Review: An investigation of single particle breakage tests for coal handling system of the gladstone port

Aspects of the literature on single particle breakage test have been reviewed in this article. The test procedures that are commonly used by the researchers in examining and measuring the breakage characteristics of the ore and coal particles are also discussed. It appears that most of the common size distribution function fitting techniques were not suitable for accurate representation of the size distributions obtained from a pendulum breaking process. The single impact test, double impact test (drop weight test, pendulum test) and slow compression test can be used to study the behaviour of the single particle breakage events. The single impact test, slow compression test and drop weight test cannot measure the energy utilization pattern in single particle breakage events, but this can be determined from the pendulum test.The energy utilized for breakage was predominantly dependent upon the size and shape of the specimen, level of input energy and the breakage properties of the specimen. This review highlights that the size distribution curves were linear in the fine particle region and have varying curvature in the coarser region, the gradient of the linear fine particle region of the size distribution curves increases with an increase in the specific comminution energy. The comminution energy increases with input energy at lower levels of input energy but at the higher levels of input energy the comminution energy did not show the same proportional increase. At a given level of input energy, the size distribution resulting from the breakage of the particles by the pendulum apparatus can be represented by a one-parameter family of curves.     

Energy and population balances in comminution process modelling based on the informational entropy

The results of theoretical and experimental studies of a comminution process are presented. There are two random functions: the selection function and the breakage function in the stochastic model based on a population balance. This model enables prediction of particle size distributions of comminution products after determination of both random functions. Maximum entropy method is used in the entropy model for determining the breakage function. Two cases are analysed, based on continuous and discrete particle size distribution functions of the fed material. Apart from mass balance, the energy balance of comminution process is also used. Searched form of breakage function is determined with the application of methodology of calculus of variations. The results of experimental identification of both models are presented. The parameters that occur in the discrete form of the selection and breakage functions were the identification objects. The results of experimental investigations of quartz sand single comminution in a laboratory jet mill provided an identification base. The experimentally identified results of the entropy model confirmed the adequacy of the theoretical analysis and demonstrated the possibility of adequate prediction of particle size distributions resulting from single comminution.     

Batch Grinding in Laboratory Ball Mills: Selection Function

The selection functions and the breakage distribution functions are based on the experimentally‐determined particle size distribution on the basis of comminution of one size fraction particles. Therefore, to obtain a clear picture of the product properties during comminution of the “real” polydisperse sample, a number of experiments are needed. This work introduces the tested methodology for the selection function determination based on the starting and maximal values of the selection function. The principle was tested on the planetary ball mill and the horizontal laboratory ball mill, and according to the results obtained, it can be concluded that the proposed methodology can be useful for the evaluation of the selection function during batch comminution in different mills.     

Strength distribution of particles under compression

From time immemorial people dealt with size reduction processes (mill, mineral liberation, etc.). As time has passed industrial units for comminution processes have become larger and more sophisticated, but still they perform with low efficiencies [1], [2] and [3]. The strength of a particle is one of its most crucial characteristics due to the mechanical stresses experienced by each particle within an industrial unit. This is because the final size of particles is mostly dependant on the strength distribution of the raw material [4]. In this present study, the ability of a number of statistical formulations to accurately describe the strength distribution of particles was examined. Additionally, selected equations were analyzed and a general expression including the effect of the material and particle size was developed. A number of approaches to define particle strength were considered, and strength in terms of crushing force was chosen. Particle strength in terms of force and in terms of energy was also compared and found to be size independent. Finally, particle strength in terms of stress was examined and compared to the particle strength in terms of force.The ability to describe the compression strength distribution will significantly improve the accuracy of the comminution processes simulation, design and optimization.     

Breakage probability of irregularly shaped particles

The investigation of breakage probability by compression of single particles was carried out. The spherical glass particles and irregularly shaped particles of NaCl, sugar, basalt and marble were subjected to a breakage test. The breakage test includes the compression up to breakage of 100 particles to obtain the distribution of the breakage probability depending on the breakage force or compression work. The breakage test was conducted for five particle size fractions from each individual material, at two stressing rates. Thus obtained 50 breakage force distributions and corresponding 50 breakage work distributions were fitted with log-normal distribution function.Usually, the breakage probability distribution can be found by means of stress or energy approach. The first one uses the stress to calculate the breakage probability distribution. The second approach uses the mass-related work done to break the particle. We prefer to use the breakage force and energy as essential variables. The correlation between the force and energy at their breakage points is obtained by integrating the characteristic force–displacement curve, i.e. the constitutive function of elastic–plastic mechanical behavior of the particle. The irregularly shaped particle is approximated by comparatively “large” hemispherical asperities. In terms of elastic–plastic deformation of the contacting asperities with the plate, a transition from elastic to inelastic deformation behavior was considered. Thus, one may apply the model of soft contact behavior of comparatively stiff hemispheres. Based on this model a relationship between the breakage force distributions and corresponding energy distributions was analyzed. Every tested material exhibits a linear relationship between average breakage energy and average breakage force calculated for every size fraction.For future consideration both force and energy distributions were normalized by division by average force or energy, consequently. The relationship between the fit parameters of normalized energy distribution and corresponding fit parameters of normalized force distribution was established. The mean value and standard deviation of normalized force distribution can be found from mean value and standard deviation of normalized energy distribution by means of system of two linear equations. The coefficients of those linear equations remain the same for all of the above tested materials; particle size fractions and stressing rates. As a result the simple transformation algorithm of distributions is developed. According to this algorithm the force distribution can be transformed into energy distribution and vice versa.     

The application of the attainable region analysis to comminution

The aim of any comminution circuit is to produce material of a desired particle size distribution (PSD) at a minimum operational cost. Currently, the comminution process is energy intensive and operates at very low efficiency when the input energy is compared to the breakage achieved. The attainable region (AR) technique has been successfully used to solve optimization problems simultaneously with the process synthesis formulation of reactor systems. The AR looks at the fundamental processes of a given system and determines all the possible outputs to which the objective function can be applied and an optimal process solution selected.Particle breakage, separation (classification) and mixing are identified as the three fundamental processes of interest taking place during comminution. Breakage and mixing processes are used in this paper to illustrate the applicability of the AR theory in comminution. We develop a fundamentally based model which is equipment independent to describe breakage. Specific energy is the independent variable and the production of particles with a certain PSD is the objective function. We use geometric construction to represent this PSD as a point in an n-dimensional space in relation to an input specific energy. Output PSDs are dependent on the input PSDs, allowing connectivity of the batch grinding stages to form a pseudo-continuous process.Specific energy is used as the control variable to obtain sharper product PSDs. It is shown that the same net energy consumed in the system can produce different product PSDs. Therefore, this implies that the design of comminution circuits should achieve better control of the specific energy. Once the candidate AR is constructed, operational process targets can be defined more accurately. This establishment of targets permits a measure of the actual process efficiency against a theoretical target. The advantage of the AR method lies in its ability to develop not only the performance of the optimal circuit but also the operational conditions to be used in the optimal process circuit. This also answers the process synthesis question of the type of equipment to be used which is a function of the specific energy.     

An investigation into the influence of microwave treatment on mineral ore comminution

The influence of microwave pre-treatment on mineral ore breakage has been investigated. Samples of lead-zinc ore were microwave pre-treated prior to strength testing and change in strength with microwave exposure time determined. Comparisons of change in strength were made between microwave-treated and -untreated material. Using a multimode microwave cavity, it was found that strength could be significantly reduced in 0.5 s when using 15 kW of microwave power. Lower powers in this type of cavity were found to be less effective. Drop weight tests were used to quantify the change in strength in terms of reduction in required comminution energy. Reductions of up to 40% were achieved for particles of mean size 14.53 mm. Preliminary tests in a single-mode microwave cavity gave strength reductions of 50% at 10 kW of microwave power with a residence time of only 0.1 s, indicating that high electric field strength is important in the failure of ore. A preliminary energy balance indicating the benefits of single-mode heating is presented.     

A mixed Weibull model for size reduction of particulate and fibrous materials

This paper describes a simple alternative to the classical population balance breakage model, which characterizes and controls the size distribution of particles submitted to a reduction process. The new approach is based on cumulative distribution functions of mixed random variables. Results indicate that a Weibull mixture distribution function adequately models the size of particles submitted to various breakage processes. The model was further applied to experimental reduction processes with apparently random breakage probability and yielded good estimates of the unbroken particle and fragment distributions. Use of these results for direct and indirect prediction of the size alteration under dimensional reduction processes is discussed.     

Comminution of Polymers – An Example of Product Engineering

Investigations into the processes of grinding and classification are presented. It is shown how the properties of filled polymer products like powder coatings or toner can be tailored through grinding and classification. A systematic approach to describe the process by a machine and a material function is introduced. Single particle comminution tests allow the determination of the material function. The breakage probability curves of different organic and inorganic materials can be transferred to one single master curve. The transfer of single particle tests to production mills seems to be possible, at least for the given example that of powder coatings. This comparison shows that the width of the final size distribution is determined in this example by the material function and not by the operation of the mill. Significant improvements were achieved for both powder quality, i.e. the amount of fines below 10 μm, and the yield by employing two new classifiers for the removal of fines. The classifiers were operated inline, directly after a classifying mill.     

Microstructure and phase evolution of micronized ceramic colorants from a pilot plant for inks production

The advent of inkjet printing as digital decoration of ceramic materials has irreversibly modified the industrial decoration technology, imposing companies to change the colorant production process. The inkjet application requires micronized particles in the ultrafine particle size range (smaller than 1 μm). Particles size reduction of ceramic colorants is performed by a high-energy comminution process in wet-operated bead mills, affecting colorants properties. Since a deep knowledge of milling-induced microstructural changes is still lacking, the micronization effects on a set of five industrial ceramic colorants are thoughtfully investigated in this work by simulating the industrial process at a pilot plant. Particle size distribution and energy consumption are monitored during the comminution process. The compositional (including crystallite size and microstrain analysis of the main phases) and morphological variation of four ceramic pigments (yellow zircon, brown spinel, pink malayaite, and green eskolaite) and one dye (blue olivine) is investigated by XRPD (Rietveld method) and SEM analyses. The analytical approach combined with a physical/semiempirical modelling of the colorants elastic features versus the energy demand for particle reduction has yielded details on the nature of the micronization-induced microstructural changes in ceramic colorants. Specifically, the comminution efficiency as well as the crystalline phase stability are related to the intrinsic properties of each colorant. Brittle breakage rather than plastic deformation on comminution are also system dependent. When an euhedral to subhedral crystal habit is maintained a brittle fracture is preserved throughout the comminution progress, while the formation of flake-like particles and particle agglomeration are strong evidences of plastic deformation. The last evidence deals with the material elastic features. Materials with high bulk modulus convert the grinding energy to lattice defects that lead to particle breakage by brittle fractures, while materials with lower bulk modulus convert/dissipate part of the supplied energy in plastic deformations, drastically decreasing the comminution process efficiency.     

Similarity Solutions for the Population Balance Equation Describing Particle Fragmentation

Similarity solutions are obtained to the population balance equation describing particulate systems undergoing fragmentation. The solutions are restricted only by the requirement that the breakage rate of particles of volume v be of the form φ(v) = Av^b and the breakage distribution function of the form ω(u, v) = ?(v/u)/u, where u is the volume of the fragmenting particle. Under such conditions, the moments of the distribution asymptotically approach the form N_i(t) α t ^(1?i)/b , and the particle size distribution function is shown to obey a first-order linear ordinary integro-diflerential equation.

For the case ?(v/u) = γ(v/u)^γ?2, analytical solutions to the above equation were obtained. Complete solutions as well as asymptotic behavior are given. The results are potentially applicable to a wide range of particle fragmentation problems, including char/ash fragmentation during pulverized coal combustion, explosively generated aerosol formation, ore comminution, powder crushing and grinding, floe breakage, and crystallization kinetics.     

Characterizing fibre shortening in low-consistency refining using a comminution model

An experimental method of determining the probability of fibre shortening in the form of a selection function during refining has been developed based on comminution models used in the crushing and grinding industries. The method was validated by comparing experimentally measured selection functions to theoretical estimates for a model refining process. Selection functions were experimentally determined for a series of pilot refining trials that examined five refiner plate patterns operating over a wide range of specific intensity and specific energy. We concluded that the probability of fibre cutting during refining is proportional to the applied energy and fibre length and that for a single refiner at constant specific energy the selection function increased with Specific Edge Load (SEL) and was approximately independent of feed consistency. For a constant specific energy, achieved using a wide range of flow rates, consistency, applied power and plate pattern, selection function was shown to strongly correlate with SEL.     

Analysis of catalyst particle strength by impact testing: The effect of manufacturing process parameters on the particle strength

The mechanical strength of porous alumina catalyst carrier beads, used in the reforming units with continuous catalytic regeneration, was measured by impact testing. With this testing method particle strength can be measured at higher strain rates than the traditional crushing test method, hence providing a better simulation of pneumatic conveying and chute flow conditions, and also a large number of particles can be tested quickly. This is important for particles with a brittle failure mode such as the alumina particles used in this work as a wide distribution of mechanical strength usually prevails. Extensive impact testing was carried out first with an industrial sample, in order to understand the failure mechanism of this type of particles and to develop a methodology for analysing the extent of breakage by impact. Then the method was used to analyse the effect of a number of process parameters, such as filler, macroporosity and drying procedure on the particle strength with the aim of optimising the manufacturing process. The impact test results were then used to test the model of breakage behaviour of particulate solids proposed by Vogel and Peukert [Vogel and Peukert, Breakage behaviour of different materials—construction of a mastercurve for the breakage probability. Powder Technol., 129 (2003) pp. 101-110].     

Modelling of comminution processes in Spex Mixer/Mill

It is well known that mathematical models which simulate comminution processes represent a useful tool in several fields of academic and industrial research, with particular emphasis on nano-material and pharmaceutical production. In the present work a mathematical model which is able to quantitatively describe comminution processes in a ball milling system (i.e., Spex-Mixer/Mill) has been developed. The proposed approach takes into account three different contributions: dynamics of the vial, dynamics of spheres motion and simulation of the comminution process. The vial dynamics has been modelled by taking advantage of an appropriate roto-translation matrix. Model results have been successfully compared with literature experimental data. The spheres motion within the Spex Mixer/Mill has been simulated using a 3D dynamic model based on classical mechanics as well as the so-called discrete element method, which is widely adopted to quantitatively describe multi-body collision behaviour. In particular, existing models of impact with dissipation as well as the classical Hertz impact theory have been taken into account. This part of the global model allows one to obtain, for different operating conditions, the impact specific energy and impact velocity as a function of time. The latter ones represent input parameters for the simulation of comminution processes that is performed through suitable population balances, where different breakage functions as well as appropriate breakage probabilities have been considered. Model results are reported in terms of granulometric distribution of powders within the mixer-mill as a function of time, minimal grain size obtainable and time needed to complete the comminution process for various operating conditions (i.e., mill frequency and charge ratio).     

Improving comminution efficiency using classification: An attainable region approach

The AR for the fundamental processes of breakage and mixing was constructed in an earlier paper (Khumalo, N.; Glasser, D.; Hildebrandt, D.; Hausberger, B.; Kauchali, S. (2006). The application of the attainable region analysis to comminution. Chem. Eng. Sci., 61, 5969-5980). This work presents the AR constructed when the process of classification is combined with the processes of breakage and mixing. The process of classification extends the AR. An additional variable of energy consumption is introduced, increasing the dimensionality of the geometric construction from 2-D to 3-D. The AR shows that there is a linear relationship between consecutive particle size distributions with grinding time. However total energy consumption results in concavities when plotted against mass fraction in the median size class.This work demonstrates the degree to which there is an advantage of including the additional fundamental process of classification to particle breakage. The attainable region (AR) of a three particle size distribution can easily be represented graphically. Process targets can be inferred from these graphs. In our chosen system, the classification process has the effect of reducing total energy consumption by 95% to reach an objective of producing 92% of the material in the fines size class. This has cost implications since energy is often the predominant operating cost in size reduction systems. This work also shows that the benefits of classification are a function of the grinding extent for a system which consists of mono-sized feed particles. This suggests that classification should be introduced after some grinding at some point which is easily identified by analysing the AR construction.     

A rigorous breakage matrix methodology for characterization of multi-particle interactions in dense-phase particle breakage

Broadbent and Calcott's breakage matrix methodology has been used for more than 50 years to model various comminution processes and to determine breakage functions from experimental data. The methodology assumes first-order law of breakage and neglects mechanical multi-particle interactions that are especially prevalent in dense-phase comminution processes and breakage tests. Although several researchers severely criticized this aspect of the methodology, Baxter et al. (2004, Powder Technol. 143–144:174–178) were the first to modify the methodology toward determining the elements of a feed-dependent breakage matrix. However, no non-linear breakage matrix has ever been constructed from experimental data using the modified approach. In this study, a critical analysis of this modified approach has been performed, and the non-linear breakage matrix was fundamentally derived from a non-linear population balance model. Different approaches were proposed to identify the breakage functions based on the nature of available breakage tests on multiple mono-dispersed feed samples and at least one poly-dispersed sample. Using the derived equations, available experimental data on the breakage of a binary mixture of coarse and fine limestone particles in uniaxial compression test were fitted to quantify the multi-particle interactions. Superior fitting capability of rational approximation to the effectiveness factor was demonstrated.     

Breakage behaviour of enzyme granules in a repeated impact test

In many industries, handling or processing of relatively fragile particles takes place and predictions are required whether a significant proportion of the particles will be damaged. These processes have been designed and controlled solely on the basis of particle size and shape. Another parameter that needs to be introduced is particle strength. The stringent environmental laws demand improved particle mechanical quality, which has given rise to the need for a more accurate and fundamental particle strength measurement and its application in modelling and control of particulate processes. Particles need to show good resistance against static and dynamic loads.

The present paper deals with the study of breakage behaviour of different enzyme granules subjected to repeated impacts using a new instrument developed at the Delft University of Technology. The impact test involves bombarding the particles against a flat target repeatedly. The main feature of this new test is its ability to impact a large number of particles against a flat target repeatedly, and generate extremely reproducible results. Testing a large number of particles has the advantage of producing statistically correct results. The repeated impacts provide information on the breakage behaviour of the particles based on their history. In the new impact test enzyme granules can undergo very low impact velocities of the order of 5 m s⁻¹. These low impact velocities lead to attrition and chipping of the granules.

The current paper presents preliminary results on the breakage behaviour of the new impact test and its basic advantages over already existing tests. Furthermore, experiments were performed on enzyme granules, and the breakage mechanisms determined, depending on the change in size and shape of the particles.