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Energy efficient comminution under high velocity impact fragmentation
Minerals Engineering 24 (2011) 1053–1061
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Energy efficient comminution under high velocity impact fragmentation Sepehr Sadrai a,⇑, John A. Meech a, Desmond Tromans b, Farrokh Sassani c a
Department of Mining Engineering, The University of British Columbia, Vancouver, BC, Canada V6T 1Z4 Department of Materials Engineering, The University of British Columbia, Vancouver, BC, Canada V6T 1Z4 c Department of Mechanical Engineering, The University of British Columbia, Vancouver, BC, Canada V6T 1Z4 b
a r t i c l e
i n f o
Article history: Received 19 October 2010 Accepted 14 May 2011 Available online 12 June 2011 Keywords: Mining Mineral Processing Comminution Crushing Grinding
a b s t r a c t In mining operations, comminution processes are responsible for most of the energy used during mineral recovery. Low fragmentation efficiency of comminution in the range of 1–2% (Tromans, 2008) occurs due to the quasi-static nature of the process which is typically accompanied by low impact velocities. Accurate estimation of efficiency requires a measurement system to account for fractal parameters such as surface roughness and fracture surface area. Continuum breakage models of single particles fail to estimate the actual stress transformation that affects bulk material during comminution. In order to study comminution in a dynamic regime at higher strain rates than those of conventional equipment, a compressed-air apparatus designed to launch a projectile at velocities as high as 450 m s1 has been developed to measure the quantitative nature of high-speed impacts on aggregated rock samples. A method to calculate the energy efficiency is also presented. The results of experiments conducted on three materials suggest the energy efficiency of rock breakage can be improved by two or three times under high velocity impact for the same energy input level. The paper reports an empirical model of impact velocity and energy input and discusses the advantages and limitations of this model. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The mining and mineral processing industry suffers from high energy costs attributed to the size reduction of large rocks to smaller fragments via compressive loading operations such as crushing and grinding. DOE (2005) reported that in the USA about 29% of the total mining industry energy or 0.4% of the total US energy consumption is used in comminution. In Canada and Australia, comminution is responsible for about 2% and 1.5% of total energy use, respectively (Tromans, 2008). In non-industrialized countries where mining constitutes a higher fraction of their industrial sector, comminution costs represent significant contribution to mine operating costs. This is compounded by the fact that comminution devices operate inefficiently since almost all the mechanical input energy is emitted as waste heat instead of generating new surface area (Austin, 1984). The energy efficiency of comminution equipment can be defined as the ratio of surface energy change to the mechanical energy input. Using this definition, the fragmentation efficiency of comminution is of the order of 1–2% (Fuerstenau and Abouzeid, 2002; Tromans and Meech, 2002). This is the typical range in efficiency of grinding that consumes most of the total energy used during mineral recovery. Crushing efficiencies are slightly higher ⇑ Corresponding author. Tel.: +1 604 822 2540; fax: +1 604 822 5599. E-mail address: [email protected] (S. Sadrai). 0892-6875/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2011.05.006
at 2–3%. High pressure grinding rolls (HPGR) and roller crushers are reported to operate at levels perhaps as much as 30–50% higher. Blasting efficiencies, ranging from 13% to 20%, are several times above that of conventional comminution equipment (Workman and Eloranta, 2003). The major mechanisms of breakage in comminution circuits such as ball and rod mills occur by both attrition (shear crushing between media sliding over each other) and impact loading. Rock fracture depends on particle size, the size and orientation of existing flaws, and the loading force. Hukki (1961) determined that more specific input energy is required as particle size decreases since smaller particles inevitably contain fewer and smaller flaws. Opposing impact forces on a particle create tensile stresses that may lead to failure depending on the distribution and orientation of flaws within the particle. The tensile strength of rock is 10% of the compressive strength (Napier-Munn et al., 1996), due to the presence of pre-existing flaws or cracks within the rock material. As compressive loading proceeds, it induces indirect tensile stresses that control rock fracture. In comminution, it seems that the low energy efficiency of rock breakage is limited by the effective transformation of compressive loading into a tensile component. The loading forces are generated in the main by gravity in a quasi-static regime at low impact velocities ranging from 1 to 10 m s1. Tromans (2008) theoretically estimated a maximum ideal energy efficiency of 5–9% for rock breakage under indirect tension, i.e., by conventional comminution. The levels of loading
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forces in mechanical devices have a wide distribution resulting in numerous impacts required before a sufficient force causes the particle to break (King and Tavares, 1997). Unsuccessful impacts generate elastic strain energy at crack tips within the particle which is released as thermal energy without producing any new surface area, thus contributing to overall inefficiency (Tromans and Meech, 2004).
Table 1 Range of typical static and dynamic loading. Operation
Feed Product Velocity (m s1) size size (mm) (mm)
Blasting New study Crushing Grinding
1 ? 400 20
400 ? 20 0.05
2000–15,000 102–103 104–1 104–1
Strain rate (s1)
Loading Energy efficiency regime (%)
100–20,000 10–102 105–101 105–101
13–20 ? 2–3 1–2
Dynamic Dynamic Static Static
2. Strain and strain rate effects In general, a stressed crack will only advance if there is a decrease in the energy of the local crack system, i.e., the decrease in local strain energy produced by crack tip advance must be sufficient to compensate for the increase in energy required to create new surface area at the propagating tip (e.g., see analysis by Courtney, 1990). The crack tip stress depends on crack length and the globally applied load, with longer cracks experiencing higher tip stresses. Consequently, for a loaded rock sample containing different sized cracks some will propagate and others will not. At low stress (load) rates, the largest cracks will propagate first. At very high stress rates, the rapidly rising load may achieve a value that allows the smaller cracks to reach the crack advance condition before the largest cracks have fully propagated to cause fracture. This is the origin of strain rate effects on fracture (e.g., see Liu et al., 1998) and it is well recognized that the mechanical properties of brittle materials such as rock strongly depend on deformation rate and strain rate (Grady and Kipp, 1979, 1980; Kipp et al., 1980; Whittles et al., 2006). Also, Zhang et al. (1999) indicated that the dynamic fracture toughness of the rock as well as crack branching increases with increasing loading rate. Studies performed by Sadrai et al. (2006) indicate that surface roughness and hence, specific surface area increases with increasing loading rate. These studies demonstrate that power efficiency (i.e., energy efficiency per unit time) or the rate of energy efficiency is significantly improved as the loading rate increases. 2.1. Static and dynamic loading Cho et al. (2003) noted that dynamic tensile strength increases at high strain rates because the existing cracks are arrested by the generation of large numbers of micro-cracks that consume energy and interfere with the formation of the fracture plane. However, violent fragmentation of a body can occur because of dynamic tensile stresses resulting from rapid energy imposition through contact forces (Grady, 1981, 1985). The strength of material increases as a function of strain rate. However, it is not well understood as to whether the process of rock fragmentation at higher strain rates is less competent than at lower rates in terms of energy efficiency. The evidence with respect to blasting would tend to support the theory that higher efficiencies accompany high strain rates. So despite an increased strength, the efficiency of energy transformation into new surface energy may also increase, possibly even more so at higher strain rate. The range of typical static and dynamic loading is shown in Table 1. In this table, the ‘‘New Study’’ refers to the velocity range covered by this research. It is evident that conventional comminution processes, which exhibit low energy efficiency, are associated with low (static) strain rates whereas blasting operations, which exhibit a higher energy efficiency, are associated with high (dynamic) strain rates or high impact velocities. In blasting, sudden increases in pressure and the rapid deposition of energy in a few milliseconds cause the rock to fracture in a dynamic environment. The explosive impact produces shock waves that move throughout the rock with high velocities (Liu and Katsabanis, 1997), while in
mechanical equipment, the impact occurs at low strain rates in a near static regime. Few studies have been done in the intermediate strain rate range between the extreme static and dynamic loading conditions. Consequently, studying the breakage function at impact velocities higher than those of comminution equipment and lower than those of blasting may clarify the energy efficiency behavior of brittle material in this range. 2.2. Breakage function testing methods The Bond work index is a suitable design criterion to determine rough energy requirements across the particle size range of interest in mining and mineral processing. However, the method provides no information regarding the effect of impact velocity governing fracture, and the amount and characteristics of fine particles that constitute much of the surface area produced (Sadrai and Meech, 2006). Other breakage testing methods utilize single particles in order to determine a particle size-energy relationship, whereas conventional comminution processes deal with bulk particulate materials with significant inter-particle effects that cannot be observed in single particle tests. Hypervelocity projectile impact has received much attention as a high loading rate technique, spurred by interest in the possible effects of meteorites and debris impacts upon space vehicles. Several methods have been explored to accelerate small projectiles. These include projection by compressed air, explosives, electromagnetic guns, as well as one and two-stage light gas guns. Limitations on the selection of a method include the strength of the gun and projectile, the length of the gun, and the attainable velocity. Projectile impact tests on single particle targets may involve impact velocities <50 m s1 (Hopkinson bar method) or more than 2 km s1 (two-stage light-gas gun, electromagnetic launcher) (Grosch and Riegel, 1993). Thornhill et al. (2006) reported a maximum velocity of about 20 km s1 is achievable for a small projectile utilizing a three-stage light gas gun. In contrast, typical impact velocities in industrial comminution equipment are well below 10 m s1 and it is desirable to study the effects of higher impact velocities in the range of 100–500 m s1 and to design experiments that provide information on the breakage of bulk materials. 2.3. Efficiency estimation under static fragmentation Conventional methods of energy estimation have not determined the influence of fractal parameters on the evaluation of rock properties. Interpretation of breakage phenomena requires measurement of surface roughness and an understanding of the influence of the resolution of the measurement technique on the precision of the measurement. Accordingly, Sadrai et al. (2006) developed a novel approach to measure surface roughness and surface area based on a fractal analysis procedure conducted on core samples of volcanic rocks. Changes in surface roughness of broken specimens under high loading rates were studied using a laser probe to generate 3D topographical maps of the fracture surfaces. It was shown that roughness and surface area measurements
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Reservoir Quick opening valve
Vacuum Projectile
Launch tube Coupling flanges
Chamber Velocity measurement
Fig. 1. Apparatus design configuration.
depend on the resolution used to produce these maps – a similar phenomenon occurs in the BET apparatus in comparing N2 gas (0.2 nm2 per molecule) versus Kr gas (0.04 nm2 per molecule) adsorption effects on the measured surface area. Surface area can be estimated based on theory, measurement, and empirical calculations. The results indicated that surface roughness and hence, specific surface area, increases with increasing loading rate by several orders of magnitude as particle size decreases. Overall accuracy of surface area measurement depends on several parameters such as shape factor estimation, weight measurement of each size fraction, assumptions inherent in a BET measurement, material porosity, and measurement resolution. Ultimately, a new method was proposed to increase the accuracy of the calculated surface area before and after breakage and to determine the amount of energy expended to create new surface area. It was concluded that high loading rates even in a static regime enhance energy efficiency and mineral liberation mainly due to significant improvement in the power efficiency as loading rate increases which suggests that productivity increases at higher loading rates (Sadrai, 2007). Power efficiency is defined as the energy efficiency per unit time or the rate of energy use. 3. Experimental procedures The present study required the design and construction of a new apparatus to comminute bulk particulate rock samples by launching a projectile at velocities between 100 and 500 m s1. The test facility can examine the influence of impact velocities on bulk materials to understand mechanisms of rock breakage similar to that in comminution equipment but at higher velocities. By testing bulk samples rather than single particles, the effect of void space for expansion of smaller broken particles can be studied. 3.1. Development of high velocity impact apparatus The compressed-air apparatus uses aggregated rock samples fragmented in a confined chamber while subjected to the transmission of stress waves produced at the point of contact by the impact of a 12-g steel projectile. The target chamber in which fragmentation occurs is able to hold 5–50 g of material with variable depths for the target bed (Fig. 1). This device is able to launch the projectile at a controlled velocity measured before impact by two pairs of laser diode detectors. Laser sensors mounted adjacent to the barrel record the projectile travel time which is used to obtain the dynamic fragmentation en-
ergy imparted to the test materials. Particle size analysis together with surface area measurements before and after breakage reveals the amount of energy resulting as new surfaces. The air inside the system and between particles is evacuated by a pump to a maximum negative pressure of 98.3 kPa to facilitate the launch of the projectile with least air resistance and to transfer the stress wave to particles located behind the point of impact. 3.2. Testwork material selection criteria Two aspects of rock behavior of particular interest include porosity and Poisson’s ratio (t) that may affect rock failure. Porosity contributes to a higher specific surface area after breakage from non-continuous pores within the particle that become exposed after breakage. This surface area is not caused by enhanced fragmentation and must be discounted from the measurements. Materials that exhibit intermediate values of Poisson’s ratio may exhibit a higher transformation of compressive forces to tensile stresses resulting in better fragmentation. For small values of t, the lateral stress induced by a given axial load is relatively small. In a dynamic experiment, material with a low Poisson’s ratio is expected to initiate failure by axial splitting since the lateral confining pressure is insufficient to suppress the tendency for crack initiation and propagation. Ceramic materials with a low Poisson ratio tend to fail by brittle cracking leading to high fragmentation. On the other hand, a material with a high Poisson’s ratio may induce higher confinement preventing microcracks from sliding and also leading to brittle failure. Thus, the failure mode is associated with plastic flow for large values of t (Chen and Ravichandran, 2000). The effect of high velocity impact on rock material properties has been suggested to mask or remove the influence of Poisson’s ratio on breakage (Katsabanis et al., 2003). Based on these considerations, as shown in Table 2, experiments were conducted on three different materials – highly porous limestone, quartz with low specific surface area (low porosity), and rock salt with the highest Poisson’s ratio of the materials selected. 3.3. Particle size distribution analysis After preparing materials to the required size, bulk samples (2 mm + 1 mm) were selected to undergo experiments in order to conduct particle breakage in the range of a typical grinding operation. Two bed depths were studied. Zone ‘‘A’’ and ‘‘B’’ were designated with a target bed depth of 75 mm (13 g) and 150 mm (25 g), respectively. Particle size distribution analysis was done after each
Table 2 Relevant Properties of rock samples used in this test work.
*
Rock type
S.G. (g cm3)
Initial bulk density (g cm3)
Poisson’s ratio
Initial specific surface area (m2 g1)
Specific surface energy (J m2)*
Limestone Quartz Rock salt
2.61 2.64 2.10
1.36 1.40 1.28
0.215 0.078 0.300
0.728 0.005 0.020
1.000 2.678 0.577
Tromans and Meech, 2004.
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Limestone (13 g)
Limestone (25 g)
100
100 90
80 70 60 50 40
LA00
30
LA80 LA110
20
LA180
10
80
Cumulative passing (%)
Cumulative passing (%)
90
70 60 50 40
LB00 LB70
30
LA270
0
LB180
20
LB240
10
LB300
0
0
500
1000
1500
2000
0
500
Particle size (micron)
1000
(a)
2000
(b)
Quartz (13 g) 100
100
90
90
80
80
70 60 50 QA00
40
QA80 QA110
30
QA140
20
QA160
Cumulative passing (%)
Cumulative passing (%)
1500
Particle size (micron)
QA190
10
Quartz (25 g)
70 60 50 40 30
QB00 QB70
20
QB110
10
QA220
QB190
0
0 0
500
1000
1500
0
2000
500
Particle Size (micron)
1000
1500
2000
Particle Size (micron)
(c)
(d) Rock Salt (13 g)
100
Cumulative Passing (%)
90 80 70 60 50 40 SA00
30
SA80
20
SA110 SA160
10
SA200
0 0
500
1000
1500
2000
Particle Size (micron)
(e) Fig. 2. Particle size analysis at variable impact velocities: (a) limestone 13 g, (b) limestone 25 g, (c) quartz 13 g, (d) quartz 25 g, (e) rock salt 13 g, (A = zone A, B = zone B, L = limestone, Q = quartz, S = salt; LA80 means limestone of zone A with a velocity of 80 m.s1).
test for all samples. The representative sample demonstrates the material size before breakage (i.e., at zero impact velocity). These analyses are shown in Fig. 2a–e as represented by the black solid lines for each test.
It can be seen that substantial improvements in breakage (reduced p80 sizes) of the 75 mm tests for all rock samples occur as the impact velocity increases, but breakage of limestone in a bed depth of 150 mm shows little improvement and exhibits erratic
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100
100
90
90
80
70
Wt % (-1 mm)
Wt % (-1 mm)
80 60 50 40 30
QA (75)
60
QB (150)
50 40 30 20
20
LA (75)
10
LB (150)
0
70
10 0
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
Velocity (m/s)
Velocity (m/s)
(a)
(b) 100 90
Wt % (-1 mm)
80 70 60 50 40 30 20 10 0
SA (75)
0
50
100
150
200
250
Velocity (m/s)
(c) Fig. 3. Weight percent of 1 mm vs. impact velocity: (a) limestone zone A and B, (b) quartz zone A and B, (c) rock salt zone A, (zone A = 13 g or 75 mm, zone B = 25 g or 150 mm, L = limestone, Q = quartz, S = salt).
behavior. The breakage of quartz in a bed depth of 150 mm also shows anomalous behavior with only a small increase in the 80% passing size as velocity increases. Breakage of rock salt in a bed depth of 150 mm was not performed since this depth was likely too far to propagate the shock wave. Fig. 3a–c presents weight percentage of 1 mm material before and after breakage as a function of impact velocity for all samples tested in both zones. Note that the percent 1 mm increases substantially with velocity indicating initial breakage likely occurs by attrition (shear breakage). At this size, more fragmentation in zone A than zone B indicates better use of energy in shallower depths particularly at high impact velocities. With increased bed depth, the impact shock wave is unable to reach the material at the end of the chamber with sufficient intensity to cause breakage. Clearly, bed depth plays an important role in determining the breakage of material at high impact velocities. 3.4. Specific surface area measurements A Quantachrome surface area analyzer (BET) was used to measure the specific surface area (SSA) of the materials before and after each test using nitrogen gas. In this way, the new surface area produced by impact can be calculated. The range of change in SSA as a function of impact velocity shows substantial improvements for all samples tested in both zones (Fig. 4). In order to measure the SSA by BET, broken material is divided into different size fractions. Therefore, it is possible to plot the SSA as a function of particle size. The particle size reported is the geometric mean of the upper and lower limit of the split size. Fig. 5 shows the results for limestone and quartz as a function of particle size for zone A breakage. Note that the SSA for the same
particle size is higher for all sizes with increasing impact velocity indicating that the surface becomes much rougher as velocity increases – particularly for the finer particles.
3.5. Energy efficiency estimation model In this model, the energy efficiency of breakage is defined as the ratio of energy output to energy input (Sadrai and Meech, 2006). Before and after each test, the surface area of material allows the total surface area produced by breakage to be calculated for the retrieved amount of material (material losses averaged 3% and showed no correlation with velocity). The new surface area provides a measure of the total energy output together with the specific surface energy of the solid (see Table 2). Energy input is calculated from the mass of the projectile and its impact velocity (see Eq. (1)). Table 3 shows the result of these calculations for all samples.
g¼
ðSSA2 SSA1 ÞW SE 1 MV 2 2
100 ¼
200ðSSA2 SSA1 ÞW SE MV 2
ð1Þ
where g = energy efficiency (%); SSA2 = specific surface area after breakage (m2 g1); SSA1 = specific surface area before breakage (m2 g1); W = weight of sample (g); SE = specific surface energy (J m2); M = projectile mass (kg); V = projectile velocity (m s1). Fig. 6 shows the influence of impact velocity on the energy efficiency of rock breakage for all samples tested in both zones. As can be seen, the efficiency of all samples is substantially improved with increased impact velocities. However, all sets of data appear to exhibit a peak efficiency within the velocity range of 180–220 m s1.
S. Sadrai et al. / Minerals Engineering 24 (2011) 1053–1061 2.50
0.45 LA (75 mm) LB (150 mm)
2.00
Specific Surface Area (m2/g)
Specific Surface Area (m2/g)
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Limestone
MAX
1.50 MIN
1.00 0.81 0.66 0.50 0.00
0
50
100
150
200
250
300
350
0.40
Quartz
QA (75 mm) QB (150 mm)
0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
0
50
100
150
Velocity (m/s)
Velocity (m/s)
(a)
(b)
200
250
Specific Surface Area (m2/g)
0.300 Rock Salt
SA (75 mm)
0.250 0.200 0.150 0.100 0.050 0.000
0
50
100
150
200
250
Velocity (m/s)
(c) Fig. 4. Specific surface area vs. impact velocity: (a) limestone zone A and B, (b) quartz zone A and B, (c) rock salt zone A, (zone A = 13 g or 75 mm, zone B = 25 g or 150 mm, L = limestone, Q = quartz, S = salt).
2.50 LA80
Limestone
LA110
2.00
LA180
SSA (m2/g)
SSA (m2/g)
LA270
1.50
1.00
0.50
0.00
0
200
400
600
800
1000
Mean Particle Size (micron)
0
200
400
600
800
1000
Mean Particle Size (micron)
Fig. 5. Specific surface area vs. particle size for limestone and quartz (zone A).
It is clear that the energy efficiency trend prior to this peak doubles or triples with increasing impact velocity. 4. Results and discussions Although fragmentation under high velocity impact has been studied for some time, it has been unclear if the observed increase in energy efficiency for a similar total energy input occurs when strain rates are increased. For years, the use of explosives has provided a way to break rock in tension with efficiencies about one order of magnitude above that of comminution. The results of this work show that higher strain rates do provide increased efficiencies in terms of generating new surface area. Strain rates higher
than those achieved by conventional comminution equipment create an opportunity to save considerable amounts of money and energy and liberate valuable minerals by processing lower grade ores more efficiently. 4.1. Impact velocity and energy input model In this study, the breakage model utilizes the kinetic energy content of the projectile (i.e. velocity and mass) to determine efficiency. We find that breakage occurs more efficiently as impact velocities increases to at least 200 m s1. The question remains whether the level of specific energy input (J g1) or velocity (m s1) causes this enhancement? These two factors are directly
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Table 3 Calculation of energy efficiency for all samples tested.
*
Produced SSA* (m2 g1)
Energy output (J)
Energy input (J)
Energy efficiency (%)
LA80 LA110 LA180 LA270
0.026 0.154 0.613 1.206
0.33 2.00 7.97 15.68
39.19 73.11 188.10 414.44
0.85 2.74 4.24 3.78
LB70 LB180 LB240 LB300
0.008 0.392 0.753 0.708
0.21 9.81 18.84 17.71
30.68 190.91 324.98 527.93
0.68 5.14 5.80 3.35
QA80 QA110 QA140 QA160 QA190 QA220
0.017 0.044 0.097 0.153 0.255 0.396
0.60 1.53 3.38 5.34 8.87 13.80
38.41 64.66 121.27 145.80 209.62 268.72
1.57 2.36 2.79 3.66 4.23 5.13
QB70 QB110 QB190
0.003 0.014 0.047
0.21 0.92 3.17
30.65 71.16 209.40
0.70 1.30 1.51
SA80 SA110 SA160 SA200
0.010 0.060 0.160 0.209
0.08 0.45 1.20 1.57
32.91 69.24 149.28 242.60
0.23 0.65 0.80 0.65
ηe = 0.59 EQ0.64
E.Eff. (%)
Sample
ηe = 0.57 EL0.64 1
Quartz
ηe = 0.19 ES0.52
Limestone Salt
0.1 1
10
100
Specific Energy Input (J.g-1) Fig. 7. Energy efficiency vs. specific energy input.
10
Specific surface area.
ηe = 0.0041 VQ1.28 ηe = 0.0042 VL1.27
E.Eff. (%)
6 QA
Energy Efficiency (%)
5
QB LA LB
4
1
SA
3
Quartz
ηe = 0.0032 V S1.05
Limestone Salt
2
0.1 10
100
1000
Impact Velocity (m.s-1)
1
Fig. 8. Energy efficiency vs. impact velocity.
0
0
50
100
150
200
250
300
350
Velocity (m/s) Fig. 6. Comparison of energy efficiencies (Q = quartz, L = limestone, S = rock salt, A = zone A, B = zone B).
related via a general energy formula. The energy efficiency as a function of specific energy input and impact velocity for all samples are shown in Figs. 7 and 8, respectively. Specific energy input is a function of velocity squared, hence one could conclude that Figs. 7 and 8 are simply plots of efficiency as a function of two dependent variables, i.e., the plots are the same graphs. However, note that the trend lines for the data in Fig. 7 exhibit slopes above 0.5 (0.64 for both limestone and quartz and 0.52 for rock salt). This indicates that the specific energy level plays a role in the overall efficiency independent of velocity.
ge ¼ K e ðEÞ0:60
gv ¼ K V ðVÞ1:2
ð3Þ
gv = energy efficiency (based on impact velocity) (%); V = impact velocity (m s1); Kv = velocity index (% (s/m)1.2). These equations are empirical with validity over the range of impact velocity measurements, (50–300 m s1), i.e., in a dynamic regime. The energy index (Ke) and velocity index (Kv) are also empirical parameters affected by many factors such as the type of material, material characteristics, mechanical properties of the material, Poisson’s ratio, grain size, density, porosity, environment, etc. To determine these factors, a large number of similar tests with different materials and different variations are required. The experiments should be extended to higher and lower velocities than those in the current study in order to measure the value of Ke and Kv over a wider dynamic range. Similarly, parallel experiments should be performed to establish Ke and Kv in the static range.
ð2Þ
where ge = energy efficiency (based on energy input) (%); E = specific energy input (J g1); Ke = energy index (% (g/J) 0.60). In a similar fashion, the trend lines for data in Fig. 8 show a slope greater than 1.0 (1.27 for limestone, 1.28 for quartz, and 1.05 for rock salt) again supporting the concept that specific surface energy plays a role independent of velocity – otherwise the slope would be 1.0.
4.2. Pressure model of work efficiency The developed model utilizes a change in surface area of rock material as the output of the fragmentation process caused by the impact energy of a projectile. The work done on the sample can also be estimated by direct measurement of pressure and volume changes during breakage. Since the material is broken in a
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Table 4 Pressure model of maximum work efficiency for all samples tested. Sample
Work output (DPV)
Work output (% of energy input)
Ratio of surface energy change to work output
LA80 LA110 LA180 LA270
1.60 3.55 8.87 19.52
4.08 4.86 4.72 4.71
0.21 0.56 0.90 0.80
LB70 LB180 LB240 LB300
1.33 11.09 22.36 28.40
4.34 5.81 6.88 5.38
0.16 0.88 0.84 0.62
QA80 QA110 QA140 QA160 QA190 QA220
0.80 2.22 7.10 11.98 13.31 19.17
2.08 3.43 5.85 8.22 6.35 7.13
0.76 0.69 0.48 0.45 0.67 0.72
QB70 QB110 QB190
0.80 2.00 9.32
2.61 2.81 4.45
0.27 0.46 0.34
SA80 SA110 SA160 SA200
1.33 3.33 8.43 17.35
4.04 4.81 5.65 7.15
0.06 0.14 0.14 0.09
confined chamber, the change in volume can be calculated by measuring the compaction level of the material during experiments. Impact pressure can also be estimated by the projection of force from the initial reading of the regulator installed in the pressure line before launching the projectile. Therefore, the work performed to compress the bulk material can be obtained. The ratio of this work to the energy input imparted by the projectile velocity represents the maximum work efficiency achievable in each test (Table 4). The ratio of energy efficiency obtained based on surface area measurements (see Table 3) to the maximum work efficiency indicates what percentage of the work done in compressing the bulk material is transferred into breakage and new surface area (or energy). It is assumed in these calculations that the loss of pressure during the flight of the projectile is negligible and that the resistance of any small amount of air during acceleration is insignificant. The total energy input to the projectile is produced as the projectile accelerates along the barrel. At the point of contact with the material, the projectile has gained its maximum energy according to its velocity. At this moment, the free traveling of the projectile is completed and it begins transferring its energy to the rock material in the form of some partially reversible work. This compression (or work) measured in the form of changes in pressure and volume is equal to DPV. Some of this work is reversible as the sample compresses to a higher bulk density and then rebounds off the walls of the target chamber. During compression, breakage occurs causing a change in surface energy (non-reversible). All of the remaining energy eventually is wasted mostly as heat and sound. As shown in Tables 3 and 4, the work done by the projectile in compressing the target bulk material is of a similar order of magnitude to that of the newly created surface energy. It is unclear if this work is a parallel energy path or a serial one, i.e., does the rebound energy result in any additional breakage? Perhaps, a combination of these two modes of transformation of compression to tension takes place. In a parallel path, the impact energy is utilized to contract the material and create new surface area both at the same time, while in a serial path the newly created surface area is the result of pressure and volume change. The ratio of surface energy change to work done is much lower for rock salt compared with quartz and limestone suggesting a parallel path dominates in the case of rock salt.
4.3. Effect of material porosity Porosity in rock particles affects the measurement of surface area by allowing nitrogen gas (absorbent) to enter the pores. The amount of adsorbed gas on the free surface of particles determines the specific surface area of the material. After breakage of highly porous rock samples, i.e., volcanic rock such as tuff, the surface area of the closed pores is considered part of the measurement despite the fact that input energy had no effect in actually creating these surfaces. In fact, the majority of the increased surface area is due to porosity and not to fragmentation since the initial measurement prior to breakage did not account for pore surface area. Porosity inflates the measurement of new surface area after breakage due to the exposure of pores and so, a high and erroneous estimate of energy efficiency results. Although pores likely decrease the overall rock strength, a cellular structure with highly porous material may prevent a crack from propagating whenever it meets a void. This could result in a strengthening of the material (a dampening effect). As such, the effect of high rock porosity on measurement of energy efficiency of breakage is yet to be fully understood because of its complex nature. In the dynamic tests, if the pores are all open prior to breakage, then the pore surfaces are measured both before and after which cancel out in terms of measuring surface area change. The vast majority of porosity in rock is open-pores so this is a reasonable assumption. The presence of non-continuous pores of total volume relative to the particle size will produce large errors in measuring energy efficiency in the way proposed in this work. 5. Conclusion Our studies have attempted to exploit impact engineering as a solution for rock breakage in mining and comminution problems. In dynamic fragmentation, a high-velocity impact comminution apparatus was designed and built to directly measure the quantitative parameters of impact velocity on aggregated rock materials. Experiments on three rock materials – porous limestone, quartz, and rock salt, were conducted at projectile velocities from 50 to 300 m s1. The results show that the energy efficiency of rock breakage is improved by as much as 2–3 times under high velocity impact. To summarize, the following conclusions can be made: 1. Utilization of high strain rates and high-velocity impact in comminution provides an opportunity to improve energy efficiency in rock breakage significantly. 2. Regardless of mineralogy, high-velocity impact helps explain the reported increase in efficiency of higher impact crushing technologies (high pressure grinding rolls (HPGR), Barmac, and roller crushers). 3. The depth of particle bed is a key variable in determining the fragmentation of rocks and minerals by high velocity impact. This may not be the case with static loading. 4. Impact velocity is a key variable in enhancing the efficiency of rock fragmentation and has an important effect independent of total energy input. 5. Future work should focus on designing new devices to increase impact intensity during comminution.
References Austin, G.L., 1984. Gaudin lecture: concepts in process design of mills. Mining Engineering 36 (6), 628–635. Chen, W., Ravichandran, G., 2000. Failure mode transition in ceramics under dynamic multiaxial compression. International Journal of Fracture 101 (1–2), 141–159.
S. Sadrai et al. / Minerals Engineering 24 (2011) 1053–1061 Cho, S.H., Ogata, Y., Kaneko, K., 2003. Strain-rate dependency of the dynamic tensile strength of rock. International Journal of Rock Mechanics and Mining Sciences 40, 763–777. Courtney, T.H., 1990. Mechanical Behavior of Materials. McGraw-Hill Publishing Company, University of Virginia. DOE, 2005. Mining Industry of the Future Fiscal Year 2004 Annual Report, Industrial Technologies Program, US Department of Energy, Energy Efficiency and Renewable Energy. Fuerstenau, D.W., Abouzeid, A.-Z.M., 2002. The energy efficiency of ball milling in comminution. International Journal of Mineral Processing 67 (1–4), 161– 185. Grady, D.E., 1981. Fragmentation of solids under impulsive stress loading. Journal of Geophysical Research 86 (B2), 1047–1054. Grady, D.E., 1985. Mechanics of Fracture under High-rate Stress Loading. Mechanics of Geomaterial: Rocks Concrete Soils. John Wiley & Sons, pp. 129–156. Grady, D.E., Kipp, M.E., 1979. The micromechanics of impact fracture of rock. International Journal of Rock Mechanics and Mining Sciences, Geomechanics Abstracts 16, 293–302. Grady, D.E., Kipp, M.E., 1980. Continuum modelling of explosive fracture in oil shale. International Journal of Rock Mechanics and Mining Sciences, Geomechanics Abstracts 17, 147–157. Grosch, D.J., Riegel, J.P., 1993. Development and optimization of a micro two-stage light gas gun. International Journal of Impact Engineering 14, 315–324. Hukki, R.T., 1961. Proposal for a solomonic settlement between the theories of von Rittinger, Kick, and Bond. Translation, Society of Mining Engineers of AIME 220, 403–408. Katsabanis, P.D., Gregersen, S., Pelley, C., Kelebek, S., 2003. Small scale study of damage due to blasting and implications on crushing and grinding. In: Proceedings of the 29th Conference on Explosives and Blasting Technique, Nashville, TN, v2, pp. 353–361. King, R.P., Tavares, L.M., 1997. Establishing the energy efficiency of a ball mill. In: Kawatra, S. (Ed.), Comminution practices. Society for Mining, Metallurgy and Exploration Inc. (SME), Littleton, CO, USA, pp. 311–316. Kipp, M.E., Grady, D.E., Chen, E.P., 1980. Strain-rate dependent fracture initiation. International Journal of Fracture 16 (5), 471–478.
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Liu, C., Knauss, W.G., Rosakis, A.J., 1998. Loading rates and the dynamic initiation toughness in brittle solids. International Journal of Fracture 90, 103–118. Liu, L., Katsabanis, P.D., 1997. Development of a continuum damage model for blasting analysis. International Journal of Rock Mechanics and Mining Sciences 34 (2), 217–231. Napier-Munn, T.J., Morrell, S., Morrison, R.D., Kojovic, T., 1996. Mineral Comminution Circuits: Their Operation and Optimization, JKMRC, Australia. Sadrai, S., 2007. High Velocity Impact Fragmentation and the Energy Efficiency of Comminution. PhD Thesis, The University of British Columbia, Vancouver, Canada. Sadrai, S., Meech, J.A., 2006. High velocity impact: what it means for comminution. In: Annual Meeting of Canadian Mineral Processors of British Columbia (CMP 2006), Canadian Institute of Mining (CIM), Vancouver, Canada. Sadrai, S., Meech, J.A., Ghomshei, M., Sassani, F., Tromans, D., 2006. Influence of impact velocity on fragmentation and the energy efficiency of comminution. International Journal of Impact Engineering 33, 723–734. Thornhill, T.F., Chabildas, L.C., Reinhart, W.D., Davidson, D.L., 2006. Particle launch to 19 km/s for micro-meteoroid simulation using enhanced three-stage light gas gun hypervelocity launcher techniques. International Journal of Impact Engineering 33, 799–811. Tromans, D., 2008. Mineral comminution: energy efficiency considerations. Journal of Minerals Engineering 21 (8), 613–620. Tromans, D., Meech, J.A., 2002. Fracture toughness and surface energies of minerals. Journal of Minerals Engineering 15 (12), 1027–1041. Tromans, D., Meech, J.A., 2004. Fracture toughness and surface energies of covalent minerals: theoretical estimates. Journal of Minerals Engineering 17, 1–15. Whittles, D.N., Kingman, S., Lowndes, I., Jackson, K., 2006. Laboratory and numerical investigation into the characteristics of rock fragmentation. Mining Engineering 19, 1418–1429. Workman, L., Eloranta, J., 2003. The effects of blasting on crushing and grinding efficiency and energy consumption. In: Proceedings of the 29th Conference on Explosives and Blasting Techniques, International Society of Explosive Engineers, Cleveland, OH, pp. 1–5. Zhang, Z.X., Kou, S.Q., Yu, J., Yu, Y., Jiang, L.G., Lindqvist, P.A., 1999. Effects of loading rate on rock fracture. International Journal of Rock Mechanics and Mining Sciences 36, 597–611.
Contents lists available at ScienceDirect
Minerals Engineering journal homepage: www.elsevier.com/locate/mineng
Energy efficient comminution under high velocity impact fragmentation Sepehr Sadrai a,⇑, John A. Meech a, Desmond Tromans b, Farrokh Sassani c a
Department of Mining Engineering, The University of British Columbia, Vancouver, BC, Canada V6T 1Z4 Department of Materials Engineering, The University of British Columbia, Vancouver, BC, Canada V6T 1Z4 c Department of Mechanical Engineering, The University of British Columbia, Vancouver, BC, Canada V6T 1Z4 b
a r t i c l e
i n f o
Article history: Received 19 October 2010 Accepted 14 May 2011 Available online 12 June 2011 Keywords: Mining Mineral Processing Comminution Crushing Grinding
a b s t r a c t In mining operations, comminution processes are responsible for most of the energy used during mineral recovery. Low fragmentation efficiency of comminution in the range of 1–2% (Tromans, 2008) occurs due to the quasi-static nature of the process which is typically accompanied by low impact velocities. Accurate estimation of efficiency requires a measurement system to account for fractal parameters such as surface roughness and fracture surface area. Continuum breakage models of single particles fail to estimate the actual stress transformation that affects bulk material during comminution. In order to study comminution in a dynamic regime at higher strain rates than those of conventional equipment, a compressed-air apparatus designed to launch a projectile at velocities as high as 450 m s1 has been developed to measure the quantitative nature of high-speed impacts on aggregated rock samples. A method to calculate the energy efficiency is also presented. The results of experiments conducted on three materials suggest the energy efficiency of rock breakage can be improved by two or three times under high velocity impact for the same energy input level. The paper reports an empirical model of impact velocity and energy input and discusses the advantages and limitations of this model. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The mining and mineral processing industry suffers from high energy costs attributed to the size reduction of large rocks to smaller fragments via compressive loading operations such as crushing and grinding. DOE (2005) reported that in the USA about 29% of the total mining industry energy or 0.4% of the total US energy consumption is used in comminution. In Canada and Australia, comminution is responsible for about 2% and 1.5% of total energy use, respectively (Tromans, 2008). In non-industrialized countries where mining constitutes a higher fraction of their industrial sector, comminution costs represent significant contribution to mine operating costs. This is compounded by the fact that comminution devices operate inefficiently since almost all the mechanical input energy is emitted as waste heat instead of generating new surface area (Austin, 1984). The energy efficiency of comminution equipment can be defined as the ratio of surface energy change to the mechanical energy input. Using this definition, the fragmentation efficiency of comminution is of the order of 1–2% (Fuerstenau and Abouzeid, 2002; Tromans and Meech, 2002). This is the typical range in efficiency of grinding that consumes most of the total energy used during mineral recovery. Crushing efficiencies are slightly higher ⇑ Corresponding author. Tel.: +1 604 822 2540; fax: +1 604 822 5599. E-mail address: [email protected] (S. Sadrai). 0892-6875/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2011.05.006
at 2–3%. High pressure grinding rolls (HPGR) and roller crushers are reported to operate at levels perhaps as much as 30–50% higher. Blasting efficiencies, ranging from 13% to 20%, are several times above that of conventional comminution equipment (Workman and Eloranta, 2003). The major mechanisms of breakage in comminution circuits such as ball and rod mills occur by both attrition (shear crushing between media sliding over each other) and impact loading. Rock fracture depends on particle size, the size and orientation of existing flaws, and the loading force. Hukki (1961) determined that more specific input energy is required as particle size decreases since smaller particles inevitably contain fewer and smaller flaws. Opposing impact forces on a particle create tensile stresses that may lead to failure depending on the distribution and orientation of flaws within the particle. The tensile strength of rock is 10% of the compressive strength (Napier-Munn et al., 1996), due to the presence of pre-existing flaws or cracks within the rock material. As compressive loading proceeds, it induces indirect tensile stresses that control rock fracture. In comminution, it seems that the low energy efficiency of rock breakage is limited by the effective transformation of compressive loading into a tensile component. The loading forces are generated in the main by gravity in a quasi-static regime at low impact velocities ranging from 1 to 10 m s1. Tromans (2008) theoretically estimated a maximum ideal energy efficiency of 5–9% for rock breakage under indirect tension, i.e., by conventional comminution. The levels of loading
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forces in mechanical devices have a wide distribution resulting in numerous impacts required before a sufficient force causes the particle to break (King and Tavares, 1997). Unsuccessful impacts generate elastic strain energy at crack tips within the particle which is released as thermal energy without producing any new surface area, thus contributing to overall inefficiency (Tromans and Meech, 2004).
Table 1 Range of typical static and dynamic loading. Operation
Feed Product Velocity (m s1) size size (mm) (mm)
Blasting New study Crushing Grinding
1 ? 400 20
400 ? 20 0.05
2000–15,000 102–103 104–1 104–1
Strain rate (s1)
Loading Energy efficiency regime (%)
100–20,000 10–102 105–101 105–101
13–20 ? 2–3 1–2
Dynamic Dynamic Static Static
2. Strain and strain rate effects In general, a stressed crack will only advance if there is a decrease in the energy of the local crack system, i.e., the decrease in local strain energy produced by crack tip advance must be sufficient to compensate for the increase in energy required to create new surface area at the propagating tip (e.g., see analysis by Courtney, 1990). The crack tip stress depends on crack length and the globally applied load, with longer cracks experiencing higher tip stresses. Consequently, for a loaded rock sample containing different sized cracks some will propagate and others will not. At low stress (load) rates, the largest cracks will propagate first. At very high stress rates, the rapidly rising load may achieve a value that allows the smaller cracks to reach the crack advance condition before the largest cracks have fully propagated to cause fracture. This is the origin of strain rate effects on fracture (e.g., see Liu et al., 1998) and it is well recognized that the mechanical properties of brittle materials such as rock strongly depend on deformation rate and strain rate (Grady and Kipp, 1979, 1980; Kipp et al., 1980; Whittles et al., 2006). Also, Zhang et al. (1999) indicated that the dynamic fracture toughness of the rock as well as crack branching increases with increasing loading rate. Studies performed by Sadrai et al. (2006) indicate that surface roughness and hence, specific surface area increases with increasing loading rate. These studies demonstrate that power efficiency (i.e., energy efficiency per unit time) or the rate of energy efficiency is significantly improved as the loading rate increases. 2.1. Static and dynamic loading Cho et al. (2003) noted that dynamic tensile strength increases at high strain rates because the existing cracks are arrested by the generation of large numbers of micro-cracks that consume energy and interfere with the formation of the fracture plane. However, violent fragmentation of a body can occur because of dynamic tensile stresses resulting from rapid energy imposition through contact forces (Grady, 1981, 1985). The strength of material increases as a function of strain rate. However, it is not well understood as to whether the process of rock fragmentation at higher strain rates is less competent than at lower rates in terms of energy efficiency. The evidence with respect to blasting would tend to support the theory that higher efficiencies accompany high strain rates. So despite an increased strength, the efficiency of energy transformation into new surface energy may also increase, possibly even more so at higher strain rate. The range of typical static and dynamic loading is shown in Table 1. In this table, the ‘‘New Study’’ refers to the velocity range covered by this research. It is evident that conventional comminution processes, which exhibit low energy efficiency, are associated with low (static) strain rates whereas blasting operations, which exhibit a higher energy efficiency, are associated with high (dynamic) strain rates or high impact velocities. In blasting, sudden increases in pressure and the rapid deposition of energy in a few milliseconds cause the rock to fracture in a dynamic environment. The explosive impact produces shock waves that move throughout the rock with high velocities (Liu and Katsabanis, 1997), while in
mechanical equipment, the impact occurs at low strain rates in a near static regime. Few studies have been done in the intermediate strain rate range between the extreme static and dynamic loading conditions. Consequently, studying the breakage function at impact velocities higher than those of comminution equipment and lower than those of blasting may clarify the energy efficiency behavior of brittle material in this range. 2.2. Breakage function testing methods The Bond work index is a suitable design criterion to determine rough energy requirements across the particle size range of interest in mining and mineral processing. However, the method provides no information regarding the effect of impact velocity governing fracture, and the amount and characteristics of fine particles that constitute much of the surface area produced (Sadrai and Meech, 2006). Other breakage testing methods utilize single particles in order to determine a particle size-energy relationship, whereas conventional comminution processes deal with bulk particulate materials with significant inter-particle effects that cannot be observed in single particle tests. Hypervelocity projectile impact has received much attention as a high loading rate technique, spurred by interest in the possible effects of meteorites and debris impacts upon space vehicles. Several methods have been explored to accelerate small projectiles. These include projection by compressed air, explosives, electromagnetic guns, as well as one and two-stage light gas guns. Limitations on the selection of a method include the strength of the gun and projectile, the length of the gun, and the attainable velocity. Projectile impact tests on single particle targets may involve impact velocities <50 m s1 (Hopkinson bar method) or more than 2 km s1 (two-stage light-gas gun, electromagnetic launcher) (Grosch and Riegel, 1993). Thornhill et al. (2006) reported a maximum velocity of about 20 km s1 is achievable for a small projectile utilizing a three-stage light gas gun. In contrast, typical impact velocities in industrial comminution equipment are well below 10 m s1 and it is desirable to study the effects of higher impact velocities in the range of 100–500 m s1 and to design experiments that provide information on the breakage of bulk materials. 2.3. Efficiency estimation under static fragmentation Conventional methods of energy estimation have not determined the influence of fractal parameters on the evaluation of rock properties. Interpretation of breakage phenomena requires measurement of surface roughness and an understanding of the influence of the resolution of the measurement technique on the precision of the measurement. Accordingly, Sadrai et al. (2006) developed a novel approach to measure surface roughness and surface area based on a fractal analysis procedure conducted on core samples of volcanic rocks. Changes in surface roughness of broken specimens under high loading rates were studied using a laser probe to generate 3D topographical maps of the fracture surfaces. It was shown that roughness and surface area measurements
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Reservoir Quick opening valve
Vacuum Projectile
Launch tube Coupling flanges
Chamber Velocity measurement
Fig. 1. Apparatus design configuration.
depend on the resolution used to produce these maps – a similar phenomenon occurs in the BET apparatus in comparing N2 gas (0.2 nm2 per molecule) versus Kr gas (0.04 nm2 per molecule) adsorption effects on the measured surface area. Surface area can be estimated based on theory, measurement, and empirical calculations. The results indicated that surface roughness and hence, specific surface area, increases with increasing loading rate by several orders of magnitude as particle size decreases. Overall accuracy of surface area measurement depends on several parameters such as shape factor estimation, weight measurement of each size fraction, assumptions inherent in a BET measurement, material porosity, and measurement resolution. Ultimately, a new method was proposed to increase the accuracy of the calculated surface area before and after breakage and to determine the amount of energy expended to create new surface area. It was concluded that high loading rates even in a static regime enhance energy efficiency and mineral liberation mainly due to significant improvement in the power efficiency as loading rate increases which suggests that productivity increases at higher loading rates (Sadrai, 2007). Power efficiency is defined as the energy efficiency per unit time or the rate of energy use. 3. Experimental procedures The present study required the design and construction of a new apparatus to comminute bulk particulate rock samples by launching a projectile at velocities between 100 and 500 m s1. The test facility can examine the influence of impact velocities on bulk materials to understand mechanisms of rock breakage similar to that in comminution equipment but at higher velocities. By testing bulk samples rather than single particles, the effect of void space for expansion of smaller broken particles can be studied. 3.1. Development of high velocity impact apparatus The compressed-air apparatus uses aggregated rock samples fragmented in a confined chamber while subjected to the transmission of stress waves produced at the point of contact by the impact of a 12-g steel projectile. The target chamber in which fragmentation occurs is able to hold 5–50 g of material with variable depths for the target bed (Fig. 1). This device is able to launch the projectile at a controlled velocity measured before impact by two pairs of laser diode detectors. Laser sensors mounted adjacent to the barrel record the projectile travel time which is used to obtain the dynamic fragmentation en-
ergy imparted to the test materials. Particle size analysis together with surface area measurements before and after breakage reveals the amount of energy resulting as new surfaces. The air inside the system and between particles is evacuated by a pump to a maximum negative pressure of 98.3 kPa to facilitate the launch of the projectile with least air resistance and to transfer the stress wave to particles located behind the point of impact. 3.2. Testwork material selection criteria Two aspects of rock behavior of particular interest include porosity and Poisson’s ratio (t) that may affect rock failure. Porosity contributes to a higher specific surface area after breakage from non-continuous pores within the particle that become exposed after breakage. This surface area is not caused by enhanced fragmentation and must be discounted from the measurements. Materials that exhibit intermediate values of Poisson’s ratio may exhibit a higher transformation of compressive forces to tensile stresses resulting in better fragmentation. For small values of t, the lateral stress induced by a given axial load is relatively small. In a dynamic experiment, material with a low Poisson’s ratio is expected to initiate failure by axial splitting since the lateral confining pressure is insufficient to suppress the tendency for crack initiation and propagation. Ceramic materials with a low Poisson ratio tend to fail by brittle cracking leading to high fragmentation. On the other hand, a material with a high Poisson’s ratio may induce higher confinement preventing microcracks from sliding and also leading to brittle failure. Thus, the failure mode is associated with plastic flow for large values of t (Chen and Ravichandran, 2000). The effect of high velocity impact on rock material properties has been suggested to mask or remove the influence of Poisson’s ratio on breakage (Katsabanis et al., 2003). Based on these considerations, as shown in Table 2, experiments were conducted on three different materials – highly porous limestone, quartz with low specific surface area (low porosity), and rock salt with the highest Poisson’s ratio of the materials selected. 3.3. Particle size distribution analysis After preparing materials to the required size, bulk samples (2 mm + 1 mm) were selected to undergo experiments in order to conduct particle breakage in the range of a typical grinding operation. Two bed depths were studied. Zone ‘‘A’’ and ‘‘B’’ were designated with a target bed depth of 75 mm (13 g) and 150 mm (25 g), respectively. Particle size distribution analysis was done after each
Table 2 Relevant Properties of rock samples used in this test work.
*
Rock type
S.G. (g cm3)
Initial bulk density (g cm3)
Poisson’s ratio
Initial specific surface area (m2 g1)
Specific surface energy (J m2)*
Limestone Quartz Rock salt
2.61 2.64 2.10
1.36 1.40 1.28
0.215 0.078 0.300
0.728 0.005 0.020
1.000 2.678 0.577
Tromans and Meech, 2004.
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Limestone (13 g)
Limestone (25 g)
100
100 90
80 70 60 50 40
LA00
30
LA80 LA110
20
LA180
10
80
Cumulative passing (%)
Cumulative passing (%)
90
70 60 50 40
LB00 LB70
30
LA270
0
LB180
20
LB240
10
LB300
0
0
500
1000
1500
2000
0
500
Particle size (micron)
1000
(a)
2000
(b)
Quartz (13 g) 100
100
90
90
80
80
70 60 50 QA00
40
QA80 QA110
30
QA140
20
QA160
Cumulative passing (%)
Cumulative passing (%)
1500
Particle size (micron)
QA190
10
Quartz (25 g)
70 60 50 40 30
QB00 QB70
20
QB110
10
QA220
QB190
0
0 0
500
1000
1500
0
2000
500
Particle Size (micron)
1000
1500
2000
Particle Size (micron)
(c)
(d) Rock Salt (13 g)
100
Cumulative Passing (%)
90 80 70 60 50 40 SA00
30
SA80
20
SA110 SA160
10
SA200
0 0
500
1000
1500
2000
Particle Size (micron)
(e) Fig. 2. Particle size analysis at variable impact velocities: (a) limestone 13 g, (b) limestone 25 g, (c) quartz 13 g, (d) quartz 25 g, (e) rock salt 13 g, (A = zone A, B = zone B, L = limestone, Q = quartz, S = salt; LA80 means limestone of zone A with a velocity of 80 m.s1).
test for all samples. The representative sample demonstrates the material size before breakage (i.e., at zero impact velocity). These analyses are shown in Fig. 2a–e as represented by the black solid lines for each test.
It can be seen that substantial improvements in breakage (reduced p80 sizes) of the 75 mm tests for all rock samples occur as the impact velocity increases, but breakage of limestone in a bed depth of 150 mm shows little improvement and exhibits erratic
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100
100
90
90
80
70
Wt % (-1 mm)
Wt % (-1 mm)
80 60 50 40 30
QA (75)
60
QB (150)
50 40 30 20
20
LA (75)
10
LB (150)
0
70
10 0
0
50
100
150
200
250
300
350
0
50
100
150
200
250
300
350
Velocity (m/s)
Velocity (m/s)
(a)
(b) 100 90
Wt % (-1 mm)
80 70 60 50 40 30 20 10 0
SA (75)
0
50
100
150
200
250
Velocity (m/s)
(c) Fig. 3. Weight percent of 1 mm vs. impact velocity: (a) limestone zone A and B, (b) quartz zone A and B, (c) rock salt zone A, (zone A = 13 g or 75 mm, zone B = 25 g or 150 mm, L = limestone, Q = quartz, S = salt).
behavior. The breakage of quartz in a bed depth of 150 mm also shows anomalous behavior with only a small increase in the 80% passing size as velocity increases. Breakage of rock salt in a bed depth of 150 mm was not performed since this depth was likely too far to propagate the shock wave. Fig. 3a–c presents weight percentage of 1 mm material before and after breakage as a function of impact velocity for all samples tested in both zones. Note that the percent 1 mm increases substantially with velocity indicating initial breakage likely occurs by attrition (shear breakage). At this size, more fragmentation in zone A than zone B indicates better use of energy in shallower depths particularly at high impact velocities. With increased bed depth, the impact shock wave is unable to reach the material at the end of the chamber with sufficient intensity to cause breakage. Clearly, bed depth plays an important role in determining the breakage of material at high impact velocities. 3.4. Specific surface area measurements A Quantachrome surface area analyzer (BET) was used to measure the specific surface area (SSA) of the materials before and after each test using nitrogen gas. In this way, the new surface area produced by impact can be calculated. The range of change in SSA as a function of impact velocity shows substantial improvements for all samples tested in both zones (Fig. 4). In order to measure the SSA by BET, broken material is divided into different size fractions. Therefore, it is possible to plot the SSA as a function of particle size. The particle size reported is the geometric mean of the upper and lower limit of the split size. Fig. 5 shows the results for limestone and quartz as a function of particle size for zone A breakage. Note that the SSA for the same
particle size is higher for all sizes with increasing impact velocity indicating that the surface becomes much rougher as velocity increases – particularly for the finer particles.
3.5. Energy efficiency estimation model In this model, the energy efficiency of breakage is defined as the ratio of energy output to energy input (Sadrai and Meech, 2006). Before and after each test, the surface area of material allows the total surface area produced by breakage to be calculated for the retrieved amount of material (material losses averaged 3% and showed no correlation with velocity). The new surface area provides a measure of the total energy output together with the specific surface energy of the solid (see Table 2). Energy input is calculated from the mass of the projectile and its impact velocity (see Eq. (1)). Table 3 shows the result of these calculations for all samples.
g¼
ðSSA2 SSA1 ÞW SE 1 MV 2 2
100 ¼
200ðSSA2 SSA1 ÞW SE MV 2
ð1Þ
where g = energy efficiency (%); SSA2 = specific surface area after breakage (m2 g1); SSA1 = specific surface area before breakage (m2 g1); W = weight of sample (g); SE = specific surface energy (J m2); M = projectile mass (kg); V = projectile velocity (m s1). Fig. 6 shows the influence of impact velocity on the energy efficiency of rock breakage for all samples tested in both zones. As can be seen, the efficiency of all samples is substantially improved with increased impact velocities. However, all sets of data appear to exhibit a peak efficiency within the velocity range of 180–220 m s1.
S. Sadrai et al. / Minerals Engineering 24 (2011) 1053–1061 2.50
0.45 LA (75 mm) LB (150 mm)
2.00
Specific Surface Area (m2/g)
Specific Surface Area (m2/g)
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Limestone
MAX
1.50 MIN
1.00 0.81 0.66 0.50 0.00
0
50
100
150
200
250
300
350
0.40
Quartz
QA (75 mm) QB (150 mm)
0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
0
50
100
150
Velocity (m/s)
Velocity (m/s)
(a)
(b)
200
250
Specific Surface Area (m2/g)
0.300 Rock Salt
SA (75 mm)
0.250 0.200 0.150 0.100 0.050 0.000
0
50
100
150
200
250
Velocity (m/s)
(c) Fig. 4. Specific surface area vs. impact velocity: (a) limestone zone A and B, (b) quartz zone A and B, (c) rock salt zone A, (zone A = 13 g or 75 mm, zone B = 25 g or 150 mm, L = limestone, Q = quartz, S = salt).
2.50 LA80
Limestone
LA110
2.00
LA180
SSA (m2/g)
SSA (m2/g)
LA270
1.50
1.00
0.50
0.00
0
200
400
600
800
1000
Mean Particle Size (micron)
0
200
400
600
800
1000
Mean Particle Size (micron)
Fig. 5. Specific surface area vs. particle size for limestone and quartz (zone A).
It is clear that the energy efficiency trend prior to this peak doubles or triples with increasing impact velocity. 4. Results and discussions Although fragmentation under high velocity impact has been studied for some time, it has been unclear if the observed increase in energy efficiency for a similar total energy input occurs when strain rates are increased. For years, the use of explosives has provided a way to break rock in tension with efficiencies about one order of magnitude above that of comminution. The results of this work show that higher strain rates do provide increased efficiencies in terms of generating new surface area. Strain rates higher
than those achieved by conventional comminution equipment create an opportunity to save considerable amounts of money and energy and liberate valuable minerals by processing lower grade ores more efficiently. 4.1. Impact velocity and energy input model In this study, the breakage model utilizes the kinetic energy content of the projectile (i.e. velocity and mass) to determine efficiency. We find that breakage occurs more efficiently as impact velocities increases to at least 200 m s1. The question remains whether the level of specific energy input (J g1) or velocity (m s1) causes this enhancement? These two factors are directly
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Table 3 Calculation of energy efficiency for all samples tested.
*
Produced SSA* (m2 g1)
Energy output (J)
Energy input (J)
Energy efficiency (%)
LA80 LA110 LA180 LA270
0.026 0.154 0.613 1.206
0.33 2.00 7.97 15.68
39.19 73.11 188.10 414.44
0.85 2.74 4.24 3.78
LB70 LB180 LB240 LB300
0.008 0.392 0.753 0.708
0.21 9.81 18.84 17.71
30.68 190.91 324.98 527.93
0.68 5.14 5.80 3.35
QA80 QA110 QA140 QA160 QA190 QA220
0.017 0.044 0.097 0.153 0.255 0.396
0.60 1.53 3.38 5.34 8.87 13.80
38.41 64.66 121.27 145.80 209.62 268.72
1.57 2.36 2.79 3.66 4.23 5.13
QB70 QB110 QB190
0.003 0.014 0.047
0.21 0.92 3.17
30.65 71.16 209.40
0.70 1.30 1.51
SA80 SA110 SA160 SA200
0.010 0.060 0.160 0.209
0.08 0.45 1.20 1.57
32.91 69.24 149.28 242.60
0.23 0.65 0.80 0.65
ηe = 0.59 EQ0.64
E.Eff. (%)
Sample
ηe = 0.57 EL0.64 1
Quartz
ηe = 0.19 ES0.52
Limestone Salt
0.1 1
10
100
Specific Energy Input (J.g-1) Fig. 7. Energy efficiency vs. specific energy input.
10
Specific surface area.
ηe = 0.0041 VQ1.28 ηe = 0.0042 VL1.27
E.Eff. (%)
6 QA
Energy Efficiency (%)
5
QB LA LB
4
1
SA
3
Quartz
ηe = 0.0032 V S1.05
Limestone Salt
2
0.1 10
100
1000
Impact Velocity (m.s-1)
1
Fig. 8. Energy efficiency vs. impact velocity.
0
0
50
100
150
200
250
300
350
Velocity (m/s) Fig. 6. Comparison of energy efficiencies (Q = quartz, L = limestone, S = rock salt, A = zone A, B = zone B).
related via a general energy formula. The energy efficiency as a function of specific energy input and impact velocity for all samples are shown in Figs. 7 and 8, respectively. Specific energy input is a function of velocity squared, hence one could conclude that Figs. 7 and 8 are simply plots of efficiency as a function of two dependent variables, i.e., the plots are the same graphs. However, note that the trend lines for the data in Fig. 7 exhibit slopes above 0.5 (0.64 for both limestone and quartz and 0.52 for rock salt). This indicates that the specific energy level plays a role in the overall efficiency independent of velocity.
ge ¼ K e ðEÞ0:60
gv ¼ K V ðVÞ1:2
ð3Þ
gv = energy efficiency (based on impact velocity) (%); V = impact velocity (m s1); Kv = velocity index (% (s/m)1.2). These equations are empirical with validity over the range of impact velocity measurements, (50–300 m s1), i.e., in a dynamic regime. The energy index (Ke) and velocity index (Kv) are also empirical parameters affected by many factors such as the type of material, material characteristics, mechanical properties of the material, Poisson’s ratio, grain size, density, porosity, environment, etc. To determine these factors, a large number of similar tests with different materials and different variations are required. The experiments should be extended to higher and lower velocities than those in the current study in order to measure the value of Ke and Kv over a wider dynamic range. Similarly, parallel experiments should be performed to establish Ke and Kv in the static range.
ð2Þ
where ge = energy efficiency (based on energy input) (%); E = specific energy input (J g1); Ke = energy index (% (g/J) 0.60). In a similar fashion, the trend lines for data in Fig. 8 show a slope greater than 1.0 (1.27 for limestone, 1.28 for quartz, and 1.05 for rock salt) again supporting the concept that specific surface energy plays a role independent of velocity – otherwise the slope would be 1.0.
4.2. Pressure model of work efficiency The developed model utilizes a change in surface area of rock material as the output of the fragmentation process caused by the impact energy of a projectile. The work done on the sample can also be estimated by direct measurement of pressure and volume changes during breakage. Since the material is broken in a
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Table 4 Pressure model of maximum work efficiency for all samples tested. Sample
Work output (DPV)
Work output (% of energy input)
Ratio of surface energy change to work output
LA80 LA110 LA180 LA270
1.60 3.55 8.87 19.52
4.08 4.86 4.72 4.71
0.21 0.56 0.90 0.80
LB70 LB180 LB240 LB300
1.33 11.09 22.36 28.40
4.34 5.81 6.88 5.38
0.16 0.88 0.84 0.62
QA80 QA110 QA140 QA160 QA190 QA220
0.80 2.22 7.10 11.98 13.31 19.17
2.08 3.43 5.85 8.22 6.35 7.13
0.76 0.69 0.48 0.45 0.67 0.72
QB70 QB110 QB190
0.80 2.00 9.32
2.61 2.81 4.45
0.27 0.46 0.34
SA80 SA110 SA160 SA200
1.33 3.33 8.43 17.35
4.04 4.81 5.65 7.15
0.06 0.14 0.14 0.09
confined chamber, the change in volume can be calculated by measuring the compaction level of the material during experiments. Impact pressure can also be estimated by the projection of force from the initial reading of the regulator installed in the pressure line before launching the projectile. Therefore, the work performed to compress the bulk material can be obtained. The ratio of this work to the energy input imparted by the projectile velocity represents the maximum work efficiency achievable in each test (Table 4). The ratio of energy efficiency obtained based on surface area measurements (see Table 3) to the maximum work efficiency indicates what percentage of the work done in compressing the bulk material is transferred into breakage and new surface area (or energy). It is assumed in these calculations that the loss of pressure during the flight of the projectile is negligible and that the resistance of any small amount of air during acceleration is insignificant. The total energy input to the projectile is produced as the projectile accelerates along the barrel. At the point of contact with the material, the projectile has gained its maximum energy according to its velocity. At this moment, the free traveling of the projectile is completed and it begins transferring its energy to the rock material in the form of some partially reversible work. This compression (or work) measured in the form of changes in pressure and volume is equal to DPV. Some of this work is reversible as the sample compresses to a higher bulk density and then rebounds off the walls of the target chamber. During compression, breakage occurs causing a change in surface energy (non-reversible). All of the remaining energy eventually is wasted mostly as heat and sound. As shown in Tables 3 and 4, the work done by the projectile in compressing the target bulk material is of a similar order of magnitude to that of the newly created surface energy. It is unclear if this work is a parallel energy path or a serial one, i.e., does the rebound energy result in any additional breakage? Perhaps, a combination of these two modes of transformation of compression to tension takes place. In a parallel path, the impact energy is utilized to contract the material and create new surface area both at the same time, while in a serial path the newly created surface area is the result of pressure and volume change. The ratio of surface energy change to work done is much lower for rock salt compared with quartz and limestone suggesting a parallel path dominates in the case of rock salt.
4.3. Effect of material porosity Porosity in rock particles affects the measurement of surface area by allowing nitrogen gas (absorbent) to enter the pores. The amount of adsorbed gas on the free surface of particles determines the specific surface area of the material. After breakage of highly porous rock samples, i.e., volcanic rock such as tuff, the surface area of the closed pores is considered part of the measurement despite the fact that input energy had no effect in actually creating these surfaces. In fact, the majority of the increased surface area is due to porosity and not to fragmentation since the initial measurement prior to breakage did not account for pore surface area. Porosity inflates the measurement of new surface area after breakage due to the exposure of pores and so, a high and erroneous estimate of energy efficiency results. Although pores likely decrease the overall rock strength, a cellular structure with highly porous material may prevent a crack from propagating whenever it meets a void. This could result in a strengthening of the material (a dampening effect). As such, the effect of high rock porosity on measurement of energy efficiency of breakage is yet to be fully understood because of its complex nature. In the dynamic tests, if the pores are all open prior to breakage, then the pore surfaces are measured both before and after which cancel out in terms of measuring surface area change. The vast majority of porosity in rock is open-pores so this is a reasonable assumption. The presence of non-continuous pores of total volume relative to the particle size will produce large errors in measuring energy efficiency in the way proposed in this work. 5. Conclusion Our studies have attempted to exploit impact engineering as a solution for rock breakage in mining and comminution problems. In dynamic fragmentation, a high-velocity impact comminution apparatus was designed and built to directly measure the quantitative parameters of impact velocity on aggregated rock materials. Experiments on three rock materials – porous limestone, quartz, and rock salt, were conducted at projectile velocities from 50 to 300 m s1. The results show that the energy efficiency of rock breakage is improved by as much as 2–3 times under high velocity impact. To summarize, the following conclusions can be made: 1. Utilization of high strain rates and high-velocity impact in comminution provides an opportunity to improve energy efficiency in rock breakage significantly. 2. Regardless of mineralogy, high-velocity impact helps explain the reported increase in efficiency of higher impact crushing technologies (high pressure grinding rolls (HPGR), Barmac, and roller crushers). 3. The depth of particle bed is a key variable in determining the fragmentation of rocks and minerals by high velocity impact. This may not be the case with static loading. 4. Impact velocity is a key variable in enhancing the efficiency of rock fragmentation and has an important effect independent of total energy input. 5. Future work should focus on designing new devices to increase impact intensity during comminution.
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