Size Specific Energy (SSE) – Energy Required to Generate Minus 75 Micron Material

Post-print copy

Title: Size Specific Energy (SSE) – Energy Required to Generate Minus 75 Micron Material

Authors: Grant R. Ballantyne1,2*, Wolfgang Peukert3 and Malcolm S. Powell1,2

1The University of Queensland, Sustainable Minerals Institute, Julius Kruttschnitt Mineral Research Centre. 40 Isles Road, Indooroopilly, Brisbane, QLD 4068, AUSTRALIA

2CRC ORE: Optimised Resource Extraction Level 7, Sir James Foots Building, The University of Queensland, St Lucia, QLD, Australia, 4072

3Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nuremberg. Cauerstrasse 4, D-91058 Erlangen, Germany

*Corresponding author | T: +61 7 3365 5839 | F: +61 7 3365 5999 | E: [email protected]

Published in: International Journal of Mineral Processing, 2015, Vol. 139, 2-6

Published version found online at: http://www.sciencedirect.com

DOI: 10.1016/j.minpro.2014.09.010

HIGHLIGHTS

 Single particles from 37.5 mm to 250 µm were comminuted via impact breakage.  The relationship between energy and the generation of -75 µm material was explored.  The initial particle size was found to influence the size specific energy.  A model was developed that accurately described the breakage results.  Size specific energy measurements enable quantification of energy efficiency.

GRAPHICAL ABSTRACT

Size specific energy

m) 40

µ 75 - 35 30 Ore 1 25 20 15 Ore 2 10

5 Size specific (kWh/t specific Size energy 0 0.1 1 10 100 Initial particle size (mm)

ABSTRACT

This paper explores the relationship between energy and the generation of minus 75 micron material. Rittinger’s law of comminution states that the energy input is proportional to the generation of new surface area. An accurate and consistent measurement of surface area, applicable across multiple size ranges is required to apply this practically. The amount of new -75 µm material generated has previously been proposed as a proxy for surface area. This has been demonstrated to some extent on a range of different laboratory equipment, but not in a manner suited to equipment-independent ore characterisation. To this end the JK Rotary Breakage Tester (JKRBT) and Schönert breakage device have been used to measure the progressive production of fines from cumulative single impacts starting with 37.5 mm particles down to 250 µm. As per expectation, the generation of -75 µm material was found to be proportional to the specific energy, but there was a secondary influence of size. A model was developed to describe the breakage and it was found that the standard t10 relationship could be used to effectively calculate the size specific energy. Measuring the intrinsic competence of an ore in this way can then be used to assess the energy efficiency of full-scale mills in relation to a lab scale test. It is envisaged that this relationship also has the potential to be used in the design of new comminution circuits. The methodology and the results from its application are presented for discussion and review.

Keywords: Comminution, Energy

INTRODUCTION

The relationship between energy and size reduction is of primary importance in the field of comminution. Rittinger (1867) was credited as proposing that the work done in crushing is proportional to the area of new surface produced. Just 18 years later, Kick (1885) proposed that for a homogeneous rock, the work input is proportional to the reduction in particle. Bond (1952) proposed the third theory, a compromise between the two earlier relationships, originally thought to infer proportionality with the length of new crack formation. Walker (1937) and later Hukki (1961) found that these three laws may not be mutually exclusive and are each applicable within a specific size range. Tavares and King (1998) proved experimentally that Kick’s assumption is valid at large sizes where the surface energy is negligible compared to the internal energy required for breakage. The results of Griffith (1921) have more recently been used to relate the increase in energy required to break smaller particles with the reduction in the probability of internal flaws and weaknesses (Napier-Munn et al., 2005; Wang and Forssberg, 2007).

This paper proposes the use of the energy required to produce new -75 µm material (hereafter referred to as size specific energy or SSE after (Powell et al., 2003-2010)) as a simplified measure across a broader range of particle sizes. Hukki (1979) first introduced this method to characterise the efficiency of closed grinding circuits. Later, Levin (1992) argued that the energy required to generate -75 µm material could be used as a competence measurement, providing similar results to the Bond work index. More recently, Hilden and Suthers (2010) found the linear relationship between energy and per cent -75µm to hold true over a wide range of machines, from crushing to ball milling (see Figure 1). Musa and Morrison (2009) found that typically 70 to 80% of the surface area of mill product existed below 75 µm. The 75 µm proxy has no intrinsic value. For circuits producing a much finer (or coarser) product, a finer (or coarser) proxy size may be more appropriate. They also found that the total surface area measured from coarse to fine was well enough limited at the fine end to justify the original Rittinger hypothesis that comminution energy generates new surface area – albeit not very efficiently. Therefore, the theory behind size specific energy may be related to the original Rittinger hypothesis.

100% 90%

80% y = 0.0228x + 0.3312

70%

75µm) - 60% y = 0.054x 50% 40% y = 0.0407x 30%

Fines (% Fines generated 20% Hilden and Suthers (2010) 10% Levin (1992) 0% 0 5 10 15 20 25 30 Specific energy (kWh/t)

Figure 1. Published size specific energy data. Currently, the standard method for calculating comminution unit energy efficiency is the ratio of operating work index and the Bond work index. This gives an indication of the efficiency of the milling circuit in relation to the Bond (1952) standard crush, rod and ball mill circuit. Observed and predicted specific energy calculations are displayed in Figure 2. The styles of the data points correspond to different databases. Filled data points were collated from the database published by Ballantyne and Powell (2014) and the unfilled data points were published in Morrell (2004). Sixty percent of the mines analysed had overall circuit efficiencies between 50 and 65 per cent. These low efficiency values indicated that there was great potential across the industry to improve efficiency of comminution equipment. However, when the efficiencies of the autogenous and semi-autogenous grinding (AG/SAG) circuits and the ball mill circuits were calculated a more complex underlying relationship was found. It is widely known that by calculating the energy efficiency using the Bond equation, AG/SAG circuits appear significantly less efficient. A number of researchers have attempted to account for this with a range of correction factors (Barratt and Allan, 1986; Rowland, 1988) and alternative power factors (Hukki, 1961; Morrell, 2004). The underlying reason for the discrepancy is that the Bond equation requires parallel feed and product size distributions in log/log space. AG/SAG mills do not fit this assumption because they tend to produce a large amount of fines without reducing the sieve size that 80% of the material passes (P80) significantly. Using the size specific energy to calculate the energy efficiency is more effective than the Bond equation because it is related to the generation of fines, not the reduction in the top size. However, a standard test procedure is required for this to be achieved (Musa and Morrison, 2009). The operating work index and size specific energy were found to be linearly related in the database published by Ballantyne et al. (2012). This linear relationship suggests similarity in the measurement of rock competence between the two methods. However, this may have been a result of the similar circuits across the sampled mines, because this would not be so if the gradient of the size distributions in log- log space changed.

Combined 25

20 AG/SAG

15 Observed kWh/t Observed 10 Ball

0 0 5 10 15 20 25 Bond predicted kWh/t

Figure 2. Comminution energy efficiency calculated using ratio between operating and Bond work indices (unfilled data points from Morrell (2004)).

METHOD

The relationship between input energy and generation of -75 µm material was tested using controlled single particle impacts. Two Australian copper-gold ores were tested and the feed particle sizes started at 37.5 mm and reduced to 250 µm over successive steps of breakage. The JKRBT was used for breaking particles larger than 4.75 mm with accurate input energies (Shi et al., 2006). Breakage of smaller particle sizes was achieved with the Schönert breakage device at Erlangen Institute of Particle Technology (Vogel and Peukert, 2005). This equipment is able to break particles in the size range 4.75 mm to 250 µm within a vacuum of 20 mbar, thus reducing errors associated with air-drag on the particles. Both machines utilise a spinning internal rotor to propel the particles outward, impacting with a stationary anvil ring (Figure 3).

Figure 3. Rotor/anvil configuration for both JKRBT and Schönert breakage device (Tavares, 2007).

The specific kinetic energy (kWh/t) of the particle before impact was determined by half the velocity of the particle squared. Theoretically, when the particle exits the rotor, its tangential and radial velocity components equal the tip speed. However, in practice the transfer of energy is not 100% efficient. For the JKRBT, these calibration factors have been established through high-speed video analysis (Shi et al., 2006). Discrete Element Modelling (DEM) was used to calculate the factors for the Schönert breakage device. Analysis of the DEM simulations allowed the velocity efficiency to be calculated for a range of particle sizes using the following equation (Weerasekara, 2013):

(1)

The breakage testwork procedure started with 90 particles between 37.5 and 26.5 mm and progressively comminuted these down through root-2 size intervals to 100% passing 250 µm (Figure 4). The methodology was repeated for energy levels between 0.4 and 3.5 kWh/t. Due to the small diameter of the rotor, the maximum input energy for the Schönert breakage device was 0.8 kWh/t. Care was taken to minimise sample losses that can occur during this type of testwork. This justified the assumption that all the material lost during the experiment was dust below 75 µm in size. On average this added 1.55 per cent to the -75 µm figures.

-37.5 mm Breakage +26.5 mm

-250 µm

-26.5 mm Breakage +19 mm

-250 µm Continue until minus 250 µm -19 mm +13.2 mm

Figure 4. Simplified testwork workflow. The Schönert breakage device replaced the JKRBT below 4.75 mm.

RESULTS

Previous work has shown linear relationships between cumulative comminution energy consumption and material generated below 75 µm (Hilden and Suthers, 2010; Hukki, 1979; Levin, 1992; Musa and Morrison, 2009). The results from this investigation have found that the generation of -75 µm is dependent on more than simply the input energy. The results for one of the two samples (Ore 1) are displayed in Figure 5. The sample was split into three and

Please reference as: Ballantyne, G.R., Peukert, W., Powell, M.S., 2015. Size specific energy (SSE)—Energy required to generate minus 75 micron material. International Journal of Mineral Processing 139, 2-6. Post-print copy progressively comminuted in the JKRBT at 1, 2 and 3 kWh/t. The generation of -75 µm material appeared relatively linear within each of these energy levels. The gradient of the relationship is consistent at different energy levels, but the y-intercept was strongly dependent on variability of the initial breakage event. Normalising the generation of -75 µm after the initial breakage event produced a linear relationship passing through the origin. However, this analysis simply proved the similarity of the gradients at different energy levels.

When the breakage was extended to finer sizes using the Schönert breakage device, the relationship visibly deviated from linearity. As the smaller particles were broken, the generation of -75 µm material for the same energy input increased.

15%

75 µm 75 - 10%

5% Cumulative of generation Cumulative

0% 0 1 2 3 4 Cumulative specific energy (kWh/t)

Figure 5. Ore-type 1: progressive generation of -75µm. The results for the second ore are displayed together with the first sample in Figure 6. Ore 2 was less competent than ore 1, producing significantly more -75 µm material at the same input energy levels. The Size Specific Energy (SSE) for the sample is the inverse of the gradient of a trendline forced to pass through the origin. For ore 1 and 2 the values are 24.9 and 11.1 kWh/t-75µm respectively. The scatter in the data results from a combination of ore variability, particle size effects and the relationship between impact velocity and specific energy. The SSE values corresponded well with historical survey results from the two mines. A comparison of the theoretical minimum energy measured through single particle breakage and mine site SSE resulted in the mines corresponding to ore 1 and 2 being 74% and 43% efficient respectively.

25% Ore 2

y = 0.09x

20%

75 µm 75 -

15% Ore 1 y = 0.04x

10%

5% Cumulative of generation Cumulative

0% 0 1 2 3 4 Cumulative specific energy (kWh/t)

Figure 6. Combined progressive generation of -75µm. The cumulative generation of -75 µm material displayed a slight non-linear relationship. To investigate this deeper, the results were analysed independently for each feed particle size. This technique revealed that the generation of -75 µm material increased with decreasing particle size. The cause of this trend is that the marker size of 75 µm corresponds to a smaller reduction ratio when the feed particle size is reduced. Therefore, since the breakage function was found to be consistent, smaller particles resulted in larger production of -75 µm material. This phenomenon was explored further through the development of a model to describe the breakage.

MODEL DEVELOPMENT

A model was developed to describe the results generated through the experimental program. The model was based on the breakage (appearance) function developed by Narayanan and Whiten (1988) and the modified Weibull (1939) distribution model developed by Vogel and Peukert (2005) and later modified by Shi and Kojovic (2007). Musa (2010) developed a similar technique to analyse the efficiency of breakage within crushers and mills. The degree of breakage was characterised using the t10 parameter which is defined as the percentage of material passing through a screen size one tenth the size of the initial geometric mean particle size. The Shi and Kojovic (2007) model (Equation 2) was used to reduce the t10 data from different input energies and initial particle sizes to one master curve (Figure 7).

t10 = M(1-exp[−fmat . x . (Ecs−Emin)]) (2)

Where M represents the maximum t10 for a material subject to breakage, fmat (1/kWh.m) is the material breakage property, x (m) the initial particle size Ecs (kWh) the mass-specific impact energy, and Emin (kWh) the threshold energy.

70%

60%

50%

40%

10 t 30%

20%

10%

0% 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Ecs.Fmat.x

Figure 7. Master curve showing the degree of breakage (t10) at different energy levels and initial particle sizes for ore 1.

Plotting of the degree of breakage (t10) parameter against the other reduction ratio parameters (t- family) provides the basis for determining the whole size distribution from the t10 parameter (Narayanan and Whiten, 1988). The results for ore 1 are displayed in Figure 8. To enable a more accurate prediction of the progeny over a wide range of t10, t1.2 and t150 values were added to the classic analysis. The t1.2 corresponds to the probability of breakage parameter as described by the proportion of material that falls through the screen below in a root two sieve series. This technique provide a method for linking the results from low energy collisions where breakage probability is the dominant descriptor and high energy impacts where t10 becomes dominant. A spline function is fitted through five chosen points that cover the whole range of t10 values. Using this technique, the whole t-family of curves can be described by a 5x7 matrix. This analysis technique is able to effectively describe the breakage progeny when self-similar breakage is apparent—as evident in this case.

100% 90% t 80% 1.2

70% t2

60% t4 50% t10 40% t

tn (% passing) (% tn 25 30% t75 20% t 10% 150 0% 0% 10% 20% 30% 40% 50% 60% 70%

Breakage Index, t10 (%)

Figure 8. Breakage (appearance) function for ore 1 in the form of the t-family of curves. Combining these t-family modeling techniques provides a robust methodology for determining the progeny from single particle impact tests over a wide range of input energies and initial particle sizes. Double parabolic interpolation functions were used to calculate the t-values from the experimental size distributions, the t-values that corresponded to the fitted t10, and the per cent passing screen sizes between the given t-values. The accuracy of the interpolation function was improved by taking the log of the particle size. The goodness of fit for this model over the range of tests completed within this experimental campaign is displayed in Figure 9. The top and bottom end of the size distribution was predicted more accurately than the intermediate sizes. This is evident in the wider scatter that is observable between the 30 and 70 per cent passing figures.

100% R² = 0.992

80%

60%

40% % passing (observed) %passing

20%

0% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% % passing (predicted)

Figure 9. Correlation between predicted and observed progeny size distributions obtained for ore 1. The model was tested to its limits by the predicting the size specific energy and its variability with initial particle size (Figure 10). As alluded to earlier, the %-75 µm corresponds to a larger t-value for coarser initial particle sizes. Therefore, since self-similar breakage is assumed in this model, the size specific energy is smaller for finer initial particle sizes. This trend matches the experimental data well across the wide range of initial particles sizes and energy levels. There is a sharp increase in the modeled SSE at the extreme coarse end of the distribution. In this range, 75 µm corresponds to large t-values and, the model under-predicts the amount of -75 µm material generated.

m) 40

µ 75

- 35

30 Ore 1 25 20 15 Ore 2 10

5 Size Size specific energy(kWh/t 0 0.1 1 10 100 Initial particle size (mm)

Figure 10. Relationship between initial particle size and size specific energy for both Ore 1 and 2. Error bars represent the standard deviation around the mean and the line is the predicted size specific energy from the model.

DISCUSSION

The SSE consumption is a useful metric for the determination of the practical comminution energy efficiency. Thermodynamic milling efficiencies are typically calculated as below 2 per cent, a value so low as to be useless (Fuerstenau and Abouzeid, 2002). Determining the practical minimum SSE from single particle impact breakage will result in a much more realistic and achievable efficiency benchmark. This can also be measured easily by sampling at different points around the comminution circuit to troubleshoot where the inefficiencies enter the system.

The SSE calculation has a key advantage over the use of t10—it can be found for single particle breakage as well as size distributions. Compared to Bond’s use of P80 it is more closely related to the surface area production than top size reduction and doesn’t rely on the assumption of parallel feed and product size distributions.

The SSE decreases with particle size—a result opposed to the traditional t10 approach. This highlights an inherent limitation in the calculation because the t10 changes with feed size, whereas the 75 µm marker does not. A factor related to the tn of the marker size may help reduce this effect, but may also affect the applicability of the results.

CONCLUSION

Single particles from 37.5 mm to 250 µm were broken using impact breakage—a wider range than previously attempted. This was achieved by combining coarse particle breakage data from the JKRBT with fine particle breakage using the Schönert breakage device. A linear relationship was observed between specific breakage energy and generation of -75 µm material for two ores comminuted via single particle impact. The inverse gradient of this relationship is

Please reference as: Ballantyne, G.R., Peukert, W., Powell, M.S., 2015. Size specific energy (SSE)—Energy required to generate minus 75 micron material. International Journal of Mineral Processing 139, 2-6. Post-print copy the SSE (kWh/t-75µm) which is a measure of the competence of an ore. This can be used as a benchmark and to provide a simple method for assessing the practical comminution energy efficiency of full scale grinding circuits. It can be used to assess energy efficiency of existing circuits, benchmark operations internationally, measure productivity improvements and assess performance of individual equipment.

A simple model relating the t10 to input energy, feed size and the resulting t-family of curves was developed to validate the results. Using this model, the size specific energy was calculated proving that the size specific energy is not independent from classical t10 analysis. Using this analysis technique, it is also possible to assess the breakage probability functions that were also previously thought of as independent variables.

ACKNOWLEDGMENTS

The authors would like to acknowledge the support of CRC ORE, established and supported by the Australian Government’s Cooperative Research Centres Program and all their sponsors who provided financial assistance for this research. We thank the research group at the Institute of Particle Technology at Erlangen University for their hospitality and the use of the Schönert breakage device. We thank JKTech management for their permission to access its database. Nirmal W contributed DEM simulations for this work

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