Indan Journal of Chemcal Technology Vol. 9, May 202, pp. 80-84 A study on the effect of ball dameter on breakage propertes of clnker and lmestone Vedat Denz* Department of Chemcal Engneerng, Htt Unversty, Çorum, Turkey Receved 9 February 20; accepted 2 February 202 Effect of ball dameter has been studed on the lmestone and clnker samples under batch grndng condtons based on a knetc model. Frstly, eght dfferent mono-sze fractons between.7 mm and 0.06 mm formed by a 2 seve seres have been prepared. Then, S and B,j equatons are determned from the sze dstrbutons at dfferent grndng tmes, and the model parameters (S, a T, α, γ and φ j ) are compared for four dfferent ball dameters (4, 25.4, 20 and 9.5 mm). The results show that the study on the effect of ball dameter on the grndng gves more dfferent results than other nvestgatons. The varaton n specfc rate of breakage wth feed sze s ndependent of ball dameters and knd of materals. Keywords: Ball mll, Ball sze effects, Clnker, Grndng, Lmestone Commnuton s extremely energy ntensve, consumng 3-4% of the electrcty generated worldwde, and comprsng up to 70% of all energy requred n a typcal mneral processng plant. Consderng these factors, a small gan n commnuton effcency can have a large mpact on the operatng cost of a plant, whle conservng resource as well. Durng the last decade there have been consderable mprovements n commnuton effcency not only due to the development of machnes wth the ablty to enhance energy utlsaton, but also due to the optmal desgn of grndng systems and operatng varables that enable more effcent use of exstng machnes 2. In the desgn of grndng crcuts n mneral processng plant, the Bond method s wdely used to evaluate the performance and determne the powder requred and mll sze for a materal. Ths method s complex and very lengthy. In addton, t s very senstve to procedural errors. For ths reason, dfferent methods have been proposed as alternatve to the Bond method by many nvestgators 3,4. In the recent years, matrx and knetc models have been used both n the laboratory and n the ndustral areas. Knetc model, an alternatve approach, s consderng commnuton as a contnuos process n *E-mal: vedatdenz@htt.edu.tr whch the rate of breakage of partcles sze s proportonal to the mass present n that sze 5. The analyss of sze reducton n tumblng ball mlls usng the concepts of specfc rate of breakage and prmary daughter fragment dstrbutons have receved consderable attenton for more than 50 years. Austn 6 has revewed the advantages of ths approach and the scale-up of laboratory data to full-scale mlls have also been dscussed n a number of papers -7. The use of Portland lmestone cements has many benefts, both techncal and economcal. The European Pre-standard pren 97- dentfes 2 types of Portland lmestone cement contanng 6-20% lmestone and 2-35% lmestone respectvely. It s expected that the future world producton and use of Portland lmestone cement wll be sgnfcantly extended. These materals have dfferent grndabltes and the ndvdual partcle sze dstrbuton of each component nfluences the cement hydraton and fnally ts performance 8. Varous laboratory studes, plot plant works and full sze plant observatons showed that ball dameter, as an operatng varable, can affect grndng effcency at a gven output fneness. Austn et al. 9 showed typcal varaton n the specfc rate of breakage versus partcle sze for varous ball dameters (wth a mxture of ball sze, 25.4 mm and 50 mm) n a tumblng mll. The best
DENIZ: BREAKAGE PROPERTIES OF CLINKER & LIMESTONE 8 estmates of the varaton of B parameters for quartz show that the greater mpact force of collson nvolvng a larger ball gves a somewhat bgger proporton of fnes,.e. lower γ and hgher φ j. Thus, the lower specfc rate of breakage due to larger balls s partally compensated by the producton of a bgger proporton of fne fragments 9. In addton, consderng a representatve unt volume of mll, the rate of ball-on-ball contacts per unt tme ncreases wth the ncrease n ball dameter, because the number of balls n the mll ncreases as /d 3. Thus, the rates of breakage of smaller szes are hgher for smaller ball dameters. The relaton wth a T and ball dameter n a 0.6 m dameter mll were gven as a T α /d 9. Ths paper reports a study on the comparson of the breakage parameters of clnker and lmestone under the standard condtons n a small laboratory ball mll. Theory When breakage s occurrng n an effcent manner, the breakage of a gven sze fracton of materal usually follows a frst order law 0. Thus, the breakage rate of materal that s n the top sze nterval can be expressed as: dw = dt S w ( t)... () Assumng that S does not change wth tme (.e. a frst-order breakage process), ths equaton ntegrates to St log[ w (t)] log[ w (0)] =... (2) 2.3 where w (t) s the weght fracton of the mll hold-up for sze at tme t; and S, the specfc rate of breakage. The formula proposed by Austn et al. 9 for the varaton of the specfc rate of breakage S wth partcle sze s gven below: S = a X (3) T α where X s the upper lmts of the sze nterval ndexed by (mm); and a T and α, the model parameters that depend on the propertes of the materal and the grndng condtons. On breakage, partcles of gven sze produce a set of prmary daughter fragments whch are mxed nto the bulk of the powder and then, n turn, have a probablty of beng refractured. The set of prmary daughter fragments from breakage of sze j can be represented by b,j, where b,j s the fracton of sze j materal, whch appears n sze on prmary fracture, n >j. It s convenent to represent these values n cumulatve form, as shown below: B j = bk, j k = n,... (4) where B,j s the sum fracton of materal less than the upper sze of sze nterval resultng from prmary breakage of sze j materal: b,j = B,j B +, j. Austn et al. 7 have shown that the values of B,j can be estmated from a sze analyss of the product from short tme grndng of a startng mll charge predomnantly n sze j (the one-sze fracton BII method). The equaton used s gven below: B log = log [( P (0))] log[ ( P ( t)) ] [( P (0))] log[ ( P ( t)) ],j n j + j+ j+... (5) where P (t) s the fracton by weght n the mll charge less than sze X at tme t. B,j can be ftted to an emprcal functon 0, as shown below: γ β [ X X ] + ( φ [ X X ] n j B, j = φ j j j ) j... (6) Where [ ] δ φ j = φ X X ; and... (7) δ, φ, γ, and β are the model parameters that depend on the propertes of the materal. It s found that B functons are the same for dfferent ball fllng ratos, mll dameters, etc. 9. If B,j values are ndependent of the ntal sze,.e. dmensonally normalzable, then δ s zero. Expermental Procedure Materals Lmestone and clnker samples, taken from Göltaş Cement Factory (Isparta/Turkey), were used as the expermental materals. Chemcal propertes of lmestone and clnker samples are presented n Table. Each sample was carred out for grndng after dryng at 05 C.
82 INDIAN J. CHEM. TECHNOL, MAY 202 Table Chemcal compostes of clnker and lmestone samples Oxdes SO 2 Al 2 O 3 Fe 2 O 3 CaO MgO SO 3 Lmestone, % 0.60.07 0.59 48.99. - Clnker, % 22.22 3.6 3.30 67.44.80.50 Mll Table 2 Standard set of grndng condtons Dameter (D), mm 200 Length, mm 200 Volume, cm 3 6280 20 Mll Crtcal (N c ) a, rpm 97, 00, 0, 06 speed Operatonal(φ c = 75 %), rpm 72, 75, 76, 80 Balls Dameter (d), mm 9.5, 20, 25.4, 4 Specfc gravty 7.8 Qualty Alloy Steel Assumed porosty, % 40 Ball fllng volume fracton (J%) b Materal Specfc gravty Clnker 3.0, Lmestone 2.69 Powder fllng volume fracton (f c, %) c 4.2 Intersttal fllng (U%) d 52.5 Fg. Frst-order plots for 20 mm ball dameter of lmestone N c = 42. 3 D d (D and d n meter) Mass of balls /Specfc gravty of balls.0 J = Mll volume 0.6 Mass of powder / Specfc gravty of powder f c = Mll volume f U = c 0.4 J.0 0.6 Grndng tests Frstly, Standard Bond Work Index tests were carred out for lmestone and clnker samples and, the bond work ndex values for both the samples are found to be 3.52 kwh/t and 3.69 kwh/t respectvely. The standard set of grndng condtons used s shown n Table 2. Eght mono-sze fractons (-.7+.8, -.8+0.850, -0.850+0.600, -0.600+0.425, -0.425 +0.300, -0.300+ 0.22, -0.22+0.50, -0.50+0.06 mm) were prepared and ground batch-wse n a laboratory-scale ball mll for the determnaton of breakage functons. Each sample was taken out of the mll and, t was dry seve for product sze analyss. Result and Dscusson Determnaton of S functon Typcal frst-order plots (d= 20 mm) for varous feed szes of lmestone and clnker samples are shown Fg. 2 Frst-order plots for 20 mm ball dameter of clnker n Fgures and 2. Smlar results are also obtaned for other ball dameters of lmestone and clnker samples. The results ndcate that for grndng of all sze fractons, two samples could be descrbed by the frst-order law. In addton, parameters of specfc rate of breakage to supply by frst-order plots are gven n Table 3. The specfc rates of breakage of each monosze fracton that exhbts frst-order grndng knetc behavour are determned from the slope of straghtlne of frst-order plots. The values of S for grndng of the four dfferent ball sze studed, as a functon of sze, are shown n Fgures 3 and 4. Determnaton of B functon By defnton, the values of B,j are determned from the sze dstrbutons at short grndng tmes. The parameters are determned accordng to the BII method 9,
DENIZ: BREAKAGE PROPERTIES OF CLINKER & LIMESTONE 83 Ball dameter d, mm -0.850+0.600 mm S (/mn) Table 3 Model parameter values for dfferent ball dameters Lmestone α a T γ φ j -0.850+0.600 mm S (/mn) Clnker α a T γ φ j 9.5 0.028-0.02 0.69 0.23 0.045 2.37 0.03 0.30 0.35 20 0.307 0.60 0.27 0.70 0.25 0.308.00 0.28 0.67 0.28 25.4 0.400 0.6 0.4 0.7 0.32 0.366.22 0.39 0.68 0.26 4 0.46.09 0.45.07 0.5 0.57 0.99 0.52 0.69 0.24 Fg. 3 Specfc rates of breakage for ball dameters wth 4, 25.4, 20 and 9.5 mm of lmestone Fg. 5 Cumulatve breakage dstrbuton functons for ball dameter of 4, 25.4, 20 and 9.5 mm of lmestone Fg. 4 Specfc rates of breakage for ball dameter of 4, 25.4, 20 and 9.5 mm of clnker and the graphcal representatons are shown n Fgures 5 and 6. Lmestone and clnker samples show a typcal normalsed behavour, and the progeny dstrbuton does not depend on the partcle sze, t shows that the parameter δ s zero. Model parameters supples by cumulatve dstrbuton are gven n Table 3. Varaton of breakage parameters wth ball dameter Austn et al. 9 demonstrated that the specfc rates of smaller szes are hgher for smaller ball dameters. The relatonshp wth a T and ball dameter gves Fg. 6 Cumulatve breakage dstrbuton functons for ball dameter of 4, 25.4, 20 and 9.5 mm of clnker a T /d. For ths, varatons n specfc rate of breakage wth ball dameter for lmestone and clnker samples have been nvestgated. As shown n Fgs 3 and 4, the specfc rate of breakage (S ) decreases wth respect to ncreases ball sze (d) for small values of partcle sze
84 INDIAN J. CHEM. TECHNOL, MAY 202 (-0.300 mm). However, S values ncrease wth respect to ncrease ball sze (d) for hgher values of partcle sze (+0.300 mm). Wth respect to ball sze, Kelsall et al. reported no effect on B,j ; but later Austn et al. 2 demonstrated that for quartz, B,j alters n a systematc manner expressed n terms of γ and φ j, wth β remanng unchanged. It appears that the greater mpact force of a collson nvolvng a larger ball sze gves a somewhat bgger proporton of fnes, that s, γ s lower and φ j s hgher -3. As dfferent from the other researches, ths study demonstrates that γ values of lmestone and clnker samples ncrease wth respect to ncreasng ball sze. Therefore, proporton of fne partcles decreases, that s, ball fllng volume fracton (J= 0.2) s low and very fne partcles are lost among larger balls. φ j values of lmestone samples ncreases wth respect to ncreased ball sze as smlar to the results obtaned by Austn et al. 2. However, φ j values of clnker sample decrease wth respect to ncreased ball sze, because clnker s formed as an artfcal materal. In other words, clnkers are produced for makng artfcal stone (mneral) wth a process, whch s partal meltng of mxed lmestone and clay, heated to ~500 C n a rotary kln. Concluson Dry grndng of sze ntervals of lmestone and clnker samples shows that these samples follow the frst-order breakage law wth constant normalsed prmary breakage dstrbutons. In addton, these samples do not depend on the partcle sze. The values of the prmary daughter fragment dstrbutons and the values of α n S = a T X α are found to be dfferent n both lmestone and clnker. Ths means that the sze dstrbuton s produced from the more dfferent materals. As the amount of S or a T values ncreases, t expresses more effectve breakage and breaks very fast n the undersze of orgnal partcle sze. Accordng to expermentally obtaned a T values, grndng s faster wth respect to ncreased ball dameter for every two samples. Although, lmestone and clnker samples have close work ndex values (3.53 kwh/t and 3.69 kwh/t), they have demonstrated entrely dfferent characterstcs n the selecton functon and the breakage functon models. Ths study shows that grndng knetc parameters could be dfferent for dfferent ball dameters. Therefore, t appears that the grndng knetcs for each materal must be evaluated n order to lower the energy costs n grndng process. References Denz V, Cem Concr Res, 33 (2003) 439. 2 Denz V, Cem Concr Res, 34 (2004a) 365. 3 Denz V & Özdağ H, Mner Eng, 6 (2003) 2. 4 Denz V, Powder Technol, 09 (2004b) 208. 5 Denz V & Onur T, Int J Mner Process, 67 (2002) 7. 6 Austn L G, Powder Technol, 5 (972). 7 Austn L G, Bagga R & Çelk M, Powder Technol, 28 (98) 235. 8 Tsvls S, Vogls N & Photou J, Mner Eng, 2 (999) 837. 9 Austn L G, Klmpel R R & Lucke P T, Process Engneerng of Sze Reducton: Ball Mllng (SME, AIME, New York), 984. 0 Austn L G & Lucke P T, Powder Technol, 5 (972) 25. Kelsall D F, Red K J & Restarck C J, Powder Technol, (967/68) 29. 2 Austn L G, Klmpel R R, Lucke P T & Rogers R S C, n Desgn and Installaton of Commnuton Crcuts, edted by A L Mular and G V Jergensen (SME, AIMM, New York), 982, 30. 3 Prasher C L, Crushng and Grndng Process Handbook (John Wley & Sons, Chchester), 987.