Fuel 92 (2012) 116–121

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Fuel

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Evaluation of a laboratory rod mill when grinding bituminous coal

Hoon Lee a, Mark S. Klima b,⇑, Paul Saylor b

a Korea Institute of Geoscience & Mineral Resources, 92 Gwahang-no, Yuseong-gu, Daejeon 305-350, Republic of Koreab John and Willie Leone Family Department of Energy and Mineral Engineering, Penn State University, University Park, PA 16802, United States

a r t i c l e i n f o

Article history:Received 14 February 2011Received in revised form 15 July 2011Accepted 1 August 2011Available online 17 August 2011

Keywords:Size-mass balanceBreakage ratesBreakage distributionGasifier feed

0016-2361/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.fuel.2011.08.006

⇑ Corresponding author. Tel.: +1 814 863 7942; faxE-mail address: msk4@psu.edu (M.S. Klima).

a b s t r a c t

Laboratory testing was conducted to evaluate the breakage of bituminous coal in a rod mill. A Pittsburghseam coal, which had been obtained from the product stream of an operating coal cleaning facility, wasused as the feed material. This material had an ash value of 6.7% and had been crushed to a nominal�6.35 mm. Grinding tests were carried out on a mono-size (2.38 � 1.68 mm) fraction. The tests were con-ducted using a 193.5 mm diameter and 245.0 mm long laboratory rod mill, which contained steel rods ata volume loading of 23%. The mill was operated at 70% of critical speed for various grind times. A locked-cycle test was also performed to simulate continuous grinding conditions.

The grinding was characterized using the population (or size-mass) balance model. The breakage dis-tribution and rates of breakage were determined from the grinding data. The results indicated first-orderbreakage. The locked-cycle results indicated that steady state was achieved in several iterations. The sim-ulated results matched the experimental results very well.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

While prices for raw materials including petroleum have oftenshown wide fluctuations, the prices for coal have been relativelystable. Moreover, because the worldwide coal reserves are large,it is likely that coal will be a key energy source for the foreseeablefuture. According to a report by United States Energy InformationAdministration, the amount of coal consumed throughout theworld is estimated to reach 206.3 quadrillion Btu by 2035 [1]. Inthe United States, approximately 90% of coal is used for power pro-duction via coal combustion. Coal gasification is also receiving re-newed interest both as a more efficient approach to electricitygeneration and a possible way to reduce CO2 emissions [2].

In the gasification process, carbonaceous material, includingcoal, is partially combusted with insufficient oxygen to generatecarbon dioxide and water. Additional water is added to producesynthesized gases composed mainly of carbon monoxide andhydrogen [3]. During gasification, organic matter is transformedinto hydrogen components at high temperature by using wateras a raw material. In addition, the sulfur and nitrogen componentsare converted into hydrogen sulfide, which can be removed andcollected as sulfur or sulfuric acid, and ammonia, and potentiallyutilized as byproducts.

Common gasifiers include the Lurgi, fluidized-bed, and en-trained-flow slagging gasifiers. In each unit, the preparation ofthe feed material, including the particle size distribution, is an

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: +1 814 865 3248.

important aspect of the overall gasification process. Improperlyprepared feed material can lead to reduced gasifier performance.In the case of entrained-flow slagging gasifiers, particles less thanapproximately 1 mm are typically used as the feed solids [4].

Wen and Chaung [5] showed that the feed particle size had asignificant effect on the carbon conversion in a pilot-scale down-flow entrainment gasifier. Large particles have greater terminalvelocities and shorter residence times than small particles,whereas the specific contact area between reacting gases and thefuel particle is inversely proportional to the particle size. Thesetwo effects combine to give a lower conversion for large particlescompared to small particles. Shannon et al. [6] analyzed the effectof size and density of coal particles during gasification at severalgasifier temperatures. They found that higher conversions wereobtained for coal that was in a density range of 1.3–1.6 g/cm3

and a size range of 0.212 mm–0.425 mm. Hanson et al. [7] trackedthe effect of coal particle size at the onset of the gasification pro-cess and found that finer coal produced char particles larger thanthe original particles whereas coarser coal showed a tendency tofragment. Interestingly, in the coal size range from 0.5 to2.8 mm, the gasification behavior did not vary significantly withthe coal size.

Prior to gasification, size reduction by grinding is required toproduce coal in the desired size range. However, during grinding,only a small fraction of the energy used to rotate the mill andgrinding media is involved in the actual breakage of the coal. Therest is lost primarily as heat. Therefore, improvements in the grind-ing process can lead to reductions in energy use, improving theoverall economics of the gasification process.

H. Lee et al. / Fuel 92 (2012) 116–121 117

An increase in grinding efficiency can be achieved by selectingthe appropriate equipment and establishing the optimum operat-ing conditions. With regards to equipment selection, the ball millis very effective in producing fine sizes. The energy used to grindthe material is created by lifting the balls and then allowing themto fall by gravity over the material. The energy in a given ball is afunction of its diameter so that large balls are required to grindlarge particles. If particles larger than expected are inputted tothe mill, the grinding efficiency will be reduced significantly [8].On the other hand, a rod mill uses large rods instead of balls asthe grinding media, which are very effective for reducing large par-ticles [9]. In addition, since relatively fewer fine particles are pro-duced by rod mills compared to ball mills, narrower sizedistributions are produced. Therefore, they are used extensivelyfor coal grinding particularly for preparing the feed for en-trained-flow gasifiers [10].

One approach for establishing the correct operating conditionsis by modeling, which reduces the need for detailed testing. Themost frequently used grinding modeling technique is the size–mass balance approach, often referred to as the population balancemodel (PBM) [8]. Unlike empirical models that provide a relation-ship between representative particle sizes and energy, the PBM canreproduce complete product size distributions based on mathe-matical functions. These in turn can be related to the different de-sign and operating conditions of the mill [11].

In this study, coal grinding experiments were conducted using alaboratory rod mill to obtain the parameters used in the PBM. Thetests were carried out using a bituminous coal at various grindtimes to generate the rates of breakage and breakage distribution.A detailed locked-cycle test was also carried out to simulate con-tinuous grinding. The results were compared to the simulated re-sults using the PBM.

2. Modeling approach

2.1. The specific rates of breakage and primary breakage distribution

The rates of grinding vary with particle size. For a given particlesize, this rate is defined as the specific rate of breakage (Sj). For agiven size of grinding media, the S value increases with increasingparticle size, passes through a maximum, and then decreases as theparticles become too large to be broken efficiently by the grindingmedia. For the particle size range below the maximum size, therelationship between the specific rate of breakage and particle sizecan be expressed by [8]

Sj ¼ Axj

xo

� �a

ð1Þ

where A is a parameter that depends on mill specifications; a is acharacteristic parameter that changes according to the material; xj

is the particle top size for size interval j; and xo is the standard par-ticle size (normally 1 mm). By convention, size interval x1 repre-sents the top size of the material, and size interval xn representsthe smallest size interval.

The primary breakage distribution (Bij) is the distribution offragments that is produced by each particle breakage. It has beenshown that typical B values can be fitted to the function [12]

Bij ¼ Ujxi�1

xj

� �cþ ð1�UjÞ xi�1

xj

� �bi > j P 1

Bij ¼ 1 i ¼ jð2Þ

where Bij is the cumulative breakage distribution, i.e., fragmentsproduced by breaking particles of size xj to sizes of xi and smaller.Uj, c, and b are constants and are characteristic of the material.The B values are considered normalized if Uj is constant for all sizes

that break, which has been found to apply for a wide range of grind-ing conditions [8].

2.2. Batch grinding process

In a batch process, the mass balance for size interval i is due tothe disappearance of material by breakage to smaller sizes and theappearance of material by breakage from larger sizes. This balancecan be expressed by

dwiðtÞdt

¼ �SiwiðtÞ þXi�1

j¼1i>1

bijSjwjðtÞ n P i P j P 1 ð3Þ

where wi(t) is the mass of material in size interval i after time t; Si

and Sj are the specific rates of breakage for material of size xi and xj,respectively; bij is the breakage distribution, which represents thebreakage of material from size xj into size xi.

It is possible to solve Eq. (3) using the Reid solution to obtainthe product size distribution as a function of grinding time [13].This solution is given by

wiðtÞ ¼Xi

j¼1

aije�Sjt n P i P 1 ð4Þ

aij ¼

0 i < j

wið0Þ �Pi�1

k¼1i>1

aik i ¼ j

1Si � Sj

Pi�1

k¼jSkbikakj i > j

8>>>>>>><>>>>>>>:

2.3. Continuous grinding process

To simulate the continuous grinding process, the concept of res-idence time is needed. The residence time distribution (RTD) is aprobability distribution function that describes the amount of timea particle could spend inside the mill. By applying the appropriateRTD model to the solution of the batch grinding equation, the con-tinuous grinding process can be simulated. The typical Reid solu-tion for continuous grinding is given by

pi ¼Xi

j¼1

cijajjej n P i P j P 1 ð5Þ

cij ¼

�Pj�1

k¼1cikcjk i < j

1 i ¼ j

1Si�Sj

Pi�1

k¼jSkbikakj i > j; Si–Sj

8>>>>>><>>>>>>:

aij ¼ fi �Xi

j¼1i>1

cijajj

where ej is used to represent the RTD model. The three models com-monly used for grinding are plug flow, fully mixed, and one large/two small (1L/2S) reactors in series. These models are given by

ej ¼ e�Sjs plug flow ð6Þ

ej ¼1

1þ Sjsfully mixed

ej ¼1

ð1þ Sjs1Þð1þ Sjs2Þ21L=2S

tion

in T

op S

ize

0.1

1

118 H. Lee et al. / Fuel 92 (2012) 116–121

The mean residence time, s, at solids mass feed rate, F, is de-fined as

s ¼WF

ð7Þ

where W is the mass holdup of material in the mill, and it is as-sumed that all material moves through the mill at the same velocityand leaves the mill with no classification at the mill exit [14].

3. Experimental approach

3.1. Sample preparation and characterization

A high-volatile bituminous coal from the Pittsburgh seam wasused in this study. The material had been obtained as the clean coalproduct from an operating coal cleaning facility. The proximateanalysis, total sulfur, and Hardgrove grindability index are givenin Table 1. The coal was crushed to a nominal �6.35 mm andstored under argon. For this testing, approximately 15,000 g werescreened at 2.38 mm (8 US mesh) and 1.68 mm (12 US mesh).The +8 mesh material was then crushed in a double roll crusherand then screened again at 8 and 12 mesh. The crushing was doneto maximize the generation of 8 � 12 mesh material. This was re-peated several times until all oversize material was reduced. The8 � 12 mesh material was saved for the grinding tests.

3.2. Conventional grinding tests

A 193.5 mm diameter and 245.0 mm long rod mill was used forthe grinding tests. The mill was equipped with six lifters, whichwere spaced evenly around the inside of the mill. Twenty-four,203 mm long steel rods were used. Nine rods had a diameter of19 mm, eight rods had a diameter of 15.9 mm, and the other eightrods had a diameter of 12.7 mm. This gave a nominal rod loading of23% by volume. The rod charge was provided by the mill supplier,and the volume loading was similar to that used by others for rodmill testing [9,15].

A 385 g sample of the 8 � 12 mesh coal was placed into the mill.This quantity was sufficient to fill the voids among the rods. Themill was placed on a roller table and operated at 67 rpm, whichcorresponded to 70% of critical speed. After each grind time, theentire mill was emptied and a representative sample of approxi-mately 90 g was obtained by riffling. The sample was screenedusing a Ro-Tap sieve shaker, and the size distribution was deter-mined. All material was returned to the mill and the grindingwas repeated at the next grind time. This procedure was carriedout for total grind times of 15 s, 30 s, 60 s, 120 s, and 240 s.

3.3. Locked-cycle test

Another series of tests was conducted for a grinding time of120 s using the same coal and grinding conditions as for the previ-ous tests. After the desired time, the entire mill contents werescreened at 0.210 mm (70 US mesh). The �70 mesh material wasremoved and replaced with the same weight of 8 � 12 mesh feed.The +70 mesh material and new feed were ground for the same

Table 1Characteristics of the Pittsburgh seam coal.

Moisture (%) 2.6Volatile matter (%) 34.9Fixed carbon (%) 55.8Ash (%) 6.7Total sulfur (%) 1.76Hardgrove grindability index 56

time and then screened at 70 mesh. The locked-cycle test wasmeant to simulate closed-circuit operation under steady-state con-ditions via batch grinding and screening [16]. Steady-state opera-tion was achieved in four cycles. As a check, two additionalcycles were carried out.

4. Results and discussion

4.1. Determination of the breakage parameters by experimentalmethod

Typically, the specific rate of breakage can be calculated usingthe ‘‘one-size-fraction’’ method [8]. After the feed sample is groundfor the desired time, the fraction remaining in the original sizeinterval is determined by sieving. The tests are repeated at longertimes and the results are plotted on a semi-log plot. Fig. 1 showsthe fraction of 8 � 12 mesh coal remaining after rod milling at dif-ferent times. As can be seen, the fraction of material remaining de-creased linearly with time, an indication of first-order breakage.After 1 min of grinding, about 10% of the 8 � 12 mesh material re-mained and only 0.5% remained after 2 min of grinding. Based onthese results, the S value for the 8 � 12 mesh material was 2.1.

The primary breakage distribution can be determined experi-mentally using the BII method [17]. This method uses the experi-mental size distribution data where particle breakage is notextensive as would be found at the short grinding times. In thisstudy, 44% of the top size particles material was broken at 15 s ofgrinding. These data were used to evaluate the primary breakagedistribution. Fig. 2 shows the plot of the primary breakage distribu-tion estimated by the BII method. From this plot, the breakageparameters, U, c, and b, were determined to be 0.6, 1.1, and 3.5,respectively.

4.2. Determination of the breakage parameters by back-calculation

In addition to determining the breakage parameters experimen-tally, a back-calculation method was also used. With this approach,the S and B parameters can be determined directly from the prod-uct size distribution data. This approach uses all of the size distri-bution data rather than just that obtained at the short grindingtimes. The back calculation technique uses a non-linear optimiza-tion technique to obtain the breakage parameters that minimizethe sum of squares of differences between the experimental andcalculated size distribution data [18].

The simplex method [19] was used to search for the optimumvalues for the five breakage parameters. These were determinedto be: A = 0.94, a = 0.85, U = 0.57, c = 1.20, and b = 3.5. Using thevalues for A and a and Eq. (1), the S value for the 8 � 12 mesh size

Grinding Time, Min0.0 0.5 1.0 1.5 2.0

Wei

ght F

rac

0.001

0.01y = 0.9681e-2.107x

R2 = 0.9967

Fig. 1. Disappearance plot for the 8 � 12 mesh material.

Relative Size0.01 0.1 1

Cum

ulat

ive

Brea

kage

Par

amet

ers,

Bij

0.01

0.1

1

Slope α

Slope β

Intercept Φ

Fig. 2. Cumulative breakage distribution for the 8 � 12 mesh material.

Number of Cycles1 2 3 4 5 6

Mas

s of

Rep

lace

men

t, g

0

20

40

60

80

100

120

140

Wei

ght P

erce

nt o

f Rep

lace

men

t

0

10

20

30

40

50

MassPercent

Fig. 4. Replacement mass and weight percent as a function of cycle number for thelocked-cycle test.

Perc

ent L

ess

Than

Siz

e10

100

123456

Number of Cycles

H. Lee et al. / Fuel 92 (2012) 116–121 119

interval was 1.95 compared to 2.1 found experimentally. Klimpeland Austin [18] showed that if the S or B values are known fromthe experimental results, the parameters from back-calculationhave realistic values. In this study, the back-calculated parametersfor the B values were nearly identical to those found experimen-tally, and it was judged that the breakage parameters from back-calculation were correct.

The actual and simulated product size distributions are com-pared in Fig. 3. As can be seen, the simulated results matched theactual size distributions quite well. This indicates that the PBMcan be used to describe rod mill grinding of coal.

Size, μm10 100 1000 10000

1

Fig. 5. Product size distribution as a function of cycle number for the locked-cycletest.

Med

ian

Size

, μm

100

200

300

400

500

4.3. Locked-cycle test

The locked-cycle test is a representative method to simulate thecontinuous grinding process using a combination of batch grindingand sieving. Six experiments were conducted for a grind time oftwo minutes, and the process reached a steady state by the fourthiteration. Fig. 4 shows the sample weights that were replaced aftereach cycle and their ratios relative to the entire mill solids. The ini-tial weight of replacement material was 104 g, which increasedand then stabilized at approximately 120 g. This represented33.7% of the entire mill solids.

The size distributions for each cycle are shown in Fig. 5. It canbe seen that after the first cycle, the size distributions rapidly con-verged and were essentially the same after the fourth cycle. Themedian particle sizes for each cycle are shown in Fig. 6. The median

Size, μm10 100 1000 10000

Wei

ght F

ract

ion

Less

Tha

n Si

ze

0.001

0.01

0.1

1

153060120240

GRINDING TIME, SEC

Fig. 3. Experimental and simulated product size distributions for various batchgrinding times (solid lines indicate the simulated results).

Number of Cycles1 2 3 4 5 6

0

Fig. 6. Product median size as a function of cycle number for the locked-cycle test.

size decreased from 450 lm after the first cycle to 300 lm after thesecond cycle and finally converged to 270 lm.

Simulation of a continuous grinding process requires a circuitconfiguration, an RTD model, and a classifier model. The configura-tion for the normal-closed circuit, which is the most widely usedgrinding circuit, is shown in Fig. 7. The performance of a classifiercan be characterized by the size selectivity curve, which depictsthe fraction of feed material of a given size that reports to the over-size stream (Fig. 8). The actual curve would be typical of a hydro-cyclone classifier. The curve not reaching zero at the finer sizes istypical for hydrocyclones and can be represented mathematically

Fig. 7. Schematic representation of a normal-closed grinding circuit.

Size, μm100 1000 10000

Size

Sel

ectiv

ity V

alue

, si

0.0

0.2

0.4

0.6

0.8

1.0

Ideal

Actual

Corrected

Fig. 8. Examples of size selectivity curves.

Size, μm10 100 1000 10000

Perc

ent L

ess

Than

Siz

e

1

10

100

Steady-State (Cycle 6)

Plug FlowFully Mixed1L/2S

Fig. 9. Comparison of the steady-state size distribution from the locked-cycle testto the simulated product size distributions for various RTD models.

Table 2Mean residence times for the various RTD models.

RTD type Mean residence time (min)

Plug flow 6.5Fully mixed 7.31 large/2 small (0.45/0.275/0.275) 6.8

120 H. Lee et al. / Fuel 92 (2012) 116–121

as though some fraction of the feed bypassed the separating actionof the cyclone [8]. The corrected curve represents classifier perfor-mance after mathematically correcting for apparent bypass. Theseparation or cut size, d50 (the size at the 50% value) and sharpnessindex, SI (the ratio of the size at the 25% value to the size at the 75%value) are derived from this curve. An ideal separation (no bypassand a sharpness index of one) would produce the vertical line atthe separation size as shown in Fig. 8.

The actual size selectivity values, si, are related to the correctedvalues, ci, by

si ¼ ð1� aÞci þ a ð8Þ

where a = apparent bypass. For this study, the Rosin–Rammler func-tion was used to represent the corrected size selectivity values andis given by

ci ¼ 1� exp � xi

xr

� �k !

ð9Þ

where xi = particle size; d50 = xr(0.693)1/k; k = �1.5725/ln(SI). For thelocked-cycle test, a sieve was used as the classifier. Hence, classifierperformance would approach an ideal separation. To simulate anideal classifier, the following values were used: d50 = 212 lm (sievesize); a = 0.0; SI = 0.99.

As noted previously, various RTD models can be used to de-scribe the movement of solids through the mill. In this study, theplug flow model, fully mixed model, and 1L/2S model were used.The plug flow model assumes that there is no axial mixing fromwhen the feed enters the mill until it exits. The fully mixed modelassumes that all particles are axially diffused as soon as they enterthe mill. The 1L/2S model is based on fully mixed reactors in series[8].

The simulation results using the three RTD models are shown inFig. 9. The weight of sample replaced at steady state was 120 g.Based on this value the mean residence time was calculated usingEq. (7), which gave an experimental mean residence time of6.4 min. The simulated mean residence times for the three modelsare given in Table 2. For the 1L/2S model, a value of 0.45 was used

for s1 of the large reactor and 0.275 for each of the smaller reactors,s2. The mean residence time for the plug flow model was approx-imately the same as the actual value and that for the 1L/2S modelwas somewhat larger.

Fig. 9 shows that the plug flow and 1L/2S models gave similarresults, which were close to the experimental results from thelocked-cycle test. It can also be seen that the fully mixed modeldid not agree with the experimental results at the coarser sizes.For the fully mixed model, the particles are diffused too rapidlyupon entry into the mill so that the particles are ground less thanexpected.

5. Summary and conclusions

Rod mill grinding tests were carried out using a high-volatilebituminous coal. From the single-size fraction tests, it was foundthat A = 0.94 and a = 0.85, which gave an S value of 2.1 for the8 � 12 mesh size fraction. The breakage distribution parameterswere found to be U = 0.57, c = 1.20, and b = 3.5, which were nearlyidentical to those determined by the back-calculation method. As aresult, the predicted size distributions were very similar to thosedetermined experimentally.

A locked-cycle test was used to simulate normal closed-circuitgrinding. It was found that steady state was obtained by four cyclesfor a grind time of two minutes. Applying the back-calculatedbreakage parameters, the locked-cycle product size distributionwas simulated for various RTD models. The predicted resultsagreed with the experimental results when using the plug flowand the 1L/2S RTD models. The fully mixed model under predictedthe grinding of the coarser particle sizes.

The results from this study indicate that rod mill grinding ofcoal can be described accurately using the population-balancemodel. This approach could provide a basis for evaluating variousoperating and design conditions of the grinding circuits. These sim-ulations in turn can play a role in optimizing the grinding processand improving the overall energy efficiency of the coal gasificationprocess.

H. Lee et al. / Fuel 92 (2012) 116–121 121

Acknowledgement

This work was supported by the Energy and Resources Engi-neering Program Grant funded by the Ministry of Knowledge Econ-omy, Korea.

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