The development of the wide-range 4D appearance function for breakage characterisation in grinding mills
Graphical abstract
Introduction
Comminution, including crushing and grinding, is an energy intensive process in the mining industry. For example, the energy used in the comminution of gold and copper ores accounts for 0.2% of global and 1.3% of Australia’s electricity consumption (Ballantyne and Powell, 2014). Thus comminution circuit optimisation is of great importance in reducing the total energy cost. In order to achieve this, it is essential to characterise the breakage properties for any ore of interest so that optimisation of the comminution circuit and operational conditions through modelling can be achieved. The relationship between the product size distribution and the applied breakage energy can be quantified through ore breakage characterisation. Based on valid breakage characterisation results used in appropriate process models, comminution circuit design, modelling, and optimisation can be achieved for a particular ore.
Ore breakage characterisation involves laboratory breakage testing work that provides the establishment of an appearance function. Among the various laboratory breakage tests, single particle breakage tests are widely used to determine the comminution characteristics of ore particles. The first single particle breakage test was the Bond Crushing Work Index Test (Bond, 1947). Subsequently, several single particle breakage tests were developed such as the Twin Pendulum Test (Narayanan, 1985, Narayanan and Whiten, 1988); the Ultrafast Load Cell test (UFLC, also called Impact Load Cell) (King and Bourgeois, 1993, Tavares and King, 2004, Weichert and Herbst, 1986); the laboratory-scale compression crushing test (Evertsson, 1999, Evertsson, 2000); the Short Impact Load Cell test (SILC) (Bourgeois and Banini, 2002); the JK Drop Weight Test (Napier-Munn et al., 1996); the SMC Test (Morrell, 2004) and the JK Rotary Breakage Test (JKRBT) (Shi et al., 2009).
The appearance function, also known as the breakage distribution function, is used to describe the size distribution of the breakage progeny as a function of input energy. It is an important sub-model in a generic model structure for tumbling mills (Yu et al., 2014) and some AG/SAG mill models (Leung, 1987). In this paper, the existing appearance function models that are widely used in industry were reviewed. A new 4D appearance function, which includes the effect of feed particle size and extends the particle size to the sub-millimetre range as well as the breakage at low energy inputs, was developed and validated.
Section snippets
Review of existing appearance function models
The JK t10 appearance function (also known as the JK breakage model (Napier-Munn et al., 1996)), the JK Mpq appearance function (also known as the JK size-dependent breakage model (Shi, 2016)), and King’s t10 based appearance function are widely used in industry.
An important concept proposed by Narayanan and Whiten is the family of tn curves (Narayanan and Whiten, 1988).
In Fig. 1, tn = percentage passing an aperture of 1/n of the original ore particle size (n = 2, 4, 10, 25, 50 and 75). t10 here is
Experiment using the Mini JK drop weight test (mini JKDWT)
In order to develop an accurate appearance function model that cover a wide range of test conditions, single particle breakage tests at a wide range of experimental conditions were conducted. The standard JK drop weight test (standard JKDWT), which was first developed at the JKMRC in 1992 (Napier-Munn et al., 1996), was used for breakage characterisation measurement in this work. 15 sets of existing data from standard JKDWT were used for analysis. The sample size ranges are −63 + 53 mm, −45 + 37.5
4D-m appearance function model
45 sets of Mini JKDWT data and the existing 15 sets of standard JKDWT data were collected. There was an overlap of the two test results for X = −16 + 13.2 mm, Ecs = 1.0 kW h/t, measured by standard JKDWT and mini JKDWT respectively and the outcome from standard JKDWT was used. Thus after eliminating overlapped data, a total of 59 sets of data were analysed to develop the 4D appearance function model.
Each set represents a product size distribution for a combination of size and energy. The product size
4D-mq appearance function model
The P80-m Weibull distribution (Rosin-Rammler distribution) is widely used in industry to describe comminution product size distribution, especially where the product size distribution curve is not so steep. However, when the feed ore size X is smaller, and the specific energy is lower (e.g. X: −2 mm, Ecs: −0.5 kW h/t), the shape of the product size distribution curve is steeper and even behave like a step in a size range (e.g. Fig. 12). The P80-m Rosin-Rammler distribution cannot describe the
Other t10 based appearance functions
In order to compare the results of the 4D appearance function models and traditional t10 based model, three t10 based appearance functions discussed in Section 2 were applied here: JK t10 (Napier-Munn et al., 1996), JK Mpq models (Kojovic et al., 2012, Shi and Kojovic, 2007) and King t10 based appearance function (King, 2012).
Based on 59 sets of experimental raw data, a series of tn-t10 family curves (Fig. 20) and a table of basic appearance function data (Table 6) were obtained through
Conclusions
In this work, two versions of the 4D appearance function model, 4D-m and 4D-mq, were developed based on a wide range of breakage test data of mini JKDWT and standard JKDWT. The 4D appearance function models can successfully characterise the breakage of different size-energy combinations (feed size from 425 μm to 63 mm and input specific energy Ecs from 0.1 kW h/t to 2.5 kW h/t). The standard errors (SE) of 4D models are 3.5% and 3.9%, which are more accurate than the JK t10, JK Mpq and King’s t10
Acknowledgements
The authors wish to acknowledge the financial support of the Commonwealth Scholarship from the Australian Government and Scholarships from the University of Queensland. The authors wish to acknowledge the partial financial support on supervision from AMIRA P9P project. The reviews and advice on this paper by Dr Marko Hilden and Dr Grant Ballantyne are highly appreciated.
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Formerly: University of Queensland, Julius Kruttschnitt Mineral Research Centre.