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A multi-component model for the vertical spindle mill

Can E. Ozer, William J. Whiten, Alban J. Lynch

PII: S0301-7516(16)30023-0DOI: doi: 10.1016/j.minpro.2016.01.024Reference: MINPRO 2860

To appear in: International Journal of Mineral Processing

Received date: 1 April 2015Revised date: 14 January 2016Accepted date: 29 January 2016

Please cite this article as: Ozer, Can E., Whiten, William J., Lynch, Alban J., A multi-component model for the vertical spindle mill, International Journal of Mineral Processing(2016), doi: 10.1016/j.minpro.2016.01.024

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A Multi-Component Model for the Vertical Spindle Mill

Can E. Özera, William J. Whitenb and Alban J. Lynchc

The University of Queensland, Sustainable Minerals Institute, Julius Kruttschnitt Mineral Research Centre, 40 Isles

Road, Indooroopilly, 4068, Queensland, Australia

Abstract

Vertical Spindle Mills (VSMs) are widely utilised in coal power plants that account for more than 40% of the electrical

energy generated worldwide. These mills can consume up to 1% of the gross power generated by the plant; and hence,

present a good scope for optimisation. However, optimisation requires better understanding of the operation of these

mills and reliable models to be used for investigating optimisation opportunities.

A new model of VSMs has been developed which enabled interlinked simulation of comminution and classification

operations that occur in the mill. The multi-component models incorporate the effects of size and ash distribution in

coal feed, air and coal flow rate and power drawn by the mill. Both models utilise the size-by-size density distribution

of the coal streams. An efficiency curve model based on settling velocity was used to describe and distinguish

difference in behaviour due to variable density of the components and their composites in the three classification

regions. The matrix comminution model works with a selection function that is only dependent on size and a three

dimensional breakage function that is size, density and energy dependent to account for the differences in breakage of

components and composite particles.

It has been demonstrated that, the particle size distributions and flow rates corresponding to the streams in the mill and

its product can be estimated with a very good accuracy. A reasonable prediction is also found for the density

distributions in these streams.

Keywords

Coal Pulverisation; Multi-Component Comminution; Multi-Component Classification; Vertical Spindle Mill;

Modelling; Simulation

1. Introduction

One of the oldest and most widely spread technology in generating electricity is the fossil fuel fired generators that

utilise steam power. Steam is produced from water in the boilers by the heat supplied from fuel burners.

In 2010, more than 40% of the world electricity generation was from coal power plants (EIA, 2013) where coal is

pulverised prior to being burnt. Pulverisation of coal in power plants is a major consumer of electrical energy that can

account up to 1% of gross generation. Therefore, optimisation of the pulverisation operation in Vertical Spindle Mills

(VSMs) is an important objective both in terms of operating costs and environmental concerns. However, optimisation

requires understanding the operation of these mills and how they react to changes in the operational variables.

a Corresponding author. Present address: Metso Minerals Oy, Lokomonkatu 3, 33900, Tampere, Finland. can.ozer@metso.com b 4 Magnet Close, Riverhills 4074, Australia. wjwhiten@tpg.com.au c 11/2 Sandford Street, St. Lucia 4067, Australia. ajlynch@tpg.com.au

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1.1. Modelling of Vertical Spindle Mills

There are studies in the literature of the operation of these mills that deal with the optimisation problem through detailed

pilot or industrial scale testing, modelling and simulation of laboratory, pilot and industrial scale mills.

Batch comminution kinetics of single-size fractions of different individual (Austin et al., 1976) and binary mixtures

(Cho, 1990; Cho and Luckie, 1995a,b) of materials and the effects of rotational speed, load, number of balls and

fractional filling of the race on specific breakage rates (Austin et al., 1981) in Hardgrove mills have been reported.

Size reduction operation in full scale mills have been described with size mass balance breakage models and

classification functions for relevant classification zones calculated either empirically (Austin et al., 1982; Sato et al.,

1996; Shoji et al., 1998; Kojovic et al., 2015) or theoretically (Masson and Sligar, 1974; Sligar, 1975; Robinson, 1985;

Lee, 1986; Zhou et al., 2000). Zhang et al. (2002) treated the mill as a black box.

In addition to the size reduction and classification operations in the mill, some of the researchers have considered the

pressure drop (Lee, 1986; Shoji et al., 1998; Zhou et al., 2000; Zhang et al., 2002) and energy transfer between air and

coal (Lee, 1986; Zhou et al., 2000; Zhang et al., 2002). Although transient state operation of the mills was also of

interest to some researchers (Robinson, 1985; Lee, 1986; Shoji et al., 1998; Zhou et al., 2000; Zhang et al., 2002)

quantitative validation was not available.

None of the above studies considered coal as a multi-component material. However, coal, mineral matter and composite

particles are substances that could be expected to behave differently both in comminution and classification processes.

2. Material & Method

The VSMs combine two interacting operations, i.e. comminution and classification processes, within single equipment

and a model for these mills require de-coupling of these processes to construct individual models of each operation and

describing the interaction between them. This exercise requires detailed sampling from the mills; and a full mill survey

comprises conventional samples (i.e. coal feed, product and mill reject), ball product and, separator feed and reject

streams. A new methodology has been developed to collect non-conventional samples, which has previously been

described in Özer et al. (2010). The effect of two of the operational variables, namely coal and air flow rate to the

pulveriser, were investigated by carrying out five sampling campaigns whereas other variables, e.g. pressure on balls,

kept constant. During these surveys steady state operation of the pulveriser was ensured by checking operational data in

the control room. Combinations of three different air and coal flow rates within the normal plant operation range were

tested. The test conditions are summarised in Table 1 as a percentage of the base condition of 28.5t/h coal and 18.6kg/s

air flow rates. The pulveriser was operated as close as possible to the base condition for repeat surveys (Surveys 1 and

3).

Samples collected utilising the newly developed method enabled separate investigation of the two operations with the

information collected during detailed sampling surveys carried out on a Babcock-Hitachi 10E10 mill in an Australian

power plant processing high-ash bituminous thermal coal (Mutton, 2003). For this coal the low density coal component

is harder than the higher density gangue component (Özer and Whiten, 2012). A schematic view of the mill and model

flow structure is illustrated in Figure 1.

Samples collected from the mill during five sampling surveys were air dried for moisture determination, analysed for

size from 90mm down to 45μm with screens and sieves in root-two progression and, five size fractions of the coal feeds

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of all of the surveys and most of the conventional and mill internal samples from survey 1 were further fractioned based

on density at six levels. Breakage characteristics of the coal in four density bins (F1.3 and F1.4/S1.3 bins were

combined) and three size fractions were determined at six different specific comminution energy (ECS) levels. Selected

size fractions of samples from all surveys, breakage test products, density fractions of the mill internal samples (i.e. mill

body feed, feed and reject of separator) and product from Survey 1 were analysed for ash content by a certified

commercial laboratory. The size fractions analysed using density fractioning, breakage tests and ash content

determinations are summarised in Table 2.

3. Results & Discussion

Construction of a multi-component model for VSMs required a number of intermediate data analysis and model

development stages as summarised in the following sections. Major findings from simulation studies are also detailed

and discussed.

3.1. Density – Ash Content Relationship

Evaluation of ash content data corresponding to the tested density fractions yielded a simple equation relating these two

parameters to each other as given in Equation 1. This type of relation has previously been reported in the literature

(Anon., 1966, Luttrell et al., 2003) and enables estimation of the average density of a sample provided that the ash

content is known; or vice versa. The predictions were found to be satisfactory in describing the measured (Figure 2a)

and variations in the intercept values (k or reciprocal density of “pure coal”) showed a logarithmic relation to particle

size (Figure 2b).

(1)

3.2. Multi-Component Appearance Function

A multi-component appearance function (MCAF) has been developed for describing the breakage characteristics of the

mill feed coal samples broken in particle beds under compression. The smallest size fraction tested was 4×2.8mm due to

difficulties in density fractionation of narrowly sized fine fractions in larger amounts either with conventional

separating funnel and the funnel-flask methods suggested in Standards Australia (AS4156.1-1994, 1994) or the method

developed during this work (Özer, 2016). The number of sizes, density fractions and energy levels tested was

considered sufficient for estimating the effect of size and density on breakage behaviour for the purpose of this study.

However, if a greater accuracy is required, particularly outside the range of the tested sizes, other fractions could be

analysed.

Equation (2) relates t10 (percent passing one tenth of the original particle size) of the progeny particle size distribution to

the ECS utilising the top size (xT) of the size fraction and average density (ρP) of the tested sample. Details of this

model development can be found in Özer and Whiten (2012).

(2)

The t10 value determines which of the family of breakage curves applies.

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3.3. The Flows within the Mill

The flow rates, particle size distributions and size-by-size ash contents of the streams entering and leaving the mill body

and separator classifiers (C2 and C3 in Figure 1, respectively) were mass balanced by using two different routines

written in Excel VBA. The details of the mass balancing procedures has been described in a previous publication (Özer

et al., 2010). The mass balance results provided the flow rates, particle size distributions and size-by-size ash contents

of the reject streams of mill body and separator which combine on the grinding race with the new feed to the mill to

produce the ball feed (Figure 3a). Since the weighted average of mill body feed and the mill reject allowed calculation

of the ball product (Figure 3b), the particle size distributions, flow rates and size-by-size ash content information

entering and leaving the grinding section (B, in Figure 1) is available to calculate the selection function (Equation 5)

using the MCAF (Section 3.2).

3.4. Prediction of Size-by-Size Ash Distribution of Streams for the Whole Size Range

The ash content estimates for some sizes of separator and mill body reject streams from Section 3.3 were used to

estimate the ash contents for the whole size fraction ranges by interpolation or extrapolation utilising Equation (3) fitted

to experimental and mass balanced ash content data. It was further assumed that the ash content of coal feed to be

constant over the size fractions and equal to the ash content of 16×11.2mm fraction. These data, together with the

associated particle size distributions and flowrates, allowed calculation of size-by-size ash content of the ball feed. For

the ball feed stream, there exists a critical size (XC) where very little or no material exists in both the mill body and

separator classifiers’ reject streams (XC = ~5mm for Survey 1); and, above XC, the curve mostly follows the ash content

distribution trend of coal feed. However, below XC the ash content increases gradually down to the top size of the

product, (i.e. higher density material accumulates in the mill), and thereafter, decreases with particle size (Özer et al.,

2010). Thus, the two separate equations (3a and 3b) were defined to predict the ash content distribution above and

below the critical size XC, by fitting coefficients a1 to a6 (Table 3)

Ash%‒ Xc = (a1 + a2x) / (1 + a3x + a4x2) (3a)

Ash%+Xc = a5 + a6x (3b)

The resulting ash distribution by size presented in Figure 4 is readily converted to density distribution data by size using

the relation in Section 3.1. The equations predicted the ash and density distributions sufficiently accurately and were

used to estimate average density in each size fraction to calculate MCAF’s.

3.5. Power Draw

The gross power drawn by the mill was found to be linearly related to the ratio of mass flow rates of coal to air; and, an

estimate of no load power (118.8kW) from y-axis intercept (i.e. extrapolation to no coal feed) enabled calculation of net

power draft of the comminution operation (Figure 5a). This provided the net specific energy (Net ECS) introduced by

the grinding balls to the grinding bed (or ball feed, BF in Figure 5b) to estimate the progeny particle size distribution for

each density fraction by calculating appropriate MCAF coefficients. The net specific energy was assumed to be split

between size and density fractions equally, based on the findings of Özer and Whiten (2012) reporting the capability of

the model predicting progeny size distributions of size and density mixtures tested.

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3.6. Back-Calculated Selection for Breakage Functions (Open Circuit)

In order to calculate selection function for each surveyed condition, t10 values for each size with its corresponding

average density in the ball feed was calculated using the size-by-size ash contents, the top size of size fractions and the

net specific comminution energy estimate. The t10 values enabled estimation of appearance functions for each density-

size fraction combination and were readily converted to matrix breakage functions (B) by discarding the unbroken

particles. The known variables f, p and B enabled calculation of the diagonal matrix selection function (S) solving

Equation (4) for each of the surveys using a simple Excel VBA routine. As seen in Figure 6a-e the back-calculated

results, shown with markers, presented somewhat a scatter; and hence, were fitted to the exponential function given in

Equation (5) to obtain smoothened values (dashed lines in Figure 6). The scale parameter (x’) was found to be a

function of gross specific energy as illustrated in Figure 7 and a value of 0.708 described the coefficient “t” sufficiently

for all surveys.

p = [BS + (I – S)] f (4)

Si = 1 – exp[–0.6931(xi / x’)t] (5)

3.7. Validation of Selection Functions

The selection functions estimated with gross ECS (Figure 7), the mass balanced ball feed particle size distribution and

breakage functions were then used to predict the size distribution of the ball product (≈mill body feed). An example for

the predicted particle size distributions for the mill body feed over the mass balanced size distribution is presented in

Figure 8.

The density of the daughter particles after breakage was assumed to be equal to the density of the mother particle based

on observations of non-preferential breakage for this specific coal (Özer and Whiten, 2012); i.e., the distribution of

daughter particles to lower sizes would have the same density or ash content as the mother particle. An Excel VBA

routine averaged the density of each component ending up in each size fraction from upper size classes based on

weight; providing better predictions for the density distribution of the ball product. An example of the predicted size-

by-size ash distribution of ball product stream compared with the observed values is presented in Figure 9.

3.8. Aerodynamic Classification Function

The conventional way of expressing the efficiency of a physical separation is to utilise either the particle size (e.g.

efficiency curve for classifiers) or density (e.g. partition curves for coal preparation plants). However, the physical

separation process in a pneumatic classifier could be described better by plotting the efficiency values against a

parameter that includes both the size and density of particles, e.g. settling velocity. The settling velocity of particles

corresponding to each size fraction and density bin combination was conveniently calculated using the Whiten and Özer

(2015) equation relating dimensionless velocity and dimensionless diameter for spherical particles (equation 6).

[ln(d*) – 0.4321ln(u*) – 0.6753][ln(d*) – 3.3597ln(u*) + 8.6976] = 10.0518 (6)

The size-by-size density fractioning of the samples around the classification regions for Survey 1 enabled construction

of size-by-size density distribution of particles in each stream which is readily converted to settling velocity

(aerodynamic size) for each size and density fractions. The mass split to fines streams for mill body and separator

classifiers is illustrated in Figure 10.

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The aerodynamic classification function is a more detailed relationship than conventional methods of describing

classification and is required for a complete multi-component simulation model, i.e. it provides the link between the

comminution and classification models both in terms of particle size and density. Since the density fractioning data for

the streams around the classifiers are only available for Survey 1, it was not possible to calculate aerodynamic

classification function using experimental density and size data for other surveys and directly relate the model

parameters to the operational variables; e.g. air flow. However, model parameters used in simulation did show a relation

with air flow rate (See Section 3.12).

3.9. Input Data for Simulation of Mill Operation

A simulation program incorporating multi-component matrix comminution and classifier models, interlinked with

aerodynamic size, have been coded in Matlab as interacting models and were tested together as a closed circuit

comminution-classification machine.

A multi-dimensional coal feed flow rate grouped in root two ratio size fractions each with four density bins (<1.4g/cm3,

1.4-1.8g/cm3, 1.8-2.0g/cm

3 and >2.0g/cm

3) was input to the simulator. For each survey the density distribution of the

16×11.2mm fraction was used for all feed fractions. This assumption was based on the ash content being found to be

similar in all size fractions of Survey 1 coal feed. Moreover, the ash content distribution of 16×11.2mm fraction for

Survey 1 and head ash content of coal feeds for all surveys are best predicted (Figure 11) utilising the coefficients for

2.0×1.4mm fraction (m=‒ 0.0048, k=0.8134) of mill interior streams in Equation (1). Thus it was assumed that there is

no preferential breakage of coal or mineral matter and thus particles from a density bin will produce daughter particles

into the same bin.

The specific comminution energy corresponding to each survey conditions were also calculated and used together with

size and density bins to construct MCAF matrices in a similar manner to open circuit (single pass) calculations

(Sections 3.6 and 3.7).

The classification operations at the mill rejects, mill body and separator classifiers (C1, C2 and C3 in Figure 1,

respectively) were simulated with three separate efficiency curves based on the settling velocity (ui) calculated from

Equation (6). The shape and location of the curves are controlled by changing the settling velocity that corresponds to

fifty percent efficiency (u50), the exponent (s) and the asymptote values which specify the classification by-pass

amounts, i.e. fine particles reporting to coarse product (EMAX) and coarse particles reporting to fine product (EMIN).

Ei = EMIN , Ei<EMIN (7a)

Ei = EMAX × exp[–ln(2) × (ui/u50)s] , EMIN < Ei (7b)

3.10. Simulator Algorithm (Closed Circuit) and Results

The simulator starts the first iteration with input feed as a size by density matrix and computes the breakage product for

each size and density bin of the coal feed with the MCAF and selection matrices. The breakage (ball) product is split

into two streams at the mill reject classifier (C1), i.e. mill reject and mill body classifier feed, utilising the corresponding

efficiency values for each size-density fraction combination. The mill body feed stream is further split into two streams,

mill body reject and separator feed, utilising the same form of efficiency curve function with parameters corresponding

to mill body classifier (C2). In the separator classifier (C3), the separator feed stream is split to product and separator

reject.

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Following the first simulation pass, the feed vectors to the comminution model are constructed by summing the

flowrates in each corresponding size and density bins of the coal feed, mill body reject and separator reject streams. The

simulator then uses the same algorithm as in the first run to calculate the new distributions for the product, reject and re-

circulating streams of the mill. The iterative calculation is terminated when the flow rate of the streams leaving the mill

differ from the coal feed flow rate no more than the allowed convergence value of 10–5

.

The parameters describing the comminution and classification models were estimated by simple manual adjustment

targeting to achieve good agreement with the experimental data and are summarised in Table 4.

The parameters reported in Section 3.6, describing the selection function, were back-calculated by solving matrix model

for a single pass (open circuit) and overlooked the progressive effects in size reduction due to circulating loads. Hence,

these values were altered for closed circuit runs.

The parameter s calculated for mill rejects classifier in Survey 2 is not consistent with other surveys since, the amount

of material rejected from the mill in Surveys 1, 3, 4 and 5 are negligible (<0.01%) compared to the rejects of about

615kg/h in Survey 2 that accounts for 0.4% of the ball product. All the parameters corresponding to mill body and

separator classifiers were found to be invariant except u50.

The mass balanced flowrates for each flow in the model structure are compared with simulation results in Table 5.

3.11. Simulation Predictions

3.11.1. Particle Size Distributions

The particle size distributions were calculated by summing flow rates across the density bins for each size and

proportioning to the total flow rate. The simulation results compared with mass balanced particle size distributions and

flow rates within the mill for Survey 1 are illustrated in Figures 12 and 13, respectively; and were found to be in

excellent agreement. Similar results were obtained for all of the surveys.

3.11.2. Density Distributions

The behaviour of different components and composite particles was investigated utilising the density distribution in

some size intervals calculated from the flow rates of material in each density bin. The results obtained from simulation

are illustrated in Figure 14 in comparison with the observed density distributions in four size fractions for Survey 1.

The density distributions in 5.6×4.0mm fraction in the mill body and separator feed streams are predicted reasonably

well (Figure 14a). The separator feed has more fractional content in the lowest density bin compared to mill body feed,

and vice versa is true for the highest density bin; and hence, denser particles are selectively directed to the mill body

reject by the model. The observed values for separator reject should have been equal to the separator feed for

5.6×4.0mm fraction, since this size is not present in the mill product. However, the departure of separator reject

prediction from observations is likely to be due to a bias in the sample at coarse sizes (Özer et al., 2010).The density

distribution predictions for the mill product shown in Figure 14c,d are in reasonable agreement with the observed

values; but, the predictions for the highest density bin are lower than observations.

Density distributions at finer sizes, reported in Figure 14b-d, are not predicted as well as the 5.6×4.0mm size fraction

especially for the lowest and highest density bins. As was previously been reported in Özer et al. (2010), in actual mill

operation, the particles that correspond to the highest density bin accumulate in the mill internal streams with increasing

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size. This is valid up to product top size; then, particles in lower density fractions dominate the flows. In contradiction

with observations, the simulations showed a decrease in the percent of the sinks 2.0 bin with increasing size in the

separator feed (also the product) as shown in Figure 15a. Looking at the separator feed flows in Figure 15b the sinks 2.0

bin initially increases with increasing size as expected, but the lighter fraction increases much more rapidly, resulting in

the decreasing percentage of heavy component seen in Figure 15a. The proportion of lowest density bin particles

leaving the mill in product to the particles present in the separator feed is more than that for the highest density bin at

each size fraction. However, the amount of highest density bin particles leaving the mill also increases with decreasing

size, resulting in increasing proportion of highest density bin particles in product.

3.11.3. Ash Distributions

The density distributions were converted to ash content distributions for each size fraction in each stream calculated by

the simulator using Equation 1. However, to preserve mass balance, rather than a size dependent density – ash relation

as described in Section 3.1, the coefficient set corresponding to the 2.0×1.4mm size fraction (m=‒ 0.0048 and

k=0.8134) was used for all size fractions.

The ash content was found to decrease with increasing size for all the streams in the mill up to about 10mm (Figure

16a,b). The reason for slight increase above 10mm is that the proportion of higher density bin particles starts to increase

as shown in Figure 17 for Survey 1 mill body feed. The abnormal heap at around 1mm for the mill reject is due to

selected parameters describing the classification to allow the negligible mill reject flowrate and predict its size

distribution.

3.12. Relationship between Model Parameters and Operating Conditions

Common sets of values for exponent term (s) and the by-pass value (EMAX) in Equation 7 for mill body and separator

classifiers were used for all surveys. However, the settling velocity that corresponds to 50 percent efficiency (u50) for

both mill body and separator classifiers, as expected, is found to be related to the air flow rate supplied to the mill

(Figure 18).

The parameters defining the selection function, x’ and t in Equation (5), were found to be strongly related to the specific

energy consumption at the grinding section. An increased specific energy consumption results in an increasing breakage

rate for all sizes and hence, decreasing selection size parameter (x’). An increasing selection exponent parameter (t)

increases the slope of the curve resulting in greater breakage rate at sizes larger than 1mm, but less breakage rate for

smaller particles, where the pivot value at 1mm is determined by the selection size parameter. The relations of

parameters x’ and t to the specific energy consumption based on ball feed flow rate are illustrated in Figure 19.

4. CONCLUSIONS

The comminution model has been combined with the classification models incorporating the effects of feed size, coal

feed ash distribution, air flow rate and power drawn by the mill. Both models utilise the size-by-size density distribution

of the coal streams; while only one survey had corresponding size by density information, it has been possible to adjust

the simulation models to agree with the available data size and ash data for the remaining surveys.

The predictions for the particle size distributions, flow rates and density distributions in the streams in the mill and its

products by the simulator have been demonstrated. The simulator utilises an efficiency curve model based on settling

velocity of particles for the three classifiers to distinguish difference in behaviour of the components and composites

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due to variable density. The matrix comminution model works with a selection function that is only dependent on size

and a three dimensional appearance function that is size, density and energy dependent to account for the differences in

breakage of components and composite particles.

It is shown that the models are capable of successfully reproducing the particle size distributions and the flow rates for

all the streams that are either sampled or calculated by mass balance. The density and ash measurements are more

difficult; but, the agreement of the models to these is considered satisfactory. While the number of tests was severely

limited by time and operational requirements, it has been possible to determine the relations between operating

variables and the model parameters so that predictions can be made. Once the feed has been characterised, the

predictions can be used to investigate mill performance for a range of different operational requirements.

5. Nomenclature

a1-6, k, m , s : Coefficients

A, b : Ore dependent model parameters

BF : Ball feed

d*, u* : Dimensionless diameter and velocity, respectively

f, p : Size fractions in feed and product

B, S : Breakage and selection functions in comminution model

ECS : Specific comminution energy (kWh/t)

Ei : Classification efficiency

EMIN, MAX : Asymptote values for Ei

kW : Kilowatts

MCAF : Multi-component appearance function

ρC,M,P : Density of pure coal, mineral matter and composite particles, respectively (g/cm3)

t, x’ : Selection exponent and size, respectively

tBF, tC : Tonnes of material in ball feed and coal feed, respectively

t10 : The cumulative percent passing the one tenth of the geometric mean of the tested size range

ui, u50 : Settling velocity and ui corresponding to 50% efficiency (m/s)

XC : Critical size for ash content distribution (mm)

xi : ith

size fraction

xT : Top size of the tested size fraction (mm)

6. Acknowledgements

Authors thank the financial support by ACARP C15079 project managed by Dr. Fengnian Shi, The University of

Queensland, Sustainable Minerals Institute, Julius Kruttschnitt Mineral Research Centre and Tarong Energy. Authors

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sincerely acknowledge Dr. Terry Dixon and Glenn Schumacher for their contributions and encouragement. The inputs

of the GEMIII

Project for supplying testing equipment, JKMRC pilot plant and workshop staff for technical support, and

Mr Weiran Zuo for assistance during plant surveys are appreciated.

7. References

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AS4156.1-1994, 1994. Coal Preparation Part 1: Higher Rank Coal — Float and Sink Testing. Standards Australia.

Austin, L., Shoji, K., Bhatia, V., Jindal, V. and Savage, K., 1976. Some Results on the Description of Size Reduction as

a Rate Process in Various Mills. Ind. Eng. Chem. 15, 187-196.

Austin, L.G., Shah, J., Wang, J., Gallagher, E. and Luckie, P.T., 1981. An Analysis of Ball-and-Race Milling. Part I.

The Hardgrove Mill. Powder Technol. 29, 263-275.

Austin, L.G., Luckie, P.T. and Shoji, K., 1982. An Analysis of Ball-and-Race Milling Part II. The Babcock E 1.7 Mill.

Powder Technol. 33, 113-125.

Cho, H., 1990. Investigation of the Grinding of Coal and Mineral Mixtures in a Batch Ball-Race Mill. PhD Thesis, The

Pennsylvania State University.

Cho, H. and Luckie, P.T., 1995a. Grinding Behaviour of Coal Blends in a Standard Ball-and-Race Mill. Energy & Fuels

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Cho, H. and Luckie, P.T., 1995b. Investigation of the Breakage Properties of Components in Mixtures Ground in a

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Lee, M.-S. 1986. Mathematical Model and Control of a Coal Pulverizer. PhD Thesis, The University of Texas at Austin.

Luttrell, G.H., Barbee, C.J. and Stanley, F.L., 2003. Optimum Cutpoints for Heavy Medium Separations, in: Honaker,

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Figure 1 – Illustration of flows in VSM (hollow circles - sample locations) and model structure

Figure 2 – (a) Density or ash content predictions (b) size dependency of intercept values

Figure 3 – Mass balanced particle size distributions of streams (a) entering and (b) leaving the grinding zone (B) for Survey 1

Figure 4 – Size-by-size ash and density distribution of ball feed for Survey 1

Figure 5 – (a) Gross & net mill power, (b) Grinding bed net ECS

Figure 6 – Selection functions for surveys (a) 1, (b) 2, (c) 3, (d) 4 and (e) 5

Figure 7 – Relation of scale parameter (x’ in equation 5) to gross ECS

Figure 8 – Mill body feed (≈ ball product) predicted particle size distribution for Survey 1

Figure 9 – Predicted size-by-size ash distribution of ball product for Survey 1

Figure 10 – Aerodynamic classification function for Survey 1

Figure 11 – Ash content distribution of 16×11.2mm fraction of the coal feed and coal feed head ash content predictions

Figure 12 – Comparison of mass balanced and simulated particle size distributions (Markers are mass balanced and lines are simulated results)

Figure 13 – Comparison of mass-balanced and simulated flowrates

Figure 14 – Experimental vs. Simulated density distributions by mass at (a) 5.6×4.0mm, (b) 2.0×1.4mm, (c) 0.180×0.125mm and (d) 0.090×0.063mm

for Survey 1

Figure 15 – Simulated separator feed and product (a) fractional Sinks 2.0 content and (b) flow rates per density bin

Figure 16 – Survey 1 ash distribution by size for streams

Figure 17 – Simulated variation of the proportions of particles in Floats 1.4 and Sinks 2.0 density bins with particle size for Survey 1 mill body feed

Figure 18 – Mill body and separator classifier settling velocity at 50% efficiency (u50) relation to air flowrate

Figure 19 – Selection function parameters in relation to specific energy consumption

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Fig. 1

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Fig. 2a

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Fig. 2b

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Fig. 3a

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Fig. 3b

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Fig. 4

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Fig. 5a

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Fig. 5b

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Fig. 6

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Fig. 7

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Fig. 8

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Fig. 9

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Fig. 10

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Fig. 11

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Fig. 12a

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Fig. 12b

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Fig. 13

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Fig. 14a

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Fig. 14b

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Fig. 14c

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Fig. 14d

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Fig. 15a

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Fig. 15b

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Fig. 16a

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Fig. 16b

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Fig. 17

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Fig. 18

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Fig. 19

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Table 1 – Operational conditions for sampling surveys

Flowrate Survey 1 Survey 2 Survey 3 Survey 4 Survey 5

Coal, % 102 81 98 82 99

Air, % 103 79 98 98 113

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Table 2 – Size and Density Fractions Tested

Test Sample Name Size Fraction Analysed

Float/Sink at Coal Feeds 63×45, 31.5×22.4, 16.0×11.2, 8.0×5.6 and 4.0×2.8mm

1.3, 1.4, 1.5, Survey 1 Mill Internal, 45×31.5, 31.5×22.4, 22.4×16, 16×11.2, 11.2×8, 8×5.6, 5.6×4, 4×2.8, 2.8×2, 2×1.4 and

1.6, 1.8 and Product and Rejects 1.4×1.0mm; x>1mm

2.0 g/cm3 0.71×0.50, 0.355×0.250, 0.180×0.125, 0.090×0.075 and 0.075×0.063mm; x<1mm

Breakage Coal Feeds 16×11.2, 8×5.6 and 4×2.8mm; each density fraction (F1.4, F1.5/S1.4, F2.0/S1.8 and S2.0)

Ash Content Coal Feeds 16.0×11.2mm; each density fraction

Survey 1 Mill Internal 2.0×1.4, 0.355×0.250, 0.180×0.125, 0.090×0.075 and 0.075×0.063mm; each density fraction

and Product 0.250×0.180, 0.125×0.090, 0.063×0.045 and ‒ 0.045mm; as bulk

Surveys 2 to 5 2.0×1.4, 0.355×0.250, 0.250×0.180, 0.180×0.125, 0.125×0.090, 0.090×0.075, 0.075×0.063,

0.063×0.045 and ‒ 0.045mm; as bulk

Breakage Products 11.2×8, 5.6×4, 2.8×2, 1.4×1.0, 0.71×0.50, 0.355×0.250, 0.180×0.125, 0.090×0.075

and ‒ 0.075mm; as bulk

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Table 3 – Coefficients in Equation 3 for Survey 1

Coefficient Ball Feed Mill Body Reject Separator Reject

a1 43.5 –8287 2.36

a2 1.8 200963 831

a3 0.35 2624 12.9

a4 0.17 1662 4.3

a5 3.14 - -

a6 17.5 - -

SSQ 59.8 85.4 28.9

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Table 4 – Size Model Parameters for Comminution and Classification Models

Survey x’ t Net Power, kW u50 s EMIN EMAX

RC MBC SC RC MBC SC RC MBC SC RC MBC SC

1 0.50 0.3 165 50 6.0 0.090 4.0 0.70 0.75 0.9995 0.0 0.0 0.9999950 0.90 0.98

2 0.15 0.5 162 140 4.0 0.070 1.3 0.70 0.75 0.9700 0.0 0.0 1.0000000 0.90 0.98

3 0.70 0.4 164 50 6.0 0.090 4.0 0.70 0.75 0.9995 0.0 0.0 0.9999950 0.90 0.98

4 0.50 0.4 166 70 6.0 0.085 4.0 0.70 0.75 0.9995 0.0 0.0 0.9999990 0.90 0.98

5 1.50 0.3 130 100 8.0 0.100 4.0 0.70 0.75 0.9995 0.0 0.0 0.9999985 0.90 0.98

RC: Reject Classifier, MBC: Mill Body Classifier, SC: Separator Classifier

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Table 5 – Comparison of Mass-Balanced and Simulated Flow Rates

Mass Balanced (MBal) and Simulated (Sim) Flow Rates, tph

Stream Survey1 Survey 2 Survey 3 Survey 4 Survey 5

MBal Sim MBal Sim MBal Sim MBal Sim MBal Sim

Coal Feed 29.1 - 23.0 - 28.0 - 23.3 - 28.2 -

Ball Feed 264.0 263.4 163.1 160.5 278.4 274.0 220.2 217.3 326.2 338.4

Ball Product 264.0 263.4 163.1 160.5 278.4 274.0 220.2 217.3 326.2 338.4

Mill Reject 0.022 0.015 0.677 0.615 0.022 0.022 0.011 0.008 0.015 0.003

Mill Body Feed 263.9 263.4 162.4 159.9 278.4 274.0 220.2 217.3 326.2 338.4

Mill Body Reject 86.7 88.1 54.5 43.9 92.6 91.5 72.3 66.8 109.1 120.7

Separator Feed 177.2 175.3 107.9 116.0 185.8 182.5 147.8 150.5 217.1 217.7

Separator Reject 148.1 146.2 85.6 93.6 157.9 154.6 124.5 127.2 188.9 189.5

Product 29.1 29.1 22.3 22.4 27.9 27.9 23.3 23.3 28.2 28.2

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Graphical abstract

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HIGHLIGHTS

A multi-component model of vertical spindle mill is developed

Interlinked comminution and classification operations in the mill are simulated

Particle size distributions and flowrates in all the streams are estimated accurately

Density distributions in these streams are also predicted reasonably well

Relation of model parameters to operating variables were determined for predictions