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.     

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.     

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).     

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.     

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.     

An experimental validation of a specific energy-based approach for comminution

In a recent paper [Khumalo, N., Glasser, D., Hildebrandt, D., Hausberger, B., Kauchali, S., 2006. The application of the attainable region analysis to comminution. Chemical Engineering Science 61, 5969-5980] it was shown that the attainable region approach could prove useful in designing better comminution circuits. Fundamental to this approach was the assumption that the rate of comminution was only determined by the specific energy within the device. This paper shows experimentally that this assumption holds for a batch ball mill.The system presented here considered breakage of mono-sized feed particles in a laboratory ball mill into two distinct progeny size classes. The population balance model was successfully used to model the experimental products and the results were represented geometrically in a two-dimensional space. The resulting geometric structure can be used to solve process synthesis and optimization problems simultaneously.It was found that the breakage rate parameter out of size class 1 changes with time but exhibits an exponential relationship with an asymptote. It is hypothesized that this asymptote is the rate of breakage at long grind times or in well-mixed, steady-state continuous systems. It is shown that the parameters of the process depend only on the specific energy. This was one of the assumptions that was made in the construction of the attainable region. Thus, equipment selection and operating conditions only require one to match the required specific energy.     

Comminution of Organic Material

The comminution of materials of bioorganic origin such as organic solids, biological agglomerates or micro‐organisms is described in this work. The intent of this disintegration process is to release products, to improve the product quality or to enhance biological degradation processes. Special analytical techniques based on biochemical parameters are required in order to characterize the result of the comminution of organic materials. These techniques supplement techniques that are known from the comminution of brittle inorganic materials. The defined stressing of single particles can be used to characterize the comminution properties of solid bioorganic materials. The disintegration of micro‐organisms has been investigated in the fields of biotechnological product release and biodegradability of wastewater sludges. It is possible to optimize the operational parameters of stirred ball mills based on stress intensity and stress number in order to reduce the energy input and to improve product release.     

Breakage and Particle Size Redistribution in an Ultrasound‐Intensified Leaching Process

The breakage and particle size redistributions in an ultrasound‐intensified leaching process were explored experimentally and analyzed statistically. It was found that particle size distributions (PSDs) of this atomic crystal silica may be changed to a certain extent by ultrasound, but the width of PSD cannot be altered under the conditions considered. Chemical reactions played an important reciprocal causality to the breakage and the particle size redistributions, and the contribution was about a half on the mean particle size. The most severe breakup happened at the maximum volume percentage of PSD rather than in the region of the largest particle size end. The ability of conventional stirring to break the silica particles may be larger as expected when the same power was used. The morphology of the silica particles verified that the change before and after leaching is small.     

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.     

Comminution of Wood – Influence of Process Parameters

An essential element for sustainable use of renewable resources is an efficient comminution process for which the relation between energy input and size reduction is of great importance. Fine comminution of beech, oak, and spruce wood chips in cutting and hammer mills at different moisture content levels is investigated. The influence of the different process parameters as well as the size reduction performed by the hammer and cutting mill on the specific comminution energy is reported and the particulate properties of the comminution products are reported. Considering the energy requirements, functional relations were derived from the experimental results, which describe the relation between comminution energy and size reduction.     

Correlation between processing conditions and fiber breakage during compounding of glass fiber‐reinforced polyamide

The inter‐relationship between processing conditions and fiber breakage has been studied for glass fiber‐reinforcedpolyamide 12, prepared using (i) an internal batch mixer, (ii) a laboratory scale corotating twin screw extruder, and (iii) an industrial scale twin screw extruder. The average fiber lengths and fiber length distributions were measured for various compounding conditions (screw or rotor speed, mixing time, feed rate). Experimental results have shown that fiber breakage depends on both screw speed and mixing time, the later being controlled, in an extruder, by the feed rate. For a given compounding system (batch mixer or twin screw extruder), the energy input (specific mechanical energy, SME) during the compounding process is found to be a reliable parameter, which governs fiber length (average, minimal, and maximal) evolution. Experimental data are correctly described with a model defining change in fiber length as a function of SME. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers     

Comparison of comminution data with analytical solutions of the fragmentation equation

Analytical solutions to the fragmentation equation are presented for specific rates of breakage and primary breakage distribution functions often used to correlate comminution data. These solutions, obtained by similarity arguments, compare favorably with the experimental data of Austin et al., and suggest that correlation of data via similarity techniques may facilitate determination of function parameters.     

Use of the attainable region analysis to optimize particle breakage in a ball mill

Particle size reduction is one of the most widely encountered, yet least energy efficient, processes. Therefore, potentially significant energy and cost savings exist with even the slightest increase in milling efficiency. Often one would like to mill particles to a certain size, and no smaller, while minimizing energy use and milling time. We use the attainable region (AR) analysis to optimize the comminution of silica sand particles in a bench top laboratory ball mill. When the mill is loaded with a large number of grinding media (J=volume of media/mill volume=10.7%), the breakage profiles are indistinguishable over all rotation rates investigated. However, operation at lower grinding media fill level (J=1.5%) reveals separation between the grinding profiles for different rotation rates, suggesting more efficient breakage occurs at a lower grinding media fill level for a given rotation rate. Our results show that operation at multiple speeds, fast at first and then slower (φ_c=0.03), takes advantage of the initially overlapping grinding profiles and produces a similar particle size distribution with a decreased amount of processing time—less than half the time required for the single rotation rate milling. A natural extension of this idea is continuous milling, where the first mill can operate at a higher energy input for a shorter amount of time and the second mill can operate at a lower energy input for a longer amount of time.     

Mechanische Aktivierung von Festkörpern

Mechanical activation of solids. The main reasons why solids are comminuted are to decrease particle size, to create new free surfaces, and to increase reactivity of solids. In most cases, the comminution process is connected with crystal lattice transformations. A part of the energy supplied increases the energy level of the lattice. Consequently, a new theory of the energy balance of comminution processes is given and verified by experiments. It is shown, by some examples, that the individual mill parameters as well as the different mill types lead to characteristic changes of the crystal lattice of solids. Energy input by comminution is of great importance because it mainly influences the attainable degree of mechanical activation of solids.     

AGGLOMERATION,BREAKAGE, POPULATION BALANCE,AND CRYSTALLIZATION KINETICS OF REACTIVE PRECIPITATION PROCESS

The agglomeration and breakage of particles play a significant role in determining final particle size distribution (PSD) and other qualities such as filtering characteristics and impurity content. In reactive precipitation processes, especially during the precipitation of fine particles, the agglomeration and breakage of particles normally cannot be neglected. In this study, the agglomeration and breakage of particles during the reactive precipitation process of procaine penicillin has been investigated experimentally through a continuous steady MSMPR crystallizer. Based on the population balance theory, a crystallization kinetics model including agglomeration and breakage is established, in which the breakage of particles is expressed by a two-body equal-volume birth function and a two-body power-law death function. The crystallization kinetics model is shown to be more suitable than size-dependent growth models as ASL and MJ2.     

AGGLOMERATION, BREAKAGE, POPULATION BALANCE, AND CRYSTALLIZATION KINETICS OF REACTIVE PRECIPITATION PROCESS

The agglomeration and breakage of particles play a significant role in determining final particle size distribution (PSD) and other qualities such as filtering characteristics and impurity content. In reactive precipitation processes, especially during the precipitation of fine particles, the agglomeration and breakage of particles normally cannot be neglected. In this study, the agglomeration and breakage of particles during the reactive precipitation process of procaine penicillin has been investigated experimentally through a continuous steady MSMPR crystallizer. Based on the population balance theory, a crystallization kinetics model including agglomeration and breakage is established, in which the breakage of particles is expressed by a two-body equal-volume birth function and a two-body power-law death function. The crystallization kinetics model is shown to be more suitable than size-dependent growth models as ASL and MJ2.     

AGGREGATION AND BREAKAGE OF SOLID PARTICLES IN SUSPENSIONS AGITATED IN A VIBRATING MIXER: A FRACTAL APPROACH

A lumped discrete population balance model has been selected for the verification of the experimental data. Solid aggregates of chalk suspended in vigorously mixed suspension were treated as fractal objects with a mass fractal dimension taken as 2.02. A specially written computer program has been used for determining the evolution of population of aggregates during the course of mixing. The PSD (particle size distribution) results obtained by numerical calculation for fractal and non-fractal approaches have been compared, showing a better fit in the case of the fractal model. The aggregation and breakage rate coefficients were correlated as a function of the average energy dissipation rate in the vibrating mixer.     

AGGREGATION AND BREAKAGE OF SOLID PARTICLES IN SUSPENSIONS AGITATED IN A VIBRATING MIXER: A FRACTAL APPROACH

A lumped discrete population balance model has been selected for the verification of the experimental data. Solid aggregates of chalk suspended in vigorously mixed suspension were treated as fractal objects with a mass fractal dimension taken as 2.02. A specially written computer program has been used for determining the evolution of population of aggregates during the course of mixing. The PSD (particle size distribution) results obtained by numerical calculation for fractal and non-fractal approaches have been compared, showing a better fit in the case of the fractal model. The aggregation and breakage rate coefficients were correlated as a function of the average energy dissipation rate in the vibrating mixer.     

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.