicability of the proposed abbreviated procedure has been proved on samples of copper ore, andesite and limestone. The differences between the values of the work index obtained in the two test procedures do not exceed 7%. The reliability of the new procedure can be finally evaluated only after more extensive testwork and by use of other materials.

The procedure presented here can be very useful for monitoring day-to-day variation of the grindability of ore and for the control of grinding at commercial operations. Its great merit is that it allows for a reduction of the number of grinding tests in the Bond test procedure.

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REFERENCES

Berry. T.F. and Bruce, R.W., 1966. A simple method of determining the grindability of ores. Can. Min..J.. 87: 63-65.

Bond, F.C., 1949. Standard grindability test tabulated. Trans. Am. Inst. Min. Eng., 183:313 329. Bond. F.(,., 1952. The third theory of communition. Trans. Am. Inst. Min. Eng., 193:484 -494. Bond, F.C., 1961. Crushing and Grinding Calculations. A-C Bulletin 07R9235B, Allis-Chalmers.

Milwaukee, Wise. Kapur, P.C., 1970. Analysis of the Bond grindability test. Trans. Inst. Min. Metall., 79: 103-107. Magdalinovi6. N. and (~umpujerovid, R., 1983. Shortened procedure for determination of Bond

work index. Collection of works 9. Yugoslav Symposium on Mineral Processing, Ljuhljana, 1983, pp. 521 541.

Ocepek, D., 1969. ('7her die Methoden der Bestimmung des Zerkleinerungswiderstandes. Aufber- eit. Tech., 6: 290- 293.

Smith, R.W. and Lee, K.H., 1968. A comparison of data from Bond type simulated closed-circuit and batch type grindability tests. Trans. Am. Inst. Min. Eng., 241: 91-99 (discussion, pp. 99-- 1()1 ~.