Understanding fine ore breakage in a laboratory scale ball mill using DEM

DEM models of fine grinding in ball and stirred mills have to date almost entirely focused on the motion of the media and their interaction with the mill configuration. For SAG mills, a large fraction of the feed material can now be accurately represented in DEM models. However, for other mill types with much finer feed materials, such as the second chamber of a cement ball mill, the vast numbers of feed particles makes their explicit inclusion in the models prohibitive. However, it is now feasible to model a periodic section of a laboratory scale ball mill and include the coarser end of the ore size distribution directly in the DEM model. This provides the opportunity to better understand the effect of media on the interstitial bed of powder and of the effect of the powder on the media. The effect of the powder fill level, which is varied between 0% and 150% of the pore space in the media charge, is explored. The distribution of the powder, its effect on power draw and the way in which it contributes to the pattern of energy utilisation is assessed. The simulation results are compared with experimental results from a test at similar ball loading and rotation rate and for several size fractions of ore at a range of powder fill fractions. Tracking the collision histories of specific ore particles within the charge allows estimates of the probability (per unit time) of collision between media and ore particles (the “Selection” function) and of the intensity of each collision which can be used to estimate the severity of breakage using the JKMRC breakage model (the “Breakage” function). The energy spectra indicate that for a typical ore, only very few collisions are large enough to cause damage to the body of each particle. This provides an estimate of the energy efficiency which is less than 10% at even the best operating conditions.     

Modeling breakage rates of coarse particles in ball mills

Breakage rates of coarse particles in ball mills generally follow non-first-order kinetics and the distribution products from batch milling are often characterized by significant contributions of abrasion besides breakage by impact, which are not well described using traditional size–mass balance formulations. Under such conditions, particles are often subject to impacts of insufficient magnitude to produce breakage in each stressing event, so that they are broken by a combination of abrasion and impact and also particles undergo weakening due to unsuccessful stressing events. The paper presents a mathematical model of batch grinding which takes into account the distribution of stressing energies in the mill, the distribution of fracture energies of particles contained in the charge, describing breakage by impacts from grinding media producing catastrophic breakage, abrasion and weakening from repeated impacts. The model has been applied to describe the rate of disappearance of two materials in batch grinding with good results.     

Modeling breakage rates in mills with impact energy spectra and ultra fast load cell data

A new era in modeling particle size distribution in grinding mills started at the beginning of 2000s. A direct estimation of breakage parameters became possible via computation of collision energy by discrete element method (DEM) and material breakage data.The material breakage data can be obtained for primary modes of breakage. In this study, impact and abrasion are assumed to be the primary modes of particle breakage, which are readily studied in the laboratory. The impact breakage mode is studied in a drop-weight apparatus and in a specialized device known as the ultra fast load cell. The abrasion mode of breakage is studied in a laboratory scale ball mill. Next, the particle breakage versus energy data is converted into breakage rates via impact energy spectra of the grinding mill computed by a DEM code. The fundamental material breakage information is converted into energy based breakage distribution function.The verification of the modeling concepts is shown for a 90 cm laboratory scale ball mill. In the batch mill, approximately a 10 kg mass of limestone in the 30 mm size is ground with around 100 kg of 50 mm steel ball charge. The breakage rate and the breakage distribution functions constitute the parameters of the energy based batch population balance model. It is shown that accurate particle size distribution predictions are possible with this modeling approach for different grinding regimes.     

Discrete element method simulation of bed comminution

This paper evaluates fragmentation behaviour, particle size distribution and liberation degree during bed comminution of particles. Three different cases of bed comminution are modelled through discrete element simulations. The role of stressing velocities on breakage, effects of crushing walls on fragmentation and influence of crushing gaps on liberation and particle size distribution are considered. The discrete element sample is modelled to represent the concrete specimens of B35 strength category.It has been observed that the particles around the stressing walls fail differently than the inner particles during bed comminution. The stressing velocity and the crushing walls have been found to affect the cracking mechanism of the particles. The liberation degree in bed comminution is less as compared to single particle crushing. The results presented in this paper can be used to model the liberation and recycling of valuable aggregates from cheaper matrixes.     

铁矿石物料颗粒床压载粉碎试验研究*

利用活塞缸体压载装置,在压力试验机上对三种铁矿石物料分别进行了窄粒级和宽粒级给料的颗粒床粒间粉碎试验研究。试验用的5个窄粒级为2.5～3.2,1.6～2.0,0.8～1.0,0.4～0.5和0.2～0.25 mm,宽粒级为0～4.0 mm;压强变化范围为30～360 MPa。结果表明,颗粒床单位质量物料吸收的能量与压强有线性关系;压载产物细度随压强的增加而提高,但提高的幅度随着压强的增加而变小;不同粒度的窄粒级颗粒床的压载产物粒度分布曲线之间不存在自相似性。试验数据可用于建立关于这三种矿石物料的粒间粉碎数学模型。     

Vertical Agitated Media Mill scale-up and simulation

Vertical Agitated Media Mill modeling has become subject of a research project due to its potential application as a secondary grinding mill as well as regrind and pellet feed preparation projects. A test campaign with a pilot scale vertical mill was carried out with five different ore samples to elaborate a simple and robust methodology to scale-up vertical mills and perform simulations. The methodology proposed considers breakage parameters determined from tests in a conventional batch ball mill and population balance model for simulations. The tests can be performed very quickly in any process laboratory with a small quantity of sample. Two different models can be used for scale-up purposes: the first is based on the specific grinding energy and the corresponding tests were carried out on samples with natural size distribution. The second is based on particle residence time distribution and the tests carried out with narrow sized particles. Breakage and selection function parameters were estimated from each test procedure. The results indicate that it is possible to perform vertical mill scale-up and simulations with acceptable accuracy using the results from laboratory ball mill tests. The data analysis showed that the ratio of grinding net powers between ball and vertical mills is approximately 1.35 for all samples tested.     

New population balance model for predicting particle size evolution in compression grinding

Population Balance Models (PBM) are widely used to predict the evolution of the particle size distribution during various grinding processes, such as ball milling. They represent breakage through the definition of particle destruction and fragments generation rates. Their application to compression grinding (HPGR, vertical mills…) has been limited, due to the complexity of interactions between particles of different sizes.In this work, we present a new PBM approach for compression grinding. Complex interactions between size classes are represented in a simplified manner by making particle destruction and fragment generation depend on the bed porosity. Model is tested by confrontation to an extensive collection of experimental results on a piston-die cell, on three different materials (cement clinker, limestone, and quartz). When properly calibrated with preliminary tests, the model is able to predict the evolution of the particle size with accuracy, for any starting grain size distribution and any load.     

Estimating energy in grinding using DEM modelling

The latest state of the art on Discrete Element Method (DEM) and the increased computational power are capable of incorporating and resolving complex physics in comminution devices such as tumbling mills. A full 3D simulation providing a comprehensive prediction of bulk particle dynamics in a grinding mill is now possible using the latest DEM software tools.This paper explores the breakage environment in mills using DEM techniques, and how these techniques may be expanded to provide more useful data for mill and comminution device modelling. A campaign of DEM simulations were performed by varying the mill size and charge particle size distribution to explore and understand the breakage environment in mills using DEM techniques. Analysis of each mill was conducted through consideration of the total energy dissipation and the nature of the collision environment that leads to comminution.The DEM simulations show that the mill charge particle size distribution has a strong influence on the mill input power and on the way the energy is distributed across the charge. The smaller particles experience higher energies while the larger experience less, but this variation is strongly dependent on the mill size. The results also showed that the average particle collision energy increases with increasing mill size, whereas its distribution over particle size is strongly influenced by the mill content particle size distribution. The simulations also captured the energy distribution within different regions of the tumbling charge, with the toe impact region having higher impact energies and the bulk shear region having higher tangential energies. Regardless of the mill size most of the energy is consumed by the particles in the mid-size range, which has the highest percentage mass of the total charge distribution.     

Comparison of different breakage mechanisms in terms of product particle size distribution and mineral liberation

The comminution process is still governed by a large number of factors that influence the liberation of the valuable components in the ore. A better understanding of these basic factors will provide more certainty about the design of equipment in order to achieve the best liberation and energy efficiency.Impact and bed breakage mechanisms were investigated as two distinctly different modes of breakage. Standard drop weight tests and hydraulic piston-die press tests were conducted with different energy intensities on samples.This paper describes the work carried out for the comparison of mineral liberation and particle size distribution in the particle bed breakage with impact breakage of two different copper ores. Ground products from these two different modes of breakage were screened into size fractions which were analyzed for the particle size distributions by sieve analysis and the degree of liberation by an image analysis system. The results of these analyses were statistically compared to make inferences in relation to the stated objective of the work. Test results indicated that compressive bed breakage mechanism gives finer product particle size distribution and provides better mineral liberation compared to impact breakage mechanism.     

The effect of particle breakage mechanisms during regrinding on the subsequent cleaner flotation

Stirred mills have been widely used for regrinding, and are acknowledged to be more energy efficient than tumbling mills. These two types of mills present different particle breakage mechanisms during grinding. In this study, the effect of regrinding by both mills on surface properties and subsequent mineral flotation was studied, using chalcocite as the mineral example. A rod mill and a stirred mill with the same stainless steel media were used to regrind rougher flotation concentrates. Different chalcocite flotation recovery was achieved in the cleaner stage after regrinding in tumbling and stirred mills. The factors contributing to the different recovery included particle size, the amount of created fresh surfaces, surface oxidation and the redistribution of collector carried from rougher flotation. All the factors were examined. It was determined that the predominating factor was the different distribution of collector resulting from different particle breakage mechanisms in the stirred and tumbling mills, in line with ToF-SIMS analysis. In the tumbling mill, the impact particle breakage mechanism predominates, causing the collector to remain on the surface of newly produced particles. In the stirred mill, the attrition breakage removes collector from the surface, and decreases particle floatability. Furthermore, the type of grinding media in the stirred mill also influences the subsequent flotation, again due to the change of particle breakage mechanisms. The results of this study demonstrate that the selection of regrinding mills and grinding media should not only depend on the required energy efficiency, but also on the properties of the surfaces produced for subsequent flotation.     

A specific energy-based size reduction model for batch grinding ball mill

A particle size reduction model has been developed as the first component of an upgraded ball mill model. The model is based on a specific energy-size reduction function, which calculates the particle breakage index, t₁₀, according to the size-specific energy, and then calculates the full product size distribution using the t₁₀–t_n relationships and the mass-size balance approach. The model employs an ore-specific and size-dependent breakage function, whose parameters are independently measured with a fine particle breakage characterisation device, the JKFBC. This has effectively overcome the limitation of using a default breakage appearance function for all ores in the perfect mixing ball mill model. Since the ore-specific characteristics and the machine-related specific energy parameters are mechanistically incorporated in the size reduction model, it has the capability to predict size reduction in response to changes in the ball mill feed breakage characteristics and the operation-related specific energy.     

Use of the attainable region method to simulate a full-scale ball mill with a realistic transport model

Optimisation and better control of milling circuits require extensive modelling of milling data. This paper extends the enquiry to the use of the attainable region (AR) technique to determine the optimal residence time of ore in a ball mill. It also evaluates the energy requirements of the mill at the set residence time to maximise the production of the desired size range which enables maximum recovery of platinum group minerals (PGM) during the flotation stage.With these purposes in mind, the breakage function and the scaled-up selection function parameters were used to simulate the operating conditions required by an industrial ball mill and the power requirements were predicted using the Morrell power model. This allowed the application of the AR methodology to be extended to a full-scale ball mill. Then a link was established between residence time to mill product specifications for a given feed size.The findings showed that the residence time required by a full-scale mill falls between those at which the fully mixed and the plug flow mills operate. The results also showed that operating the ball mill at a lower mill speed and a higher ball filling saves energy. Mill speed was again found to be a key operational factor for controlling the retention time of particles inside the mill. This yielded valuable insight for the importance of optimally controlling both the residence time of the material inside the mill and the amount of energy required to maximise the desired size range, in this case −75 + 9 μm.     

DEM modelling of non-spherical particle breakage and flow in an industrial scale cone crusher

Predictions of particle flow and compression breakage of non-round rock passing through an industrial scale cone crusher are presented. The DEM (Discrete Element Method) particle breakage model is generalised to allow non-round particles to be broken into non-round progeny. Particles are broken in this DEM model when the elastic energy of a contact is sufficiently high to initiate fracture. Progeny size distribution data from JKMRC Drop Weight Test (JKDWT) or JKMRC rotary breakage test (JKRBT) is used to generate the specific daughter fragments from each breakage event. This DEM model is able to predict the production of both coarser progeny which are resolved in the DEM model and finer progeny which are not. This allows the prediction of product down to very small sizes, limited only by the fineness of the fragments measured in the breakage characterisation. The predicted flow of material through the crusher, product size distribution and liner wear are discussed. The generalised breakage model demonstrated here is suitable for modelling all forms of crushers.     

Tracer studies and breakage testing in pilot-scale stirred mills

A tracer technique is used to provide parameters that describe mixing and breakage in stirred mills. The results are also used to test the accuracy of mixing and breakage models.Tracer studies have been undertaken using a 39-litre vertical Sala agitated mill and a 4-litre horizontal Netzsch mill. The experimental residence time distribution (RTD) of the mills is analysed both in terms of a single mean residence time and a non-linear least squares fit to an optimal number of perf ect mixers of unequal size in series. Results show a strong dependence of RTD on flow rate, minimal dependence on stirrer speed, and support the concept that the RTD's of liquid tracers and solid tracers subject to breakage are similar. A very accurate match to the experimental RTD curves car be achieved with the multiple uneven mixers in series model.Size distribution results from solid tracer tests are used to determine the breakage characteristics of the pilot-scale Sala mill. The population balance model for a single perfect mixer with steady state hold-up is used as the basis for solution of a constrained non-linear optimisation inverse problem for mill breakage rate and breakage function. Experimental results indicate that the breakage rate is first order as hypothesised. The population balance model using optimal breakage parameters provides a reasonable fit to experimental data for cumulative passing percentage as a function of particle size for discrete times. Both the breakage rates and cumulative breakage functions are roughly power law dependent on particle size. Analysis of the size distribution of breakage products indicates that the mode of particle breakage, as indicated by the tracer breakage parameters, is a function of time. This demonstrates that the assumption of time independent breakage parameters in the population balance model may not be valid. Accurate determination of breakage parameters is strongly influenced by the transport characteristics of the slurry through the mill.The work shows that particle breakage in pilot-scale stirred mills is a complex function of both particle and specific mill characteristics. Therefore, in order to gain insight into the appropriate physical processes at work in an industrial scale mill, it is important to perform experiments with and analyse a system that matches the real mill as closely as possible.     

Characterisation of superficial breakage using multi-size pilot mills

Low energy surface breakage has a high frequency of occurrence and thus plays a significant role in grinding processes. Yet this superficial breakage is poorly understood, measured and modelled – forming the focus of this work.Pilot mills of 0.8–1.8 m diameter, designed to provide a predominantly surface breakage environment with efficient removal of the resultant progeny, are utilised to characterise superficial breakage. A new rate, that of superficial breakage (1/(kW h/m²)), is introduced which measures fractional superficial breakage rate per energy provided to the surface of the material. This methodology is proposed as being suitable for understanding and characterising the surface breakage behaviour of ores.Tests were conducted on two ores with different hardness. Superficial breakage rates varied from 2 to 16 (1/(kW h/m²)) for the different ores and mill sizes, indicating a good sensitivity to ore type and the need to understand the applied stress – related to mill size. The results show that a single ‘surface breakage rate for use in mill modelling is incorrect as the rate of superficial breakage is dependent on the size of the mill and therefore the inter-particle stressing conditions.     

基于矿石冲击破碎特性提高球磨机磨矿效率的探讨

针对提高球磨机磨矿效率问题,提出了矿石冲击破碎特性的简易测定方法,构建了依据矿石冲击破碎特性数据,通过确定钢球在落回点与被磨颗粒接触瞬间的动量法向分量,使之更有效地对矿粒实施冲击破碎和研磨。研究结果表明,本文采用的测定装置,可以较为方便地获取体现矿石样品冲击破碎特性的数据,进而得出矿石样品的适宜冲击破碎动量;针对拟采用的球磨机规格,据此可以较为方便地确定适宜采用的钢球尺寸和球磨机的转速率,以便获得较为理想的磨矿效率。      

Ore impact breakage characterisation using mixed particles in wide size range

The Drop Weight Tester (DWT) for ore impact breakage characterisation uses particles in five narrow size fractions, and the JKMRC Rotary Breakage Tester (JKRBT) uses four size fractions, both with three impact energy levels for each size fraction. It is time consuming to prepare these narrowly sized particles and to carry out size analysis on the 15 DWT or 12 JKRBT products, so a Wide-size JKRBT characterisation method was developed. In this method, the mixed particles in 13.2–45 mm size range are tested as one size class in the JKRBT by single-particle breakage mode. The wide-size feed is then divided into several virtual narrow size fractions by simulation, based on which the impact product size distributions are calculated using a size-dependent breakage model. Four sets of measurement data, consisting of two feed samples in the 13.2–45 mm size range with different size distributions tested with two impact energy levels, are adequate to determine the three model parameters. In the case where a benchmark ore of known breakage characteristic parameters is available, one Wide-size JKRBT impact treatment can determine the ore competence change parameter using a t₁₀-based model.     

Confined particle bed breakage of microwave treated and untreated ores

The effect of microwave treatment on the processing of mineral ores was investigated through simulations of microwave heating, thermal damage and confined particle bed breakage test on bonded-particle models. The simulations were undertaken on two-phase mineral ore consisting of a microwave-absorbing mineral in a non-absorbing matrix. The microwave heating was simulated by dissipating a volumetric heat source in the absorbent phase. The progeny size distribution and degree of liberation for the untreated and microwave treated ores after breakage tests were determined by undertaking image analysis of the model outputs. It was shown that microwave treatment at high power density considerably changed the progeny size distribution and enhanced the degree of liberation in confined particle bed breakage tests. It was also found that crushing velocity has a significant effect on both progeny size distribution and liberation, particularly for the ore treated at high power density.     

粒度对方解石冲击粉碎影响研究

JK标准落重试验的样品粒度范围为-63.0+13.2mm。为了研究粒度尺寸对颗粒抗冲击粉碎能力的影响,以天然方解石为研究对象,将矿石粒度范围拓展到-13.2+4.75mm。通过JK落重试验方法分别测定-63.0+13.2mm和-13.2+4.75mm两个粒级范围内矿石抗冲击粉碎特性参数,以此来分析研究不同试验条件下颗粒抗冲击粉碎能力的变化。试验结果表明,方解石物料的冲击粉碎存在较明显的粒度效应,且随着粒度的减小,颗粒抵抗冲击粉碎的能力增大。这为运用JKSimMet软件中的变速率模型进行模拟时,粒度效应对模拟结果的影响提供了理论支持。