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Modelling iron ore degradation using a twin pendulum breakage device
Int. J. Miner. Process. 59 Ž2000. 195–213 www.elsevier.nlrlocaterijminpro
Modelling iron ore degradation using a twin pendulum breakage device D.M. Weedon a,) , F. Wilson b a
Department of Mechanical and Materials Engineering, UniÕersity of Western Australia, Nedlands, Perth, Western Australia 6907, Australia b QCL, Norton Centre, Poyernook Road, Aberdeen, Scotland AB115RW UK Received 30 March 1999; received in revised form 8 July 1999; accepted 1 October 1999
Abstract The breakage rates of three different types of iron ore D2, D4 and Joffre from the Brockman Iron Formation, Western Australia were investigated. Batch milling tests were undertaken to determine breakage rates as well as breakage tests using a computer monitored laser detected twin pendulum breakage device. The results showed that Joffre ore was more friable than D4, which was more friable than D2. A set of t-curves were calculated from the pendulum breakage data and a new model was developed. This model was used to satisfactorily predict fines generation from handling and dropping ore samples over a series of 1.8, 5 and 10 m drops. The model developed different degradation matrices for each ore type at the three drop heights and for a given feed. A parameter was also included to account for fines generation due to handling. q 2000 Elsevier Science B.V. All rights reserved. Keywords: iron ore; lumps; fines; degradation
1. Introduction Iron ore production is a significant part of the mining operations of Broken Hill Proprietary ŽBHP. at Mt. Whaleback at Newman, Western Australia, which is one of the largest single open cut metalliferous mine in the world. It is currently 5.5 km long and 1.5 km wide with production of ; 62 million tons Ž1998.. Its ore is railed to Port )
Corresponding author. Fax: q61-8-9380-1024. E-mail address: [email protected] ŽD.M. Weedon..
0301-7516r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 7 5 1 6 Ž 9 9 . 0 0 0 6 6 - 6
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headland and shipped to plant operators in Japan, Taiwan, Korea, Pakistan, Europe and China. During the processes of mining, crushing and transporting iron ore, the material is subjected to loads and impacts which increase the production of fines ŽWilson, 1998.. The ore is predominately hematite–martite and exists as the Dales Gorge and Joffre members of the Brockman Iron Formation lying within the Hamersley Iron outcrop. The Dales Gorge ore contains four zones D1, D2, D3 and D4, which are of premium quality with high grades and low impurities. D2 has the highest grade and lowest impurity and D4 is of similar grade and appearance but is significantly more friable. Enriched D1 is not very common and D3 contains thick shale bands and were therefore not examined in this research. The lower bands of the Joffre member are also enriched and are mined at Mt. Whaleback but are of lower grade than Dales Gorge and contain more impurities. It is also considerably more friable and yields a low lumpsrfines ratio. Two products are sold, lumps which range in size from 6.4 to 30 mm and fines which are smaller than 6.4 mm. Lumps command a premium price so size degradation is a significant cost factor for BHP. The degradation of lump material into fines is undesirable because with an oxidizing ore, when processing in furnaces, any fine material cannot penetrate the slag layer and is partly lost through the exhaust ports resulting in economic loss. The predominant problem with ores of high fines content, however, is that the yield of an oxidizing furnace rapidly diminishes with an increased percentage of fines due to restrictions to the flow of reducing gases through the reactor. There have been many previous studies on the causes of iron ore lumps degradation. The Swedish Mining Association ŽFaberberg and Sandberg, 1973. carried out extensive investigations of the degradation of lump iron ore Žpredominately magnetite. while in transport. The samples were taken from a number of lump ore shipments ranging in size from 2000 to 20,000 tons from mines to various blast furnaces on the European continent. The ore was divided into categories of varying degrees of hardness and softness based on strength tests and chemical composition. The fines generation testing mainly consisted of a series of drop and abrasion tests. The drop tests were undertaken predominately from a 20-m high chute with inlet ports at different levels. The abrasion tests were performed in a standardized tumbler drum 1.0 = 0.5 m with two 50-mm high lifters. The speed was 25 rpm and the rotation time was 8 min. No model was developed for the breakage process. The results concluded that the main cause of degradation was impact when the material was dropped from a significant height, usually during transportation and unloading. However, degradation from abrasion due to gravity flow through bins and other devices also occurred but only to a minor extent ŽFaberberg and Sandberg, 1973.. In a series of drops, as the total drop height increased, the large sizes gradually decreased and the fines increased in percentage. The medium sizes remained fairly stable. It was estimated that a total drop of 100 m represented 0.3 kW hrton which is a significant amount of energy considering that the crushing energy required to reduce an ore from 100 to 30 mm is approximately 0.5 kW hrton. The results also showed that a few large drops were equivalent to several smaller drops of the same total height providing the smaller drops were greater than 5 m. The study generally found increased fines generation with the weaker ores than the stronger ores and that a cushioning effect
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started to occur as the percentage of initial fines increased with 40% less fines produced as the initial fines percentage increased from 0% to 30%. Norgate et al. Ž1986. undertook a study to investigate the breakage properties of two ores, one ‘hard’ and one ‘soft’, from the Pilbara region in Western Australia. A series of drop tests were carried out from heights ranging from 0.9 to 32 m. They found that ore type was a significant factor in predicting the percentage of fines produced with the softer ores producing an extra ; 12% in comparison to the hard ores after completing the maximum number of drops. Norgate et al. Ž1986. also concluded that the total drop height was the major factor affecting the generation of fines. It was stated that a drop height of a given value will cause more degradation earlier in a handling system rather than later because of conditioning of the ore removing the weaker particles, although the difference seems to be only of the order of 1–2%. Norgate et al. Ž1986. also found that the degree of degradation can be reduced if a large drop was replaced with a series of smaller drops, in the vicinity of 1 m or less. This seems to concur with the findings of Faberberg and Sandberg Ž1973. although the exact mechanical reason why this should be so is uncertain. Norgate et al. Ž1986. also found a cushioning effect to exist with initial fines of 12% or more. A semi-empirical model was developed by Norgate et al. Ž1986., which related the breakage out c i from size fraction i containing mass si to the mean tensile strength a i and co-ordination number CN Žthe number of contact points between each particle and its neighbour.,
c i1r2 s d Ž hy1 . g
si
ai
CN
Ž 1.
where h is the drop height, and g and d are model parameters. The Austin et al. Ž1984. breakage distribution function: g
Bs j , s i s f Ž s jrsi . q Ž 1 y f . Ž s jrsi .
b
Ž 2.
was used to determine the amount of material distributing to various size fractions after breakage where f , g and b are parameters and Bs j , s i is the mass fraction of material of size s j or smaller resulting from breakage of particles of initial size si . The model assumed that the value of the breakage function was the same for all size fractions. This assumption is probably incorrect. Waters et al. Ž1986. undertook repeated drop shatter tests on Pilbara iron ore samples ranging in size from 90 to 16 mm. The drops were onto steel plates from a height of 1.8 m. The results indicated that different first-order breakage rates were observed for different particle sizes. The coordination number CN and the mean tensile strength a i were not measured experimentally and were arbitrarily assigned a value of unity for the y10 q 6 mm size fraction and then fitted for all the other size fractions during parameter fitting exercises. This process in itself is acceptable and in reality, simply represents a size-dependent lumped parameter. The model’s value as a simulator depends on whether CN and the mean tensile strength a i can be predicted from theoretical or empirical tests on ore samples. No
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mention is made as to whether this was attempted in the study. However, in general, the model seems to predict the degradation of lump ore to fines reasonably well and should be useful in predicting fines production during transport from mine to port. In an internal BHP Žunpublished. report conducted by Vince et al. Ž1987. on Mt. Newman ore, a drop test procedure similar to Norgate et al. was used. Two different types of drop towers were used, a 1.8-m tower and a 15-m tower. Two different sets of results were obtained. The first dropped six sets of samples a total height of 30 m each but split the test heights into 2 = 15, 3 = 10, 6 = 5, 10 = 3, 15 = 2 and 30 = 1 m tests. Some unusual results were obtained with the greatest fines generation occurring at 2 = 15 m and an apparent minimum fines generation noted for the 10 = 3 m tests. Both the 15 = 2 and 30 = 1 m tests had a higher percentage fines than the 10 = 3 m but were not as large as the 2 = 15 m tests. The increased fines generation for the lower drop heights was attributed to increased handling of approximately 0.6% extra fines per handling. The final adjusted results, where the percentage due to handling was removed, indicated decreased breakage with decreasing test height. This result tends to confirm the findings of Faberberg and Sandberg Ž1973. and Norgate et al. Ž1986., that a minimum height is required to achieve fines generation. As a result, the report recommended that drops above 3 m should be replaced with smaller staged drops such as in a rock box. However, the results leave uncertain the exact nature of the degradation effects of handling. Nor does it address the problem of how different types of handling affect the percentage of fines generated. These tests should be repeated over a wide range of handling situations and the results carefully analysed. The second set of tests confirmed those of Norgate et al. Ž1986., and indicated that the primary factor affecting the degree of degradation was drop height. They involved repeated dropping of different samples from heights of Ži. 1.8 m, Žii. 5 m, and Žiii. 10 m. The results clearly show increased generation of fines as the number of drops increased. The tests were carried out on a ‘blend’ of Mt. Whaleback iron ores but the exact composition was not mentioned. The report also found that the presence of iron ore fines greater than 10% had a cushioning effect and significantly reduced the production of fines. The present study carefully selected samples from the open cut pit at Newman permitting easy geological identification. The samples were later assayed and XRF tests conducted to confirm their type. The samples tested were the D2, D4 and Joffre ore types. The ore types individually had not been investigated before to any significant degree. In this research, it was decided not to use tumble tests to measure the degree of degradation experienced by lump ore during the breakage process. Two reasons for this were that as particles are tumbled, the sharp edges of the particles are removed and so the generation of fines is reduced as the particles become rounded. There is no evidence to suggest that this is the degradation process experienced by particles during handling in real plant situations. The second reason was that, as the percentage of fines increases in the tumbling mill, the ‘cushioning’ effects of fines reduces further degradation of the ore. It is now well known that fine material has the effect of cushioning the level of impact between larger particles and may spread the impact loads and stress experienced
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by the particles. It was decided therefore to use a more direct method of applying a breakage force where the exact amount of breakage energy could be carefully controlled and the final breakage product could reflect the amount of breakage energy applied, For this reason, a computer monitored, laser detected twin pendulum breakage apparatus was used for all the tests used in developing the model.
2. Results 2.1. Microstructure An analysis of the microstructure of the three ores using scanning electron microscopy was undertaken in order to assist in understanding the possible differences between the three types of ore. They are presented here simply to assist the reader, in a qualitative way, of appreciating the differences in the ore types. Further detailed investigations are proceeding into the fracture properties of these ores and the results of this work will be presented at a future date. D2 indicated clearly defined microplaty haematite with good crystal form dispersed between apparently massive regions of dense microplaty haematite or martite. The smaller more needle-like shapes seen in Fig. 1 are microplaty haematite and it is thought
Fig. 1. Scanning electron micrograph images of D2 ore showing microplaty haematite regions and more apparently massive regions of dense microplaty haematite or martite. ŽScale: 1 cm s1 mm..
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that the larger white areas are predominantly denser martite. The porosity of this ore is low with small irregularly shaped pores and not interconnected, which may inhibit crack propagation and account for the low friability of the ore. The D4 ore ŽFig. 2. is very similar to D2 and it also seems to consist of microplaty haematite and martite with significant crystalline intergrowth of the two. However, there appears to be more and larger pores than D2 which may make D4 more susceptible to breakage. Further research is required to confirm this. The Joffre ore consisted mainly of martite with some microplaty haematite with very little intergrowth between the two. There also appears to be many pores with interconnecting cracks ŽFig. 3.. 2.2. Batch grinding tests In the literature, batch grinding tests have frequently been used to determine specific rates of breakage si that are usually first-order in nature, at least for initial Žshort. grinding times ŽAustin, 1971; Austin et al., 1984., for a given size fraction, mill type and weight of feed size wi . wi Ž t . s wi Ž 0 . exp Ž ysi t .
Ž 3.
Batch grinding tests were carried out on the three iron ores under investigation and the results are shown in Fig. 4. The tests were carried under identical conditions in order
Fig. 2. Scanning electron micrograph images of D4 ore showing microplaty haematite regions but more porous regions. ŽScale: 1 cm s1 mm..
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Fig. 3. Scanning electron micrograph images of Joffre ore showing many interconnected porous regions. ŽScale: 1 cm s1 mm..
Fig. 4. First-order plots for various size fractions of iron ore samples from ŽBHP. Mt. Whaleback, Newman, Western Australia in a 200=200 mm ball mill, running at 75% critical speed with a 10-kg ball charge of 25 mm balls.
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to compare the breakage rates. Distinct groupings were observed for each ore type, D2, D4 and Joffre with some variation for feed size within a group as would be expected. The average specific rates of breakage for D2, D4 and Joffre were 0.36, 0.77, and 1.23 miny1 , respectively. The results strongly suggest that the rate of breakage of the three different ores are different and therefore, the amount of fines produced as a result of handling in each case should also be different ŽFig. 4.. The twin pendulum breakage device ŽFig. 5. breaks ore samples with carefully controlled breakage energies. The device is first calibrated by raising the rebound pendulum to various heights and measuring the period of the pendulum after release. This is done as a fin at the bottom of the pendulum interrupts the light from a laser to a detector which is monitored by a computer. No particles are actually crushed during calibration. The data collected in this way is then used later to calculate the comminution energy Ec . An individual particle of known mass is then secured to the face of the rebound pendulum and the input pendulum is drawn back to a prescribed height before being released to crush the particle. A test sample consists of 25 closely sized particles, which are each crushed in an identical manner using the same height of the input pendulum on each particle. After crushing, the subsequent oscillations of the rebound pendulum are measured using the laser and the computer. The exact amount of energy absorbed by a particle in crushing can then be determined by subtracting the energy in the rebound pendulum from the energy applied via the input pendulum. All other energy losses due to factors like noise and heat are considered constant. The average mass per sample is
Fig. 5. The twin pendulum breakage device showing the laser detector and sample position.
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Table 1 Samples of iron ore crushed using the twin pendulum breakage device using a constant input energy Žthe test numbers are only for reference purposes. Constant input pendulum heights 0.3125 m. Ore type
Size fraction Žmm.
Mass Žg.
Specific comminution energy Ecs ŽkW hrton.
Product P80 Žmm.
D2 Žtest a4. D2 Žtest a1. D2 Žtest a7. D4 Žtest a5. D4 Žtest a2. D4 Žtest a8. Joffre Žtest a6. Joffre Žtest a3. Joffre Žtest a9.
y16.00q13.2 y13.2q11.2 y11.2q9.5 y16.00q13.2 y13.2q11.2 y11.2q9.5 y16.0q13.2 y13.2q11.2 y11.2q9.5
191.4 125.8 77.7 195.9 125.2 71.8 174.5 122.8 73
0.282 0.430 0.696 0.276 0.432 0.751 0.310 0.441 0.727
10.24 7.7 6.5 7.9 5.4 5.5 5.36 3.56 3.34
calculated Žtons. and the amount of energy applied specifically to the sample, the specific comminution energy Ecs , is determined. Full details of the twin pendulum can be found in the literature ŽNarayanan, 1985, 1987a,b; Narayanan and Whiten, 1988; Weedon and Napier-Munn, 1990. and details of the method of calculating the breakage energy are outlined in Appendix A. In order to investigate extensively the breakage characteristics of the three different types of iron ore, a large number of test samples were selected. The test samples selected are shown in Tables 1 and 2. In Table 1, the sample sizes shown were broken using a constant height of the input pendulum of 0.3215 m. In Table 2, the same sized samples were broken using different input pendulum heights.
Table 2 Samples of iron ore of the same size fraction crushed using the twin pendulum breakage device at the input heights of 0.2525, 0.3615, 0.4135 and 0.4805 m for each ore type Constant size fraction. Ore type
Size fraction Žmm.
Mass Žg.
Specific comminution energy Ecs ŽkW hrton.
Product P80 Žmm.
D2 Žtest a13. D2 Žtest a19. D2 Žtest a10. D2 Žtest a16. D4 Žtest a14. D4 Žtest a20. D4 Žtest a11. D4 Žtest a17. Joffre Žtest a15. Joffre Žtest a21. Joffre Žtest a12. Joffre Žtest a18.
y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2
131.7 127 127.3 132.4 111.4 122.1 115.9 114.2 120 114.3 116.1 107.1
0.322 0.479 0.544 0.609 0.037 0.498 0.598 0.706 0.354 0.528 0.594 0.750
8.85 7.6 7.6 7.3 7.7 6.2 5.5 4.5 4.35 3.8 3.1 2.86
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Fig. 6. The breakage product from pendulum tests on samples of D4 and Joffre ores as listed in Table 1.
As mentioned, the Ecs value is the specific comminution energy, which is the comminution energy applied to a sample, taking into consideration the mean mass of the 25 particles in the sample. The different specific comminution energies shown in the tables therefore reflect the differences in mass of the samples used in the tests ŽWhiten and Kavetsky, 1984.. The product from the breakage tests was collected and sized and the distributions are shown in Figs. 6 and 7 Žfor the sake of clarity, the D2 product is shown on a separate
Fig. 7. The breakage product from pendulum tests on samples of D2 ore as listed in Table 1.
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graph.. The geometric mean size of the breakage products was plotted against the percentage passing the lower sieve size. This procedure was found to provide the most consistent set of results, especially in the smaller size fractions. It also facilitated the calculation of several mathematical parameters. It is clear from Figs. 6 and 7 that, in general, the same order of breakage exists as seen in the batch milling tests. In each case, the D2 ore seems to be more competent than the D4 which in turn is more competent than the Joffre. Although several different size fractions were broken at various breakage energies, in a qualitative sense it can be seen that the P80 values ŽTable 1. tend to finer sizes for the D4 and finer again for the Joffre. Results of the breakage tests of the samples indicated in Table 2 are shown in Figs. 8–10. As with the previous tests, it is clear that, in general, the product and P80 values become finer with increasing specific comminution energy. In this case, because the size fractions broken were all the same size, it can be shown that the mean P80 values decrease in the order D2 ) D4 ) Joffre, i.e. 7.8, 6.0, and 3.5 mm, respectively, as would be expected from previous results. 2.3. t-CurÕes In order to normalize the results from the many breakage tests, it was decided to generate a series of t-curves. In Table 3, the results of a pendulum breakage test Žtest a17. are provided. The test was conducted on a D4 ore sample, size fraction y13.2 q 11.2 mm Žgeometric mean 12.16 mm.. After breakage, the geometric mean sizes of the
Fig. 8. Pendulum breakage product from tests on D2 ore samples indicated in Table 2. The size fraction was the same in each test but the specific comminution energy Ecs was increased.
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Fig. 9. Pendulum breakage product from tests on D4 ore samples indicated in Table 2. The size fraction was the same in each test but the specific comminution energy Ecs was increased.
product was calculated along with the cumulative percentage passing ŽCPP. for each size. To normalize the product, the parameter t was used, which is the feed size divided by the geometric mean size. The values for t can be seen in Table 3. By cubic spline interpolation, it is possible to find the CPP for all other values for t. ŽNote, a large number of ‘‘Matlab’’ spline knots were used to ensure accuracy with the splines.. For example, the CPPs for t s 2, 3, 5, 7, 15, and 50 are 97.01%, 87.57%, 66.11%, 52.33%, 33.98%, and 19.8%, respectively ŽThese values of t were selected for mathematical simplicity in later modelling..
Fig. 10. Pendulum breakage product from tests on Joffre ore samples indicated in Table 2. The size fraction was the same in each test but the specific comminution energy Ecs was increased.
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Table 3 Breakage product from the pendulum test on a sample of D4 ore Žtest a17, D4; feed sizes12.16 mm. Sieve size Žgeometric mean. Žmm. Parameter t s Žfeed sizersieve size. Cumulative percentage passing Ž%. 6.718 3.348 1.669 0.841 0.424 0.212 0.106 0.053 0.020
1.8 3.63 7.29 14.46 28.68 57.35 114.7 229.4 607.95
100 84.28 50.98 34.64 25.58 18.83 12.08 7.99 5.77
For modelling purposes, the CPPs for these values of t were calculated for all test samples outlined in Tables 1 and 2. By using t50 as x values and plotting them against the respective t 2, t3, t5, t 7 and t15 values, Fig. 11 was obtained. Note that previous research in the literature has tended to use the parameter t10 on the x-axis. However, using t50 provides better spline interpolations in the lower values ŽNarayanan, 1985, 1987a,b; Narayanan and Whiten, 1988.. All three ore types are presented in Fig. 11 with the D2 and D4 values tending towards the smaller t50 values, and the Joffre values the larger t50 values. The specific comminution energies for each test can be related to the t50 parameter as shown in Fig. 12. Again, the same sequence of ores as discussed previously was
Fig. 11. The t-curve representations of the product distributions from breakage tests on D2, D4 and Joffre iron ore samples.
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Fig. 12. The specific comminution energy and t50 parameter for the tests outlined in Tables 1 and 2.
observed. For most Ecs values, the sequence of values of the t50 parameters were D2 - D4 - Joffre. This means that for the same breakage energy input per ton of ore, Joffre would produce a finer product than the D4 which in turn would produce a finer product than the D2. The pendulum breakage device is being modified to apply breakage energies of 0.1 kW hrton and lower. The present lower limit is about 0.2 kW hrton. All energy values used in the modelling that were lower than this were found by interpolation, assuming zero energy at zero t50. In the work carried out by Vince et al. Ž1987., three drop heights were chosen. They were 1.8, 5 and 10 m. Samples of known size distribution were used, namely, y45 q 32, y32 q 21, y21 q 16, y16 q 11, y11 q 8, y8 q 5.5 mm and the fines y5.5 mm. The samples were taken from a feed stock totalling 50 tons, but it is unclear from the literature exactly what mass of material was dropped per test. Based simply on the drop heights involved, the equivalent breakage energies would have been as indicated in Table 4, which also includes the respective t50 values taken from ŽMatlab. splines fitted to the data shown in Fig. 12. Again, a large number of spline knots were used, especially in the lower regions to ensure accuracy.
Table 4 From the drop heights used in the research conducted by Vince et al. Ž1987., the corresponding specific comminution energy were calculated and t50 values were determined using cubic splines Drop height Žm.
Specific comminution energy Ecs ŽkW hrton.
1.8 5 10
0.0049 0.0135 0.027
t50 D2
D4
Joffre
0.08 0.21 0.42
0.11 0.30 0.61
0.27 0.75 1.51
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Ore shipped from the mine at Newman to the port at Port Headland contains varying percentages of different ore types, predominately D2, D4 and Joffre. Because the friability of these ores is considerably different, it was necessary to account for the percentage f i j of each ore type j, in each feed size fraction i. The percentage of each ore type was estimated from plant data for 1997 showing the split in ore types arriving at Port Headland ready for loading for export. It was assumed that these percentages were typical of the type of ore tested by Vince et al. A semi-empirical model was developed from the t50 values and the breakage energies outlined in Table 4. For a particular drop height and ore type, the percentage of each size fraction that would appear in the fines Žy6 mm. was m i j . In fact, it was relatively easy to produce degradation rates for any drop height or feed size distribution using the methods outlined above. Vince et al. Ž1987. also showed that an increase in fines production due to handling could be expected. From Vince et al.’s data, taking into account the number of handling events and the total percentage increase in fines from handling, it was calculated that the increase in percentage of fines per handling, per size fraction per ore type was approximately 0.6%. A handling parameter h ij was introduced, and given the same value of 0.6% for all size fractions and the three ore types. However, it should be noted that this parameter probably varies with feed size and type of handling. Further research is being undertaken to quantitfy the degradation due to handling. The model can be expressed as follows: D
F sÝ j
N
Ý wi j fi j Ž mŽ i j.qh i j . 4
Ž 4.
t
Where F is the additional fines produced as a result of a drop, wi j is the weight percent of ore in feed size i, N is the number of feed size fractions and D is the number of ore
Fig. 13. A comparison of the degradation model of Eq. Ž4. using the data of Vince et al. Ž1987. for the 1.8-m series of drops.
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Fig. 14. A comparison of the degradation model of Eq. Ž4. using the data of Vince et al. Ž1987. for the 5-m series of drops.
types j. Using this equation, calculations were carried out for the 1.8, 5 and 10 m series of drops using the data provided by Vince et al. The results are shown in Figs. 13–15. The results of the modelling can be seen in Figs. 13–15. There is a close agreement between the model and the raw data. Most of the data points lie within experimental error of the model points. From these results, it is clear that the use of degradation parameters, one for each ore type, provides a close agreement with reality, despite the assumptions regarding the percentages of each ore type present in the feed.
Fig. 15. A comparison of the degradation model of Eq. Ž4. using the data of Vince et al. Ž1987. for the 10-m series of drops.
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In Fig. 13, at the first drop test Ž1.8 m series., the raw data point differs from the model by 1.1%. The reason for this is unclear. It could be due to excess handling during the loading and unloading into the 1.8 m tower. The samples were dropped into the tower from a height of about 0.1 m. However, this height alone does not seem to account for the extra fines generation. It could possibly be due to ‘‘piggy back’’ fines on the first pre-dropped sample, which are only dislodged after the first drop. However, similar results are not seen on the 5 and 10 m tests. Also, the findings of Faberberg and Sandberg Ž1973. implied that a minimum drop of 5 m was required to achieve significant breakage. Additional research is required to find the cause of this deviation or whether it is due to experimental error. The additional fines generation predicted by the model in Figs. 12 and 13 for the 5 and 10 m seems to follow the raw data up to about the 5th drop. The reason for the deviation after this point is unclear. It could possibly be due to cushioning by fines. The percentage of fines generated after the 5th drop increased to 15.36% and 20.69% for the 5 and 10 m tests, respectively. Vince et al. Ž1987. found very little cushioning effects under 10% fines, but at 20% fines, the cushioning effect became obvious. Further research is being undertaken at the University of Western Australia to determine the exact effects of cushioning on fines generation.
3. Conclusion Lumps attract a premium price when selling iron ore for blast furnace smelting. It is therefore important for economic reasons that the lumpsrfines ratio be predictable and controllable. However, it has been known for some time that some ore types are more friable than others and so create more fines for the same degree of handling. Batch milling test results showed different breakage rates for the three different types of iron ores D2, D4 and Joffre. These differences were again seen in breakage tests carried out on a computer monitored laser detected twin pendulum breakage device. A set of t-curves was calculated from the pendulum breakage data and a new degradation model developed to predict fines generation from handling which included drops from various heights. In the model, different degradation parameters were established which incorporated the breakage rates for different ore types when subjected to breakage energies from different drop heights. However, the model is set up so that degradation rates can be determined for any typical drop height and feed distribution. A parameter was also included to account for fines generation due to handling. The model satisfactorily predicted the fines generation from a series of tests conducted by Vince et al. Ž1987..
Acknowledgements This research was in part funded by BHP and the authors would sincerely like to thank BHP for their financial assistance. The authors would particularly like to thank Dr. Marcel Kamperman for his coordination, planning and general helpful advice. The authors would also like to thank Dr. Laurence Spencer, Department of Mechanical and
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Materials Engineering for organizing the funding, and the Centre for Microscopy and Microanalysis, for all the SEM work. Thanks must also go Allison Low for assisting with some of the microscopy.
Appendix A Conservation of Momentum m 1 u 1 q m 2 u 2 s m 1Õ 1 q m 2 Õ 2
Ž A1.
where u1 and u 2 are the input and rebound pendulum velocities before impact; m1 and m 2 are the mass of input Ž4.108 kg. and rebound Ž6.234 kg. pendulum, respectively; Õ 1 and Õ 2 are the input and rebound pendulum velocities after impact. Newton’s Law of Restitution Õ 2 y Õ 1 s ye Ž u 2yu1 .
Ž A2.
where e is the coefficient of restitution. Substituting Õ 1 in Eq. ŽA1. with u 2 s 0 gives e s Ž m1 q m 2 .rm1Ž Õ 2ru1 y 1. s 0 for inelastic collisions. Energy equation Žassuming system losses are constant.; Input energy Ž EI . s output energy Ž Eoc . q comminution energy Ž Ec .: 1r2 Ž m1 u12 q m1 u 22 . s 1r2 Ž m1Õ 12qm 2 Õ 22 . q Ec
Ž A3.
Combining Eqs. ŽA1. – Ž3., the specific comminution energy, Ecs s m 2rŽ m1 q m 2 .4Ž1 y e 2 . E I . ŽFull details including worked examples can be found in Narayanan, 1987a..
References Austin, L.G., 1971. A review. An introduction to the mathematical description of grinding as a rate process. Powder Technol. 5, 1–15. Austin, L.G., Klimpel, R.R., Luckie, P.T., 1984. The process engineering of size reduction. In: Ball Milling. New York. SMErAIME Vol. 1, 87 pp. Faberberg, B., Sandberg, N., 1973. Minerals transport. In: Proc. 2nd Int. Symp. Transport and Handling of Materials Vol. 2. Narayanan, S.S., 1985. PhD Thesis, University of Queensland. 209 pp. Narayanan, S.S., 1987a. Modelling performance of industrial ball mills using single particle breakage tests. Int. J. Miner. Process. 20, 211–228. Narayanan, S.S., 1987b. Relationship between breakage parameters and process variables in ball milling — an industrial case study. Int. J. Miner. Process. 20, 241–251. Narayanan, S.S., Whiten, W.J., 1988. Determination of comminution characteristics of ores from single particle breakage tests, and its applications to ball mill scale-up. Trans. Inst. Min. Metall., Sect. C 97, 115–124. Norgate, T.E., Tompsitt, D.F., Batterham, R.J., 1986. Computer simulation of the degradation of lump ore during transportation and handling. In: Proc., 2nd Int. Conf. on Bulk Materials Storage, Handling and Transportation, Wollongong. . Vince, A., Mahoney, M., Waters, A.G., 1987. An evaluation of the factors affecting the degradation of Mt Newman lump ore, Internal report.
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Waters, A.G., Vince, A., Lister, J.D., 1986. Measuring the strength with agglomerate. Proc. Chemeca 86 Adelaide, Australia, pp. 118–123, 19–22 August. Weedon, D.M., Napier-Munn, T.J., 1990. Sulphide deposits — their origin and processing. IMM, 137–154. Whiten, W.J., Kavetsky, A., 1984. In: Studies on Scale-Up of Ball Mills. SME Fall Meeting, Salt Lake City, UT, Oct.. . Wilson, F., 1998. An investigation into the nature of friable iron ore at Mt Whaleback, Western Australia. Honours Thesis ŽBachelor of Engineering., University of Western Australia.
Modelling iron ore degradation using a twin pendulum breakage device D.M. Weedon a,) , F. Wilson b a
Department of Mechanical and Materials Engineering, UniÕersity of Western Australia, Nedlands, Perth, Western Australia 6907, Australia b QCL, Norton Centre, Poyernook Road, Aberdeen, Scotland AB115RW UK Received 30 March 1999; received in revised form 8 July 1999; accepted 1 October 1999
Abstract The breakage rates of three different types of iron ore D2, D4 and Joffre from the Brockman Iron Formation, Western Australia were investigated. Batch milling tests were undertaken to determine breakage rates as well as breakage tests using a computer monitored laser detected twin pendulum breakage device. The results showed that Joffre ore was more friable than D4, which was more friable than D2. A set of t-curves were calculated from the pendulum breakage data and a new model was developed. This model was used to satisfactorily predict fines generation from handling and dropping ore samples over a series of 1.8, 5 and 10 m drops. The model developed different degradation matrices for each ore type at the three drop heights and for a given feed. A parameter was also included to account for fines generation due to handling. q 2000 Elsevier Science B.V. All rights reserved. Keywords: iron ore; lumps; fines; degradation
1. Introduction Iron ore production is a significant part of the mining operations of Broken Hill Proprietary ŽBHP. at Mt. Whaleback at Newman, Western Australia, which is one of the largest single open cut metalliferous mine in the world. It is currently 5.5 km long and 1.5 km wide with production of ; 62 million tons Ž1998.. Its ore is railed to Port )
Corresponding author. Fax: q61-8-9380-1024. E-mail address: [email protected] ŽD.M. Weedon..
0301-7516r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 7 5 1 6 Ž 9 9 . 0 0 0 6 6 - 6
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headland and shipped to plant operators in Japan, Taiwan, Korea, Pakistan, Europe and China. During the processes of mining, crushing and transporting iron ore, the material is subjected to loads and impacts which increase the production of fines ŽWilson, 1998.. The ore is predominately hematite–martite and exists as the Dales Gorge and Joffre members of the Brockman Iron Formation lying within the Hamersley Iron outcrop. The Dales Gorge ore contains four zones D1, D2, D3 and D4, which are of premium quality with high grades and low impurities. D2 has the highest grade and lowest impurity and D4 is of similar grade and appearance but is significantly more friable. Enriched D1 is not very common and D3 contains thick shale bands and were therefore not examined in this research. The lower bands of the Joffre member are also enriched and are mined at Mt. Whaleback but are of lower grade than Dales Gorge and contain more impurities. It is also considerably more friable and yields a low lumpsrfines ratio. Two products are sold, lumps which range in size from 6.4 to 30 mm and fines which are smaller than 6.4 mm. Lumps command a premium price so size degradation is a significant cost factor for BHP. The degradation of lump material into fines is undesirable because with an oxidizing ore, when processing in furnaces, any fine material cannot penetrate the slag layer and is partly lost through the exhaust ports resulting in economic loss. The predominant problem with ores of high fines content, however, is that the yield of an oxidizing furnace rapidly diminishes with an increased percentage of fines due to restrictions to the flow of reducing gases through the reactor. There have been many previous studies on the causes of iron ore lumps degradation. The Swedish Mining Association ŽFaberberg and Sandberg, 1973. carried out extensive investigations of the degradation of lump iron ore Žpredominately magnetite. while in transport. The samples were taken from a number of lump ore shipments ranging in size from 2000 to 20,000 tons from mines to various blast furnaces on the European continent. The ore was divided into categories of varying degrees of hardness and softness based on strength tests and chemical composition. The fines generation testing mainly consisted of a series of drop and abrasion tests. The drop tests were undertaken predominately from a 20-m high chute with inlet ports at different levels. The abrasion tests were performed in a standardized tumbler drum 1.0 = 0.5 m with two 50-mm high lifters. The speed was 25 rpm and the rotation time was 8 min. No model was developed for the breakage process. The results concluded that the main cause of degradation was impact when the material was dropped from a significant height, usually during transportation and unloading. However, degradation from abrasion due to gravity flow through bins and other devices also occurred but only to a minor extent ŽFaberberg and Sandberg, 1973.. In a series of drops, as the total drop height increased, the large sizes gradually decreased and the fines increased in percentage. The medium sizes remained fairly stable. It was estimated that a total drop of 100 m represented 0.3 kW hrton which is a significant amount of energy considering that the crushing energy required to reduce an ore from 100 to 30 mm is approximately 0.5 kW hrton. The results also showed that a few large drops were equivalent to several smaller drops of the same total height providing the smaller drops were greater than 5 m. The study generally found increased fines generation with the weaker ores than the stronger ores and that a cushioning effect
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started to occur as the percentage of initial fines increased with 40% less fines produced as the initial fines percentage increased from 0% to 30%. Norgate et al. Ž1986. undertook a study to investigate the breakage properties of two ores, one ‘hard’ and one ‘soft’, from the Pilbara region in Western Australia. A series of drop tests were carried out from heights ranging from 0.9 to 32 m. They found that ore type was a significant factor in predicting the percentage of fines produced with the softer ores producing an extra ; 12% in comparison to the hard ores after completing the maximum number of drops. Norgate et al. Ž1986. also concluded that the total drop height was the major factor affecting the generation of fines. It was stated that a drop height of a given value will cause more degradation earlier in a handling system rather than later because of conditioning of the ore removing the weaker particles, although the difference seems to be only of the order of 1–2%. Norgate et al. Ž1986. also found that the degree of degradation can be reduced if a large drop was replaced with a series of smaller drops, in the vicinity of 1 m or less. This seems to concur with the findings of Faberberg and Sandberg Ž1973. although the exact mechanical reason why this should be so is uncertain. Norgate et al. Ž1986. also found a cushioning effect to exist with initial fines of 12% or more. A semi-empirical model was developed by Norgate et al. Ž1986., which related the breakage out c i from size fraction i containing mass si to the mean tensile strength a i and co-ordination number CN Žthe number of contact points between each particle and its neighbour.,
c i1r2 s d Ž hy1 . g
si
ai
CN
Ž 1.
where h is the drop height, and g and d are model parameters. The Austin et al. Ž1984. breakage distribution function: g
Bs j , s i s f Ž s jrsi . q Ž 1 y f . Ž s jrsi .
b
Ž 2.
was used to determine the amount of material distributing to various size fractions after breakage where f , g and b are parameters and Bs j , s i is the mass fraction of material of size s j or smaller resulting from breakage of particles of initial size si . The model assumed that the value of the breakage function was the same for all size fractions. This assumption is probably incorrect. Waters et al. Ž1986. undertook repeated drop shatter tests on Pilbara iron ore samples ranging in size from 90 to 16 mm. The drops were onto steel plates from a height of 1.8 m. The results indicated that different first-order breakage rates were observed for different particle sizes. The coordination number CN and the mean tensile strength a i were not measured experimentally and were arbitrarily assigned a value of unity for the y10 q 6 mm size fraction and then fitted for all the other size fractions during parameter fitting exercises. This process in itself is acceptable and in reality, simply represents a size-dependent lumped parameter. The model’s value as a simulator depends on whether CN and the mean tensile strength a i can be predicted from theoretical or empirical tests on ore samples. No
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mention is made as to whether this was attempted in the study. However, in general, the model seems to predict the degradation of lump ore to fines reasonably well and should be useful in predicting fines production during transport from mine to port. In an internal BHP Žunpublished. report conducted by Vince et al. Ž1987. on Mt. Newman ore, a drop test procedure similar to Norgate et al. was used. Two different types of drop towers were used, a 1.8-m tower and a 15-m tower. Two different sets of results were obtained. The first dropped six sets of samples a total height of 30 m each but split the test heights into 2 = 15, 3 = 10, 6 = 5, 10 = 3, 15 = 2 and 30 = 1 m tests. Some unusual results were obtained with the greatest fines generation occurring at 2 = 15 m and an apparent minimum fines generation noted for the 10 = 3 m tests. Both the 15 = 2 and 30 = 1 m tests had a higher percentage fines than the 10 = 3 m but were not as large as the 2 = 15 m tests. The increased fines generation for the lower drop heights was attributed to increased handling of approximately 0.6% extra fines per handling. The final adjusted results, where the percentage due to handling was removed, indicated decreased breakage with decreasing test height. This result tends to confirm the findings of Faberberg and Sandberg Ž1973. and Norgate et al. Ž1986., that a minimum height is required to achieve fines generation. As a result, the report recommended that drops above 3 m should be replaced with smaller staged drops such as in a rock box. However, the results leave uncertain the exact nature of the degradation effects of handling. Nor does it address the problem of how different types of handling affect the percentage of fines generated. These tests should be repeated over a wide range of handling situations and the results carefully analysed. The second set of tests confirmed those of Norgate et al. Ž1986., and indicated that the primary factor affecting the degree of degradation was drop height. They involved repeated dropping of different samples from heights of Ži. 1.8 m, Žii. 5 m, and Žiii. 10 m. The results clearly show increased generation of fines as the number of drops increased. The tests were carried out on a ‘blend’ of Mt. Whaleback iron ores but the exact composition was not mentioned. The report also found that the presence of iron ore fines greater than 10% had a cushioning effect and significantly reduced the production of fines. The present study carefully selected samples from the open cut pit at Newman permitting easy geological identification. The samples were later assayed and XRF tests conducted to confirm their type. The samples tested were the D2, D4 and Joffre ore types. The ore types individually had not been investigated before to any significant degree. In this research, it was decided not to use tumble tests to measure the degree of degradation experienced by lump ore during the breakage process. Two reasons for this were that as particles are tumbled, the sharp edges of the particles are removed and so the generation of fines is reduced as the particles become rounded. There is no evidence to suggest that this is the degradation process experienced by particles during handling in real plant situations. The second reason was that, as the percentage of fines increases in the tumbling mill, the ‘cushioning’ effects of fines reduces further degradation of the ore. It is now well known that fine material has the effect of cushioning the level of impact between larger particles and may spread the impact loads and stress experienced
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by the particles. It was decided therefore to use a more direct method of applying a breakage force where the exact amount of breakage energy could be carefully controlled and the final breakage product could reflect the amount of breakage energy applied, For this reason, a computer monitored, laser detected twin pendulum breakage apparatus was used for all the tests used in developing the model.
2. Results 2.1. Microstructure An analysis of the microstructure of the three ores using scanning electron microscopy was undertaken in order to assist in understanding the possible differences between the three types of ore. They are presented here simply to assist the reader, in a qualitative way, of appreciating the differences in the ore types. Further detailed investigations are proceeding into the fracture properties of these ores and the results of this work will be presented at a future date. D2 indicated clearly defined microplaty haematite with good crystal form dispersed between apparently massive regions of dense microplaty haematite or martite. The smaller more needle-like shapes seen in Fig. 1 are microplaty haematite and it is thought
Fig. 1. Scanning electron micrograph images of D2 ore showing microplaty haematite regions and more apparently massive regions of dense microplaty haematite or martite. ŽScale: 1 cm s1 mm..
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that the larger white areas are predominantly denser martite. The porosity of this ore is low with small irregularly shaped pores and not interconnected, which may inhibit crack propagation and account for the low friability of the ore. The D4 ore ŽFig. 2. is very similar to D2 and it also seems to consist of microplaty haematite and martite with significant crystalline intergrowth of the two. However, there appears to be more and larger pores than D2 which may make D4 more susceptible to breakage. Further research is required to confirm this. The Joffre ore consisted mainly of martite with some microplaty haematite with very little intergrowth between the two. There also appears to be many pores with interconnecting cracks ŽFig. 3.. 2.2. Batch grinding tests In the literature, batch grinding tests have frequently been used to determine specific rates of breakage si that are usually first-order in nature, at least for initial Žshort. grinding times ŽAustin, 1971; Austin et al., 1984., for a given size fraction, mill type and weight of feed size wi . wi Ž t . s wi Ž 0 . exp Ž ysi t .
Ž 3.
Batch grinding tests were carried out on the three iron ores under investigation and the results are shown in Fig. 4. The tests were carried under identical conditions in order
Fig. 2. Scanning electron micrograph images of D4 ore showing microplaty haematite regions but more porous regions. ŽScale: 1 cm s1 mm..
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Fig. 3. Scanning electron micrograph images of Joffre ore showing many interconnected porous regions. ŽScale: 1 cm s1 mm..
Fig. 4. First-order plots for various size fractions of iron ore samples from ŽBHP. Mt. Whaleback, Newman, Western Australia in a 200=200 mm ball mill, running at 75% critical speed with a 10-kg ball charge of 25 mm balls.
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to compare the breakage rates. Distinct groupings were observed for each ore type, D2, D4 and Joffre with some variation for feed size within a group as would be expected. The average specific rates of breakage for D2, D4 and Joffre were 0.36, 0.77, and 1.23 miny1 , respectively. The results strongly suggest that the rate of breakage of the three different ores are different and therefore, the amount of fines produced as a result of handling in each case should also be different ŽFig. 4.. The twin pendulum breakage device ŽFig. 5. breaks ore samples with carefully controlled breakage energies. The device is first calibrated by raising the rebound pendulum to various heights and measuring the period of the pendulum after release. This is done as a fin at the bottom of the pendulum interrupts the light from a laser to a detector which is monitored by a computer. No particles are actually crushed during calibration. The data collected in this way is then used later to calculate the comminution energy Ec . An individual particle of known mass is then secured to the face of the rebound pendulum and the input pendulum is drawn back to a prescribed height before being released to crush the particle. A test sample consists of 25 closely sized particles, which are each crushed in an identical manner using the same height of the input pendulum on each particle. After crushing, the subsequent oscillations of the rebound pendulum are measured using the laser and the computer. The exact amount of energy absorbed by a particle in crushing can then be determined by subtracting the energy in the rebound pendulum from the energy applied via the input pendulum. All other energy losses due to factors like noise and heat are considered constant. The average mass per sample is
Fig. 5. The twin pendulum breakage device showing the laser detector and sample position.
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Table 1 Samples of iron ore crushed using the twin pendulum breakage device using a constant input energy Žthe test numbers are only for reference purposes. Constant input pendulum heights 0.3125 m. Ore type
Size fraction Žmm.
Mass Žg.
Specific comminution energy Ecs ŽkW hrton.
Product P80 Žmm.
D2 Žtest a4. D2 Žtest a1. D2 Žtest a7. D4 Žtest a5. D4 Žtest a2. D4 Žtest a8. Joffre Žtest a6. Joffre Žtest a3. Joffre Žtest a9.
y16.00q13.2 y13.2q11.2 y11.2q9.5 y16.00q13.2 y13.2q11.2 y11.2q9.5 y16.0q13.2 y13.2q11.2 y11.2q9.5
191.4 125.8 77.7 195.9 125.2 71.8 174.5 122.8 73
0.282 0.430 0.696 0.276 0.432 0.751 0.310 0.441 0.727
10.24 7.7 6.5 7.9 5.4 5.5 5.36 3.56 3.34
calculated Žtons. and the amount of energy applied specifically to the sample, the specific comminution energy Ecs , is determined. Full details of the twin pendulum can be found in the literature ŽNarayanan, 1985, 1987a,b; Narayanan and Whiten, 1988; Weedon and Napier-Munn, 1990. and details of the method of calculating the breakage energy are outlined in Appendix A. In order to investigate extensively the breakage characteristics of the three different types of iron ore, a large number of test samples were selected. The test samples selected are shown in Tables 1 and 2. In Table 1, the sample sizes shown were broken using a constant height of the input pendulum of 0.3215 m. In Table 2, the same sized samples were broken using different input pendulum heights.
Table 2 Samples of iron ore of the same size fraction crushed using the twin pendulum breakage device at the input heights of 0.2525, 0.3615, 0.4135 and 0.4805 m for each ore type Constant size fraction. Ore type
Size fraction Žmm.
Mass Žg.
Specific comminution energy Ecs ŽkW hrton.
Product P80 Žmm.
D2 Žtest a13. D2 Žtest a19. D2 Žtest a10. D2 Žtest a16. D4 Žtest a14. D4 Žtest a20. D4 Žtest a11. D4 Žtest a17. Joffre Žtest a15. Joffre Žtest a21. Joffre Žtest a12. Joffre Žtest a18.
y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2 y13.2q11.2
131.7 127 127.3 132.4 111.4 122.1 115.9 114.2 120 114.3 116.1 107.1
0.322 0.479 0.544 0.609 0.037 0.498 0.598 0.706 0.354 0.528 0.594 0.750
8.85 7.6 7.6 7.3 7.7 6.2 5.5 4.5 4.35 3.8 3.1 2.86
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Fig. 6. The breakage product from pendulum tests on samples of D4 and Joffre ores as listed in Table 1.
As mentioned, the Ecs value is the specific comminution energy, which is the comminution energy applied to a sample, taking into consideration the mean mass of the 25 particles in the sample. The different specific comminution energies shown in the tables therefore reflect the differences in mass of the samples used in the tests ŽWhiten and Kavetsky, 1984.. The product from the breakage tests was collected and sized and the distributions are shown in Figs. 6 and 7 Žfor the sake of clarity, the D2 product is shown on a separate
Fig. 7. The breakage product from pendulum tests on samples of D2 ore as listed in Table 1.
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graph.. The geometric mean size of the breakage products was plotted against the percentage passing the lower sieve size. This procedure was found to provide the most consistent set of results, especially in the smaller size fractions. It also facilitated the calculation of several mathematical parameters. It is clear from Figs. 6 and 7 that, in general, the same order of breakage exists as seen in the batch milling tests. In each case, the D2 ore seems to be more competent than the D4 which in turn is more competent than the Joffre. Although several different size fractions were broken at various breakage energies, in a qualitative sense it can be seen that the P80 values ŽTable 1. tend to finer sizes for the D4 and finer again for the Joffre. Results of the breakage tests of the samples indicated in Table 2 are shown in Figs. 8–10. As with the previous tests, it is clear that, in general, the product and P80 values become finer with increasing specific comminution energy. In this case, because the size fractions broken were all the same size, it can be shown that the mean P80 values decrease in the order D2 ) D4 ) Joffre, i.e. 7.8, 6.0, and 3.5 mm, respectively, as would be expected from previous results. 2.3. t-CurÕes In order to normalize the results from the many breakage tests, it was decided to generate a series of t-curves. In Table 3, the results of a pendulum breakage test Žtest a17. are provided. The test was conducted on a D4 ore sample, size fraction y13.2 q 11.2 mm Žgeometric mean 12.16 mm.. After breakage, the geometric mean sizes of the
Fig. 8. Pendulum breakage product from tests on D2 ore samples indicated in Table 2. The size fraction was the same in each test but the specific comminution energy Ecs was increased.
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Fig. 9. Pendulum breakage product from tests on D4 ore samples indicated in Table 2. The size fraction was the same in each test but the specific comminution energy Ecs was increased.
product was calculated along with the cumulative percentage passing ŽCPP. for each size. To normalize the product, the parameter t was used, which is the feed size divided by the geometric mean size. The values for t can be seen in Table 3. By cubic spline interpolation, it is possible to find the CPP for all other values for t. ŽNote, a large number of ‘‘Matlab’’ spline knots were used to ensure accuracy with the splines.. For example, the CPPs for t s 2, 3, 5, 7, 15, and 50 are 97.01%, 87.57%, 66.11%, 52.33%, 33.98%, and 19.8%, respectively ŽThese values of t were selected for mathematical simplicity in later modelling..
Fig. 10. Pendulum breakage product from tests on Joffre ore samples indicated in Table 2. The size fraction was the same in each test but the specific comminution energy Ecs was increased.
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Table 3 Breakage product from the pendulum test on a sample of D4 ore Žtest a17, D4; feed sizes12.16 mm. Sieve size Žgeometric mean. Žmm. Parameter t s Žfeed sizersieve size. Cumulative percentage passing Ž%. 6.718 3.348 1.669 0.841 0.424 0.212 0.106 0.053 0.020
1.8 3.63 7.29 14.46 28.68 57.35 114.7 229.4 607.95
100 84.28 50.98 34.64 25.58 18.83 12.08 7.99 5.77
For modelling purposes, the CPPs for these values of t were calculated for all test samples outlined in Tables 1 and 2. By using t50 as x values and plotting them against the respective t 2, t3, t5, t 7 and t15 values, Fig. 11 was obtained. Note that previous research in the literature has tended to use the parameter t10 on the x-axis. However, using t50 provides better spline interpolations in the lower values ŽNarayanan, 1985, 1987a,b; Narayanan and Whiten, 1988.. All three ore types are presented in Fig. 11 with the D2 and D4 values tending towards the smaller t50 values, and the Joffre values the larger t50 values. The specific comminution energies for each test can be related to the t50 parameter as shown in Fig. 12. Again, the same sequence of ores as discussed previously was
Fig. 11. The t-curve representations of the product distributions from breakage tests on D2, D4 and Joffre iron ore samples.
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Fig. 12. The specific comminution energy and t50 parameter for the tests outlined in Tables 1 and 2.
observed. For most Ecs values, the sequence of values of the t50 parameters were D2 - D4 - Joffre. This means that for the same breakage energy input per ton of ore, Joffre would produce a finer product than the D4 which in turn would produce a finer product than the D2. The pendulum breakage device is being modified to apply breakage energies of 0.1 kW hrton and lower. The present lower limit is about 0.2 kW hrton. All energy values used in the modelling that were lower than this were found by interpolation, assuming zero energy at zero t50. In the work carried out by Vince et al. Ž1987., three drop heights were chosen. They were 1.8, 5 and 10 m. Samples of known size distribution were used, namely, y45 q 32, y32 q 21, y21 q 16, y16 q 11, y11 q 8, y8 q 5.5 mm and the fines y5.5 mm. The samples were taken from a feed stock totalling 50 tons, but it is unclear from the literature exactly what mass of material was dropped per test. Based simply on the drop heights involved, the equivalent breakage energies would have been as indicated in Table 4, which also includes the respective t50 values taken from ŽMatlab. splines fitted to the data shown in Fig. 12. Again, a large number of spline knots were used, especially in the lower regions to ensure accuracy.
Table 4 From the drop heights used in the research conducted by Vince et al. Ž1987., the corresponding specific comminution energy were calculated and t50 values were determined using cubic splines Drop height Žm.
Specific comminution energy Ecs ŽkW hrton.
1.8 5 10
0.0049 0.0135 0.027
t50 D2
D4
Joffre
0.08 0.21 0.42
0.11 0.30 0.61
0.27 0.75 1.51
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Ore shipped from the mine at Newman to the port at Port Headland contains varying percentages of different ore types, predominately D2, D4 and Joffre. Because the friability of these ores is considerably different, it was necessary to account for the percentage f i j of each ore type j, in each feed size fraction i. The percentage of each ore type was estimated from plant data for 1997 showing the split in ore types arriving at Port Headland ready for loading for export. It was assumed that these percentages were typical of the type of ore tested by Vince et al. A semi-empirical model was developed from the t50 values and the breakage energies outlined in Table 4. For a particular drop height and ore type, the percentage of each size fraction that would appear in the fines Žy6 mm. was m i j . In fact, it was relatively easy to produce degradation rates for any drop height or feed size distribution using the methods outlined above. Vince et al. Ž1987. also showed that an increase in fines production due to handling could be expected. From Vince et al.’s data, taking into account the number of handling events and the total percentage increase in fines from handling, it was calculated that the increase in percentage of fines per handling, per size fraction per ore type was approximately 0.6%. A handling parameter h ij was introduced, and given the same value of 0.6% for all size fractions and the three ore types. However, it should be noted that this parameter probably varies with feed size and type of handling. Further research is being undertaken to quantitfy the degradation due to handling. The model can be expressed as follows: D
F sÝ j
N
Ý wi j fi j Ž mŽ i j.qh i j . 4
Ž 4.
t
Where F is the additional fines produced as a result of a drop, wi j is the weight percent of ore in feed size i, N is the number of feed size fractions and D is the number of ore
Fig. 13. A comparison of the degradation model of Eq. Ž4. using the data of Vince et al. Ž1987. for the 1.8-m series of drops.
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Fig. 14. A comparison of the degradation model of Eq. Ž4. using the data of Vince et al. Ž1987. for the 5-m series of drops.
types j. Using this equation, calculations were carried out for the 1.8, 5 and 10 m series of drops using the data provided by Vince et al. The results are shown in Figs. 13–15. The results of the modelling can be seen in Figs. 13–15. There is a close agreement between the model and the raw data. Most of the data points lie within experimental error of the model points. From these results, it is clear that the use of degradation parameters, one for each ore type, provides a close agreement with reality, despite the assumptions regarding the percentages of each ore type present in the feed.
Fig. 15. A comparison of the degradation model of Eq. Ž4. using the data of Vince et al. Ž1987. for the 10-m series of drops.
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In Fig. 13, at the first drop test Ž1.8 m series., the raw data point differs from the model by 1.1%. The reason for this is unclear. It could be due to excess handling during the loading and unloading into the 1.8 m tower. The samples were dropped into the tower from a height of about 0.1 m. However, this height alone does not seem to account for the extra fines generation. It could possibly be due to ‘‘piggy back’’ fines on the first pre-dropped sample, which are only dislodged after the first drop. However, similar results are not seen on the 5 and 10 m tests. Also, the findings of Faberberg and Sandberg Ž1973. implied that a minimum drop of 5 m was required to achieve significant breakage. Additional research is required to find the cause of this deviation or whether it is due to experimental error. The additional fines generation predicted by the model in Figs. 12 and 13 for the 5 and 10 m seems to follow the raw data up to about the 5th drop. The reason for the deviation after this point is unclear. It could possibly be due to cushioning by fines. The percentage of fines generated after the 5th drop increased to 15.36% and 20.69% for the 5 and 10 m tests, respectively. Vince et al. Ž1987. found very little cushioning effects under 10% fines, but at 20% fines, the cushioning effect became obvious. Further research is being undertaken at the University of Western Australia to determine the exact effects of cushioning on fines generation.
3. Conclusion Lumps attract a premium price when selling iron ore for blast furnace smelting. It is therefore important for economic reasons that the lumpsrfines ratio be predictable and controllable. However, it has been known for some time that some ore types are more friable than others and so create more fines for the same degree of handling. Batch milling test results showed different breakage rates for the three different types of iron ores D2, D4 and Joffre. These differences were again seen in breakage tests carried out on a computer monitored laser detected twin pendulum breakage device. A set of t-curves was calculated from the pendulum breakage data and a new degradation model developed to predict fines generation from handling which included drops from various heights. In the model, different degradation parameters were established which incorporated the breakage rates for different ore types when subjected to breakage energies from different drop heights. However, the model is set up so that degradation rates can be determined for any typical drop height and feed distribution. A parameter was also included to account for fines generation due to handling. The model satisfactorily predicted the fines generation from a series of tests conducted by Vince et al. Ž1987..
Acknowledgements This research was in part funded by BHP and the authors would sincerely like to thank BHP for their financial assistance. The authors would particularly like to thank Dr. Marcel Kamperman for his coordination, planning and general helpful advice. The authors would also like to thank Dr. Laurence Spencer, Department of Mechanical and
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Materials Engineering for organizing the funding, and the Centre for Microscopy and Microanalysis, for all the SEM work. Thanks must also go Allison Low for assisting with some of the microscopy.
Appendix A Conservation of Momentum m 1 u 1 q m 2 u 2 s m 1Õ 1 q m 2 Õ 2
Ž A1.
where u1 and u 2 are the input and rebound pendulum velocities before impact; m1 and m 2 are the mass of input Ž4.108 kg. and rebound Ž6.234 kg. pendulum, respectively; Õ 1 and Õ 2 are the input and rebound pendulum velocities after impact. Newton’s Law of Restitution Õ 2 y Õ 1 s ye Ž u 2yu1 .
Ž A2.
where e is the coefficient of restitution. Substituting Õ 1 in Eq. ŽA1. with u 2 s 0 gives e s Ž m1 q m 2 .rm1Ž Õ 2ru1 y 1. s 0 for inelastic collisions. Energy equation Žassuming system losses are constant.; Input energy Ž EI . s output energy Ž Eoc . q comminution energy Ž Ec .: 1r2 Ž m1 u12 q m1 u 22 . s 1r2 Ž m1Õ 12qm 2 Õ 22 . q Ec
Ž A3.
Combining Eqs. ŽA1. – Ž3., the specific comminution energy, Ecs s m 2rŽ m1 q m 2 .4Ž1 y e 2 . E I . ŽFull details including worked examples can be found in Narayanan, 1987a..
References Austin, L.G., 1971. A review. An introduction to the mathematical description of grinding as a rate process. Powder Technol. 5, 1–15. Austin, L.G., Klimpel, R.R., Luckie, P.T., 1984. The process engineering of size reduction. In: Ball Milling. New York. SMErAIME Vol. 1, 87 pp. Faberberg, B., Sandberg, N., 1973. Minerals transport. In: Proc. 2nd Int. Symp. Transport and Handling of Materials Vol. 2. Narayanan, S.S., 1985. PhD Thesis, University of Queensland. 209 pp. Narayanan, S.S., 1987a. Modelling performance of industrial ball mills using single particle breakage tests. Int. J. Miner. Process. 20, 211–228. Narayanan, S.S., 1987b. Relationship between breakage parameters and process variables in ball milling — an industrial case study. Int. J. Miner. Process. 20, 241–251. Narayanan, S.S., Whiten, W.J., 1988. Determination of comminution characteristics of ores from single particle breakage tests, and its applications to ball mill scale-up. Trans. Inst. Min. Metall., Sect. C 97, 115–124. Norgate, T.E., Tompsitt, D.F., Batterham, R.J., 1986. Computer simulation of the degradation of lump ore during transportation and handling. In: Proc., 2nd Int. Conf. on Bulk Materials Storage, Handling and Transportation, Wollongong. . Vince, A., Mahoney, M., Waters, A.G., 1987. An evaluation of the factors affecting the degradation of Mt Newman lump ore, Internal report.
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Waters, A.G., Vince, A., Lister, J.D., 1986. Measuring the strength with agglomerate. Proc. Chemeca 86 Adelaide, Australia, pp. 118–123, 19–22 August. Weedon, D.M., Napier-Munn, T.J., 1990. Sulphide deposits — their origin and processing. IMM, 137–154. Whiten, W.J., Kavetsky, A., 1984. In: Studies on Scale-Up of Ball Mills. SME Fall Meeting, Salt Lake City, UT, Oct.. . Wilson, F., 1998. An investigation into the nature of friable iron ore at Mt Whaleback, Western Australia. Honours Thesis ŽBachelor of Engineering., University of Western Australia.