Using the discrete element method to analyze the breakage rate in a centrifugal/vibration mill

The grinding characteristics of a centrifugal mill with varying G/D (gyration/mill diameter) ratios were investigated using the population balance model and the discrete element method (DEM). A series of grinding tests were conducted on illite samples using a centrifugal mill under various conditions, and the breakage parameters were calculated. Three-dimensional DEM simulations were also conducted. It was found that the specific rates of breakage estimated for various grinding conditions correlated well with the impact energy calculated from DEM simulations. This information was used to develop scale-up functions for the centrifugal mill in terms of G/D ratio, rotational speed, mill diameter, grinding media diameter, and ball loading.     

Effect of media size in stirred ball mill grinding of coal

As a prerequisite to producing super-clean coal with any physical coal-cleaning process, such as microbubble flotation, the feed coal must be micronized to liberate finely disseminated mineral matter. The stirred ball mill is regarded as one of the most efficient devices for micronizing coal. Using a 13.4 cm batch mill, the optimum operating conditions have been determined in terms of media size, feed size and media type. The rate of breakage determined with monosized feeds are compared on the basis of specific energy consumption. It has been found that a 20:1 ball size/particle size ratio gives optimum grinding conditions.     

A comparison of dry and wet grinding of a quartzite ground in a small batch ball mill

Classical grinding models involve the selection function (S), which gives the rates of breakage of particles of each screen size fraction, and the breakage function (B), which describes the instantaneous size distributions of fragments produced when the particles of each fraction are broken. In order to investigate the differences between dry and wet grinding as far as the selection and breakage functions are concerned, batch grinding experiments were performed on both dry and wet bases, on the same material, a quartzite, in a small ball mill under similar experimental conditions.On a dry basis, the rates of breakage were found to be time invariant and independent of the size environment in the mill. It is logical to postulate a similar behavior for the breakage function. On a wet basis (65% solids), an increase of the rates of breakage was observed as grinding proceeds. This behavior is essentially due to the variation of the size environment within the mill. This increase in breakage rates was, however, less and less important as the particle size decreased and was not observed for the smallest particles tested. These points were confirmed by considering the disappearance kinetics of samples of different screen size fractions of quartzite injected in the mill during the batch grinding of a limestone. Moreover, it is not impossible that the breakage function could also vary with grinding time, giving rise to finer instantaneous size distributions of fragments as the size environment in the mill becomes finer. As an overall result, wet grinding has appeared more selective than dry grinding for coarse material, while it did not produce more schlamms.     

Investigations of autogenous and semi-autogenous grinding in tumbling mills

A model based on the specific rates of breakage of each size in a mill as affected by balls and large lumps has been developed. Three mechanisms of breakage are recognized: ‘normal’ fracture of smaller sizes by balls and larger pebbles, ‘chipping’ of raw feed to give rounded pebbles and ‘abrasion’ from the surfaces of pebbles. A tracing technique was developed to distinguish these contributions to autogenous breakage in batch grinding tests. It was found that the accumulation of finer material strongly cushions the impact between pebbles and pebbles and pebbles and balls. Empirical relations were developed to describe this cushioning effect. It was also found that chipping breakage is first order for short times of grinding. The mathematical model lumps fracture and chipping in a single contribution and considers the material as if it were a mixture of fast- and slow-breaking components. Breakage rates and primary breakage distributions measured on an ore in batch tests were used to predict the performance of a 1.8-m diameter pilot-scale mill, and predictions compared to the pilot-scale data on the same ore.     

Calibration of the perfect mixing model to a dry grinding mill

The perfect mixing model is calibrated to a dry grinding mill used to prepare iron powder for powder metallurgy applications. The calibration procedure was modified to account for possible error on both the mill feed and discharge size distributions, while the usual calibration criterion is based on the estimation error of the mill product size distribution. The calibration criterion was also modified to allow the simultaneous processing of several sampling campaigns to estimate common appearance, breakage and discharge rate functions. Calibration results are analysed in terms of reproducibility of model estimates and model capacity to predict the mill powder content as a function of the mill throughput and power drawn.     

Crushing characteristics

A method of measuring the basic characteristics of comminution was developed. These characteristics are expressed by the major comminution functions: crushing probability function, energy function and breakage function. The crushing probability function is the strength distribution of particles of a given size. The energy function is the strength of the particles as a function of their sizes. And finally, the breakage function is the size distribution of the crushed material. The functions are defined mathematically. Several natural minerals were tested by drop tests in order to determine their individual comminution functions. From the tests, several crushing properties of the particulate materials can be derived. The comminution functions given in this paper would be the basic elements in developing mathematical models for various crushing and grinding processes.     

Grindability of lateritic nickel ores in Cuba

The purpose of this paper is to outline the findings of the evaluation of the grinding process of limonite and serpentine minerals present in oxidized Ni-Co ores, which are contained in the lateritic soils of the north-eastern region of Cuba.The grindability study supporting this paper was based on the execution of various tests aiming to determine the influence of mineral content in breakage and selection functions, and in the Bond work index. The results obtained shows that grinding behaviour of each mineral component does not depend on the mineral content in the sample.     

Application of grinding kinetics analysis of inorganic powders by a stirred ball mill

The need for ultra fine particles has been increasing in the preparation field of raw powders such as fine ceramics and high functional products. A series of wet grinding experiments were carried out on inorganic powders such as calcite, pyrophyllite and talc by a stirred ball mill. The grinding rate constant K’ in the equation of grinding kinetics was examined based on the grinding kinetics analysis as the same type of function of a previous paper on a vertical type planetary ball mill. The experimental particle size distribution of the ground products was obtained in various grinding conditions. The grinding rate constants K and K’ were expressed by empirical equation involving experimental conditions by a stirred ball mill. The empirical equation on the grinding rate constant was expressed in terms of a function involving the ball diameter of grinding balls, the median diameter of feed material, and Bond’s work index of material, in the experimental conditions. The values of empirical constants C1 and C₂ were 21.13 and 0.0109 on K, while C₁ and C₂ were 120.99 and 0.0192 on K′, respectively. And the particle size distribution of ground products of each test material for a given grinding time was found to be expressing the selection function (the specific rate of breakage) which was obtained from the grinding kinetics analysis. In this study, the grinding rate change on calcite and pyrophyllite was similar at the same experimental operation condition. However, in the case of talc, it was observed that the grinding rate was not increased compared with other samples.     

Inferring the distribution of iron oxidation species on mineral surfaces during grinding of base metal sulphides

Electrochemistry plays an important role in the flotation of base metal sulphide minerals. During grinding a galvanic interaction occurs between minerals and grinding media and controls the iron contamination on mineral surfaces, which depresses mineral flotation significantly. In this study, the galvanic interaction was quantified by measuring the iron oxidation species originated from grinding media by ethylene diamine-tetra acid (EDTA) extraction in single mineral and mixed mineral systems. It was found that the extent of galvanic interaction between minerals and grinding media was intimately associated with the electrochemical reactivity of minerals. The nobler the mineral, the stronger the galvanic interaction with grinding media, and the higher the amount of iron oxidation species from grinding media. For both galena and chalcopyrite a linear relationship was observed between the amount of iron oxidation species and flotation recovery in single mineral systems. This relationship was able to predict the iron oxidation species on galena and chalcopyrite surfaces when they were mixed with pyrite separately. The distribution of iron oxidation species onto the two minerals in the mixture changed with the ratio of the mineral surface areas and was correlated with mineral flotation recovery. The major cathodic mineral in the mixture was dictated by the combination of mineral surface area and reactivity and drew iron oxidation species from the grinding media.     

Energy efficiency of cement finish grinding in a dry batch ball mill

Dry grinding experiments on cement clinker were carried out using a laboratory batch ball mill equipped with torque measurement. The specific energy was found to be dependent on operating parameters and clinker environment. Additional compounds such as gypsum and pozzolanic tuff improve energy efficiency. The optimal parameters allowing maximising the energy efficiency factor were determined. Energy efficiency factors were obtained both on the crude material (size minus 2.8 mm) and on a sieved fraction (1-0.71 mm). They demonstrate that a low initial rate of breakage implies higher energy efficiency. On the contrary, conditions ensuring an initial maximal rate of breakage lead to an increase of the energy consumption.     

Continuous grinding in a small wet ball mill. Part IV. A study of the influence of grinding media load and density

TXX influence of changes in grinding media load and density on the grinding behaviour of trace quantities of quartz within an environment of calcite in a small continuous wet ball mill have been studied using (a) ball loads ranging from 45% to 100% of the standard load of 1-in. balls, (b) a standard load of 1-in. pebbles and (c) standard loads of equicylinders with specific gravities ranging from 2.82 to 9.49. A mill overload condition (125% ball load) has also been studied using a feed comprising 5% by weight of full-size-range quartz and 95% standard calcite.The results show that variations in breakage behaviour were best followed by a comparison of the adjusted breakage rate constants (k′) for individual sizes corresponding to a standard hold-up-weight. The changes in k′ with ball load could be explained in terms of changes in number of impacts per unit time and in the environmental size distribution. A reduction in the density of the grinding media caused a disproportionate decrease in k′ for the coarse sizes compared with the fine sizes, and breakage rates tended to zero for all sizes as the density of the medium approached that of the pulp.Whilst under some of the test conditions the flow of tracer solids behaved anomalously, under most conditions there was an approximately linear relationship between average residence time and total weight of media charged to the mill.Media density per se had no effect on breakage function, but there was a distinct change due to change in media shape.     

Continuous grinding in a small wet rod mill Part I. Comparison with a small ball mill

Tests have been done with a small continuous wet rod mill in order to characterise its dynamic behaviour in terms of the type of model previously developed for a small continuous wet ball mill. The three functions studied were the distribution of residence time, the breakage function and the breakage rate as a function of size.Distribution of residence time data showed that flow through the rod mill was similar to that through the ball mill and the contents of the mill were very well mixed. The breakage function results showed that any breakage event statistically produced less fines than in a ball mill. Breakage rate data showed that the coarsest sizes were broken more selectively, thus resulting in less fines in the product than would have been obtained if the breakage had been a result of ball action. Nevertheless it was shown that, overall, breakage in the rod mill could be described in similar terms to breakage in the ball mill, and the models were very similar.     

Influence of process parameters on breakage kinetics and grinding limit at the nanoscale

In long‐term milling experiments, in a stirred media mill, a grinding limit where no further particle breakage occurs was identified. During mechanical stressing of the particles, defects are generated in the crystalline lattice, which allows real fracture of nanoparticles. Below a critical size, defects cannot be stored or generated in the crystallites and the overall limit of grinding is reached. This limit is strongly influenced by material properties and hardly affected by most of the process conditions. However, the breakage kinetics strongly depend on the process parameters and suspension conditions as long as the grinding limit is not reached. Based on these findings, two mechanisms of nanoparticle breakage are proposed. Proper choice of process parameters saves not only up to 90% of the energy input to reach the grinding limit but also leads to a higher product quality in terms of crystallinity and less milling bead wear. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

A study on the specific rate of breakage of cement materials in a laboratory ball mill

The specific rate of breakage (S_i) in the widely accepted first-order expression of grinding rate is one of the important factors required to evaluate a grinding process, particularly for the initial grinding stage in various mill types.In this study, the effects of ball diameter and feed size on the specific rate of breakage were investigated on limestone, trass and clinker samples at batch grinding conditions based on a kinetic model. Eight different monosize fractions were prepared between 1.7 and 0.106 mm, using a √2 sieve series. The specific rates of breakage (S_i) were determined from the size distributions at different grinding times, and the specific rates of breakage were compared for three different ball diameters (41, 25.4 and 9.5 mm).The results indicated that the variation of the specific rate of breakage with feed size of cement materials could be expressed. For the specific rate of breakage of each material, empirical equations were developed to express it as a function of feed size and ball diameter.     

Dry grinding kinetics of binary mixtures of ceramic raw materials by Bond milling

The kinetics of batch dry grinding of binary mixtures of ceramic raw materials, namely quartz–kaolin, quartz–potassium feldspar and kaolin–potassium feldspar, from the feed sizes of −3.350 + 2.360, −2.000 + 1.400, −0.850 + 0.600, −0.500 + 0.355 and −0.300 + 0.212 mm have been determined using a Bond mill with a mixture of ball sizes of 38.10, 31.75, 25.40, 19.05 and 12.70 mm diameter and total mass of 22.648 kg. The Bond mill used was a size of 30.5 cm diameter, 30.5 cm length, with a total volume of 22,272 cm³. The fractional ball filling was 22% of mill volume and the mill speed was 70 rpm. The breakage parameters were obtained for those mineral mixtures to predict the product size distributions. As the feed sized given above, which were ground in the mill, increase, the specific rate of breakage (S_i) values also increase, which means faster breakage with higher S_i value occurs in the order of quartz–kaolin, quartz–potassium feldspar and kaolin–potassium feldspar mixtures when comparing the characteristic values (slope of S_i versus size relationship with higher value). The cumulative breakage distribution function (B_i,j) values obtained for these mineral mixtures were slightly different in terms of the fineness factor, γ. This means that quartz–potassium feldspar mixture produced less fines with higher γ value, while kaolin–potassium feldspar gave more fines with lower γ value. The simulations of the product size distribution for these mixing were very close to the experimental data. Finally, slowing down effect, treated with false time concept, started earlier than the expected for these binary mixtures. There were some correlations found between the simulated time (θ) and experimental time (t).     

Mathematical modeling of fluid energy milling based on a stochastic approach

In this study, the stochastic method is used to simulate the grinding process in a fluid energy mill: the product particle size distribution is regarded as the result of repeating elementary breakage events, i.e. M_p=M₀[T_m]^m, where M₀ is the row vector of the size distribution of feed particles, M_p is the row vector of the size distribution of product particles, m is the number of elementary steps, and T_m is the matrix of transition probabilities representing the elementary breakage event. The matrix of transition probabilities can be related to the breakage rate function and the breakage distribution function of the elementary breakage event. A specially designed apparatus, named single-event fluid mill, was employed to experimentally estimate those two breakage functions of the elementary breakage event with a breakage rate correction factor θ. The classification effect is taken into consideration by defining a cutting size under which the particle will not break any more. Using this strategy, the product particle size distribution is calculated. The good consistency between the simulation and the experimental results indicates that this model is valid to quantitatively estimate the grinding performance of the fluid energy mill.     

The influence of grinding mechanism on the liberation characteristics of clinker minerals

This study deals with the characterization of narrowly sized fractions of clinker ground by ball mill and high-pressure grinding rolls. Chemical, physical and mineralogical characterizations were made by using XRF, laser sizing, Blaine, BET, SEM, and image analysis techniques. The emphasis was given to the preferential liberation of the constituent clinker phases. High-pressure grinding rolls gave higher degrees of liberation of mineral phases arising from the intergranular breakage along the grain boundaries compared to ball mill grinding. This is expected to influence the downstream service properties of cement.     

氧化硼研磨的实验与理论研究

用行星式球磨机对13个不同尺寸区间氧化硼的研磨过程进行了实验与理论研究. 实验测量了13个不同尺寸区间氧化硼的粉碎速率常数及其分布系数,通过对测量结果的分析得到了不同尺寸氧化硼的粉碎速率函数及其分布系数函数,进而建立了粉碎过程质量分数的积分微分方程. 用四阶龙格-库塔法对氧化硼研磨过程的质量分数积分微分方程进行了数值计算,并与实验结果进行了比较. 计算与比较结果表明,氧化硼的研磨过程具有时变特征.     

Batch grinding kinetics in the presence of two active zones

It is shown that the presence of two active zones in a grinding mill leads to apparent non-first-order breakage of the top feed size in batch grinding. The equations to describe the kinetics of the breakage of the top size and of the total size distribution are obtained, and an analytical solution is given. Parametric analysis shows the influences of the relative magnitudes of the two active zones, the rates of breakage and the rate of mass transfer between the two active zones on the mill product. The concepts may be applicable to any type of mill where two active zones can exist.     

Laboratory studies of the grinding and rheology of coal—water slurries

The laboratory ball mill grinding of coal—water slurries is described for three coals. Emphasis is placed on the measurement of specific rates of breakage for various operating conditions. Corresponding rheological information is also presented based on data collected using a rotational viscometer. A rheological explanation of the influence of various slurry fluidity conditions on the specific rates of breakage is presented. This rheological approach has proved useful in both the identification of suitable chemicals for increasing breakage rates in coal—mineral slurry grinding and in the plant scale implementation of dense slurry grinding systems.