The dependence of specific discharge and breakage rate functions on feed size distributions, operational and design parameters of industrial scale multi-compartment cement ball mills

Powder Technology 239 (2013) 137–146

Contents lists available at SciVerse ScienceDirect

Powder Technology journal homepage: www.elsevier.com/locate/powtec

The dependence of specific discharge and breakage rate functions on feed size distributions, operational and design parameters of industrial scale multi-compartment cement ball mills Ö. Genç a,⁎, Ş.L. Ergün b, A.H. Benzer b a b

Muğla Sıtkı Koçman University, Department of Mining Engineering, 48170, Kötekli, Muğla, Turkey Hacettepe University, Department of Mining Engineering, 06800, Beytepe, Ankara, Turkey

a r t i c l e

i n f o

Article history: Received 28 May 2012 Received in revised form 13 January 2013 Accepted 19 January 2013 Available online 1 February 2013 Keywords: Discharge rate Breakage rate Modelling Ball mill Cement

a b s t r a c t Calculating specific discharge and breakage rates is an essential part of developing a grinding model for dry ball milling. With this purpose, detailed sampling surveys were performed to collect size distribution data at the steady state conditions of the cement grinding circuits at different plants. Effects of operational and design parameters on specific discharge and breakage rate of particles in geometrically different multi-compartment ball mills were evaluated. Results indicated that, effects of mill throughput rate, compartment length and mill feed size distribution on discharge rate function and effects of mill diameter and ball size distribution parameters on breakage rate function could be reflected using the industrial scale data directly. Crown Copyright © 2013 Published by Elsevier B.V. All rights reserved.

1. Introduction Application of modelling and simulation techniques to cement grinding presents an opportunity to optimise circuits and decrease the power consumption per ton of cement produced. Energy consumptions of conventional cement grinding ball mills usually lie between 32 and 37 kWh/ton for cements ground to a Blaine fineness within the range of 2950 to 3200 cm 2/g [1]. The energy consumption of grinding mills could be optimised by mathematical modelling and simulation techniques which require models capable of reflecting the effects of operational and design characteristics of the ball mill on breakage and discharge rates of particles. Such models have been developed using laboratory scale tests. However, they are not directly applicable to industrial systems without scale-up as reported by Austin et al. [2]. According to size-mass balance modelling approach, model parameters are determined based on laboratory scale batch grinding tests and the calculated rates have to be scaled-up. Ability of batch grinding parameters to describe continuous grinding systems has been discussed in the literature [2–10]. In this study, perfect mixing model [11] was chosen in breakage rate calculation due to its simplicity among the models that were used to define size reduction in ball mills. Perfect mixing model constitutes a few parameters for the estimation of breakage rates as compared to ⁎ Corresponding author. E-mail address: [email protected] (Ö. Genç).

size-mass balance batch models [12]. Relations between the mill operational and design variables were defined using the perfect mixing modelling approach for wet ball mill grinding systems [13]. Operational and design parameters were related to mill model parameter which was defined by a ratio of breakage rate (r) to discharge rate (d) function and identified by r/d. Such models were developed using laboratory scale tests. However, they are not directly applicable to industrial systems without scale-up as discussed by Austin et al. [2]. In this study, mill inside load and size distributions were measured directly in industrial scale sampling surveys. Thus, discharge and breakage rate functions could have been established individually based on the ball mill model structure proposed by Benzer [14] instead of defining the grinding performance in terms of r/d function. It was established how these functions were affected by the operational and design parameters in different mills. This is an essential part of developing a predictive grinding model. 2. Sampling surveys and laboratory studies Circuit and mill inside sampling surveys were conducted at the steady state condition of the cement grinding circuits. Steady state conditions were determined by examining the variations in the values of important variables of mills and separators in the control room. For this purpose, important variables of the operation were recorded in every 5 min from the process control system during the sampling studies. The variables include tonnage flow rates of clinker and cement additive materials, circulating load flow rate, mill motor (kW) etc. When

0032-5910/$ – see front matter. Crown Copyright © 2013 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.powtec.2013.01.061

138

Ö. Genç et al. / Powder Technology 239 (2013) 137–146

the stable values were observed in the variables, it was decided that the steady state condition was achieved and the samples from the circuit were collected within the possible shortest time interval. All the sampled cement mills were fully dry grinding mills. As soon as the circuit sampling was completed, the mill was crash-stopped to perform inside mill sampling. Sampled mills were cooled down for 3–4 h ahead of inside mill sampling. Before collecting inside mill samples, measurements related to length over the material in the x-axis, free height in the y-axis were performed. Height above the ball charge level was also measured in case of material above the ball charge. Related measurements were used in the calculation of charge (material + ball) filling to estimate hold-up in the compartments. Following inside mill measurements, each compartment was sampled by 1 m on the average along the long axis of the mill. In the context of laboratory studies, size distribution analysis of the samples from the top size down to 150 μm was performed by dry screening while − 150 μm sub-sieve sample was sized down to 1.8 μm with a SYMPATHEC® laser diffractometer in dry mode. Agglomeration of fine particles was observed in the measurement of some of the samples. This problem was solved by setting the operational pressure to an appropriate value which provided a normal distribution. Particle size distribution of each sample was determined from the top size down to 1.8 μm so that to be used in mass balance calculations. Single particle impact breakage functions of mill feeds were determined by drop-weight test method [15–17] and used in the calculation of breakage rates. Mill feed grindabilities were determined by laboratory scale standard bond work index test procedure as explained by Austin et al. [2]. Mass balance module of the JKSimMet simulation and modelling software package was used to determine statistically adjusted size distribution values and tonnage flowrates of all streams. Mill feed and discharge size distributions obtained from mass balance calculations were used in the calculation of discharge and breakage rate functions [17]. Basic design and operational characteristics of the mills in the regarding surveys are given in Table 1 and some of the operational parameters of the circuits in Table 2 respectively. Intermediate and discharge diaphragm designs are also different in the investigated mills.

rate and breakage distribution function which varies depending on the material. A number of researchers have used this model in modelling of cement mills [14,17–22]. Discharge rate of i th size fraction from the mill is defined by Eq. (1) in the perfect mixing model. di ¼

ð1Þ

In Eq. (1), si is the mass of size fraction (i) as tons in the mill hold-up (S), pi is the mass flow rate of particle fraction (i) out of the mill as product in t/h. Determination of inside mill size distributions is essential to estimate mill hold-up which could also be defined as the mass of powder material in a mill as tons (powder load). If mill hold-up could be determined sensitively, discharge rate function could be established from Eq. (1). As it is difficult to measure mill hold-up and size distribution accurately, ball mills used in wet and dry grinding applications were modelled by back-calculating the ratio of breakage rate to discharge rate (r/d) in the literature [13,14,18–20,22–24]. Ball mill model parameter r/d can be back-calculated from Eq. (2) if breakage function, mill feed and product size distributions are determined [13].

f i −ri

i pj pi X þ a r −pi ¼ 0 di j¼1 ij j dj

ð2Þ

where, fi pi pj ri rj aij

di 3. Mill modelling approach dj Perfect mixing model was developed by Whiten [11] and defines the size reduction process in terms of three parameters; breakage rate (selection function) which defines the breakage probability in the equipment; discharge rate which defines the transportation

pi si

Mass flow rate of size fraction i in the mill feed (t/h) Mass flow rate of size fraction i in the mill discharge (t/h) Mass flow rate of size fraction j in the mill discharge (t/h) Specific breakage rate of size fraction i (ton broken per hour per ton in the mill, h −1) Specific breakage rate of size fraction j (h −1) Breakage or appearance function representing the mass fraction of size fraction j that appears in size fraction i after breakage (breakage function is in the form of triangular matrix) Specific discharge rate of size fraction i (ton discharged per hour per ton in the mill, h −1) Specific discharge rate of size fraction j (h −1)

For the correction of variations in residence time, di is scaled in terms of mill volume and volumetric feed rate (Q) to the term di* where D and L are the diameter and length of the mill respectively.

Table 1 Single and two-compartment ball mill design parameters.

a

Sampling survey/mill

Mill brand

Nominal diameter (m)

Comp-1 nominal length (m)

Comp-2 nominal length (m)

Comp-1 ball filling %

Comp-2 ball filling %

Operating mill power (kW)

Survey-1/mill-1 Survey-2/mill-1 Survey-3/mill-2 Survey-4/mill-3 Survey-5/mill-4 Survey-6/mill-4 Survey-7/mill-4 Survey-8/mill-4 Survey-9/mill-5 Survey-10/mill-6 Survey-11/mill-7 Survey-12/mill-8 Survey-13/mill-8 Survey-14/mill-9 Survey-15/mill-9

– – FLSmidth® FLSmidth® Krupp Polysius® Krupp Polysius® Krupp Polysius® Krupp Polysius® FLSmidth® Humboldt Wedag® Humboldt Wedag® – – Humboldt Wedag® Humboldt Wedag®

4.8 4.8 3.5 3.5 4.8 4.8 4.8 4.8 3.5 3.5 3.2 4 4 4 4

11 11 10.5 10.5 4.25 4.25 4.25 4.25 3.85 3.60 3.27 4.75 4.75 3.15 3.15

– – – – 10 10 10 10 5.8 5.75 7.25 6.9 6.9 5.18 5.18

32 32 – – 31 31 31 31 23 30 29 29 29 32 32

– – – – 31 31 30 31 31 30 30 28 28 33 33

– – 1545 1582 4764 4766 4581 – 1401 1488 – 3283 3280 1969 1951

In survey-8, mill-7 was operated in open circuit mode. Liner thickness range: 0.24–0.16 m.

b

Ö. Genç et al. / Powder Technology 239 (2013) 137–146

139

Table 2 Single and two-compartment ball mill operational parameters. Sampling survey/mill

Mill throughput rate (t/h)

Circulating load (air classifier reject) (t/h)

Standard bond work index (kWh/t)

F80

Survey-1/mill-1 Survey-2/mill-1 Survey-3/mill-2 Survey-4/mill-3 Survey-5/mill-4 Survey-6/mill-4 Survey-7/mill-4 Survey-8/mill-4 Survey-9/mill-5 Survey-10/mill-6 Survey-11/mill-7 Survey-12/mill-8 Survey-13/mill-8 Survey-14/mill-9 Survey-15/mill-9

316.21 210.03 174.20 221.21 469.45 542.95 712.53 160.00 86.70 136.82 79.34 251.95 357.08 471.01 392.74

147.11 94.03 – – 325.00 383.97 520.68 – 34.01 86.65 31.34 149.76 276.10 380.97 307.68

9.15 9.15 11.53 12.45 14.87 13.86 13.86 14.87 14.46 16.34 14.80 15.86 14.12 15.88 16.19

1.6 1.5 0.085 0.063 13 0.6 1 10.5 9 1.5 15.5 10 0.425 0.350 0.400

mill feed

(mm)

P80 mill

discharge

0.900 0.050 0.065 0.055 0.100 0.100 0.130 0.055 0.076 0.102 0.072 0.100 0.100 0.15 0.12

(mm)

Air classifier fine +45 μm% 15 24 9 6 11 11 14 25 15 11 – 10 6 10 1.4

c In survey-11, two ball mills (mill-1 and mill-2) fed from different silos were operating in the circuit. Mill-2 was closed circuited with an air classifier. Load which was provided from both mills to the air classifier was classified and the circulating load refers to the reject of that air classifier which was combined with the fresh feed of mill-2 circuit.

Formulation of normalized discharge rate function is given by Eq. (3) [13]. " # 2 D L di  ¼ di 4Q

ð3Þ

contents of liquid phase, MgO, periclase, free lime, alumina (Al2O3), and iron oxide (Fe2O3) of the clinker minerals. Their effects on grindability were discussed in the literature [27,28]. Single particle breakage functions were used to characterise grindability of clinkers provided from different cement plants by Genç and Benzer [29]. In the related study, the effect of mineralogical and chemical compositions of clinkers on grindability, which was determined based on the single particle breakage functions, was evaluated.

3.1. Breakage function Breakage function is a material specific parameter of grinding models and represents the proportion of particles after breakage. The values of breakage distribution function are assumed to be invariant with grinding process conditions. Breakage function changes with breakage energy level. However, it may or may not change with particle size depending on the material tested [25]. Different breakage mechanisms such as impact, compression and shear affect breakage within the ball mill. However, in this study breakage was assumed to be predominantly affected by the impact and the effects of other breakage mechanisms were assumed to be eliminated. If samples were tested under all the mentioned mechanisms, each mechanism would result in different breakage functions. A different methodology defined to combine the effects of different mechanisms such as impact and abrasion as in the work of Hashim [22]. By this way, effect of each breakage mechanism could be reflected on r/d functions. In this study, drop-weight technique was used for experimental measurement of single particle impact breakage function of mill feed clinker and cement additive materials which were used to calculate specific breakage rates [15,17]. In the calculation of size normalized breakage functions, top size of each mill feed was assumed to be 38 mm. Particle sizes were determined based on a √2 series from the top size down to 0.0016 mm. The breakage function values were calculated for thirty size fractions and extrapolated linearly from 2.38 mm down to 0.0016 mm. Appearance values were defined as a ratio of weight per cent of each size to 100 which form the single column of the triangular breakage matrix. Appearance values of the test clinkers were given from the top size down to 0.052 mm in Table 3. Differences in single particle breakage functions (Table 3) were observed which could be linked to the probable differences in microstructure, mineralogical and chemical compositions of clinkers provided from different plants. It is known that, clinker minerals such as alite and belite are known to be strength giving minerals whereas tricalcium aluminate and tetracalcium aluminoferrite are the flux minerals [26]. Important parameters that affect grindability are macro and microstructural arrangement (texture), composition, porosity, crystal size,

4. Data evaluation and discussions In order to be able to model any segment of a grinding compartment, size reduction should occur within that segment. In this respect, size reduction in the segments was analysed based on the mill inside size distributions. The ball mill model structure proposed for the calculation of breakage and discharge rate functions was explained in the literature [17]. Schematical representation of the proposed two-compartment ball mill model structure is given in Fig. 1. As shown, first and second compartments are divided into perfectly mixed mill segments. In this representation: s1 p1 s2 p2 s3 s4 p3 d1 d2 d3

Mill hold-up of segment-1 in compartment-1 Mill inside particle size distribution corresponding to last 1 or 2 m of the compartment length Mill hold-up of segment-2 in compartment-1 Mill inside particle size distribution corresponding to sample collected from the inlet of compartment-2 Mill hold-up of segment-1 in compartment-2 Mill hold-up of segment-2 in compartment-2 Mill discharge particle size distribution Discharge rate of particles through segment-1 compartment-1 Discharge rate of particles through segment-2 compartment-1 Discharge rate of particles through compartment-2

the

the

of of

In the first compartments, specific breakage rate in segment-2 was characterized by the rates calculated for segment-1 by assuming that, particles in segment-2 of compartment-1 have the same rate. Breakage characteristics of each clinker sample was assumed to be represented by single particle breakage functions determined by drop weight test technique. Breakage function is known to be material dependent and required in perfect mixing mill model to back-calculate mill model parameter (ri/di). By this way, breakage

140

Ö. Genç et al. / Powder Technology 239 (2013) 137–146

Table 3 Size normalised single particle impact breakage functions. Size (mm)

Survey1

Survey 2

Survey 3

Survey 4

Survey 5-8-9

Survey 6-7

Survey 10

Survey 11

Survey 12-13

Survey 14-15

38 26.87 19 13.44 9.5 6.72 4.75 3.36 2.38 1.68 1.19 0.840 0.594 0.420 0.297 0.210 0.148 0.105 0.074 0.052

0.00000 0.04501 0.09795 0.26000 0.19893 0.11301 0.07180 0.04887 0.03200 0.02504 0.01929 0.01448 0.01110 0.01130 0.00875 0.00726 0.00602 0.00499 0.00414 0.00343

0.0000 0.0450 0.0980 0.2600 0.1989 0.1130 0.0718 0.0489 0.0320 0.0250 0.0193 0.0145 0.0111 0.0113 0.0088 0.0073 0.0060 0.0050 0.0041 0.0034

0.0000 0.0000 0.0000 0.1390 0.1692 0.1573 0.1337 0.0947 0.0579 0.0384 0.0397 0.0307 0.0257 0.0210 0.0171 0.0140 0.0114 0.0093 0.0076 0.0062

0.0000 0.0000 0.1087 0.2105 0.2043 0.1216 0.0881 0.0644 0.0360 0.0296 0.0246 0.0202 0.0165 0.0135 0.0111 0.0091 0.0075 0.0061 0.0050 0.0041

0.0000 0.0600 0.1100 0.2700 0.1800 0.1000 0.0800 0.0450 0.0275 0.0225 0.0150 0.0167 0.0169 0.0130 0.0100 0.0077 0.0059 0.0046 0.0035 0.0027

0.0000 0.0000 0.0624 0.2214 0.1997 0.1432 0.0914 0.0651 0.0406 0.0333 0.0235 0.0183 0.0225 0.0175 0.0136 0.0106 0.0082 0.0064 0.0050 0.0039

0.0000 0.0000 0.0000 0.2220 0.2272 0.1462 0.1108 0.0657 0.0444 0.0326 0.0280 0.0195 0.0184 0.0152 0.0125 0.0103 0.0084 0.0069 0.0057 0.0047

0.0000 0.0000 0.0069 0.0832 0.1390 0.1600 0.1591 0.0938 0.0637 0.0484 0.0465 0.0338 0.0286 0.0237 0.0196 0.0162 0.0134 0.0111 0.0092 0.0076

0.0000 0.0339 0.0931 0.2435 0.2059 0.1110 0.0898 0.0471 0.0387 0.0251 0.0216 0.0166 0.0123 0.0125 0.0092 0.0075 0.0061 0.0049 0.0040 0.0033

0.0000 0.0603 0.1175 0.2573 0.1900 0.1033 0.0693 0.0474 0.0299 0.0259 0.0169 0.0131 0.0114 0.0095 0.0080 0.0066 0.0055 0.0046 0.0039 0.0032

characteristics were reflected on combined mill model parameter (ri/di) through single particle impact breakage functions. In the estimation of hold-up (si) in compartment-1, size distribution of the final meter sample in the first compartment was not considered due to the diaphragm reject effect. The concept of diaphragm reject effect was explained in the literature [14,17,29,30]. However, size distributions of the whole length were considered in the estimation of mill hold-up in the second compartments as discussed by Genç [17]. Related calculations were all done in Excel®. Mass of each size fraction in mill hold-up (si) of each compartment was calculated using the average of the inside mill particle size distributions, mill and ball filling percent values. Average of the inside mill particle size distributions was calculated by taking the arithmetic mean of the size distribution data of samples collected along the long axis of the compartments at the crash-stop condition. Breakage and discharge rates were established based on the mill model structure given in Fig. 1. for the mill segments where size reduction was achieved. Discharge and then breakage rates were calculated for geometrically different ball mills operating at different conditions. The procedure for calculating specific breakage rates was as follows: • Combined mill model parameter (ri/di) was back-calculated from the perfect mixing model using the single particle breakage distribution function, mill feed, mill inside, and mill discharge size distributions. • Specific discharge rate (di) was determined based on the mass of size fraction (i) in the mill hold-up, and then specific breakage rates (ri) in the compartments were back-calculated by solving the combined breakage rate parameter (ri/di) and discharge rate function (di) using Eq. (2).

Mill inside size distributions in a mill with dimensions of Ø4.8× L14.25 m is shown in Fig. 2 to demonstrate the characteristic mill inside size distribution patterns and typical trends observed in the other investigated mills. In Fig. 2, labelled as compartment-1 (1.m) sample corresponds to the sample collected from the sampling location at the first meter of the compartment length. Other samples were collected and labeled with the same methodology. In the study of Genç [17], size reduction progress in two-compartment type mills were analysed for 17 mills and evaluated by determining the particle size distribution change in each meter through a single size distribution parameter such as 80% passing particle size. In the related study, it was demonstrated that when the size reduction ratio in a mill segment is determined based on the 80% passing particle size, size reduction in the first meters of compartment-1 will be higher as compared to the one in the second compartment. In general, when the change in size distributions of the first and the last meter sample, which are determined from the top size down to sub-sieve range, were analysed in each compartment. Size distributions in the second compartment of different mills were found to be close to each other which indicated a lower size reduction performance. It was observed that, coarse particles such as 25 mm, 16 mm, 9.5 mm exist at the last meter of the first compartment length, the condition of which could be linked to the diaphragm reject effect. Discharge rate of particles was expected to be affected from the presence of the intermediate diaphragm located between the first and second compartments. Intermediate diaphragm slot positions, slot and grate aperture shape, open area percent, classification performance of diaphragms are important parameters which are expected to affect particle discharge rate through the first compartment. In the second compartments, particles coarser than the discharge diaphragm grate openings

Fig. 1. Two-compartment ball mill model structure. (Redrawn after Genç [17]).

Ö. Genç et al. / Powder Technology 239 (2013) 137–146

Fig. 2. Size distributions inside a cement mill with dimensions of Ø4.8 × L14.25 m.

were observed to be ground in the first meters of compartment-2 length. In this respect, diaphragm reject effect could be considered to be not significant as grate opening sizes of the discharge diaphragms were recorded to be typically within the range of 8–12 mm which allowed the free passage of finely ground particles through the compartment. Thus, discharge rate was assumed to be not significantly affected by the presence of the discharge diaphragm. 4.1. Effects of design and operational parameters on discharge rate function Material transport through the mill was characterized by residence time distribution functions which were defined as a ratio of mass of powder material in a mill (tons) to feed rate (tons/hour) in size-mass balance models [2]. On the other hand, material transport was characterized by a specific discharge rate function as defined by the ratio of feed rate to mill hold-up in perfect mixing models [13]. Specific discharge rate is considered to be the product of two mechanisms such that, transport and classification by the grate. Typical discharge rate function pattern in a single compartment cement ball mill is given in Fig. 3 which was characterised based on the mill model structure given in Fig. 1. Similar discharge rate function pattern was observed in the second compartments of the mills. However, in the first compartments a different pattern was observed as discussed in detail by Genç [17]. The discharge rate function pattern observed in cement grinding ball mills was found to be similar to that observed in industrial scale wet ball milling [31] and semi-autogenous

Fig. 3. Typical discharge rate function in a single compartment cement grinding ball mill.

141

grinding mills [31]. In wet ball milling, [13] defined an average discharge function based on the average size distribution of the mill hold-up. Typical specific discharge rate function given in Fig. 3 was explained in the literature [13]. As presented in Fig. 3, Xc is the critical particle size at which the particles finer than this size behave like a water and discharge at a constant rate. Rates of particles coarser than this size progressively decrease. Particles coarser than Xc size was assumed to be subjected to the classifying effect of the discharge grate. Rates for particles coarser than the grate size (Xg) will be zero as these particles will not be able to pass through the grate. Classification behaviour of multi-compartment ball mill diaphragms used in the cement industry was extensively discussed by [32]. In this study, the effect of mill length, mill throughput rate (tons/hour) and mill feed size distributions on discharge rate function were discussed. Due to the intermediate diaphragm reject effect, discharge rate function was established for all particle sizes towards the last 1 or 2 m of the compartment length. Mill filling level and hold-up in the compartments were calculated using the inside mill measurements at the crash-stop condition and are presented in Table 4. Considered segment lengths denoted by “L” for defining the discharge rate functions are given in Table 4. Bulk density of cement was measured as 1.8 ton/m3 and this value was used in the calculations. 4.1.1. Effect of mill length Effect of mill length on discharge rate was discussed for a constant mill throughput rate condition. Data related to mill-5 which is a two-compartment mill was used in the discussion. In this respect, discharge rates of particles defined for the first segment (L= 2.2 m) of compartment-1 and for the whole length of compartment-2 (L= 10 m) were compared for the same mill. Characteristic patterns of discharge rate functions in each compartment is given in Fig. 4. Discharge rates of particles were determined to decrease systematically coarser than the critical size (Xc). Similar discharge function pattern which was observed in single compartment cement ball mill was also observed in the second compartment of a two-compartment mill. Systematical decrease in discharge rates could not have been observed in the first compartment such that, slight increase was observed for particles coarser than 10 mm. This is an unexpected pattern in discharge function which could be attributed to the accumulation of coarse particles at the last meter of compartment-1. Accumulation was expected to be affected from the classification performance of the intermediate diaphragm located between the first and second compartments. Physical conditions on the diaphragm such as blockage of slots and grates with material and grinding balls are expected to affect classification performance of the diaphragms. However, it is also expected to be closely related to the grindability of the material which may vary depending on the operational conditions in the clinker feed preparation stages such as burning, cooling or storage. In the investigated ball mill, some coarse particles were rejected after screening on the intermediate diaphragm and accumulated at the last 1 m of the first compartment. However, the amount of these particles which are coarser and equal to a particle size of 13.2 mm was found to be not in significant amount as recorded to be 13.34%. Discharge rate of particles was assumed to be not affected by the presence of discharge diaphragms due to the fineness of material in the second compartment. Thus it was assumed that, mill discharge size distribution (p3) was not affected by the discharge diaphragm. In the second compartment, discharge of material is only through the discharge grate which have coarser grate opening size as compared to the intermediate diaphragm grate and slot openings. Compartment feed sizes represented by the mill feed stream in compartment-1 and stream p2 in compartment-2 are different. It should be mentioned that, discharge rate functions given in Fig. 4 could be normalized according to the mill length by using Eq. (3). However, the effect of feed sizes could not be determined exactly as the intermediate diaphragm affects

142

Ö. Genç et al. / Powder Technology 239 (2013) 137–146

Table 4 Calculated mill filling level % and hold-up as tons at the crash-stop condition. Sampling survey

Mill throughput rate (t/h)

Comp-1 segment-1 mill filling (%)

Comp-1 segment-1 hold-up (ton)

Comp-2 mill filling (%)

Comp-2 hold-up (ton)

Survey-1/mill-1 Survey-2/mill-1 Survey-3/mill-2 Survey-4/mill-3 Survey-5/mill-4 Survey-6/mill-4 Survey-7/mill-4 Survey-8/mill-4 Survey-9/mill-5 Survey-10/mill-6 Survey-11/mill-7 Survey-12/mill-8 Survey-13/mill-8 Survey-14/mill-9 Survey-15/mill-9

316.21 210.03 174.20 221.21 469.45 542.95 712.53 160.00 86.70 136.82 79.34 251.95 357.08 471.01 392.74

32 32 39 34 31 31 35 31 27 40 29 29 29 35 34

L= 11 m (41.39) L= 11 m (41.39) L= 10.5 m (25.83) L= 10.5 m (22.52) L= 2.2 m (8.02) L= 3 m (10.94) L= 3 m (14.46) L= 3 m (10.94) L= 2.6 m (5.65) L= 2 m (6.82) L= 2.8 m (4.24) L= 2 m (4.84) L= 2 m (4.84) L= 2 m (6.59) L= 2 m (6.17)

– – – – 31 36 37 31 32 41 30 28 28 34 34

– – – – L = 10 m (36.45) L = 10 m (51.15) L = 10 m (55.85) L = 10 m (36.45) L = 5.8 m (12.85) L = 5.75 m (21.87) L = 7.25 m (11.37) L = 8.5 m (19.85) L = 8.5 m (19.85) L = 5.18 m (15.33) L = 5.18 m (15.33)

mill hold-up, segment feed (p1 and p2) size distributions. Specific discharge rate functions established for each compartment also indicated that, as the mill length increases discharge rates of each size decreases by a certain ratio.

of operational parameters such as mill feed fineness, airflowrate. It was observed that, differences in the mill throughput rate (t/h) as in the case of mill-4 in survey-8 resulted in a big difference in the Xc sizes as compared to the case in survey-5, 6 and 7 which were performed in mill-4. This difference could be attributed to the circuit configuration as mill-4 was operated in open circuit mode in survey-8 to achieve the similar circuit product fineness specifications obtained in survey-5.

4.1.2. Effect of mill throughput rate Characteristic patterns of discharge rate functions in the second compartments of mills which have the same compartment dimensions have shown that, as the mill throughput rate increases discharge rates of particles also increase by a certain ratio. Mills which have the same diameter and length were selected to establish the relationship between the mill throughput rate increase ratio and discharge rate increase ratio. Discharge rate functions in the first compartments were not considered due to the diaphragm reject effect in establishing the relation. The mathematical relationship between the dimensionless mill throughput rate increase ratio and discharge rate increase ratio is given in Fig. 5. Critical particle sizes (Xc) in the mills which were selected to establish the relation given in Fig. 5 are tabulated in Table 5. However, the data related to mill-7 in survey-11 was excluded in establishing this relation as mill-7 was operated at one capacity condition. It should be mentioned that, there is not any other mill with the similar geometry which could be paired so that to be included in the evaluation of the capacity effect. The correlation given in Fig. 5 was based on physical conditions as considered to be dependent on the parameters such as intermediate diaphragm classification performance, airflow rate through the mill, application of grinding aid. Xc sizes were found to be the same in different mills which emphasises the effects

4.1.3. Effect of mill feed size distribution Effect of mill feed size distribution on discharge rate was discussed on normalized discharge rate functions of a single compartment mill with dimensions of ∅4.8 m × L11 m. The circuit was operated at two different mill throughput rate conditions and portland cement production modes. Portland cement types CEM I 42.5R in survey-1 and CEM IV/ A 32.5R in survey-2 which were classified according to the Turkish Standards EN 197–1 [33], were produced. It was recorded that, air flowrate through the mill did not change much during the sampling surveys. Calculated mill filling level percent and hold-up in the mill at the crash-stop condition were estimated to be 32% and 41.39tons respectively at throughput rate conditions of 316.21 t/h and 210.03 t/h. Specific discharge rate functions were normalized according to Eq. (3) and are given in Fig. 6. Mill feed size distributions are given in Fig. 7. Discharge rate functions given in Fig. 6 indicated that, as the mill feed size distribution gets coarser, discharge rates of particles increase for particles coarser than the critical particle size (Xc). Findings on cement grinding were found to be in accordance with that of wet mills [13].

Fig. 4. Typical patterns of specific discharge rate functions in grinding compartments of mill-5.

Fig. 5. Mill throughput rate increase ratio versus discharge rate increase ratio.

Ö. Genç et al. / Powder Technology 239 (2013) 137–146

143

Table 5 Typical critical particle sizes (Xc) observed both in single compartment and in the second compartments of mills. Sampling survey

Mill throughput rate (t/h)

Single compartment mill Survey-1/mill-1 Survey-2/mill-1 Survey-3/mill-2 Survey-4/mill-3

316.21 210.03 174.20 221.21

Second compartment of two-compartment mill Survey-5/mill-4 469.45 Survey-6/mill-4 542.95 Survey-7/mill-4 712.53 Survey-8/mill-4 160.00 Survey-9/mill-5 86.70 Survey-10/mill-6 136.82 Survey-11/mill-7 79.34 Survey-12/mill-8 251.95 Survey-13/mill-8 357.08 Survey-14/mill-9 471.01 Survey-15/mill-9 392.74

Xc (μm) 10 10 12 12

102 102 102 25 25 25 300 25 25 600 300

4.2. Effects of design and operational parameters on specific breakage rate function Empirical relations among specific breakage rate, ball and mill diameter parameters were identified on the basis of laboratory scale batch grinding test results [2]. However, breakage rates have to be scaled-up to industrial scale grinding conditions by a series of correlations defining the effects of mill operational design conditions. Based on perfect mixing modelling approach, scale-up correlations among ball mill model parameter (r/d), mill diameter, mill load fraction, critical speed, work index and maximum ball diameter were established and used in simulation of ball mills [13]. In this study, specific breakage rates were evaluated independent of the discharge rates instead of evaluating r/d model parameter relations. Experimental work carried out by Hashim [22] on laboratory scale grate discharge mill showed that, discharge rate is a function of fine particle content in mill feed, ball load and material filling. Process variables such as accumulation of coarse particles due to mill feed grindability, screening performance of the intermediate and discharge diaphragms, intermediate and discharge grate design parameters, air flowrate, grinding aid are all expected to affect material filling in the mill. In this respect, flow of particles through the mill which is characterised by the discharge rate pattern was affected indirectly from the stated parameters. It was also shown that, feed size distribution has an effect on discharge rate function (Fig. 6).

Fig. 7. Mill feed size distributions of mill-1 at different production modes.

4.2.1. Effect of ball size distribution and intermediate grate According to size-mass balance modelling approach, ball size effect was related to specific particle breakage rate through the relationship between particle size and specific breakage rate which was established based on the batch grinding test results conducted using a single sized ball charge having a ball diameter (d) Austin et al. [2]. Well known relationship is given in Eq. (4). Si has the unit of min−1, xi is given as the upper size of ith test size interval in mm, α is a parameter that depends on the material characteristics. Empirical range for α is given as 0.5 to 1.5. The parameter “a” depends on the mill conditions and related to ball diameter (d) as given in Eq. (5). Particle size (Xm) which has the maximum breakage rate is related to ball diameter to demonstrate the ball size effects. The relation obtained from batch tests is given in Eq. (6). Given relations are all empirical. α

Si ¼ aðxi Þ aα

xi ≤d

ð4Þ

1 d

Xm α d

ð5Þ 2

ð6Þ

Ball mass and ball surface area effects were related to impact and attrition breakage respectively as given in Eqs. (7) and (8). According to these relations, impact breakage mechanism predominates above Xm size whereas attrition breakage below this size. Ball size distributions were characterised by the maximum ball size and Xm was related to this size as given in Eq. (9). Xm particle sizes were determined from the perfect mixing mill model parameter (r/d*) versus particle size relationships [13]. 3

Impact breakage α b

ð7Þ

Attrition breakage α 1=b

ð8Þ

2

Xm ¼ K:b

Fig. 6. Normalised discharge rate variation in mill-1 at different production modes.

ð9Þ

In Eq. (9), b is the maximum ball diameter in the ball charge distribution in a pilot scale batch mill in mm and K is the maximum breakage rate factor which could be calculated if Xm is determined from r/d* versus particle size relationship. r/d* versus particle size relationships could be scaled by calculating the value of Xm based on the value of K when the maximum ball size is changed. Impact breakage was related to ball mass whereas attrition breakage to ball surface area. These assumptions are used in scale up of perfect mixing mill model parameter (r/d) in simulation of mills. Perfect mixing mill model was used by Erdem and Ergün [34] to establish the

144

Ö. Genç et al. / Powder Technology 239 (2013) 137–146

relationship between maximum ball diameter (Db) and particle size (Xm) using the pilot scale batch ball mill test results. The resulting relationship is given in Eq. (10) which was proposed to scale the r/d* functions to predict specific breakage rates (r) when the mill content (hold-up) size distribution was measured at a constant discharge rate in a batch test. 0:0346ðDb Þ

Xm ¼ 0:2971e

ð10Þ

In this study, effect of ball size distribution and intermediate diaphragm middle grate free surface area percent on specific breakage rates were evaluated in mill-4 with a second compartment dimension of Ø4.8 × 10 m. The mill was operated with different ball size distributions in the second compartment and intermediate diaphragm middle grate free surface area percent in survey-6 and 7. Ball size distributions in the first and second compartments at the sampling conditions are presented in Table 6. In survey-7, 60–50– 40–30 mm ball size class in the second compartment was eliminated and clinker was pre-crushed in HPGR. Back-calculated specific breakage rates in the second compartments of mill-4 are compared in Fig. 8. Agreement between experimental and calculated (fitted) particle size distributions of the mill discharge in the estimation of the related rates are given in Fig. 9. Specific breakage rate versus particle size relationships given in Fig. 8 indicated that, finer ball size distribution application could increase the rates in the grinding compartment by a certain ratio. The increase could be attributed to the total grinding surface area which could be increased by decreasing the ball size distribution. Increase in specific breakage rates was found to increase the circuit capacity at the same circuit product size specifications. Energy consumptions at the mill motor were calculated as 30 kWh/ton and 24 kWh/t in sampling survey-6 and 7 respectively. Production capacity increase by 20.75% was recorded in survey-7 as compared to survey-6. It should be mentioned that, finer ball size application was not the only cause of the mill capacity increase as the mill was operated with different intermediate diaphragm middle grate free area percent in both surveys. Free area of intermediate diaphragm middle grate (perforated screen) with aperture dimensions of 6 × 25 mm was recorded to be 53% in survey-6 whereas a grate with 9.5 mm square aperture size having a free area of 72% was used in survey-7. Grate free surface area percent in survey-7 was expected to increase the material discharge rate through the mill to a considerable extent. 4.2.2. Effect of mill diameter According to size-mass balance modelling approach, mill diameter effect was related to breakage rate based on the batch grinding test

Fig. 8. Specific breakage rates in the second compartments of mill-4.

results by Austin et al. [2] and given in Eq. (11) where Si is the specific breakage rate and D is the mill diameter. 0:5

Si αD

ð11Þ

Perfect mixing mill model parameter (r/d*) was related to mill diameter as given in Eq. (12) [13]. r 2:5 αD d

ð12Þ

A few claims were made related to mill diameter effects on grinding performance (efficiency) of industrial scale mineral grinding ball mills. Rowland [35] reported that, grinding efficiencies do not increase in wet grinding ball mills with diameter above 3.81 m which was linked to the reduced available volume for material and the number of ball to ore contacts as the mill diameter was increased. Breakage rate versus mill diameter curves showed that, grinding efficiencies decrease above a diameter around 4 m in wet grinding ball mills [5]. However, findings on diameter effects in industrial scale dry ball milling case did not indicate the similar findings related to the wet grinding ball mill efficiencies [17]. It should be mentioned that, wet grinding environment is completely different than that of dry grinding as the velocity and viscosity of the slurry is expected to affect the action of grinding media. Parameters that affect specific breakage rates are mill diameter, speed, hold-up, load and grinding ball size. Mill length does not

Table 6 Ball size distributions in survey-6, survey-7 and survey-11. Ball size (mm)

Compartment-1 (mill-4)

Compartment-2 (mill-4)

Compartment-1 (mill-7)

Weight % Survey-6 (542.95 t/h) 100 90 80 70 60 50 40 30 25 20 17 15

15.26 30.28 27.25 14.97 12.24

Survey-7 (712.53 t/h)

Survey-6 (542.95 t/h)

2.57 7.66 9.59 19.18 23.03 22.61 14.52 0.86

Survey-7 (712.53 t/h)

Survey-11 (79.34 t/h) 16.67 33.33 30.56 19.44

11.75 43.15 17.68 27.42

Ö. Genç et al. / Powder Technology 239 (2013) 137–146

Fig. 9. Agreement between experimental and calculated particle size distributions of mill-4 discharge in survey-6 and survey-7.

have an effect on breakage rates however affects discharge rate functions [13]. In this study, specifically mills with different diameters were selected to demonstrate the significant effect of mill diameter. In the investigated ball mills, ball size distributions in the first compartments did not vary significantly as most of them were determined to have similar distribution slopes. Classification in ball size did not take place as classifying liners were not applied in the first compartments. However, ball size classification took place due to the classifying liner effect and this physical condition was expected to affect specific breakage rates in different segments of second compartment as discussed by Genç [17]. Thus, effect of mill diameter on breakage rates was investigated considering the first compartments. Mills with compartment-1 dimensions of Ø4.8 × L4.25 m (mill-4) and Ø3.2 × L3.27 m (mill-7) were selected to demonstrate the mill diameter effect on breakage rates. Selected mills were determined to operate at similar grinding ball load and mill filling levels. Grinding ball loads in the first compartments of mill-4 (survey-6) and mill-7 (survey-11) were calculated to be 31% and 29% respectively. Mill filling levels which affect hold-up were estimated to be 31% and 29% based on the geometrical mill inside measurements in the first compartments of mill-4 (survey-6) and mill-7 (survey-11) respectively. Thus, effects of the related parameters on breakage rates were eliminated. Critical mill speeds were calculated based on the mill diameters and recorded to be 77% and 72% in mill-4 and mill-7 respectively. The production type in both mills were CEM I 42.5R Portland cement which were classified according to the Turkish Standards EN 197–1. Ball size distributions in the first compartments of the mills were given in Table 6. Weighted average ball size in the first compartments are calculated as 82.14 mm in mill-4 (survey-6) and 74.72 mm in mill-7 (survey-11). Cumulative weight percent passing size distributions were found to have close slopes as modelled and presented in Fig. 10 which indicated similar distributions. Thus, it was assumed that effect of the ball size could be eliminated. As stated by Austin et al. [2], mean number of balls tumbled per mill revolution per unit mill volume is constant irrespective of mill diameter. However, the mean number of impacts which a ball makes on particles is proportional to the mill diameter (D) which will have an effect on breakage rates. Breakage rates in the first compartments are compared in Fig. 11. Agreement between experimental and calculated particle size distributions of mill discharge are given in Fig. 12. Although the ball size distribution in mill-7 is finer than that of mill-4, specific breakage rate in mill-7 was found to decrease for each size as compared to

145

Fig. 10. Cumulative ball size distributions and regression equations.

that of mill-4. Breakage rates demonstrated the significant effect of mill diameter.

5. Conclusions The methodology proposed enabled the calculation of discharge and breakage rates individually using the industrial scale data. Basically, the following conclusions were drawn: • Specific discharge rates of particles increase by a certain ratio at a constant mill volume as the mill throughput rate increases, • Specific discharge rates of particles decrease by a certain ratio as the mill length increases at the same throughput rate condition in the same mill, • Specific discharge rates of particles increase systematically for particles coarser than the critical particle size (Xc) as the mill feed size distribution gets coarser, • Finer ball size distribution application in addition to higher free surface area per cent of intermediate diaphragm middle grate lead to an increase in breakage rates of particles, • Specific breakage rates of particles increase as the mill diameter increases in the first compartments where ball size classification does not take place.

Fig. 11. Variation of specific breakage rate of particles with mill diameter.

146

Ö. Genç et al. / Powder Technology 239 (2013) 137–146

Fig. 12. Agreement between experimental and calculated particle size distributions of mill-4 in survey-6 and mill-7 discharge in survey-11.

Nomenclature d Specific discharge rate p Mass flowrate out of the mill s Mass of powder load (hold-up) f Mass flowrate of mill feed r Specific breakage rate a Breakage function i Particle fraction i j Particle fraction j Q Volumetric feed rate D Mill diameter L Mill length S Specific breakage rate a Parameter that depends on the mill conditions α Parameter that depends on material characteristics d Ball diameter b Maximum ball size K Maximum breakage rate factor

Acknowledgements Authors would like to acknowledge the Turkish Scientific and Technical Research Council (Projects: MISAG 190 and MAG 104M369), Hacettepe University Research Unit (Project no: 0202602020) and the researchers involved for their valuable effort. Prof.A.J.Lynch is gratefully acknowledged for his valuable discussions and contributions throughout the research. References [1] H.M. Seebach, E. Neumann, L. Lohnherr, State-of-the-art of energy-efficient grinding systems, ZKG 49 (2) (1996) 61–67. [2] L.G. Austin, R.R. Klimpel, P.T. Luckie, Process Engineering of Size Reduction: Ball Milling, AIME Publ., NY, 1984, pp. 205–223. [3] C.C. Harris, A method for determining the parameters of the 3-parameters size distribution equation, Technical Note, Transactions of Society of Mining Engineers AIME, vol. 244, 1969, pp. 187–190. [4] P. Fruhwein, Algorithm for estimating the process parameters of continuous grinding, Zerkleinern Dechema Monographien 79 (1976) 505–518, (1576-1588, part 2). [5] A.J. Lynch, Mineral Crushing and Grinding Circuits, their Simulation, Optimization, Design and Control, Elsevier Scientific Publishing Co, Amsterdam, 1977, pp. 1–65.

[6] A. Jowett, K.R. Weller, A critical assessment of comminution test methods, 4th Tewksbury Symposium, University of Melbourne, 1979, pp. 18.1–18.25. [7] M.A. Berube, Y. Berube, R. Le Houillier, A comparison of dry and wet grinding of quartzite ground in a small batch ball mill, Powder Technology 23 (1979) 169–179. [8] V.K. Gupta, An appraisal of the linear first order kinetic model based ball mill design correlations, First World Particle Technology Part II, 6th European Symposium, Nurembery, 1986, pp. 605–620. [9] R.E. Hopple, Energy efficient ball mills, Min. Symposium on Mill Design and Grinding Performance of Large Ball Mills, I, SME/AIME, Salt Lake City, Utah, 1983, pp. 65–84. [10] D.W. Fuerstenau, A.-Z.-M. Abouzeid, Effect of fine particles on the kinetics and energetics of grinding coarse particles, International Journal of Mineral Processing 31 (1991) 151–162. [11] W.J. Whiten, Simulation and model building for mineral processing. PhD Thesis, 1972, The University of Queensland: Australia. [12] R.P. Gardner, L.G. Austin, A chemical engineering treatment of batch grinding. Part I, A radioactive tracer technique for determination of breakage function; Part II, Prediction of size weight distributions from selection and breakage data. Symposium Zerkleinern-First European Symposium on Size Reduction, 1962, Frankfurt, Editor, Rumpf H., Verlag Chemie, Dusseldorf; pp.217-231 & pp.232-248. [13] T.J. Napier-Munn, S. Morrell, R.D. Morrison, T. Kojovic, Mineral comminution circuits their operation and optimization, JKMRC Monograph Series in Mining and Mineral Processing, No.2, The University of Queensland, Brisbane, Australia, 2005, p. 413. [14] A.H. Benzer, Mathematical modelling of clinker grinding process, PhD Thesis, 2000, Hacettepe University, Mining Engineering Department, Turkey (In Turkish). [15] Ö. Genç, Investigation of the breakage distribution functions of clinker and additive materials, MSc Thesis, 2002, Hacettepe University, Mining Engineering Department, Turkey (In Turkish). [16] Ö. Genç, A.H. Benzer, Analysis of single particle breakage characteristics of cement clinker and cement additives by drop-weight technique, The Journal of the Chamber of Mining Engineers of Turkey 1 (47) (2008) 13–26, (Published by Chamber of Mining Engineers of Turkey, In Turkish). [17] Ö. Genç, An Investigation on the effect of design and operational parameters on grinding performance of multi-compartment ball mills used in the cement industry, PhD Thesis, 2008, Hacettepe University, Mining Engineering Department, Turkey (In English). [18] Y.M. Zhang, Simulation of comminution and classification in cement manufacture, Ph.D.Thesis, 1992, South University B.E. (Central-South University of Technology), China. [19] A.J. Lynch, M. Oner, H. Benzer, Simulation of a closed cement grinding circuit, ZKG No. 10 (2000) 560–568. [20] A.H. Benzer, Ş.L. Ergun, M. Öner, A.J. Lynch, Simulation of open circuit clinker grinding, Minerals Engineering 14 (7) (2001) 701–710. [21] A.H. Benzer, Modelling and simulation of a fully air swept ball mill in a raw material grinding circuit, Powder Technology 150 (2004) 145–154. [22] S. Hashim, Mathematical modelling the two-compartment mill and classification, PhD Thesis, 2003, Julius Kruttschnitt Mineral Research Centre, The University of Queensland, Australia. [23] D.M. Weedon, A perfect matrix model for ball mills, Minerals Engineering 14 (10) (2001) 1225–1236. [24] S. Morrell, Y.T. Man, Using modelling and simulation for the design of full scale ball mill circuits, Minerals Engineering 10 (12) (1997) 1311–1327. [25] S.S. Narayanan, Development of a laboratory single particle breakage technique and its application to ball mill modelling and scale-up, PhD Thesis, 1986, The University of Queensland, Australia. [26] W.H. Duda, Cement-Data-Book, International Process Engineering in the Cement Industry, vol.1, Bauverlag GmbH, Berlin, 1976, pp. 4–5. [27] M.L. Hills, The Effect of Clinker Microstructure on Grindability: Literature Review Database, Portland Cement Association, 1995, pp. 3–8. [28] M. Tokyay, Effect of chemical composition of clinker on grinding energy requirement, Cement and Concrete Research 29 (1998) 531–535. [29] Ö. Genç, A.H. Benzer, Single particle impact breakage characteristics of clinkers related to mineral composition and grindability, Minerals Engineering 22 (13) (2009) 95–1180. [30] Ö. Genç, A.H. Benzer, Horizontal roller mill (Horomill®) application versus hybrid HPGR/ball milling in finish grinding of cement, Minerals Engineering 22 (15) (2009) 1271–1358. [31] Y.T. Man, Model-based procedure for scale-up of wet, overflow ball mills, part 1: outline of the methodology, Minerals Engineering 14 (10) (2001) 1237–1246. [32] C. Özer, Modelling of the classification behaviour of the diaphragms used in multi-compartment ball mills, MSc Thesis, 2002, Mining Engineering Department, Hacettepe University, Ankara, Turkey. (In Turkish). [33] Turkish Standards EN 197–1, Cement-Part-1: Compositions and conformity criteria for common cements. [34] A.S. Erdem, Ş.L. Ergün, The effect of ball size on breakage rate parameter in a pilot scale ball mill, Minerals Engineering 22 (7–8) (2009) 660–664. [35] C.A. Rowland, Comparison of work indices calculated from operating data with those from laboratory test data, Proceedings 10th International Minerals Processing Congress, London, The Institution of Mining and Metallurgy, 1973, pp. 47–61.