Primary Breakage Distribution Research Articles

Application of artificial neural network method to predict the breakage properties of PGE bearing chromite ore

In the present investigation, systematic grinding experiments were conducted in a laboratory ball mill to determine the breakage properties of low-grade PGE bearing chromite ore. The population balance modeling technique was used to study the breakage parameters such as primary breakage distribution (Bi, j) and the specific rates of breakage (Si). The breakage and selection function values were determined for six feed sizes. The results stated that the breakage follows the first-order grinding kinetics for all the feed sizes. It was observed that the coarser feed sizes exhibit higher selection function values than the finer feed size. Further, an artificial neural network was used to predict breakage characteristics of low-grade PGE bearing chromite ore. The predicted results obtained from the neural network modeling were close to the experimental results with a correlation of determination R2 = 0.99 for both product size and selection function.

Grinding kinetics of coal in wet ball-milling using the Taguchi method

ABSTRACT In this study, the Taguchi method was used to study the influence of feed size, ball diameter, pulp density and grinding time on the grinding performance of wet ball-milling. According to P-values, the final ranking of the significance of factors in grinding efficiency was as follows: pulp density > feed size > grinding time > ball diameter. Results of signal-to-noise ratio (S/N ratio) and analysis of variance (ANOVA) indicated that the minimum mass fraction remaining in the top size interval was produced for the −3.0 + 1.0 mm feed size, 75 wt. % pulp density, 50 min grinding time and 35 mm balls. Grinding kinetics of −3.0 + 1.0 mm coal in wet ball-milling were investigated using the breakage rate and primary breakage distribution functions. The deceleration effect for the wet grinding of this coal sample was due to the relatively stronger material (quartz), which had a slower breakage rate compared to the weaker material (organic matter). Moreover, the Mohs’ hardness of the material had a significant influence on the parameters of the primary breakage distribution function according to experimental results and literature data. Finally, the morphology and shape of ground particles were analyzed to determine the breakage characteristics.

Breakage Characteristics of Heat-Treated Limestone Determined via Kinetic Modeling

In recent years, heat treatment has attracted attention as a means to improve the color sorting technology with the aim of improving the quality of low-grade limestone. The crucial stage in this technique is to evaluate the breakage characteristics of the sample materials after color sorting. In this study, the breakage characteristics of samples showing color differences after heat treatment and of the original raw material were investigated using a laboratory ball mill. The grinding was characterized using the population balance model. Specific rates of breakage and the primary breakage distribution were experimentally determined by first-order kinetic plots and the BII method. The breakage parameters were also back-calculated by employing a simplex method. Grinding of the three materials indicated first-order kinetics, and the experimental results were well described by the model with parameters obtained by back-calculating.

Grinding of Class-F fly ash using planetary ball mill: A simulation study to determine the breakage kinetics by direct- and back-calculation method

Dry grinding of Class F fly ash (FA) was carried out using the planetary ball mill to obtain mechanically activated nanostructured FA particles. The resulting FA powders were characterized for (i) particle size: dynamic light scattering and sieve analyzer, (ii) specific surface area: BET-analyzer, (iii) structure: X-ray diffractometer, (iv) chemical composition: field emission scanning electron microscope with the electron diffraction spectrum analyzer and x-ray fluorescence analyzer, and (v) aggregation and shape of the particles: Fourier-transformed infra-red spectrometer and scanning electron microscope. A significant enhancement in surface and bulk properties of milled FA was obtained over fresh FA. The breakage parameters (i.e., the specific rate of breakage and primary breakage distribution function) of FA were determined by the direct experimental method using the narrowly-sized fraction of FA over the short grinding period under identical milling environment. A relatively simple back-calculation method was employed to determine above breakage parameters of FA also using time-variant milling data that were obtained after the grinding of distributed-sized FA feed. The parameters obtained from the direct experimental and back-calculation method yielded comparative milling simulation results with the acceptable accuracy.

Simulation and optimization of a two-stage ball mill grinding circuit of molybdenum ore

A two-stage ball milling circuit for the grinding of molybdenum ore was investigated based upon the grinding kinetic model. To this end, batch grinding tests at the laboratory-scale were conducted to obtain the specific rate of breakage and the primary breakage distribution in wet and dry environments. The test results were then scaled-up to the conditions of a full-scale ball milling circuit for grinding molybdenum ores. A two-stage ball milling circuit algebra was employed to predict the capacity, circulation ratio, and size distributions. Comparison of the simulated results and the observed values showed that the model represents accurately the actual milling process in the plant. Simulation results indicated that the classification in the milling process was operated under non-optimal conditions, and that an increase in the mill output of more than 47% was possible simply by modifying the cut size of the classifier.

The effects of grinding media shapes on the grinding kinetics of cement clinker in ball mill

To investigate the effects of grinding media shapes on the grinding kinetics of ball mill cement clinker, the grinding effects with ϕ20 mm balls and ϕ20 × 20 mm cylinders on six different size fractions, i.e. − 4.75 + 4.00 mm, − 4.00 + 3.35 mm, − 3.35 + 2.36 mm, − 2.36 + 2.00 mm, − 2.00 + 1.70 mm and − 1.70 + 1.18 mm of cement clinkers, were studied in a laboratory scale ball mill. The specific rate of breakage and the primary breakage distribution function were compared for the balls and cylinders. Result shows that cement clinker obeys first-order grinding kinetics in the case of both balls and cylinders. The specific rate of breakage of cylinders is higher than that of balls. The primary breakage distribution parameters are dependent on the initial feed size. The φ value of cylinders is higher than that of balls.

The investigation of grinding kinetics of power plant solid fossil fuel in ball mill

The kinetics of batch dry grinding of power plant solid fossil fuel, from the feeds of sieve sizes −3.350 + 2.360, −2.360 + 1.700, −1.180 + 0.850, −0.425 + 0.300 and −0.212 + 0.150 mm have been determined using a Bond ball mill with a mixture of five ball sizes. The mill used has a diameter of 30.5 cm, length of 30.5 cm, providing a total mill volume of 22.272 cm 3 with a total mass of 20.125 g steel ball mixtures of 38.10, 31.75, 25.40, 19.05 and 12.70 mm diameters. The balls occupied 22% of mill volume. The speed of rotation of the mill was chosen as 70 rpm. The specific rates of breakage ( S i ) and primary breakage distribution ( B i , j ) values, called as grinding breakage parameters, were determined for those feed size fractions to simulate the product size distributions for comparison to the experimentally obtained data. As the feed sizes increase, the S i values also increase, that is, faster breakage values from higher to lower values were in the order of solid fossil fuel by comparing to its α values. Breakage distribution functions were found non-normalizable. It is dependent upon the initial feed particle sizes. In other words, the simulations of product size distributions for fossil fuels were in good agreement with the experimental data using a ball mill simulation program, called JKSimMet.

Kinetics of fine wet grinding of zeolite in a steel ball mill in comparison to dry grinding

Batch wet grinding of zeolite was studied with emphasis on a kinetic study in a laboratory size steel ball mill of 200 mm diameter. The breakage parameters were determined by using the single sized feed fractions of − 850 + 600 µm, − 600 + 425 µm and − 425 + 300 µm for the zeolite samples. The S i (specific rate of breakage) and B i , j (primary breakage distribution) values were obtained for those feed size fractions in order to predict the product size distributions by simulation for comparison to the experimental data. The specific rates of breakage values for wet grinding in the first-order breakage region were higher than the dry values reported previously by a factor 1.7 at the same experimental conditions, but the primary breakage distribution ( B i , j ) values were approximately the same. The simulations of the product size distributions of zeolite were in good agreement with the experimental data using a standard ball mill simulation program. The wet grinding of zeolite was subjected to slowing-down effect in the mill at 2 min of grinding, corresponding to an 80% passing size of about 400 µm. On the other hand, the slowing down effect in the dry grinding of zeolite was also seen at 4 min of grinding. In addition, effects of some operational parameters on dry and wet grinding of zeolite were determined by simulation using the breakage parameters obtained experimentally.

Effect of Grinding Media Shapes on Breakage Parameters

AbstractIn the present study, the effect of grinding media shape on breakage parameters was investigated. Balls and cylpebs were used as the grinding media. It was observed that the grinding of quartz obeyed first‐order breakage kinetics in the case of balls and cylpebs. Higher breakage rates were noted with cylpebs than with balls. Furthermore, it was found that the primary breakage distribution function is dependent on the feed size (i.e., non‐normalizable), but independent of the grinding media shape. The effect of grinding time on the product size distribution has also been investigated. Following four and ten minute grindings, cylpebs produced a relatively finer product compared to balls.

Dry grinding kinetics of colemanite

The specific rates of breakage ( S i ) and primary breakage distribution ( B i,j ) values of colemanite were determined and compared to quartz ground under the same grinding conditions. It was found that colemanite follows a first-order breakage behavior for all feed sizes and is broken faster than quartz. Breakage function of colemanite is non-normalizable similar to quartz. [Display omitted]

Simulation of wet ball milling of iron ore at Carajas, Brazil

Laboratory-scale batch grinding tests were performed on 2 sieve size fractions of the almost pure hematite mined at the Carajas mine of CVRD Brasil. Good first-order kinetics of grinding were obtained, both for dry grinding and for grinding with water, using the Bond test levels of ball load and powder load. However, the primary breakage distribution functions were not dimensionally normalized, as smaller particles produced proportionally more fines on primary breakage, possibly due to internal porosity of the ore. The test results were scaled to the conditions of a pilot-scale mill in normal closed circuit, and a ball mill simulator was used to predict the capacity, circulating load and size distributions, employing the size selectivity values calculated from the balance around the hydrocyclone. The simulation results were in reasonable agreement with the observed values. The technique was then extended to predict the behavior of a full-scale mill at a capacity of 308 metric tons/h and a circulating load of nearly 600%. Agreement between simulated results and plant test results was reasonable except that the simulator predicted a product (overflow) size distribution with a higher sharpness index than observed. The reason for this discrepancy is not known.

Grinding of ceramic raw materials by a standard Bond mill: quartz, kaolin and K-feldspar

The kinetics of batch dry grinding of ceramic raw materials, which are quartz, kaolin and K-feldspar, from the feeds of sieve sizes −3·350+2·360, −2·360+1·400, −1·400+0·850, −0·850+0·600, −0·500+0·425 and −0·300+0·212 mm have been determined using a Bond mill with a mixture of five ball sizes. The mill used was a size of 30·5 cm diameter, 30·5 cm length, providing a total mill volume of 22 272 cm3 with a total mass of 22 648 g steel ball mixtures of 38·10, 31·75, 25·40, 19·05 and 12·70 mm diameters, occupying 22% of mill volume and with a speed of rotation of 70 rpm. The specific rates of breakage (Si) and primary breakage distribution (Bi,j) values, called grinding breakage parameters, were determined for those feed size fractions to predict the product size distributions by simulation for comparison to the experimentally obtained data. As the feed sizes increase, the Si values also increase, that is, faster breakage values from higher to lower values were in the order of quartz, K-feldspar and kaolin by comparison with their α values. The Bi,j values obtained for these minerals were different in terms of characteristic fineness factor, γ. Thus, kaolin produced more fines, while K-feldspar and quartz produced less fines in the mill. In other words, the simulations of product size distributions for these minerals were in good agreement with the experimental data using a ball mill simulation program, called PSUSIM. However, the slowing down effect in the mill started earlier than expected for the minerals studied, unlike the laboratory size ball mill used extensively in our studies. Nevertheless, there exist linear relationships between the simulated time (θ) and experimental time (t) for these minerals.

Effect of Medium Viscosity on Breakage Parameters of Quartz in a Laboratory Ball-Mill

The role and effect of liquid medium viscosity on breakage parameters (S and B values) of the batch grinding kinetic model was investigated by grinding a single feed fraction of quartz (20 × 30 mesh) in a batch ball-mill at fixed mill loadings and at 45 vol % solid concentration, using glycerol−water mixtures of different proportions. The primary breakage distributions (B values) were normalized and separated into three different groups for grinding in media viscosities of 0.001(water), 0.002−0.03, and 0.08−0.16 Pa·s, respectively, with higher viscosity range giving proportionally finer products. The disappearance grinding kinetics of the top size showed that the specific breakage rates (S values) depended both on the viscosity of the liquid medium and on the extent of grinding. The specific breakage rates of the top size increased with the fineness of grinding while the breakage of the smaller sizes proceeded approximately in a first-order manner as characterized by a characteristic breakage rate constant. The acceleration of the top-size breakage rates as grinding proceeded was represented by a parameter called the acceleration factor, which correlated reasonably well with the changing slurry effective viscosity. Alternatively, the acceleration factor can be presented in the form of a single generalized first-order plot for grinding at different medium viscosities. The first-order breakage rate constant decreased with increasing medium viscosity over the range from 0.001 to 0.16 Pa·s but not linearly. The proportional variation of net mill power did not match exactly with that of the breakage rate constant on increasing medium viscosity. On the basis of the analysis of grinding results, three grinding regimes were identified relative to the change in medium viscosity but their existence was not confirmed experimentally.

Fine Dry Grinding of Zeolite in a Laboratory Ball Mill

AbstractThis paper presents the importance and usage of natural zeolites, which was recently recognized in the industry. Therefore, the grinding properties of natural zeolite were studied with the emphasis on a kinetic study in a ball mill. The experimental mill employed was laboratory sized, 200 mm diameter, 191 mm length, providing a total mill volume of 6000 cm3, with a total mass of 5.62 kg of steel balls of 25 mm diameter with a charge of 20% of the mill volume and with a rotation speed of 76 rpm. The breakage parameters were determined by using single sized feed fractions of −850+600 μm, −600+425 μm, and −425+300 μm for the zeolite samples. The Si (specific rate of breakage) and Bi, j (primary breakage distribution) values were obtained for those feed size fractions in order to predict the product size distributions by simulation for comparison to the experimental data. From the experimental results, Si values increased as the feed sizes became coarser, i.e., the highest Si value was 0.85 min−1 for −850+600 μm, while the lowest Si value was 0.65 min−1 for −425+300 μm feed ground in the mill. The Bi, j values obtained for the zeolite sample were γ=0.84, ϕ=0.61, and β=4.25. The breakage parameters obtained showed that the zeolite is broken faster than quartz and slower than calcite and barite in terms of the aT values reported previously at the same experimental conditions. The simulations of the product size distributions of zeolite were in good agreement with the experimental data using a standard ball mill simulation program. The slowing‐down effect was also seen in the mill after 4 min. of grinding.

Correlation of the breakage parameters with the critical surface tension for wetting of barite

In this paper, we present a correlation and experimental data for a relationship between the breakage and the wettability for barite mineral. The breakage parameters, which are readily obtained from grinding test, are the specific rates of breakage ( S i ) and the fineness value ( γ) of the primary breakage distribution function ( B i, j ). The wettability parameter, which is easily obtained from contact angle measurements or flotation tests, is the critical surface tension for wetting of any mineral ( γ c). The barite sample studied for the correlations was ground in a laboratory-size porcelain ball mill and tested extensively for wettability using a contact angle goniometer and our newly designed micro-column flotation cell. There is a significant relationship between the S i and γ c values from our experimental work on the barite sample, where the higher S i means lower γ c, i.e., a mineral was more hydrophobic when it had a higher S i value, or a more rapid breakage of the top sizes leads to better hydrophobicity or floatability. Another relationship was found between the fineness value ( γ) of the breakage and the critical surface tension for wetting ( γ c), which indicates that as the γ value increases (meaning less fines produced), the γ c increases (meaning less hydrophobicity) based on the contact angle and flotation tests.

Investigation of the breakage kinetics of pumice samples as dependent on powder filling in a ball mill

In this study, the effect of powder filling was investigated on a pumice sample from the Karakaya region of Isparta in Turkey using dry batch grinding conditions and a kinetic model. Eight different mono-size fractions, between 1.7 and 0.106 mm, were prepared using a √2 sieve series. The specific rates of breakage ( S i ) and the primary breakage distribution ( B i,j ) equations were determined from the size distributions at different grinding times, and the model parameters were compared for the five different powder filling levels. In many investigations, it has been found that an interstitial filling fraction of U=0.6 to 1.1 is a good powder-ball loading ratio to give an efficient breakage in a ball mill. In this research, it was found that U=0.4 is a good ratio for the pumice sample.

A treatment of impact breakage of particles

Particles of a given size and material have a distribution of strengths so that some fractions break at low specific strain energies, more at higher strain energies, and all break at sufficient strain energy. Those fragments from breakage at a low specific strain energy produced during a higher specific energy impact will have relaxed their stored strain energy but will be recompressed and rebroken by the remaining impact energy. Thus, a size/mass/energy balance must be performed where the remaining specific impact energy of fragments is their original specific impact energy minus that required for fracture. An algorithm for this balance is presented and a computed example given. It is shown that the apparent primary breakage distribution from impact at a given specific impact energy will become finer as the energy is higher. These so-called “energy-dependent” primary breakage distributions ( B values) can be computed using a known distribution of strengths as a function of particle size and specific energy and a true primary breakage distribution.

Kinetics of dry grinding of industrial minerals: calcite and barite

This paper presents the kinetics study of dry ball milling of calcite and barite minerals. The experimental mill used was a laboratory size of 209 mm diameter, 175 mm length, providing a total mill volume of 6001 cm 3, with a total mass of 5.6 kg of steel balls of 46, 26 and 12.8 mm diameter, so as to occupy 20% of the mill volume and with a speed of rotation of 74 rpm. The breakage parameters were determined by using the single sized feed fractions of −850+600, −600+425, −425+300 and −300+212 μm for calcite and −850+600, −600+425, −425+300 μm for barite mineral. The S i (specific rates of breakage) and B ij (primary breakage distribution) values were obtained for those feed size fractions in order to predict the product size distribution by simulation for comparison to the experimental data. As the feed size fractions become coarser, the S i values increase. The highest S i value obtained for calcite was 0.86 min −1 for the −850+600 μm feed fraction, while it was 0.42 min −1 for the −300+212 μm feed when 26-mm ball sizes were used in the mill. The ball size effect was also investigated against the S i values in where the S i value increases when the ball sizes become smaller. The B ij values remained essentially the same for each feeds; the average of φ, γ and β values for all feed sizes of calcite were 0.65, 0.95 and 4.40, respectively. On the other hand, the highest S i value obtained for barite was 0.99 min −1 for the −850+600 μm feed fraction, while it was 0.66 min −1 for the feed size fraction of −425+300 μm when 26-mm ball sizes were used in the grinding mill. The B ij values also remained unchanged for each feeds; φ, γ and β values of barite for the average of all sizes were obtained to be 0.69, 0.81 and 3.94, respectively. The simulations of the product size distributions of both calcite and barite minerals were in good agreement with the experimental data using a standard ball mill simulation program. The slowing down effect was seen in the mill after 4 min of grinding for calcite and after 2 min of grinding for barite.

Kinetics of fine wet grinding in a laboratory ball mill

The kinetics of batch wet grinding of quartz from a feed of 600×425 μm to a product of 80% less than 8 μm have been determined using sieving and laser diffractometer sizing for size analysis. A dispersing agent was added while proceeding to longer grinding times to prevent particle agglomeration in the mill. The specific rates of breakage ( S i ) values obtained were higher than those of dry grinding of quartz at the same experimental conditions, but the primary breakage distribution ( B i, j ) values were the same. Non-first order grinding was observed with continued decrease of the specific rates of breakage for finer grinding. The simulations of the product size distributions were in good agreement with the experimental data, providing the decrease in rates was included.

The modeling of dry grinding of quartz in tumbling media mills

The grinding of quartz sand to produce high purity silica flour was studied using ceramic balls, ceramic cylinders or flint pebbles in a laboratory mill and three full-scale closed circuit mills of 2.2, 2.3 and 2.8 m internal diameter. The primary breakage distribution determined in laboratory tests was the same for the three media types but the characteristic slope ( γ) was changed from 1.05 to 0.95 to fit the full-scale results. An approximate correction was used for non-first order breakage kinetics. Simulation models were developed for the air separator and the mills. Simulations indicated that a mill lining of smooth ceramic gave media slip and was less efficient than flint linings. Higher circulating loads reduced specific grinding energy even though the recycle of fine mill product to mill feed increased. Ceramic balls gave the lowest grinding energy, wear rate and cost per ton of product.