Minerals Engineering 22 (2009) 104–106
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Technical Note
Procedure for determination of ball Bond work index in the commercial operations R. Ahmadi , Sh. Shahsavari *
Iran Mineral Processing Research Center (IMPRC), Karaj, Tehran, Islamic Republic of Iran
a r t i c l e
i n f o
Article history: Received 2 March 2008 Accepted 11 April 2008 Available online 3 June 2008 Keywords: Iron ores Grinding Modelling Mineral processing
a b s t r a c t
The Bond ball mill grindability test is run in a laboratory until a circulating load of 250% is developed. It provides the Bond Ball Mill Work Index which expresses the resistance of material to ball milling. This happens 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 and Iron ores that are located in Iran. The values obtained by this procedure do not differ by more than 7% from those obtained in the standard Bond test. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction
A Bond Ball Mill Work Index test is a standard test for determining the ball mill work index of a sample of ore. It was developed by Fred Bond in 1952 and modified in 1961 ( ( JKMRC CO., 2006). 2006). This index is widely used in the mineral industry for comparing the resistance of different materials to ball milling, for estimating the energy required for grinding, and for ball mill scale-up. The test has existed for more than 40 years (Man, ( Man, 2002). 2002). Because of the difficulty in determination of this index, alternatives to the standard method method have been developed developed by many researchers researchers (Veda ( Vedatt and Huseyin, 2003). 2003). In the determination of ball mill work index 15 kg of representative ore at 100% + 3.35 mm is crushed to 100% À 3.35 mm mm (Amtech, 2006). 2006). 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 Fresh feed feed mater material ial is added added to the oversize oversize to bring 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 ing cycl cycle e is calc calcul ulat ated ed so as to grad gradua uall lly y prod produc uce e the the 250% 250% circulatin circulating g load. load. After the second second cycle, cycle, the same procedure of screening and grinding is continued until the test-sieve under size produced per mill revolution becomes constant for the last three grinding grinding cycles. cycles. This will give the 250% circulating circulating load (Bond, 1961). 1961 ). The Bond test takes 7–10 cycles. The test-sieve undersize from the last last grindi grinding ng cycle cycle is analy analyzed zed by scree screenin ning, g, (Magdalinovi,
*
Corresponding author. Tel.: +98 261 4790010; fax: +98 261 4790019. E-mail address:
[email protected] (R. Ahmadi).
0892-6875/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2008.04.008
1989 ). The work index (Wi) is calculated in a laboratory-scale ball 1989). mill with Bond equation. The Bond work index has been widely used in designing full-scale mills but the Bond test is rather complex, lengthy susceptible to procedural errors and this is why attempts tempts have have been been made made to abbre abbrevia viate te and simpli simplify fy Bond Bond test test procedure (Weiss, (Weiss, 1985). 1985). 2. Grinding kinetics in the Bond ball mill
Tests of grinding kinetics in the Bond ball mill ( Figs. 1 and 2) 2) has shown that over a shorter grinding period, the process follows the law of first order kinetics R ¼ R0 eÀkt
ð1Þ
where R = test-sieve oversize at the time ( t ); ); R0 = test sieve 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. (1) it follows that: k¼
ln R0 À ln R t
ð2Þ
This makes it possible to achieve substantial time savings and simplifications in the procedure for determining the work index (Wi). 3. Simulation of the standard bond test for finding the index
In the standard Bond test at a standard 250% circulating load: R ¼ 2:5 U U þ U þ R ¼ M
ð3Þ ð4Þ
105
R. Ahmadi, Sh. Shahsavari/ Minerals Engineering 22 (2009) 104–106 100
) % ( e z i s r e v o e 10 v i t a l u m u C
pc =150 m pc = 500 μm pc = 38 m
1 0
5
10
15
20
25
Grinding Time (minutes) Fig. 1. The kinetics of iron ore grinding.
100
) % ( e z i s r e v o 10 e v i t a l u m u C
pc= 500 m pc= 315 m pc=160 m
1 0
1
2
3
4
5
Grinding Time (minutes) Fig. 2. The kinetics of copper ore grinding.
where R: weight of the test sieve oversize ( g ), U : weight of the new feed ( g ), M : weight of the mill feed ( g ). From Eqs. (3) and (4) it follows that:
2:5 M 3:5 1 R¼ M 3:5
ð5Þ
R¼
ð6Þ t ¼
In a standard grinding cycle at the 250% circulating load, the weight of the test sieve oversize at the beginning of grinding ( R0) is 2:5 1 M þ R ¼ Mr 0 3:5 3:5 2:5 1 þ R0 ¼ r 0 M 3:5 3:5 R0 ¼
ð7Þ ð8Þ
2:5 2:5 1 þ M ¼ r 0 M eÀkt 3:5 3:5 3:5 2:5 2:5 1 ¼ þ r 0 eÀkt 3:5 3:5 3:5 lnð1 þ 0:4r 0 Þ t c ¼ k
ð9Þ ð10Þ ð11Þ
N n
ð12Þ
By substituting the expression of the t from Eq. (12) into (2) and (11), it follows that: nðln R0 À ln RÞ N lnð1 þ 0:4r 0 Þ N c ¼ n k k¼
where r 0 = the proportion of test sieve oversize in the new feed (expressed in parts of unity). From Eq. (1) which gives the grinding cycle, the following expression can be derived for the 250% circulating load:
where t c = grinding time in a standard grinding cycle after which the oversize (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 (2). With the Bond ball mill, the total number of mill revolutions (N ) is taken into account rather than the grind time (t ). Since
ð13Þ ð14Þ
where n = number of mill revolutions per minute; N : total number of mill revolutions; N c: total number of mill revolutions giving the (2.5/3.5)M test sieve oversize, which corresponds to the 250% circulating load. The derived Eqs. (7), (13), and (14) 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% À 3.327 mm (the same as for the standard Bond test).
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R. Ahmadi, Sh. Shahsavari/ Minerals Engineering 22 (2009) 104–106
2. The feed is screened to determine its size distribution which is then plotted on a graph. 3. A 700 cm3 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 oversize has to be prepared for the two grinding tests. 6. Two separate samples, weighting (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 oversize weighting (2.5/3.5) M (item 3) with the sample weighting (1/3.5) M (item4). 8. The proportion of the coarse size (R0) 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 revolutions (N = 50,100,150, . . .). 10. After grinding, the entire sample is screened on a test sieve and the oversize is weighed (R). 11. The oversize grinding rate constant (k) is calculated from Eq. (13). 12. The total number of mill revolutions (N c) for the second grinding test is calculated from Eq. (14). 13. The second sample is fed into Bond mill and is ground for N c mill revolutions. 14. After grinding, the entire sample is screened on the test sieve. Both the oversize and the undersize are weighed. The weight of the oversize should be equal or approximately equal to (2.5/3.5) M whereas the weight of the undersize ( m) should be: m = (1/3.5)M . 15. Size distribution of the undersize 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 undersize obtained per mill revolution in the second test is calculated from: 1 m À 3:5 M ð1 À r 0 Þ G¼ N c
ð15Þ
17. The work index (Wi) is derived from the Bond formula. The work index (Wi) has been obtained for the sample of iron and copper ore following both the standard Bond procedure and the abbreviated procedure as described in this paper. The results are given in Table 1. 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. The proposed procedure can be very useful in routine monitoring of ore grindability and for the control of the abbreviated proce-
Table 1
Comparative presentation of the work index values obtained by means of the Bond and the abbreviated procedures
Sample
Pc (lm)
Work index (kw h/t)
Difference (%)
Bond test, Wi(B)
Abbreviated test, Wi(A)
D
Iron ore
500 150 38
8.10 12.20 15.10
8.46 11.55 15.86
À4.4 +5.3 À5.0
Copper ore
500 315 160 80
15.40 13.79 11.84 12.90
14.57 12.83 11.46 13.07
+5.4 +7.0 +3.2 À1.3
ÞÀWiðAÞ ¼ WiðBWi  100 ðBÞ
dure can indicate the initial number of mill revolutions derived from Eq. (14), 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. 4. Conclusions
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 and iron ore. The differences between the values of the work index obtained in the two test procedures do not exceed 7%. The procedure presented here can be very useful for monitoring day-to-day variation of the grindability of ore and for 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. Acknowledgement
The authors gratefully acknowledge the Iran Mineral Processing Research Center (IMPRC) for this work. References Amtech CO., 2006. Western Australia, Technical features – Bond Ball Mill Work Index (BWI). Bond, F.C., 1961. Crushing and grinding calculations part I and II. British Chemical Engineering 6 (6 and 8). JKMRC CO., 2006. Procedure for BBMWI Test. Magdalinovi, N., 1989. A procedure for rapid determination of the Bond work index. International Journal of Mineral Processing 27 (1-2), 125–132. Man, Y.T., 2002. Why is the Bond Ball Mill Grindability Test done the way it is done? European journal of mineral processing and environmental protection 2 (1). Vedat, Deniz, Huseyin, Ozdag, 2003. A new approach to Bond grindability and work index: dynamic elastic parameters. Minerals Engineering Journal 16 (3), 211– 217. Weiss, N.L., 1985. Mineral Processing Handbook. Society of Mining Engineers, AIMM, New York. 2078.
