Media Charge_Optimal Ball Size

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		Moly-Cop Tools, Version 3.0
		About the Media Charge_Optimal Ball Size Spreadsheet ...
&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F		&8&D / &T
Scope :
The Media Charge_Optimal Ball Size spreadsheet was designed to estimate the ideal make-up ball size to any given grinding application, on the basis of the empirical correlations independently proposed by Ettore Azzaroni and Allis Chalmers. In the normal case that such ideal ball size is not commercially available, this spreadsheet also allows for the design of a mix recharge policy (maximum 2 different make-up sizes) with the same ideal ball charge area.
Theoretical Framework :
In a first attempt to provide an answer as to what would be the ideal size (diameter) of balls to be continuously recharged to any given grinding mill - in order to achieve maximum performance out of such mill - the following two (amongst others) independent empirical correlations have been proposed in the literature :
Ettore Azzaroni's Formula : (3rd ARMCO-Chile Symposium, Nov. 10-14, 1980)
 dB* = 6.06 F800.263 ( rs Wi )0.4 / (N D)0.25
Allis Chalmers' Formula : (Mineral Processing Plant Design, Chapter 12, SME of AIME, 1980)
 dB* = 1.354 (F80)0.5 [ rs Wi / (Nc D0.5) ]1/3 
where :
 dB* = Ideal Make-up Ball Size, mm
 F80 = 80% Passing Size in the Fresh Feed Stream, microns
 rs = Ore Density, ton/m3
 Wi = Bond's Work Index of the ore, kWh/ton (metric)
 N = Rotational Mill Speed, rpm
 Nc = Rotational Mill Speed, as a percentage of the Mill Critical Speed.
 D = Effective Mill Diameter, feet.
For further background references on this sort of calculations, see Moly-Cop Tools spreadsheet Media Charge_Strings.
Data Input :
All input data required must be defined in each corresponding unprotected white background cell of the here attached Optimal Ball Size worksheet. Gray background cells contain the results of the corresponding formulas there defined and are protected to avoid any accidental editing.
New Moly-Cop Tools users are invited to explore the brief inserted comments in the most relevant cells, rendering the use of the attached worksheet self-explanatory.
Optimal Ball Size
			Moly-Cop Tools TM (Version 3.0)
			OPTIMAL MAKE-UP BALL SIZE
			Remarks : 	 Mirabela
				 
			Mill Dimensions and Operating Conditions :
			Eff. Diameter, ft	10.00 	 Eff. Diameter, m	3.05 
			Eff. Length, ft	14.00 	 Eff. Length, m	4.27 
			% Critical Speed	74.00 	 Mill Speed, rpm	17.93 
			Ball Dens., ton/m3 (app)	4.65 
jsepulveda: Apparent Density of a Ball Charge, not including ore slurry in the interstitial voids.	 Mill Volume, m3	31.20 
			Ball Filling, % (app)	40.00 	 Charge Weight, tons	57.98 
			Scrap Size, in 	0.50 
			Ore Properties :
				Ore Density	Work Index	Feed Size, F80
				ton/m3	kWh/ton (metric)	microns
				2.70 	14.50 	2500 
			RECOMMENDED OPTIMAL BALL SIZE :
			AZZARONI's Formula :
			Optimal Ball Size, in	2.21 
Jaime E. Sepúlveda J.: In case this recommended size is not commercially available, use attached Mixed_Strings worksheet to design a composite recharge policy with 2 of the commercially available ball sizes, generating the same optimal overall charge area.	 String Area, m2/m3	84.68 
			, mm 	56 
			ALLIS CHALMERS' Formula :
			Optimal Ball Size, in	1.47 
Jaime E. Sepúlveda J.: In case this recommended size is not commercially available, use attached Mixed_Strings worksheet to design a composite recharge policy with 2 of the commercially available ball sizes, generating the same optimal overall charge area.	
Jaime E. Sepúlveda J.: In case this recommended size is not commercially available, use attached Mixed_Strings worksheet to design a composite recharge policy with 2 of the commercially available ball sizes, generating the same optimal overall charge area.	
jsepulveda: Apparent Density of a Ball Charge, not including ore slurry in the interstitial voids.	 String Area, m2/m3	125.32 
			, mm 	37 
&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F		&8&D / &T
Mixed_Strings
			Moly-Cop Tools TM (Version 3.0)
			BALL CHARGE COMPOSITION AT EQUILIBRIUM
			Remarks : 	 Mirabela
				 
			Mill Dimensions and Operating Conditions :
			Eff. Diameter, ft	10.00 
Jaime E. Sepúlveda J.: As defined in the attached Optimal Ball Size worksheet.	 Eff. Diameter, m	3.05 
			Eff. Length, ft	14.00 
Jaime E. Sepúlveda J.: As defined in the attached Optimal Ball Size worksheet.	 Eff. Length, m	4.27 
			% Critical Speed	74.00 
Jaime E. Sepúlveda J.: As defined in the attached Optimal Ball Size worksheet.	 Mill Speed, rpm	17.93 
			Ball Dens., ton/m3 (app)	4.65 
Jaime E. Sepúlveda J.: As defined in the attached Optimal Ball Size worksheet.	 Mill Volume, m3	31.20 
			Ball Filling, % (app)	40.00 
Jaime E. Sepúlveda J.: As defined in the attached Optimal Ball Size worksheet.	 Charge Weight, tons	57.98 
			Scrap Size, in 	0.50 
Jaime E. Sepúlveda J.: As defined in the attached Optimal Ball Size worksheet.
			Balanced Charge :			Overall
				String 1	String 2	Charge Area
			Top Size, in	3.00 
Jaime E. Sepúlveda J.: Commercially available sizes only !	2.00 
Jaime E. Sepúlveda J.: Commercially available sizes only !	Indicated Mix
			Specific Area, m2/m3	62.75 	93.38 	65.60 
			Recharge Policy, %	86.74 	13.26 	Target Value
			Mill Charge Content, %	90.68 	9.32 	65.60 
Jaime E. Sepúlveda J.: As recommended by the user, with the aid of the attached Optimal Ball Size worksheet.
					 Excess Area	0.00 
Jaime E. Sepúlveda J.: To determine the proper combination of the 2 strings to yield the Target Area level, set this value to zero using the function Tools / Goal Seek, by changing Cell D21. 
						Balanced Charge,																			Initial
			Ball Size, in	% Passing	% Passing	% Retained															Mid-Points	String 1	String 2	Combined	Charge
			3.0 	100.00 	100.00 	27.73 
jsepulveda: If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.															3.0 	100	100	100	27.7304348789
			2.5 	48.19 	100.00 	35.01 
jsepulveda: If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.															2.7386127875	69.4208494208	100	72.2695651211	35.0131753521
			2.0 	19.69 	100.00 	22.02 
jsepulveda: If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.															2.2360679775	30.8108108108	100	37.256389769	22.0184245797
			1.5 	6.18 	31.37 	11.51 
jsepulveda: If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.															1.7320508076	11.0424710425	56.0784313725	15.2379651893	11.5083932898
			1.0 	1.16 	5.88 	3.41 
jsepulveda: If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.															1.2247448714	2.7027027027	13.7254901961	3.7295718995	3.4098943081
			0.5 	0.00 	0.00 	0.32 
jsepulveda: If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.															0.7071067812	0.2316602317	1.1764705882	0.3196775914	0.3196775914
			0.5 	0.00 	0.00 	0.00 
jsepulveda: If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.															0.5	0	0	0	0
			0.5 	0.00 	0.00 	0.00 
jsepulveda:If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.	
Jaime E. Sepúlveda J.: As defined in the attached Optimal Ball Size worksheet.	
Jaime E. Sepúlveda J.: As defined in the attached Optimal Ball Size worksheet.	
Jaime E. Sepúlveda J.: As defined in the attached Optimal Ball Size worksheet.	
Jaime E. Sepúlveda J.: As defined in the attached Optimal Ball Size worksheet.	
Jaime E. Sepúlveda J.: As defined in the attached Optimal Ball Size worksheet.	
Jaime E. Sepúlveda J.: As defined in the attached Optimal Ball Size worksheet.	
Jaime E. Sepúlveda J.: Commercially available sizes only !	
Jaime E. Sepúlveda J.: Commercially available sizes only !	
Jaime E. Sepúlveda J.: As recommended by the user, with the aid of the attached Optimal Ball Size worksheet.	
Jaime E. Sepúlveda J.: To determine the proper combination of the 2 strings to yield the Target Area level, set this value to zero using the function Tools / Goal Seek, by changing Cell D21. 	
jsepulveda: If less than 10%, it is recommended to simply add this proportion to the neighboring ball size fractions.															0.5	0	0	0	0
																								0
																									100
			Weight, tons	52.58 	5.40 	57.98 
			Volume, m3 (app)	11.32 	1.16 	12.48 
			Area, m2	710 	109 	819 
			# Balls per ton	1860 	5666 	2214 
&"Arial,Bold"&8Moly-Cop Tools&"Arial,Regular" / &F		&8&D / &T