Modelling of vertical spindle mills. Part 1: Sub-models for comminution and classification

Shi, Fengnian; Kojovic, T.; Brennan, Matthew

doi:10.1016/j.fuel.2014.10.085

Cited by 35 publications

(12 citation statements)

References 13 publications

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“…Shi and Kojovic (2007) extrapolated this approach to model the effect of feed size (x) on the generation of t 10 material in high energy impact breakage. More recently, Shi et al (2015), Bonfils et al (2016) and Nadolski et al (2014) independently found that an additional power term on the feed particle size is required to accurately represent the degree of breakage. The final breakage model is represented below:…”

Section: A C C E P T E D Mmentioning

confidence: 99%

Evolution of impact breakage characterisation: Re-defining t-family relationship

Ballantyne

Bonfils

Powell

2017

International Journal of Mineral Processing

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HIGHLIGHTS A new two-parameter model is presented to fully describe the progeny size resulting from single sided impact breakage.  The model provides an accurate fit over a wide range of sizes and energies -tested on 5 ores from 37.5 mm to 250 µm and energies from 0.02 to 3.5 kWh/t.  This approach provides a link between low energy, probability of breakage and high energy, t 10 models.  This technique reduced the number of model parameters from 18 to 2 or 3 and reduced the average standard error 6.3% to 3.6%. GRAPHICAL ABSTRACTExample of the model relationship between feed particle size and percentage passing t 1.2 (probability of breakage) and t 10 (traditional degree of breakage). ABSTRACTAccurate characterisation of ore competence through controlled single particle impact can enable improved modelling of comminution process response to ore variability. A simple relationship is presented to relate the energy input and feed particle size to the breakage progeny with two fitting parameters. Previous techniques have focused either on low energy repeated impacts or high energy single impacts and have been applied over relatively small ACCEPTED MANUSCRIPTA C C E P T E D M A N U S C R I P T ranges of particle sizes. The method presented builds on previous understanding to unite these two disparate fields on feed particle sizes over more than two orders of magnitude. The method has been tested on 5 ores from 37.5 mm to 250 μm over energies from 0.02 to 3.5 kWh/t. The resultant standard error of 3.6% is lower than other benchmarked models, with considerably fewer fitting parameters and no use of splining functions required. The direct calculation of appearance function for any feed size and input energy renders the proposed model well suited to incorporation in comminution process models. Further testing is required on additional ores, and further interpretation is required to obtain mechanistic explanations for the empirical fits to the model parameters.

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Section: A C C E P T E D Mmentioning

confidence: 99%

Evolution of impact breakage characterisation: Re-defining t-family relationship

Ballantyne

Bonfils

Powell

2017

International Journal of Mineral Processing

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“…Classification in the elutriator was modelled using a Rosin-Rammler efficiency curve, and the air classifier was modelled using Sproull's gas cyclone model (Sproull, 1970). Details of the two classification functions can be found in Shi et al, (2015a) and Kojovic et al (2015).…”

Section: Fig 4 Schematic Of the Grinding Elutriation And Main Clasmentioning

confidence: 99%

A review of the applications of the JK size-dependent breakage model part 3: Comminution equipment modelling

Shi

2016

International Journal of Mineral Processing

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It has been 10 years since the JK size-dependent breakage model was developed (Shi and Kojovic, 2007). This series of papers present 20 applications of the model for the mineral and coal industries. Part 3 of this series reviews its application to modelling comminution equipment. It is demonstrated that the JK size-dependent breakage model not only can be used for modelling particle breakage, but also can be employed as a basic structure for modelling comminution equipment. This is different to the traditional equipment modelling approaches, in which the population balance models are dominant. In this energy-size reduction modelling approach, the JK size-dependent breakage model provides a key mathematical template to rationally link the size reduction as the equipment model output with ore breakage property and specific energy as the two model inputs. Five case studies are reviewed, which includes modelling of a hammer mill for coke feed preparation, a vertical spindle mill for coal pulverised fuel grinding, a ball mill for batch grinding and continuous operation, HPGR simulations based on piston press testing data, and high voltage pulse disintegration of ores. A common feature of these models is that they all incorporate the measured material breakage characteristic parameters and machine operational conditions that are represented by the size-specific energy relation. The energy-size reduction modelling approach permits the simulations of the effects of changes in ore/coal and machine operating conditions on comminution product size distribution.

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“…Later, theories which incorporated the concept of particle size distribution were developed [9,10], while recently research focused on the use of the mechanistic approach which is based on the recognition of physical events that take place during grinding [11][12][13]. The mechanistic approach includes the matrix model, which considers grinding as a series of breakage events and the population balance model, which considers grinding as a continuous process.…”

Section: Introductionmentioning

confidence: 99%

Correlation between Material Properties and Breakage Rate Parameters Determined from Grinding Tests

Petrakis

Komnitsas

2018

Applied Sciences

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Abstract:The present study investigates four materials, namely quartz, marble, quartzite and metasandstone and aims to establish correlations, with the use of simple and multiple regression analysis, between their properties and breakage rate parameters. The material properties considered in this study derived from the application of destructive and non-destructive tests and include P-wave velocity (V p ), Schmidt rebound value (R L ), uniaxial compressive strength (UCS) and tangent modulus of elasticity (E t ), while the breakage rate parameters determined from batch grinding tests, include breakage rate S i , maximum breakage rate S m , α T and α, and optimum particle size x m . The results indicate that the properties of all materials examined show very good correlation and can be used to predict S i or α T . Furthermore, parameter α is well correlated with V p , R L and E t using inverse exponential functions, while S m is strongly correlated with R L and UCS. Overall, it is deduced that multiple regression analysis involving two independent variables is a reliable approach and can be used to identify correlations between properties and breakage rate parameters for quartz, quartzite and metasandstone, which are silica rich materials. The only exception shown is the determination of x m for marble.

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Modelling of vertical spindle mills. Part 1: Sub-models for comminution and classification

Cited by 35 publications

References 13 publications

Evolution of impact breakage characterisation: Re-defining t-family relationship

Evolution of impact breakage characterisation: Re-defining t-family relationship

A review of the applications of the JK size-dependent breakage model part 3: Comminution equipment modelling

Correlation between Material Properties and Breakage Rate Parameters Determined from Grinding Tests

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