Effect of fine particles on the kinetics and energetics of grinding coarse particles

International Journal of Mineral Processing, 31 ( 1991 ) 151-162

151

Elsevier Science Publishers B.V., Amsterdam

Effect of fine particles on the kinetics and energetics of grinding coarse particles D.W. F u e r s t e n a u a n d A.-Z.M. A b o u z e i d 1 Department of Materials Science and Mineral Engineering, University of California, Berkeley, CA 94720, USA (Received October 11, 1989; accepted after revision December 6, 1990)

ABSTRACT Fuerstenau, D.W. and Abouzeid, A.-Z.M., 1991. Effect of fine particles on the kinetics and energetics of grinding coarse particles. Int. J. Miner Process., 31: 151-162. To delineate the effect of material environment on grinding parameters and specific energy distribution, mixtures of coarse (10X 14 mesh) and fine (minus 100 mesh) material at different mass ratios were comminuted in a dry-batch ball mill. Data analysis showed that the breakage distribution function is environment-independent,whereas the breakage rate function of the coarse particles increases as the fraction of coarse material in the feed is decreased. Furthermore, the energy split factors indicate that the specific energy consumed by coarse material increases as the ratio of coarse-to-fine material in the mill feed decreases. If the grinding of coarse-fine particle mixtures is carried out wet, the breakage rate of the coarse particles is markedly enhanced over all feed compositions, probably because the fines are suspended in the liquid and thereby effectively removed from the grinding zone.

INTRODUCTION

Over the years there has been a fairly extensive amount of work directed towards ascertaining whether the breakage rate function of feed in a grinding mill is dependent on the mill environment. Several investigations (Gardner and Austin, 1962; Mika et al., 1967; Gupta and Kapur, 1974; Herbst and Fuerstenau, 1968, 1973, 1980) showed that when the operating conditions in a dry-batch ball mill are held constant, the breakage rate function of feed particles remains unchanged over relatively long grinding times. That is, this breakage parameter is time-independent and thereby is independent of the size consist of the material charge inside the mill. This is exemplified by the linear disappearance kinetics observed for the dry-batch milling of closely sized feed particles over quite long grinding times (Herbst and Fuerstenau, 1968; Malghan, 1976 ). Furthermore, for feeds having a distribution of particle sizes, ~Visiting research engineer from the University of Cairo, Egypt.

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D.W. FUERSTENAU AND A.-Z.M. ABOUZEID

radioactive tracers show that the intermediate sizes of the fed exhibit linear disappearance in an environment in which the amounts of both smaller and larger sizes change with time (Austin et al., 1984). More recently, Gupta ( 1986 ) has questioned the concept that the breakage rate function is independent of the size distribution of the charge in a mill. He based his objection on several sets of published grinding data which appear to exhibit nonlinear kinetics as a function of time (Mika et al., 1967; Shoji et al., 1976; Smaila, 1982; Austin et al., 1984). Gupta noted that the size distributions generated by grinding narrowly sized feeds are not representative of those obtained under industrial milling conditions, and that the size distribution range considered in numerous investigations corresponds to a very small volume of the wide size distribution normally dealt with in an industrial grinding operation. Gupta's argument was supported by a series of experiments in which he changed the proportion of the top size fraction in a feed with a specific size distribution. After studying the breakage kinetics of the top size fraction in the feed as a function of its ratio in the feed, he reported that the top size fraction in a natural size-distribution environment grinds at rates different from those observed for a narrowly sized feed charge. The objective of this present investigation has been to determine how the addition of fine particles to closely sized coarse particles of the same material affects the comminution behavior of the coarse material. For this purpose, feeds consisting of monosized ( I 0 X 14 mesh ) dolomite with various proportions of fine (minus 100 mesh) dolomite were ground and the breakage parameters were obtained from the results using the Herbst-Fuerstenau technique ( 1968 ). A similar series of experiments was also carried out with quartz. Kapur and Fuerstenau (1988) recently proposed the concept of an energy split factor to assess the distribution of grinding energy to different materials during the milling of multicomponent feed mixtures. The energy split factor provides an opportunity to assess how the presence of one material in a feed affects the energy consumption by another material in the feed, in this case how the presence of fines affects the energy consumed by the coarse particles during grinding. EXPERIMENTALTECHNIQUE Batch grinding tests were carried out in a laboratory ball mill, 25.4 cm in diameter and 29.2 cm in length, using 459 stainless steel balls of 2.54-cm diameter as the grinding media. The ball load (39.97 kg) filled the mill to 50% of its struck volume. The feed charge was held constant at 4.00 kg, which occupied 120% of the interstices between the balls at rest. During all experiments, the mill was rotated at 54 rpm (60% of the critical speed). The mill was connected to a torque-measuring system, which is attached directly to the

EFFECT OF FINE PARTICLES ON THE KINETICS OF GRINDING COARSE PARTICLES

153

mill to measure exclusively the mill torque without external mechanical losses (Yang et al., 1968). A 10 X 14-mesh size fraction of dolomite was prepared to serve as the coarse component of the mill feed in this investigation and a minus 100-mesh fraction of the same dolomite was used as the fine component. These two components, coarse (C) and fine (F), were prepared separately and mixed at different ratios to prepare the feeds for the grinding experiments. The percentage of the coarse dolomite in the mill feed was varied between 100% and 15% of the total material charge. Feed at each composition was ground for 1, 2 and 4 min. After each grinding period, the mill was stopped, the material and balls discharged, and the balls were then separated from the dolomite. The ground material was split into eight approximately equal samples using a rotating riffler sampler, and one of the samples was taken for size analysis. The screened sample was subsequently put back into the mill with the rest of the material charge for further grinding. The sieve analysis was carried out on 14, 20, 28, 35, 48, 65 and 100 Tyler mesh sieves. A similar series of experiments was conducted using mixtures of 10 X 14mesh quartz and minus 100-mesh quartz. Each of the two quartz fractions in the feed was prepared separately and mixed into feeds of different compositions. In one series of tests with dolomite, the experiments were performed by adding sufficient water to 4.00 kg of solids such that the slurries were 60% solids by weight. RESULTS AND DISCUSSION

Mathematical analysis of the batch grinding kinetics in this study was carried out using the size-discretized/time-continuous population balance model in the form: dmi(t)

d~-

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(1)

j=l

where mi(t) is the mass fraction of the material in the ith size class at time t, k~(t) is the breakage rate function for material in the ith size class at time (t), and b~jis the breakage distribution function which gives the fraction of material reporting to size class i when material in thejth size class is comminuted. Figure 1 shows the rate of disappearance of 10 × 14 mesh dolomite at different ratios of coarse ( 10× 14 mesh) and fine (minus 100 mesh) dolomite in the feed as a function of grinding time. As can be seen from these plots, the rate of grinding of the coarse fraction increases as the ratio of that fraction in the feed decreases. This is directly reflected in the magnitude of the breakage rate function of the 10 × 14 mesh material. Figure 2 shows how the initial breakage rate function changes with the fraction of coarse material in the feed. As the percentage of coarse material in the feed is decreased down to 50%, the change in the breakage rate is small, increasing only from 0.51 to about 0.6

154

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Fig. 1. The disappearance of 10 × 14 mesh dolomite when mixed with minus 100-mesh dolomite as a function of grinding time at different feed compositions.

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EFFECTOF FINE PARTICLESON THE KINETICSOF GRINDING COARSEPARTICLES

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min- 1 As a matter of fact, this is the region where all the laboratory grinding kinetics studies using single size fraction material havc bccn conducted. Because the variation in the breakage rate function is not very sensitive to variations in the feed composition in this region, investigators have generally observed environment-invariant breakage rate functions in their grinding experiments. However, when the fraction of very fine feed in the mill charge exceeds about 50%, the rate of change of the breakage rate function for the coarse material increases sharply, reaching 1.06 rain- ~when the 10 × 14 mesh material comprises only 15% of the new feed. Under thesc conditions, the breakage rate function is nearly twice that whcn 10 × 14 mesh material is ground alone. In spite of the fact that thc brcakage rate function changes with the feed environment inside the mill, the breakage mechanisms appear not to have changed. As can bc seen from the plot of the breakage distribution function of the 10 X 14 mesh material given in Fig. 3, the breakage distribution function is independent of the feed composition. These results were calculated by the Herbst-Fuerstenau method from the zero-order-production plots, using short grinding times because grinding rates deviate from linearity for long i.O

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156

P.W. FUERSTENAUAND A.-Z.M.ABOUZEID

times in the presence of fine particles in the feed. This result shows that there is self-similarity in the breakage process of coarse particles irrespective of the wide range of variations in feed composition. The amounts of fines produced by grinding the 10 × 14 mesh dolomite particles are plotted as a function of time for two different feed compositions in Fig. 4. These plots show that the rate of the production of fines is enhanced by increasing the fraction of fine particles in the feed. This is a direct effect of changes in the breakage rate of the top size with the feed composition, as presented in the foregoing paragraphs. After the experiments reported here had been completed, Celic ( 1988 ) published a paper in which he similarly demonstrated that the addition of fine quartz enhances the kinetics of grinding coarse coal. When excess minus 100-mesh fines are present in the dry tumbling mill together with the coarse 10 × 14 mesh material, the fines appear to offer little resistance to the falling balls at the toe of the mill charge. This situation suggests that the energy associated with the balls entering the grinding zone is then mostly consumed in breaking the coarse material present in the comminution zone. The frequency at which balls impact the grinding zone is deter-

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Fig. 4. The production of fines as a function of the grinding time for two different feed compositions: 100% coarse and 25% coarse dolomite material ( 10 × 14 mesh) mixed with minus 100mesh dolomite.

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Fig. 7. The rate of production of fines as a function of specific energy consumed by the coarse fraction for two different feed compositions: 100% coarse and 25% coarse dolomite with 75% fine dolomite. m i n e d by mill speed, ball load, and ball size. Fixing these parameters means that the energy transferred to the grinding zone as a result o f the m o v e m e n t of the balls is independent of the material environment in the mill. The coarse particles may tend to segregate or float on the mass of fine particles as the feed charge enters the toe o f the mill. Alternatively, coarse particles m a y tend to grind as if the fine particles were absent. Following this argument, we can conclude that the fewer coarser particles present in the grinding zone (the toe of the mill) under such conditions, the more energy per unit mass they will receive. To test this, the energy split between coarse and fine material in the mill was calculated. The energy split factor ( K a p u r and Fuerstenau, 1988) was used to calculate the specific energy consumption by the coarse material at various feed compositions. According to Kapur and Fuerstenau: Ecm (t) = ScEca (/)

(2)

where Ecm(t) is the specific energy consumption by the coarse fraction when ground as an admixture for time t, Eca (t) is the specific energy consumed by the coarse fraction when ground alone, Sc is specific energy split factor for the

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coarse component when it is ground in the mixture. The energy split factor for the coarse size fraction was evaluated by means of the Kapur and Fuerstenau expression for Sc in terms of feed disappearance rates: S¢=

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where mcm and me, are the mass fractions of the coarse feed size initially or at time t. From this, the proportion of the grinding energy consumed by the I0 ~< 14 mesh material in the feed could be calculated. As can be seen from the results plotted in Fig. 5, the specific energy consumed by the coarse dolomite (as calculated from eq. 2 ) increases as the initial fraction of coarse material in the feed decreases. This is basically the reason why the rate of breakage increases as the amount of coarse material in the feed decreases. However, under these circumstances, the breakage of the coarse material as well as the rate of fines production are still normalizable with respect to the specific energy consumed by the coarse fraction, as demonstrated by the plots given in Figs. 6 and 7. To confirm these findings an additional series of dry-batch grinding tests was carried out using a very hard mineral, namely quartz. When 10 × 14-mesh quartz was ground with minus 100-mesh quartz fines, the rate of breakage of the l 0)< 14 mesh material was found to be linear for almost all feed compo-

160

D.W. FUERSTENAUAND A.-Z.M. ABOUZEID I

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sitions tested up to 4 min of grinding time. The trend of the breakage rate function for quartz in the presence of added fines was also found to be similar to that of dolomite, namely that it increases as the amount of the fine material in the feed is increased (Fig. 8 ). The rate of change of the breakage rate, here also, is not large until the fraction of fine particles in the feed exceeds 50%. It reaches 0.6 min-1 at 15% coarse material in the feed as compared with 0.34 m i n - ~ when 10 X 14 mesh quartz is ground alone. This indicates that the increase in the breakage rate function is a p h e n o m e n o n that applies to both hard and soft materials. To test the concept that the dry coarse particles tend to grind as if the fines were removed from the grinding zone, one series of experiments was carried out wet at 60% solids, with all other conditions being the same. Wet grinding is generally considered to be more efficient than dry grinding because the fine particles are suspended in the liquid and are effectively removed from the grinding zone. The breakage rate functions for 10 × 14 mesh dolomite that was wet-ground in coarse-fine mixtures were determined from the disappearance plots in the usual manner, and the results are plotted in Fig. 9. Comparing the behavior of wet grinding with dry grinding, Fig. 9 shows that the breakage rate of the coarse material is accelerated over all compositions tested.

EFFECTOF FINEPARTICLESON THE KINETICSOF GRINDINGCOARSEPARTICLES

161

In the absence of fines, the breakage rate function of 10 X 14 mesh dolomite is 0.66 min-~ when ground wet in comparison to 0.51 min-1 when ground dry. This is in keeping with the usual observation of increased grindability in wet systems. The liquid apparently suspends all of the minus 100-mesh material, thereby enhancing the grinding rate in the experiments conducted at all additions of fine material to the feed. CONCLUSIONS

The results presented in this paper show that the addition of fine particles can markedly enhance the grinding kinetics of coarse particles in the feed. The feed material investigated in this work was a mixture of coarse ( 10 X 14 mesh ) and fine (minus 100 mesh ) particles of the same material at different mass ratios. The minerals used were dolomite and quartz. Measurement of the kinetics and energetics of comminution of the coarse fraction showed that the breakage rate function of 10 X 14 mesh material increases as the amount of minus 100-mesh material in the feed is increased. The breakage distribution function is not affected by changes in the material environment in the mill, which is an indication of the self-similarity of the breakage process inside the mill. In other words, the grinding path of a mineral is environmentinvariant. The breakage rate of the coarse size fraction as well as the rate of production of fines is normalizable with respect to the specific energy consumption of the coarse size fraction at all feed mixture compositions. When the coarse-fine particle mixtures are ground wet, the addition of fines enhances the grinding rate over all compositions, probably because the fines are suspended and removed from the grinding zone. ACKNOWLEDGMENT

The authors express appreciation to the United States Bureau of Mines for support of this research under the Generic Mineral Technology Center Program in Comminution (Grant No. G 1125149 ).

REFERENCES Austin, L.G., Klimpel, R.R. and Luckie, P.T., 1984. Process Engineering of Size Reduction: Ball Milling. SME/AIME, New York, NY. Celic, M.S., 1988. Acceleration of breakage rates of anthracite during grinding in a bull mill. Powder Technol., 54: 227-233. Gardner, R.P. and Austin, L.G., 1962. Proceedings First European Comminution Symposium, pp. 217-248. Gupta, V.K. and Kapur, P.C., 1974. Empirical correlations for the effects of particulate rr~ass

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and ball size on the selection parameters in discretized batch grinding equation. Powder Technol., 10: 217. Gupta, V.K., 1986. An appraisal of the linear first order kinetic model based ball mill design correlations. First World Particle Technology Part II Comminution, 6th European Symposium, Nuremberg, pp. 605-620. Herbst, J.A. and Fuerstenau, D.W., 1968. The zero order production of fines in comminution and its implications in simulation. Trans. AIME, 241: 538-549. Herbst, J.A. and Fuerstenau, D.W., 1973. Mathematical simulation of dry ball milling usingg specific power information. Trans. AIME, 254: 343-348. Herbst, J.A. and Fuerstenau, D.W., 1980. Scale-up procedure for continuous grinding mill design using population balance modules. Int. J. Miner. Process., 7:1-31. Kapur, P.C. and Fuerstenau, D.W., 1988. Energy split in multicomponent grinding. Int. J. Miner. Process., 24: 1-18. Malghan, S.G., 1976. The scale-up of ball mills using population balance. D. Eng. Dissertation, University of California, Berkeley, CA. Mika, T.S., Berlioz, L.M. and Fuerstenau, D.W., 1967. DECHEMA Monogr., 57: 205-240. Shoji, K., Lohrasb, S. and Austin, L.G., 1976. The effect of ball size on mill performance. Powder Technol., 14(1 ): 71-79. Smaila, F.M., 1982. M.S. Dissertation, Pennsylvania State Univ., University Park, PA. Yang, D.C., Mempel, G. and Fuerstenau, D.W., 1968. A laboratory mill for batch grinding experimentation. Trans. AIME, 238: 273-275.