Ball Mill Guia
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
1-1. Ball Milling including Separators
© Copyright 1990-2010, Lafarge SA. All rights reserved. INTERNAL USE ONLY
BALL MILLING incl. SEPARATORS – Page 1/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Table of Contents 1.
Ball Mill General ............................................................................... 3 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8.
2.
Ball Charge and Internals ................................................................ 6 2.1. 2.2. 2.3. 2.4.
3.
BB10 Test ......................................................................................................13 Bond Test.......................................................................................................13 Hardgrove Test ..............................................................................................14 Parameters Affecting the Clinker Grindability................................................14
Mill Performance Benchmarking .................................................. 15 6.1. 6.2.
7.
Absorbed Power of a Mill...............................................................................11 Charles, Bond, Kick & Rittinger Laws............................................................12
Grindability Measurement ............................................................. 13 5.1. 5.2. 5.3. 5.4.
6.
Recommended volume loading .......................................................................8 Ball charge design for new mill without pre-existing experience.....................8 Polysius Design ...............................................................................................9 Slegten Model ................................................................................................10 Fineness in Finish Mills:.................................................................................11
Grinding Laws ................................................................................ 11 4.1. 4.2.
5.
Largest Ball ......................................................................................................6 Grinding Balls Data..........................................................................................6 Other internals .................................................................................................7 Mill Internal Inspection Sheet...........................................................................7
Ball Charge Design (Finish Mill) ..................................................... 8 3.1. 3.2. 3.3. 3.4. 3.5.
4.
Comparison of Grinding Equipment ................................................................3 Mill Design .......................................................................................................3 Percent loading of mill .....................................................................................3 Mill Critical Speed ............................................................................................4 Retention Time ................................................................................................5 Mill Throughput ................................................................................................5 Required air velocities for mill ventilation ........................................................5 Optimum filling ratio: ........................................................................................5
Performance Indicator Finish Mills Absorbed (PIFMA) .................................15 Benchmarking Ball Mills with Bond Wi ..........................................................16
Separator ........................................................................................ 17 7.1. 7.2. 7.3. 7.4.
Circulating Load (CL).....................................................................................17 Tromp Curve ..................................................................................................17 Indicators for Cement Milling and Typical Values .........................................19 Recommended Sizing for a HES...................................................................20
8.
Grinding Aid ................................................................................... 21
9.
Other Data....................................................................................... 22 9.1. 9.2. 9.3.
Sieve Sizes ....................................................................................................22 Bulk Densities ................................................................................................22 Residue Conversion Chart ............................................................................23
10. References...................................................................................... 24
© Copyright 1990-2010, Lafarge SA. All rights reserved. INTERNAL USE ONLY
BALL MILLING incl. SEPARATORS – Page 2/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
1.
Ball Mill General
1.1.
Comparison of Grinding Equipment
The priority study cement grinding shop compares the full shop power consumption using the 3 main types of technology, see the table below:
Power Consumption kWh/t Relative Consumption
Closed Circuit Ball Mill 40.2 1.0
Vertical Mill
Roller Press *(Integral Grinding) 26.9 0.67
27.4 0.68
* Integral grinding is not used for cement grinding due mainly to quality issues with the narrow particle size distribution of the product. Hence semi-integral grinding using a closed circuit roller press and closed circuit ball is more common with a circuit power consumption of around 30 kWh/t.
1.2.
Mill Design
General L/D ratio
• Raw mills: 1.5 < L/D < 3.2 • Finish / cement mills: 2.5 < L/D < 3.0 L/D vs specific power consumption for different volume loads The optimum specific energy and the highest output for cement grinding is reached with an L/D ratio of 2,5 to 3.
Length of first Compartments relative to total mill length
• Raw mills: First compartment length equals 35 – 45% of total mill effective length. • Cement mill: First compartment length equals 30 – 35% of total mill effective length. • When L/D>1.5, classifying liners might be used. • The lower the L/D, the higher the circulating load needs to be (see below).
1.3.
Percent loading of mill 2π αr 2 − r sin α (h − r ) • % volume load = 360 πr 2 where: r is the radius h is the free height
α (degrees) = arccos
0.9 h/d 0.8 0.7 0.6
h−r r
© Copyright 1990-2010, Lafarge SA. All rights reserved. INTERNAL USE ONLY
0.5 0
10
20
30
40
50%
% volume load
BALL MILLING incl. SEPARATORS – Page 3/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Rules of thumb
• % vol. Load = 111.87 – 123.98 (h/d), 25 – 50%: error max 0.6%. • It is estimated that material increases the actual ball filling ratio by about 2%. • Another method (quick but not as accurate) consists in counting the number of visible shell liner plates (n) and to divide by the total number of shell liner plates per circumference (N): Angle x 360 / N.
α
=n
Values of angle h/d ratio in relation to the ball load (% filling degree) Ball load (%) 20 21 22 23 24 25 26 27 28 29 30
1.4.
h/d .7459 .737 .7281 .7193 .7106 .702 .6926 .685 .6765 .6682 .6598
n/N .667
Ball load (%) 31 32 33 34 35 36 37 38 39 40 41 42
.653 .639 .625 .611 .601
h/d .6516 .6434 .6352 .627 .6189 .6109 .6028 .5948 .5868 .5789 .5709 .563
n/N .590 .580 .569 .558 .549 .539
Mill Critical Speed •
C
C = mω 2 r =
m
Gω 2 r g
where: G = Weight of grinding ball in kg
P r
ω = angular velocity of mill tube (rad/sec) n = rev per minute C = centrifugal force kg
Ž G
•
P = G * sin ∂ (P is the resulting force of gravity)
• To maintain the ball in this position on the mill wall, it is necessary that C ≥ P. • Mill critical speed: nc =
60 2 g 4 π2 r
=
42.3 D
with D in meters
% Critical speed:
• Practically, mill speed between 68 and 82% of critical speed. • % critical speed is the mill actual speed in RPM divided by nc. Example: 3.98 meter mill with rotational speed of 15.6 rpm then nc = 21.2, % critical speed = 73.6 %.
© Copyright 1990-2010, Lafarge SA. All rights reserved. INTERNAL USE ONLY
BALL MILLING incl. SEPARATORS – Page 4/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
1.5.
Retention Time
Rules of thumb:
• Retention time in mill:
Open circuits: ~ 12 min Closed circuits: ~ 5 min
• Feed is pushing the material through the mill, If mill throughput increases: retention time decreases: C < 12 where: C is the ball charge weight, M is the material weight 8< M Fluoroscein Tracer test:
• 2g/t of mill production. Prepare the fluoroscein with 800-ml alcohol and impregnate 2 kg of mill feed material (in a plastic bag).
• Put the material at mill inlet, start the time and sample every 30 s during 30 min. (others use salt).
1.6.
Mill Throughput
• Using elevator power and after calibrating we have:
A=
(kW − kW0 ). 3600 .η 9,81. H
Where:
A kW kW0 η H
1.7.
=
Material flow (mtph)
=
Actual elevator power
=
Elevator power empty
=
Elevator efficiency
=
Inter axis elevator height
Required air velocities for mill ventilation
Rules of thumb
• Recommended 1.5 m/s above the ball charge: -
inside the trunnion: 22-25 m/s. partitions: 8-14 m/s (<20 m/s). hood: <5 m/s to prevent dust from being sucked up (dust pick-up is proportional to speed^2). dropout box: <2 m/s.
• 0.3-0.5 Nm3/kg cement 0.6-0.8 Nm3/kg raw mix (depending upon drying needs)
• Wet bulb temperature should be at least 25°C higher then dew point temperature. • False air at mill outlet is usually >25%. Consider high false air volume in heat balance and in mill ventilation design.
1.8.
Optimum filling ratio:
• U= (volume of powder in the mill)/ (volume of voids in the charge): between 60% and 110%, optimum around 90%.
• In practical terms, material level should equal ball level in the first compartment • In practical terms, material level should be higher than ball level in the second compartment • The expansion of the ball charge due to the material in between would not exceed 3% in an optimised mill (measurement of the ball charge level of the empty and the filled mill)
• The material filling in the first compartment can be adjusted with flow control devices in modern diaphragms. (scoops, flaps)
© Copyright 1990-2010, Lafarge SA. All rights reserved. INTERNAL USE ONLY
BALL MILLING incl. SEPARATORS – Page 5/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
2.
Ball Charge and Internals
2.1.
Largest Ball
Bond Formula
•
d KMAX
-
d Wi ρ = 20.17 20 .3 K Ψ. Du
-
where: d KMAX is the largest ball diameter (mm) -
d 20 is the sieve dimension (µ)
K is a constant (350 for a dry mill open or close circuit, 300 for wet) ρ is the specific mass of material (g/cm3)
-
Wi is the Bond work index (kWh/t) Du is the mill inside diameter (m)
Ψ is the ratio between the actual / critical speed (%)
with 20% retained
B = 24 d 80 (Other formula exist that result in value differences of ± 5%) B = ball dimension (mm) d 80 is the sieve with 80% passing
2.2.
Optimum Ball Diameter (mm)
Grinding Ball vs Clinker Size
Quick evaluation • For clinker:
100
10 1
.1
10
100
Clinker Size d80
Grinding Balls Data
Grinding Ball dimensions Weight Surface Number of balls per Diameter (g) (cm2) metric tons mm inch 4,001.153 314.159 250 100.00 ± 4" 2,916.841 254.469 343 90.00 ±3½" 2,048.590 201.062 488 80.00 1,826.658 186.265 548 77.00 ±3½" 1,372.396 153.938 729 70.00 1,048.878 128.680 954 64.00 ±2½" 864.249 113.097 1,157 60.00 500.144 78.540 2,000 50.00 ±2" 256.074 50.265 3,905 40.00 219.551 45.365 4,555 38.00 ±1½" 171.549 38.485 5,830 35.00 128.061 31.669 7,809 31.75 ±1¼" 108.031 28.274 9,257 30.00 62.518 19.635 15,996 25.00 ±1" 48.682 16.619 20,542 23.00 43.895 15.511 22,782 22.22 =7/8" 32.009 12.566 31,242 20.00 ±3/4" 19.658 9.079 50,870 17.00 ±5.8" (Unit weight and specific surface of MAGOTTEAUX grinding media)
Weight of 1 m3 of balls (kg) 4560 4590 4620 4640 4660 4708 4760
4850 4894
4948 4989
Specific surface 2 (m / mt) 7.854 8.728 9.812 10.207 11.222 12.276 13.085 15,708 19.628 20.664 22.437 24.730 26.173 31.408 34.139 35.337 39.259 46.185
Quick calculation:
•
Ball diameter (mm) =
•
Specific surface of balls of diameter =
3
250 P
(P = weight in g)
785 2 m / mt d
© Copyright 1990-2010, Lafarge SA. All rights reserved. INTERNAL USE ONLY
(d = diameter in mm)
BALL MILLING incl. SEPARATORS – Page 6/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Wear rates: In the 1st compartment the wear rate is correlated with the average ball weight (positive correlation), whereas in the 2nd compartment it is correlated with the ball charge surface area (positive correlation as well). Below are general guidelines for raw as well as cement grinding wear rates: Raw grinding • Raw mix with free silica (quartz) content <5%: 30-60 g/t • Raw mix with free silica (quartz) content >5%: 50-100 g/t Cement • CEM I, clinker >90%, 300 m2/kg : 30-60 g/t • CEM I, clinker >90%, 450 m2/kg: 60-100 g/t • CEM III, slag 70%, 300 m2/kg: 60-120 g/t • CEM III, slag 70%, 450 m2/kg: 120-200 g/t • Suppliers would typically guarantee <40 g/t for CEM I Bulk density for ball load (Coarse to medium ball size distribution): • Chamber 1: 4.3 – 4.5 t/m3 • Chamber 2: 4.5 – 4.65 t/m3 • Single Chamber mill: 4.5 – 4.55 t/m3
2.3.
Other internals
Partitions • Total slot area: 10 to 20 cm²/tph production: Slot Size Central Part Discharge Part FM 7 mm ± 1 mm 9 mm ± 1 mm RM 10 mm ± 1 mm 12 mm ± 1 mm
Max opening: ½ min ball size
Liners • Liners replaced when 60% of their effective lifting height has worn away: Reduction 8 to 10 % production reference points to measure lifting height are the lowest point on the liner to the highest release point (contact points between grinding ball and liner plate) • American Lorrain pattern: diameter (ft)*2=# bolt holes/row, 18.8” centre to centre. • DIN pattern: diameter (m)*10= # bolt holes/row, 31.4 cm centre to centre. • Classifying liners if L/D>1.5 and volume load<35%. • Without classifying liners, keep a maximum of 3-4 ball sizes.
2.4.
Mill Internal Inspection Sheet
Shell Liner Thickness Shell Liner Lifter Thickness Shell Liner Remarks – crack, gaps…. Inlet Head Liner Thickness Inlet Head Liner Remarks Inlet Opening Remarks Height Liner, to Balls – Average Width Across Balls – Average Calculated Percent Fill – mill ran out Build up on water injection lance Presence of material nibs
© Copyright 1990-2010, Lafarge SA. All rights reserved. INTERNAL USE ONLY
Ball Charge Remarks – sizes, shape, contamination, breakages Ball Coating Remarks Ball Classification Remarks Discharge Grate Slot Size-Average Discharge Grate Slot Size-Maximum Discharge Grate Metal Thickness – gaps etc. Discharge Grate Percent Blinded Discharge/Centre Screen Percent Blinded Height of Material relative to media Calculated Percent Fill – mill crash stopped
BALL MILLING incl. SEPARATORS – Page 7/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
3.
Ball Charge Design (Finish Mill)
3.1.
Recommended volume loading
(see “How to Optimise Ball Charge”) Recommended Volume Loading 1st Compartment 2nd Compartment 3rd Compartment 1 Minimum kWh/t 26 – 28% 28 – 30% 28 – 30% Maximum Production 32 – 34 % 34 – 36% 34 – 36% (Ball level in the trunnion should not be higher than 50 to 75 mm.)
3.2.
Ball charge design for new mill without pre-existing experience
Closed circuit finish mill Chamber 1 Coarse charge %
Fine charge %
90
40
21
80 70 60
29 19 12
38 25 16
Average ball weight (kg/ball)
1.83
1.63
Ball size (mm)
Ball size (mm) 40 (transition zone) 30 25 20 17 Average ball weight (g/ball)
Chamber 2 Coarse charge %
Fine charge %
10 25 25 20 20
15 15 30 40
47
34
Specific surface 32 37 (m2/t) Note: With high circulating loads, as with oversized separators the coarser grading in the 2nd chamber is more suitable to help maintain charge permeability 1
The recommended volume loading for minimum kWh/t is based on an acceptable compromise with production. For minimum kWh/t the volume loading can be as low as 22% in the second compartment. Due to risk of breakage the minimum volume loading in first compartment shall not underpass 25%.
© Copyright 1990-2010, Lafarge SA. All rights reserved. INTERNAL USE ONLY
BALL MILLING incl. SEPARATORS – Page 8/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Open circuit finish mills
Ball size (mm) 90 80 70 60 Average ball weight (kg/ball)
Chamber 1 Coarse charge % 40 29 19 12
Fine charge % 21 38 25 16
Chamber 2
1.83
1.63
Ball size (mm)
%
30 25 20 17 Average ball weight (g/ball)
10 10 20 60
Specific surface (m2/t)
30 39
Raw mills Chamber 1 Ball size (mm)
%
Ball size (mm)
90 80 70 60 Average ball weight (kg/ball)
40 29 19 12
60 50 40 30 Average ball weight (g/ball)
1.83
Specific surface (m2/t)
Chamber 2 Coarse charge % 20 30 30 20
Fine charge % 30 30 40
260
186
18
21
Note: Up to 50% 90 mm are used in some mills
3.3. •
•
•
Polysius Design
As a rule of thumb, it suits raw mills and especially mono-chambers very well, especially if no classifying liners are used.
⎡ D ⎤ ln ⎢ 9.6 ⎥⎦ D = 9.6 e −013.x ⇔ x = ⎣ − 0.13 where: D = Ø ball (cm) x = effective mill length (m) Process step-by-step, calculating each effective length starting from the input and with the largest ball: 1. Calculate effective lengths and the ball sizes you plan to use. 2. Double the first effective length which is both the first interval width and the first cumulative length. 3. Calculate each succeeding interval width by taking the effective length and subtract the preceding cumulative length and doubling it. Add this value to the previous cumulative length to get the new one. 4. If an interval overlaps with the partition divide the interval at the point of overlap. The excess is carried over to the next compartment. At the end of the mill, the interval is truncated at the point of overlap. 5. Once the intervals have been adjusted for compartment lengths as described in step (4), divide the adjusted interval by compartment length and multiply by 100. This is the percent weight for each size to be used in the compartment.
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BALL MILLING incl. SEPARATORS – Page 9/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Slegten Model •
Compatible mostly with classifying linings in the second compartment.
First Compartment – Crushing Same number (n) of balls in each size range.80, 70 and 60 mm Ø and then add some 90 mm Ø to deal with oversize clinker. This equilibrium charge will not change as you add 90 mm Ø make-up balls to maintain volume load. Ø Ball (mm) % of Weight (x) % of Weight Number/ 10 t of Charge 90 100-5x 20.0 670 80 2*4x 38.4 1820 70 1.6x 25.6 1820 60 X 16.0 1820 - x = is taken to be the number of balls in the last size. • In recent years, Slegten has favoured a 3-ball size distribution in first compartments over a 4- ball size as shown in table above.
•
Transition Zone • This is the start of the second compartment and its job is to crush any oversize that penetrated the diaphragm • The design for this area is to use "n" balls of 50 and 40 mm. Ø Ball (mm) Number/ 10 t of Charge 50 1820 40 1820 •
The largest ball size used in this transition zone can be identical to the smallest ball size used in the first compartment.
Second Compartment – Fine Grinding • The envelope curve for the balls smaller than 40 mm follows the following formula: where: • D = 3.3e −010.x D = Ø ball (cm) x = distance from transition zone finish (m) • The 30 mm balls start at the completion of the transition zone and the exponential curve follows. Rule of thumb: • The smallest ball size should, as a minimum, be at least twice the width of the slots in the grates (ex. ≥16 mm balls if slots are ≤8 mm wide). For this reason, it is generally recommended to use ¾” (19 mm) balls as the smallest size in Finish mills. 5/8” balls are fine when the grates are new but often become problematic as the grate slots enlarge. Example: Comparison Slegten & Polysius 1st compartment useful length = 3.81 m, 2nd compartment useful length = 7.66 m Using an average ball weight of 1.65 kg per ball and 3 ball sizes in the first compartment for the Slegten model. Ball size and % Polysius Slegten compartment load design design 1st compartment 3 ½” 31.0% 32.1% 3” 31.2% 43.1% 2 ½” 37.8% 24.8 % Transition zone 2nd compartment 2” 2.31% 7.67% 1 ½” 23.73% 2.94% 1 ¼” 34.05% 10.08% 1” 2.57% 48.18% ¾” 37.34% 31.13% 5/8” (Some)1 A limited amount of 5/8” balls should theoretically be added but the designer decided to use ¾” as the smallest ball size.
© Copyright 1990-2010, Lafarge SA. All rights reserved. INTERNAL USE ONLY
BALL MILLING incl. SEPARATORS – Page 10/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
3.4.
Fineness in Finish Mills:
In the first compartment before intermediate diaphragm • 95% passing of 2.365 mm (2360 μm or 8 mesh) for the material leaving the first compartment • Particle size distribution recommended on other sieves: - 86 – 92 % passing 1.0 mm (1000 μm or 18 mesh) - 80 – 90 % passing 0.6 mm (595 μm or 30 mesh) - 75 – 85 % passing 0.5 mm (500 μm or 35 mesh) In the second compartment before discharge diaphragm • 95% passing 0.5 mm (500 μm or 35 mesh) • 70 - 80 % passing 0.2 mm (212 μm or 70 mesh)
4.
Grinding Laws
4.1. • •
Absorbed Power of a Mill
Only 5-10 % of the energy is used for grinding, 90% is wasted into heat, wear, noise… With similar ball charge gradation and similar liners' lifting effect, the absorbed power is related to: Tonnage of balls Mill rpm % volume load Mill diameter
Slegten formula
•
⎛ rpm ⎞ ⎟ P = W * ⎜⎜ ⎟ ⎝ Vcr ⎠
1.27
* K j * K Fr
and
W=
π 4
* Fr 2 * L * J * d
where: P : the motor absorbed power (kW) J : the ratio between the apparent ball volume and the internal volume W : the weight of the load (T) - rpm: is mill speed (rpm) Fr : internal diameter (inside liners) (m) d is the apparent density of load (t/m3) #1 comp : d = 4.5 #2 comp : d = 4.65, if fine ball size distribution (average ball weight < 40 g) d = 4.6, if coarser ball size distribution (average ball weight > 40 g) Average : d = 4.6 -
⎛ 42.3 Vcr is the critical speed inside liners= ⎜ ⎜ F r ⎝
-
K j = 1.36 − 1.2 J , K Fr = C.Fr
-
•
⎞ ⎟ , L : the useful length of mill (m) ⎟ ⎠
0.379
K Fr is the influence of the location of the center of gravity for the moving ball charge vs. the mill center (C is a constant depending on the material and the liners). C= 11.262 for Clinker mill closed circuit with Slegten equipment 10.7 for clinker + slag, 12.16 for raw mix, 10.1 for slurry
⎛ rpm ⎞ ⎟ P = L * ⎜⎜ ⎟ V ⎝ cr ⎠
1.27
* J* K j *
π 4
* Fr2.379 * d * C
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BALL MILLING incl. SEPARATORS – Page 11/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Simplified formula
Fr ⎡ RPM ⎤ 100 P =T *⎢ *Kj * * 9.5 ⎥* 1.366 ⎣ Vcr ⎦ 75
•
Kj Function of Volume Load Volume load Kj 40% 30% 20%
0.9 1 1.1
Rules of Thumb • One metric tonne of balls increases the mill power draw by 10 kW. • Usually, 8 to 12 kWh/t is absorbed in the first compartment for clinker grinding (approximately 1/3 of the mill power)
4.2.
Charles, Bond, Kick & Rittinger Laws
General Law: Charles • dW = cx −n dx -
If W = Comminution work, particles (initial, final)
Value of n Energy Law Rittinger Kick Bond
Value of n: 2 1 1.5
x = Size of
Applies well over range of: 10 – 1000 μm
Normalized Blaine fineness equation • Fineness equation, generally accepted within Lafarge:
⎡ SA ⎤ W2 = W1 ⎢ 2 ⎥ ⎣ SA 1 ⎦ -
n
n = 1.3 for high efficiency separator (HES) circuit, n = 1.4 for second generation separators, n = 1.5 for Sturtevant separators, bearing in mind that 16’ and 18’ Sturtevant separators are more efficient than the larger 20’ and 22’ Sturtevant. n = 1.6 for open circuit mills W1 and W2,are the initial and resulting specific power consumption kWh/t, W is inversely proportional to production rates. SA1 and SA2 are the initial and final product surface areas m2/kg 0.43( SA1 − SA2 ) / 1000
•
Proposed by Polysius: C 2 = C1 * e
•
where C2 and C1 are production capacities Rene’s Study: +1% passing at 10µm: +10.8 SSB [m²/kg]
Rules of thumb Raw material: 10-16 kWh/t (mill motor) target fineness: passing 200µm>99%, passing 90µm>88% depending upon burnability of raw mix) • Clinker: 45 ± 15 kWh/t at 350 m2/kg (mill motor). For a pure cement (95% clinker) at <400 m2/kg, the mill motor consumption should be <40 kWh/t.
•
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BALL MILLING incl. SEPARATORS – Page 12/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
5.
Grindability Measurement
5.1. BB10 Test Idea:
Correlate the number of revolutions of a lab mill for a given fineness with the industrial energy to obtain the same fineness. The material is crushed to everything passing 3.15 mm. The number of mill revolutions is measured to obtain a given fineness. Revolutions are converted to industrial power consumption. Lab Mill Characteristics: Diameter: 40 cm Length: 12 cm Speed: 55 rpm Ball volume load: 14 % Ball weight: 10 kg
Material load: 1kg Balls: 20-25 mm : 2.5 kg 20-35 mm : 3 kg 50 mm : 4.5 kg
Lafarge Data
•
60 clinkers. Typical results are 48-60 kWh/t 3500 m2/kg. BB10 kWh/t Minimum Average Maximum
for 250 m2/kg kWh/t 21 29.2 43
for 300 m2/kg kWh/t 30 39.8 56
for 350 m2/kg kWh/t 39 51.8 68
for 400 m2/kg kWh/t 49 65.3 83
Remark: An average CEM I 32,5 at 300 m²/t can be ground with 28kWh/t related to the mill main drive. The additional energy for finer grinding should not exceed the Normalized Blaine fineness equation described in chapter 4.2.
5.2.
Bond Test
Lab Mill Characteristics Diameter: 30.5 cm Length: 30.5 cm Ball weight: 20 kg Material quantity: 700 cm3 Speed: 70 rpm
Formula
Wi =
44.5 ⎛ 10 10 − d p 100 0.23 • P 0.82 * ⎜⎜ ⎜ d p 80 d f 80 ⎝
⎞ ⎟ ⎟⎟ ⎠
dp100 is the sieve with 100% passing feed material dp80 80% feed material df80 80% finish material P is the production (g/rev of mill) of product at the level the circulating load is requested. Wi is the Bond work index kWh/short ton.
•
Developed to predict energy requirements of 2.44m diameter, wet, closed circuit, ball mill at a fineness of either 65 mesh (220 µm) or 100 mesh(150 µm).
•
Pre-crush feed to #6 (3.35 mm). Maintain 700g sample in test mill. Turn mill 100-150 rev.
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BALL MILLING incl. SEPARATORS – Page 13/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
•
Remove undersize (dp100 – 65 or 100 mesh) and replace with fresh feed (300 – 400 g). 1st cycle is now completed. Repeat procedure until steady state is reached. Typically 6-8 cycles so that 200 g are removed at each cycle, which equals 250% circulating load or 30% of “P”.
•
The Work index expresses the specific net energy needed to grind a material from indefinite feed size to dp80 =100 µm
•
Wi for Raw materials for cement plants are usually in the range of 8 – 16 kWh/st
Typical Values for Wi for common materials:
Wi Clinker: Limestone Shale Slag Sand stone Silica sand Coal Clay Gypsum Kiln feed
kWh/st*
ρ (g/cm3)
13.49 10.18 16.40 15.76 11.53 16.46 11.37 7.10 8.16 10.57
3.09 2.68 2.58 2.93 2.68 2.65 1.63 2.23 2.69 2.67
*Clearly
the Wi can vary significantly from these figures depending upon the nature of the materials and material testing is necessary for each particular case when assessing a mill.
5.3.
Hardgrove Test
The Hardgrove test was originally developed for determination of coal grindability, using a laboratory scale ring ball mill. Feed size is prepared in the range 600 – 1180 µm. The mill is charged with 50g of feed and operated for 50 revolutions. The result is calculated from the proportion of material passing 75µm. The figure is meant to compare the grindability with a standard American coal with an index of 100. Bond gave the following equation to convert HGI into a Bond Wi:
Wi =
435 HGI 0.91
Other similar relationships can be found in the literature. Ranges of HGI found in cement plant raw materials are given below: Material Clay Coal Limestone Shale Silica Sand
HGI* 130 – 160 35 – 90 60 – 120 60 - 170 30 - 100
*Clearly
the HGI can vary significantly from these figures depending upon the nature of the materials and material testing is necessary for each particular case when assessing a mill.
5.4. Parameters Affecting the Clinker Grindability 1 point increase of Î produces a variation of
C3S
Exc SO3 /tot.alk. (%)
W250 (kWh/t @ 250 m2/kg ) W300 W350 W400
-0.3 -0.5 -0.6 -0.7
4 4 5 5
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CaOl (%)
D75 alite (µm)
Alite C3S x100
-0.9
0.1 0.1 0.2 0.2
-0.1 -0.2 -0.3
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
6.
Mill Performance Benchmarking
6.1.
Performance Indicator Finish Mills Absorbed (PIFMA)
The PIFMA is used to benchmark finish mill performance:
PIFMA =
Where: PA – actual specific power consumption mill drive PT – quasi theoretical specific power consumption, calculated from standard grindability figures
PA PT
An efficient mill will have a PIFMA close to unity The theoretical power consumption at a standard surface of 300 m2/kg calculated by:
(
1 P = • X C • SPC C + X G • SPC G + X S • SPC S + X A • SPC A + X P • SPC P + X L • SPC L + X O • SPC O T 300 MF
)
Where: XC, XG, XS, XA, XP, XL and XO are the weight fractions of clinker, gypsum, slag, flay ash, pozzolan, limestone and other components in the product. MF is the mill type factor = 1 for a ball mill, =1.6 for a Horomill, = 1.7 for Vertical mill and 1.8 for a roller press SPC refers to the standard grindability kWh/t of the components at 300 m2/kg. The standard figures used are: SPCC SPCG SPCS
Clinker Gypsum Slag
28 10 43
SPCA SPCP SPCL
Fly Ash Pozzolan Limestone
2 10 10
Note the low figure used for fly ash is to adjust for it’s initial surface The theorectical specific power consumption at 300 m2/kg is then corrected to the actual product surface area SA, by the following equation:
P = P T T 300
⎛ SA • (1 − 0.1 * ( X G + X A •⎜ 300 ⎝
+ X P + X L )) ⎞
fs
⎟ ⎠
Where: fs = Factor Separator (1.6 for open circuit, 1.5 for first, 1.4 for second, 1.3 for third generation separator, 1.0 for roller press, 1.10 for vertical mill & 1.05 for Horomill) Subtraction of the term 0.1*(XG+XA+XP+XL) from the surface area is meant to correct for over-grinding of the softer components. The resulting PIFMA will be influenced by the mill efficiency and by the grindability of the cement. Therefore especially in cases of high PIFMA (>1.15) the grindability of the components and the condition of the milling system will need to be investigated to find improvement potential. Example Calculation of PIMFA
Determine the PIFMA of a closed circuit ball mill with 3rd generation separator produces 86.2 tph @ 369 m2/kg with a power consumption at the main motor of 35.6 kWh/t. The product components are 88.29% clinker, 3.47% gypsum, 6.56% limestone and 1.68% blast furnace slag.
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Calculate the theoretical power consumption at a standard surface of 300 m2/kg by:
(
1 P = • X C • SPC C + X G • SPC G + X S • SPC S + X A • SPC A + X P • SPC P + X L • SPC L + X O • SPC O T 300 MF
(
)
1 P = • 0.8829 • 28 + 0.0347 • 10 + 0.0168 • 43 + 0.0656 • 10 = 26.4 kWh / t T 300 1
Next calculate the theoretical power consumption at the actual product surface area using:
⎛ SA • (1 − 0.1 * ( X G + X A •⎜ 300 ⎝
P = P T T 300
P T
+ X P + X L )) ⎞
⎛ 369 • (1 − 0.1 * ( 0.0347 + 0.0656)) ⎞ = 26.4 • ⎜ ⎟ 300 ⎠ ⎝
fs
⎟ ⎠
1.3 = 34.2 kWh / t
Finally calculate the PIFMA PIFMA =
6.2.
P A = 35.6 = 1.04 34.2 P T
Benchmarking Ball Mills with Bond Wi
Bond is most useful for assessing the power consumption of ball raw mills and coal mills since both target product particle size rather than surface area: The power consumption for a new mill can be estimated from the Bond Equation:
⎛ 10 10 ⎞⎟ − Ws = FB • 1.102 • Wi • ⎜ ⎜ P 80 F80 ⎟⎠ ⎝
Where: Ws – calculated industrial mill shaft power kWh/t P80 – Product 80% passing size µm F80 – Feed 80% passing size µm FB - Bond Factor for dry grinding normally 1.3
The 1.102 is the conversion from kWh/short ton to kWh/t (metric) . For grinding finer than 70µm Bond proposed a fine grinding correction factor, calculated from:
⎛ 10.3 + P80 FP = ⎜⎜ ⎝ 1.145 • P80
⎞ ⎟⎟ ⎠
The Bond equation can also be used for benchmarking existing mills in conjunction with actual mill shaft power consumption (WSA kWh/t) to compute the Bond factor:
FB =
WSA ⎛ 10 10 ⎞⎟ − 1.102 • Wi • ⎜ •F ⎜ P 80 ⎟ P F 80 ⎠ ⎝
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)
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Values of less than 1.3 would normally indicate an efficient mill. Typical values determined for specific mill types grinding cement raw materials are: 1. 2. 3. 4.
Bucket elevator ball mill Tandem Hammer / Airswept mill Airswept Mill Double Rotator Mill (Central discharge)
1.2 – 1.3 1.4 – 1.5 1.4 – 1.55 1.2 – 1.3
The Bond equation is also useful to assess the potential impact of changes to mill feed or product size.
7.
Separator
7.1.
Circulating Load (CL)
Junction with Three Streams • A, R, F are the feed, rejects and fines of the separator A ai , ri , f i are the cumulated % passing at a defined sieve(i).
F
R
-
da, dr, df are the % retained corresponding to the sieve interval dx.
-
A=R+F A da = Rdr + Fdf
With:
da = a i + 1 − ai ,
R df − da = , A df − dr
Drawing • Plot ( f i − a ) vs ( f i − ri ) If the mill circuit is steady, the graph has to be a straight line:
( f − a) = α + β( f − r )
-
α should be close to 0
-
β is the most probable value of
-
The circulating load is defined as:
7.2.
CL calculation • Using the least square line calculations, with α = 0 Quick CL calculation • With one set of results of sieving: R f −a = F a−r
β R = F 1− β
Tromp Curve
a) •
R A
F dr − da = A dr − df
Creating the Tromp Curve On the Gauss-logarithmic paper, let's plot the probability for a given particle of a certain size entering the separator to go to the rejects =
dr( x )* R with: da( x )* A
n
∑
( f i − ai )( f i − ri ) R i =0 = n A ( f i − ri ) 2
∑
i =0
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
The Tromp curve can be divided into two straight lines The higher sieve fractions have a slope which is representative of the separator efficiency (a perfect one would be vertical).
•
Tromp Curve Representation
OSEPA N1500
99.8 99.5 99 98 95 % Probability of Rejection
•
90 80 70 60 50 40 30 20 10 5
1.0
10.0
100.0
1000.0
Particle Size
b) •
Imperfection d 75 − d 25 I= 2 * d 50
where: - d25 is the size of the particle which has 25 % chance of going to rejects - d50 is the size of the particle which has 50 % chance of going to rejects - d75 is the size of the particle which has 75 % chance of going to rejects
Imperfection vs Circulation Load 0.44 Imperfection 0.42 0.40 0.38 0.36 0
c) • •
d)
100
200 300 Circ. load (%)
400
Acuity Limit AL is the abscissa of the intersection of the two Tromp curve lines. It’s the size at which selection is initiated
Bypass
Definition: • By-pass is the ordinate of the intersection of the two Tromp curve lines. • The bypass is the lowest percentage of feed that will go to the separator rejects.
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Bypass vs. feed rate – Sturtevant • The following graph shows the Bypass of an 18’Sturtevant versus its feed rate.
Bypass vs. feed rate O’Sepa/Sturtevant 80
100
70 Bypass (%)
Bypass (%)
Sturtevant
60
80 60 40
50 40 30 20
O-Sepa
10
20
0 1.0
100 150 200 250 Feedrate to Separator (t/h)
QF/Qa vs. bypass • If Qf is the separator feed rate (kg/h) and Qa the separator ventilation (m3/h), • Qf/Qa is an important ratio for the separator efficiency.
•
⎛ Qf ⎞ ⎜⎜ − f1 ⎟ Qa ⎟⎠ ⎝
•
•
2.0
2.5
3.0
3.5
40 30 20 10
Bypass = 1 + e - f1: coefficient for the separator
7.3.
1.5
Qf/Qa (kg feed/m3 separator sweep)
300
Rosin Rammler Number (RR#)
The steeper the particle size distribution (RR# high) the more efficient the grinding and separating process. Raw mix RR# are usually lower than those for cement grinding
0 0
1
2 Qf/Qa (kg/m3)
3
4
RRnumber vs. Feed to Air Ratio 1.20 Rosin-Ramler Number (n)
50
Bypass (%)
0
1.15 1.10 1.05 1.00 1.0
1.5
2.0
2.5
3.0
3.5
4.0
Qf/Qa (kg/m3)
Separator Performance • Rate of recuperation in the fines of particles smaller than a given dimension.
r=
7.4.
F f * A a
Indicators for Cement Milling and Typical Values
Slope Rosin Rammler fines: % recovery, 45 μm: Acuity: Imperfection:
Bypass: Circulating load: HES Qf/Qa: % Passing 45 μm:
1.1 – 1.4 for HES 0.85 – 1.0 for 1st generation separators (Sturtevant, Raymond) 1.2 for second generation separators 45 to 55% for Sturtevant and >65% for HES 20 – 30μm for Sturtevant and <0.30μm for HES <0.35 for HES 0.45 – 0.6 for Raymond separators 0.6 –0.7 for Sturtevant separators 5 – 10% range for HES 150 –200 % with HES 1.5 – 2.0 range 93% minimum (45 μm = 325 mesh)
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7.5.
Recommended Sizing for a HES Parameter
Recommended
Possible (Min/Max)
Industrial Range
Cage loading
20-23 t/h/m2
less than 30
11-36 t/h/m2
Qf/Qa
2 kg/m3
less than 2,2
0,7-3,0 kg/m3
Radial velocity at the inlet of the cage
3,6-4,3 m/s
x
2,9-4,5 m/s
Ratio Am3/h/m2 Gas volume / Cage Area
14 000 Am3/h/m2
13000-15000 Am3/h/m2
10500-16300 Am3/h/m2
Circulating load
100%-250%
x
45%-270%
1,0 m/min Pulse jet H.P.
less than 1,2 m/min
Filtration Velocity or Air to cloth ratio
a) • • • • •
•
0,8-1,3 m/min 1,1 m/min Pulse jet L.P.
less than 1,2 m/min
Fan and Bag House Sizing Use the production rate (T/h), Qf/Qa (kg/ Am3) and circulating load (%) to specify the air flow. Most separators can operate at +/- 20% of nominal. Only a margin of 5 - 8% above the separator airflow is recommended for the BH. Margin of 5-10% is recommended on top of the BH for the fan. Correctly specifying the static pressure: - Pressure drop can be estimated by the dP of the separator (2.5 – 3 kPa), Dust Collector (2 – 2.5 kPa), ducting. (1-1.5 kPa) and if present, silencer (250 – 500 Pa). - The recommendation is 6.5 kPa with a minimum of 600 kPa. Include in the circuit design, the possibility for recirculation of up to 80% of the separator airflow.
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
8.
Grinding Aid
Type of Products • Surface active agents tend to saturate the free valence and inhibit the pack-set. Typical surfaceactive agents are: - ligno-sulphonates - polyoils - amines - organic acids • Polar compounds (water, ammonia) are known to have some action on such bonds through their polar moment. However, their practical use as surface agents is limited by their other impacts on the cement properties. • Other agents, particularly coal dust, have been used in the past. • Commercial products available as grinding aids are essentially (60-800 g/t ck): - Triethanolamine - Polypropylene glycols and polyethylene • HEA2, DDA& and other products cause a definite reduction of pack-set but do not prevent agglomeration or lump-formation problems that are caused by: - Alkalis ( K 2 SO4 ) - Moisture The effect of grinding aid on milling process: - Enhances the flowability and prevents agglomeration - Prevents coating on liners and grinding media - Lower effect on coarser product (below 320 m2/kg) - Reduces contraction - Increased production (5-7%)
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
9. 9.1.
Other Data Sieve Sizes
Sieve Screen #400 #325 #270 #230 #200 #170 #140 #120 #100 #80 #70 #60 #50 #45 #40 #35 #30 #25 #20 #18 #16
9.2.
Micron 37 44 53 63 74 88 105 125 149 177 210 250 297 354 420 500 595 707 1000
Iso alter 38 45 53 63 75 90 106 125 150 180 212 250 300 355 425 500 600 710 850 1000 1180
Screen #14 #12 #10 #8 #7 #6 #5 #4 #3.5 1/4" 5/16" 3/8" 7/16" 1/2" 5/8" 3/4" 7/8" 1" 1"1/4 1"1/2 2"
Micron 2000
6350 8000 9510 11200 12700 16000 19000 22600 25400 32000 38100 50800
Iso alter 1400 1700 2000 2360 2800 3350 4000 4750 5600 6300 8000 9500 11200 12500 16000 19000 22400 25000 31500 38100 50000
Bulk Densities Bulk density Sand Sand Iron Bauxite Brick Gypsum Fluid coke Limestone (crushed) Silica fume Bottom Ash Cement T I-II T 10 T III Clinker Clinker (underburnt) Raw mix
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kg/m3 1387 1679 2629 1980 1502 1677 926 1803 1024 1241 1234 1207 1054 1575 1400 1041
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9.3.
Residue Conversion Chart CONVERSION OF SIEVE RESIDUES
% residue at 90μm 70
50 40
30
355 μm 20
250 μm 12.0% 10 200 μm 7
5
180 μm
150 μm
4
3 125 μm 2
106 μm 1
0.7
0.5
90 μm
0.4 80 μm 14.22%
63 μm 0.2
75 μm
56 μm
% residue
0.3
12.0%
50 μm 25 μm
45 μm 0.1
0.7
1
2
3
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4
5
7
10
20
30
40
50
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10. References ¾
Cement Portal Grinding Domain How to manage the ball charge level How to check the airflow through the mill How to do a routine stop inspection How to do a mill crash stop inspection How to optimise a ball charge How to manage liner wear in a ball mill How to conduct a ball mill audit How to remove scrap from a ball mill circuit How to check the separator efficiency Procedure for audit of Ball Mill Circuits Global mixing grinding media recommendations Technical agenda study – formalisation of knowledge on grinding aids Guide – ball mill optimisation Post Sevilla module 5 Priority study cement grinding workshop Priority study – separators
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
My notes:
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BALL MILLING incl. SEPARATORS – Page 25/25 Version September 2010
1-1. Ball Milling including Separators
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Table of Contents 1.
Ball Mill General ............................................................................... 3 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8.
2.
Ball Charge and Internals ................................................................ 6 2.1. 2.2. 2.3. 2.4.
3.
BB10 Test ......................................................................................................13 Bond Test.......................................................................................................13 Hardgrove Test ..............................................................................................14 Parameters Affecting the Clinker Grindability................................................14
Mill Performance Benchmarking .................................................. 15 6.1. 6.2.
7.
Absorbed Power of a Mill...............................................................................11 Charles, Bond, Kick & Rittinger Laws............................................................12
Grindability Measurement ............................................................. 13 5.1. 5.2. 5.3. 5.4.
6.
Recommended volume loading .......................................................................8 Ball charge design for new mill without pre-existing experience.....................8 Polysius Design ...............................................................................................9 Slegten Model ................................................................................................10 Fineness in Finish Mills:.................................................................................11
Grinding Laws ................................................................................ 11 4.1. 4.2.
5.
Largest Ball ......................................................................................................6 Grinding Balls Data..........................................................................................6 Other internals .................................................................................................7 Mill Internal Inspection Sheet...........................................................................7
Ball Charge Design (Finish Mill) ..................................................... 8 3.1. 3.2. 3.3. 3.4. 3.5.
4.
Comparison of Grinding Equipment ................................................................3 Mill Design .......................................................................................................3 Percent loading of mill .....................................................................................3 Mill Critical Speed ............................................................................................4 Retention Time ................................................................................................5 Mill Throughput ................................................................................................5 Required air velocities for mill ventilation ........................................................5 Optimum filling ratio: ........................................................................................5
Performance Indicator Finish Mills Absorbed (PIFMA) .................................15 Benchmarking Ball Mills with Bond Wi ..........................................................16
Separator ........................................................................................ 17 7.1. 7.2. 7.3. 7.4.
Circulating Load (CL).....................................................................................17 Tromp Curve ..................................................................................................17 Indicators for Cement Milling and Typical Values .........................................19 Recommended Sizing for a HES...................................................................20
8.
Grinding Aid ................................................................................... 21
9.
Other Data....................................................................................... 22 9.1. 9.2. 9.3.
Sieve Sizes ....................................................................................................22 Bulk Densities ................................................................................................22 Residue Conversion Chart ............................................................................23
10. References...................................................................................... 24
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
1.
Ball Mill General
1.1.
Comparison of Grinding Equipment
The priority study cement grinding shop compares the full shop power consumption using the 3 main types of technology, see the table below:
Power Consumption kWh/t Relative Consumption
Closed Circuit Ball Mill 40.2 1.0
Vertical Mill
Roller Press *(Integral Grinding) 26.9 0.67
27.4 0.68
* Integral grinding is not used for cement grinding due mainly to quality issues with the narrow particle size distribution of the product. Hence semi-integral grinding using a closed circuit roller press and closed circuit ball is more common with a circuit power consumption of around 30 kWh/t.
1.2.
Mill Design
General L/D ratio
• Raw mills: 1.5 < L/D < 3.2 • Finish / cement mills: 2.5 < L/D < 3.0 L/D vs specific power consumption for different volume loads The optimum specific energy and the highest output for cement grinding is reached with an L/D ratio of 2,5 to 3.
Length of first Compartments relative to total mill length
• Raw mills: First compartment length equals 35 – 45% of total mill effective length. • Cement mill: First compartment length equals 30 – 35% of total mill effective length. • When L/D>1.5, classifying liners might be used. • The lower the L/D, the higher the circulating load needs to be (see below).
1.3.
Percent loading of mill 2π αr 2 − r sin α (h − r ) • % volume load = 360 πr 2 where: r is the radius h is the free height
α (degrees) = arccos
0.9 h/d 0.8 0.7 0.6
h−r r
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0.5 0
10
20
30
40
50%
% volume load
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Rules of thumb
• % vol. Load = 111.87 – 123.98 (h/d), 25 – 50%: error max 0.6%. • It is estimated that material increases the actual ball filling ratio by about 2%. • Another method (quick but not as accurate) consists in counting the number of visible shell liner plates (n) and to divide by the total number of shell liner plates per circumference (N): Angle x 360 / N.
α
=n
Values of angle h/d ratio in relation to the ball load (% filling degree) Ball load (%) 20 21 22 23 24 25 26 27 28 29 30
1.4.
h/d .7459 .737 .7281 .7193 .7106 .702 .6926 .685 .6765 .6682 .6598
n/N .667
Ball load (%) 31 32 33 34 35 36 37 38 39 40 41 42
.653 .639 .625 .611 .601
h/d .6516 .6434 .6352 .627 .6189 .6109 .6028 .5948 .5868 .5789 .5709 .563
n/N .590 .580 .569 .558 .549 .539
Mill Critical Speed •
C
C = mω 2 r =
m
Gω 2 r g
where: G = Weight of grinding ball in kg
P r
ω = angular velocity of mill tube (rad/sec) n = rev per minute C = centrifugal force kg
Ž G
•
P = G * sin ∂ (P is the resulting force of gravity)
• To maintain the ball in this position on the mill wall, it is necessary that C ≥ P. • Mill critical speed: nc =
60 2 g 4 π2 r
=
42.3 D
with D in meters
% Critical speed:
• Practically, mill speed between 68 and 82% of critical speed. • % critical speed is the mill actual speed in RPM divided by nc. Example: 3.98 meter mill with rotational speed of 15.6 rpm then nc = 21.2, % critical speed = 73.6 %.
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
1.5.
Retention Time
Rules of thumb:
• Retention time in mill:
Open circuits: ~ 12 min Closed circuits: ~ 5 min
• Feed is pushing the material through the mill, If mill throughput increases: retention time decreases: C < 12 where: C is the ball charge weight, M is the material weight 8< M Fluoroscein Tracer test:
• 2g/t of mill production. Prepare the fluoroscein with 800-ml alcohol and impregnate 2 kg of mill feed material (in a plastic bag).
• Put the material at mill inlet, start the time and sample every 30 s during 30 min. (others use salt).
1.6.
Mill Throughput
• Using elevator power and after calibrating we have:
A=
(kW − kW0 ). 3600 .η 9,81. H
Where:
A kW kW0 η H
1.7.
=
Material flow (mtph)
=
Actual elevator power
=
Elevator power empty
=
Elevator efficiency
=
Inter axis elevator height
Required air velocities for mill ventilation
Rules of thumb
• Recommended 1.5 m/s above the ball charge: -
inside the trunnion: 22-25 m/s. partitions: 8-14 m/s (<20 m/s). hood: <5 m/s to prevent dust from being sucked up (dust pick-up is proportional to speed^2). dropout box: <2 m/s.
• 0.3-0.5 Nm3/kg cement 0.6-0.8 Nm3/kg raw mix (depending upon drying needs)
• Wet bulb temperature should be at least 25°C higher then dew point temperature. • False air at mill outlet is usually >25%. Consider high false air volume in heat balance and in mill ventilation design.
1.8.
Optimum filling ratio:
• U= (volume of powder in the mill)/ (volume of voids in the charge): between 60% and 110%, optimum around 90%.
• In practical terms, material level should equal ball level in the first compartment • In practical terms, material level should be higher than ball level in the second compartment • The expansion of the ball charge due to the material in between would not exceed 3% in an optimised mill (measurement of the ball charge level of the empty and the filled mill)
• The material filling in the first compartment can be adjusted with flow control devices in modern diaphragms. (scoops, flaps)
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
2.
Ball Charge and Internals
2.1.
Largest Ball
Bond Formula
•
d KMAX
-
d Wi ρ = 20.17 20 .3 K Ψ. Du
-
where: d KMAX is the largest ball diameter (mm) -
d 20 is the sieve dimension (µ)
K is a constant (350 for a dry mill open or close circuit, 300 for wet) ρ is the specific mass of material (g/cm3)
-
Wi is the Bond work index (kWh/t) Du is the mill inside diameter (m)
Ψ is the ratio between the actual / critical speed (%)
with 20% retained
B = 24 d 80 (Other formula exist that result in value differences of ± 5%) B = ball dimension (mm) d 80 is the sieve with 80% passing
2.2.
Optimum Ball Diameter (mm)
Grinding Ball vs Clinker Size
Quick evaluation • For clinker:
100
10 1
.1
10
100
Clinker Size d80
Grinding Balls Data
Grinding Ball dimensions Weight Surface Number of balls per Diameter (g) (cm2) metric tons mm inch 4,001.153 314.159 250 100.00 ± 4" 2,916.841 254.469 343 90.00 ±3½" 2,048.590 201.062 488 80.00 1,826.658 186.265 548 77.00 ±3½" 1,372.396 153.938 729 70.00 1,048.878 128.680 954 64.00 ±2½" 864.249 113.097 1,157 60.00 500.144 78.540 2,000 50.00 ±2" 256.074 50.265 3,905 40.00 219.551 45.365 4,555 38.00 ±1½" 171.549 38.485 5,830 35.00 128.061 31.669 7,809 31.75 ±1¼" 108.031 28.274 9,257 30.00 62.518 19.635 15,996 25.00 ±1" 48.682 16.619 20,542 23.00 43.895 15.511 22,782 22.22 =7/8" 32.009 12.566 31,242 20.00 ±3/4" 19.658 9.079 50,870 17.00 ±5.8" (Unit weight and specific surface of MAGOTTEAUX grinding media)
Weight of 1 m3 of balls (kg) 4560 4590 4620 4640 4660 4708 4760
4850 4894
4948 4989
Specific surface 2 (m / mt) 7.854 8.728 9.812 10.207 11.222 12.276 13.085 15,708 19.628 20.664 22.437 24.730 26.173 31.408 34.139 35.337 39.259 46.185
Quick calculation:
•
Ball diameter (mm) =
•
Specific surface of balls of diameter =
3
250 P
(P = weight in g)
785 2 m / mt d
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(d = diameter in mm)
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Wear rates: In the 1st compartment the wear rate is correlated with the average ball weight (positive correlation), whereas in the 2nd compartment it is correlated with the ball charge surface area (positive correlation as well). Below are general guidelines for raw as well as cement grinding wear rates: Raw grinding • Raw mix with free silica (quartz) content <5%: 30-60 g/t • Raw mix with free silica (quartz) content >5%: 50-100 g/t Cement • CEM I, clinker >90%, 300 m2/kg : 30-60 g/t • CEM I, clinker >90%, 450 m2/kg: 60-100 g/t • CEM III, slag 70%, 300 m2/kg: 60-120 g/t • CEM III, slag 70%, 450 m2/kg: 120-200 g/t • Suppliers would typically guarantee <40 g/t for CEM I Bulk density for ball load (Coarse to medium ball size distribution): • Chamber 1: 4.3 – 4.5 t/m3 • Chamber 2: 4.5 – 4.65 t/m3 • Single Chamber mill: 4.5 – 4.55 t/m3
2.3.
Other internals
Partitions • Total slot area: 10 to 20 cm²/tph production: Slot Size Central Part Discharge Part FM 7 mm ± 1 mm 9 mm ± 1 mm RM 10 mm ± 1 mm 12 mm ± 1 mm
Max opening: ½ min ball size
Liners • Liners replaced when 60% of their effective lifting height has worn away: Reduction 8 to 10 % production reference points to measure lifting height are the lowest point on the liner to the highest release point (contact points between grinding ball and liner plate) • American Lorrain pattern: diameter (ft)*2=# bolt holes/row, 18.8” centre to centre. • DIN pattern: diameter (m)*10= # bolt holes/row, 31.4 cm centre to centre. • Classifying liners if L/D>1.5 and volume load<35%. • Without classifying liners, keep a maximum of 3-4 ball sizes.
2.4.
Mill Internal Inspection Sheet
Shell Liner Thickness Shell Liner Lifter Thickness Shell Liner Remarks – crack, gaps…. Inlet Head Liner Thickness Inlet Head Liner Remarks Inlet Opening Remarks Height Liner, to Balls – Average Width Across Balls – Average Calculated Percent Fill – mill ran out Build up on water injection lance Presence of material nibs
© Copyright 1990-2010, Lafarge SA. All rights reserved. INTERNAL USE ONLY
Ball Charge Remarks – sizes, shape, contamination, breakages Ball Coating Remarks Ball Classification Remarks Discharge Grate Slot Size-Average Discharge Grate Slot Size-Maximum Discharge Grate Metal Thickness – gaps etc. Discharge Grate Percent Blinded Discharge/Centre Screen Percent Blinded Height of Material relative to media Calculated Percent Fill – mill crash stopped
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
3.
Ball Charge Design (Finish Mill)
3.1.
Recommended volume loading
(see “How to Optimise Ball Charge”) Recommended Volume Loading 1st Compartment 2nd Compartment 3rd Compartment 1 Minimum kWh/t 26 – 28% 28 – 30% 28 – 30% Maximum Production 32 – 34 % 34 – 36% 34 – 36% (Ball level in the trunnion should not be higher than 50 to 75 mm.)
3.2.
Ball charge design for new mill without pre-existing experience
Closed circuit finish mill Chamber 1 Coarse charge %
Fine charge %
90
40
21
80 70 60
29 19 12
38 25 16
Average ball weight (kg/ball)
1.83
1.63
Ball size (mm)
Ball size (mm) 40 (transition zone) 30 25 20 17 Average ball weight (g/ball)
Chamber 2 Coarse charge %
Fine charge %
10 25 25 20 20
15 15 30 40
47
34
Specific surface 32 37 (m2/t) Note: With high circulating loads, as with oversized separators the coarser grading in the 2nd chamber is more suitable to help maintain charge permeability 1
The recommended volume loading for minimum kWh/t is based on an acceptable compromise with production. For minimum kWh/t the volume loading can be as low as 22% in the second compartment. Due to risk of breakage the minimum volume loading in first compartment shall not underpass 25%.
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Open circuit finish mills
Ball size (mm) 90 80 70 60 Average ball weight (kg/ball)
Chamber 1 Coarse charge % 40 29 19 12
Fine charge % 21 38 25 16
Chamber 2
1.83
1.63
Ball size (mm)
%
30 25 20 17 Average ball weight (g/ball)
10 10 20 60
Specific surface (m2/t)
30 39
Raw mills Chamber 1 Ball size (mm)
%
Ball size (mm)
90 80 70 60 Average ball weight (kg/ball)
40 29 19 12
60 50 40 30 Average ball weight (g/ball)
1.83
Specific surface (m2/t)
Chamber 2 Coarse charge % 20 30 30 20
Fine charge % 30 30 40
260
186
18
21
Note: Up to 50% 90 mm are used in some mills
3.3. •
•
•
Polysius Design
As a rule of thumb, it suits raw mills and especially mono-chambers very well, especially if no classifying liners are used.
⎡ D ⎤ ln ⎢ 9.6 ⎥⎦ D = 9.6 e −013.x ⇔ x = ⎣ − 0.13 where: D = Ø ball (cm) x = effective mill length (m) Process step-by-step, calculating each effective length starting from the input and with the largest ball: 1. Calculate effective lengths and the ball sizes you plan to use. 2. Double the first effective length which is both the first interval width and the first cumulative length. 3. Calculate each succeeding interval width by taking the effective length and subtract the preceding cumulative length and doubling it. Add this value to the previous cumulative length to get the new one. 4. If an interval overlaps with the partition divide the interval at the point of overlap. The excess is carried over to the next compartment. At the end of the mill, the interval is truncated at the point of overlap. 5. Once the intervals have been adjusted for compartment lengths as described in step (4), divide the adjusted interval by compartment length and multiply by 100. This is the percent weight for each size to be used in the compartment.
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Slegten Model •
Compatible mostly with classifying linings in the second compartment.
First Compartment – Crushing Same number (n) of balls in each size range.80, 70 and 60 mm Ø and then add some 90 mm Ø to deal with oversize clinker. This equilibrium charge will not change as you add 90 mm Ø make-up balls to maintain volume load. Ø Ball (mm) % of Weight (x) % of Weight Number/ 10 t of Charge 90 100-5x 20.0 670 80 2*4x 38.4 1820 70 1.6x 25.6 1820 60 X 16.0 1820 - x = is taken to be the number of balls in the last size. • In recent years, Slegten has favoured a 3-ball size distribution in first compartments over a 4- ball size as shown in table above.
•
Transition Zone • This is the start of the second compartment and its job is to crush any oversize that penetrated the diaphragm • The design for this area is to use "n" balls of 50 and 40 mm. Ø Ball (mm) Number/ 10 t of Charge 50 1820 40 1820 •
The largest ball size used in this transition zone can be identical to the smallest ball size used in the first compartment.
Second Compartment – Fine Grinding • The envelope curve for the balls smaller than 40 mm follows the following formula: where: • D = 3.3e −010.x D = Ø ball (cm) x = distance from transition zone finish (m) • The 30 mm balls start at the completion of the transition zone and the exponential curve follows. Rule of thumb: • The smallest ball size should, as a minimum, be at least twice the width of the slots in the grates (ex. ≥16 mm balls if slots are ≤8 mm wide). For this reason, it is generally recommended to use ¾” (19 mm) balls as the smallest size in Finish mills. 5/8” balls are fine when the grates are new but often become problematic as the grate slots enlarge. Example: Comparison Slegten & Polysius 1st compartment useful length = 3.81 m, 2nd compartment useful length = 7.66 m Using an average ball weight of 1.65 kg per ball and 3 ball sizes in the first compartment for the Slegten model. Ball size and % Polysius Slegten compartment load design design 1st compartment 3 ½” 31.0% 32.1% 3” 31.2% 43.1% 2 ½” 37.8% 24.8 % Transition zone 2nd compartment 2” 2.31% 7.67% 1 ½” 23.73% 2.94% 1 ¼” 34.05% 10.08% 1” 2.57% 48.18% ¾” 37.34% 31.13% 5/8” (Some)1 A limited amount of 5/8” balls should theoretically be added but the designer decided to use ¾” as the smallest ball size.
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
3.4.
Fineness in Finish Mills:
In the first compartment before intermediate diaphragm • 95% passing of 2.365 mm (2360 μm or 8 mesh) for the material leaving the first compartment • Particle size distribution recommended on other sieves: - 86 – 92 % passing 1.0 mm (1000 μm or 18 mesh) - 80 – 90 % passing 0.6 mm (595 μm or 30 mesh) - 75 – 85 % passing 0.5 mm (500 μm or 35 mesh) In the second compartment before discharge diaphragm • 95% passing 0.5 mm (500 μm or 35 mesh) • 70 - 80 % passing 0.2 mm (212 μm or 70 mesh)
4.
Grinding Laws
4.1. • •
Absorbed Power of a Mill
Only 5-10 % of the energy is used for grinding, 90% is wasted into heat, wear, noise… With similar ball charge gradation and similar liners' lifting effect, the absorbed power is related to: Tonnage of balls Mill rpm % volume load Mill diameter
Slegten formula
•
⎛ rpm ⎞ ⎟ P = W * ⎜⎜ ⎟ ⎝ Vcr ⎠
1.27
* K j * K Fr
and
W=
π 4
* Fr 2 * L * J * d
where: P : the motor absorbed power (kW) J : the ratio between the apparent ball volume and the internal volume W : the weight of the load (T) - rpm: is mill speed (rpm) Fr : internal diameter (inside liners) (m) d is the apparent density of load (t/m3) #1 comp : d = 4.5 #2 comp : d = 4.65, if fine ball size distribution (average ball weight < 40 g) d = 4.6, if coarser ball size distribution (average ball weight > 40 g) Average : d = 4.6 -
⎛ 42.3 Vcr is the critical speed inside liners= ⎜ ⎜ F r ⎝
-
K j = 1.36 − 1.2 J , K Fr = C.Fr
-
•
⎞ ⎟ , L : the useful length of mill (m) ⎟ ⎠
0.379
K Fr is the influence of the location of the center of gravity for the moving ball charge vs. the mill center (C is a constant depending on the material and the liners). C= 11.262 for Clinker mill closed circuit with Slegten equipment 10.7 for clinker + slag, 12.16 for raw mix, 10.1 for slurry
⎛ rpm ⎞ ⎟ P = L * ⎜⎜ ⎟ V ⎝ cr ⎠
1.27
* J* K j *
π 4
* Fr2.379 * d * C
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Simplified formula
Fr ⎡ RPM ⎤ 100 P =T *⎢ *Kj * * 9.5 ⎥* 1.366 ⎣ Vcr ⎦ 75
•
Kj Function of Volume Load Volume load Kj 40% 30% 20%
0.9 1 1.1
Rules of Thumb • One metric tonne of balls increases the mill power draw by 10 kW. • Usually, 8 to 12 kWh/t is absorbed in the first compartment for clinker grinding (approximately 1/3 of the mill power)
4.2.
Charles, Bond, Kick & Rittinger Laws
General Law: Charles • dW = cx −n dx -
If W = Comminution work, particles (initial, final)
Value of n Energy Law Rittinger Kick Bond
Value of n: 2 1 1.5
x = Size of
Applies well over range of: 10 – 1000 μm
Normalized Blaine fineness equation • Fineness equation, generally accepted within Lafarge:
⎡ SA ⎤ W2 = W1 ⎢ 2 ⎥ ⎣ SA 1 ⎦ -
n
n = 1.3 for high efficiency separator (HES) circuit, n = 1.4 for second generation separators, n = 1.5 for Sturtevant separators, bearing in mind that 16’ and 18’ Sturtevant separators are more efficient than the larger 20’ and 22’ Sturtevant. n = 1.6 for open circuit mills W1 and W2,are the initial and resulting specific power consumption kWh/t, W is inversely proportional to production rates. SA1 and SA2 are the initial and final product surface areas m2/kg 0.43( SA1 − SA2 ) / 1000
•
Proposed by Polysius: C 2 = C1 * e
•
where C2 and C1 are production capacities Rene’s Study: +1% passing at 10µm: +10.8 SSB [m²/kg]
Rules of thumb Raw material: 10-16 kWh/t (mill motor) target fineness: passing 200µm>99%, passing 90µm>88% depending upon burnability of raw mix) • Clinker: 45 ± 15 kWh/t at 350 m2/kg (mill motor). For a pure cement (95% clinker) at <400 m2/kg, the mill motor consumption should be <40 kWh/t.
•
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
5.
Grindability Measurement
5.1. BB10 Test Idea:
Correlate the number of revolutions of a lab mill for a given fineness with the industrial energy to obtain the same fineness. The material is crushed to everything passing 3.15 mm. The number of mill revolutions is measured to obtain a given fineness. Revolutions are converted to industrial power consumption. Lab Mill Characteristics: Diameter: 40 cm Length: 12 cm Speed: 55 rpm Ball volume load: 14 % Ball weight: 10 kg
Material load: 1kg Balls: 20-25 mm : 2.5 kg 20-35 mm : 3 kg 50 mm : 4.5 kg
Lafarge Data
•
60 clinkers. Typical results are 48-60 kWh/t 3500 m2/kg. BB10 kWh/t Minimum Average Maximum
for 250 m2/kg kWh/t 21 29.2 43
for 300 m2/kg kWh/t 30 39.8 56
for 350 m2/kg kWh/t 39 51.8 68
for 400 m2/kg kWh/t 49 65.3 83
Remark: An average CEM I 32,5 at 300 m²/t can be ground with 28kWh/t related to the mill main drive. The additional energy for finer grinding should not exceed the Normalized Blaine fineness equation described in chapter 4.2.
5.2.
Bond Test
Lab Mill Characteristics Diameter: 30.5 cm Length: 30.5 cm Ball weight: 20 kg Material quantity: 700 cm3 Speed: 70 rpm
Formula
Wi =
44.5 ⎛ 10 10 − d p 100 0.23 • P 0.82 * ⎜⎜ ⎜ d p 80 d f 80 ⎝
⎞ ⎟ ⎟⎟ ⎠
dp100 is the sieve with 100% passing feed material dp80 80% feed material df80 80% finish material P is the production (g/rev of mill) of product at the level the circulating load is requested. Wi is the Bond work index kWh/short ton.
•
Developed to predict energy requirements of 2.44m diameter, wet, closed circuit, ball mill at a fineness of either 65 mesh (220 µm) or 100 mesh(150 µm).
•
Pre-crush feed to #6 (3.35 mm). Maintain 700g sample in test mill. Turn mill 100-150 rev.
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
•
Remove undersize (dp100 – 65 or 100 mesh) and replace with fresh feed (300 – 400 g). 1st cycle is now completed. Repeat procedure until steady state is reached. Typically 6-8 cycles so that 200 g are removed at each cycle, which equals 250% circulating load or 30% of “P”.
•
The Work index expresses the specific net energy needed to grind a material from indefinite feed size to dp80 =100 µm
•
Wi for Raw materials for cement plants are usually in the range of 8 – 16 kWh/st
Typical Values for Wi for common materials:
Wi Clinker: Limestone Shale Slag Sand stone Silica sand Coal Clay Gypsum Kiln feed
kWh/st*
ρ (g/cm3)
13.49 10.18 16.40 15.76 11.53 16.46 11.37 7.10 8.16 10.57
3.09 2.68 2.58 2.93 2.68 2.65 1.63 2.23 2.69 2.67
*Clearly
the Wi can vary significantly from these figures depending upon the nature of the materials and material testing is necessary for each particular case when assessing a mill.
5.3.
Hardgrove Test
The Hardgrove test was originally developed for determination of coal grindability, using a laboratory scale ring ball mill. Feed size is prepared in the range 600 – 1180 µm. The mill is charged with 50g of feed and operated for 50 revolutions. The result is calculated from the proportion of material passing 75µm. The figure is meant to compare the grindability with a standard American coal with an index of 100. Bond gave the following equation to convert HGI into a Bond Wi:
Wi =
435 HGI 0.91
Other similar relationships can be found in the literature. Ranges of HGI found in cement plant raw materials are given below: Material Clay Coal Limestone Shale Silica Sand
HGI* 130 – 160 35 – 90 60 – 120 60 - 170 30 - 100
*Clearly
the HGI can vary significantly from these figures depending upon the nature of the materials and material testing is necessary for each particular case when assessing a mill.
5.4. Parameters Affecting the Clinker Grindability 1 point increase of Î produces a variation of
C3S
Exc SO3 /tot.alk. (%)
W250 (kWh/t @ 250 m2/kg ) W300 W350 W400
-0.3 -0.5 -0.6 -0.7
4 4 5 5
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CaOl (%)
D75 alite (µm)
Alite C3S x100
-0.9
0.1 0.1 0.2 0.2
-0.1 -0.2 -0.3
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
6.
Mill Performance Benchmarking
6.1.
Performance Indicator Finish Mills Absorbed (PIFMA)
The PIFMA is used to benchmark finish mill performance:
PIFMA =
Where: PA – actual specific power consumption mill drive PT – quasi theoretical specific power consumption, calculated from standard grindability figures
PA PT
An efficient mill will have a PIFMA close to unity The theoretical power consumption at a standard surface of 300 m2/kg calculated by:
(
1 P = • X C • SPC C + X G • SPC G + X S • SPC S + X A • SPC A + X P • SPC P + X L • SPC L + X O • SPC O T 300 MF
)
Where: XC, XG, XS, XA, XP, XL and XO are the weight fractions of clinker, gypsum, slag, flay ash, pozzolan, limestone and other components in the product. MF is the mill type factor = 1 for a ball mill, =1.6 for a Horomill, = 1.7 for Vertical mill and 1.8 for a roller press SPC refers to the standard grindability kWh/t of the components at 300 m2/kg. The standard figures used are: SPCC SPCG SPCS
Clinker Gypsum Slag
28 10 43
SPCA SPCP SPCL
Fly Ash Pozzolan Limestone
2 10 10
Note the low figure used for fly ash is to adjust for it’s initial surface The theorectical specific power consumption at 300 m2/kg is then corrected to the actual product surface area SA, by the following equation:
P = P T T 300
⎛ SA • (1 − 0.1 * ( X G + X A •⎜ 300 ⎝
+ X P + X L )) ⎞
fs
⎟ ⎠
Where: fs = Factor Separator (1.6 for open circuit, 1.5 for first, 1.4 for second, 1.3 for third generation separator, 1.0 for roller press, 1.10 for vertical mill & 1.05 for Horomill) Subtraction of the term 0.1*(XG+XA+XP+XL) from the surface area is meant to correct for over-grinding of the softer components. The resulting PIFMA will be influenced by the mill efficiency and by the grindability of the cement. Therefore especially in cases of high PIFMA (>1.15) the grindability of the components and the condition of the milling system will need to be investigated to find improvement potential. Example Calculation of PIMFA
Determine the PIFMA of a closed circuit ball mill with 3rd generation separator produces 86.2 tph @ 369 m2/kg with a power consumption at the main motor of 35.6 kWh/t. The product components are 88.29% clinker, 3.47% gypsum, 6.56% limestone and 1.68% blast furnace slag.
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Calculate the theoretical power consumption at a standard surface of 300 m2/kg by:
(
1 P = • X C • SPC C + X G • SPC G + X S • SPC S + X A • SPC A + X P • SPC P + X L • SPC L + X O • SPC O T 300 MF
(
)
1 P = • 0.8829 • 28 + 0.0347 • 10 + 0.0168 • 43 + 0.0656 • 10 = 26.4 kWh / t T 300 1
Next calculate the theoretical power consumption at the actual product surface area using:
⎛ SA • (1 − 0.1 * ( X G + X A •⎜ 300 ⎝
P = P T T 300
P T
+ X P + X L )) ⎞
⎛ 369 • (1 − 0.1 * ( 0.0347 + 0.0656)) ⎞ = 26.4 • ⎜ ⎟ 300 ⎠ ⎝
fs
⎟ ⎠
1.3 = 34.2 kWh / t
Finally calculate the PIFMA PIFMA =
6.2.
P A = 35.6 = 1.04 34.2 P T
Benchmarking Ball Mills with Bond Wi
Bond is most useful for assessing the power consumption of ball raw mills and coal mills since both target product particle size rather than surface area: The power consumption for a new mill can be estimated from the Bond Equation:
⎛ 10 10 ⎞⎟ − Ws = FB • 1.102 • Wi • ⎜ ⎜ P 80 F80 ⎟⎠ ⎝
Where: Ws – calculated industrial mill shaft power kWh/t P80 – Product 80% passing size µm F80 – Feed 80% passing size µm FB - Bond Factor for dry grinding normally 1.3
The 1.102 is the conversion from kWh/short ton to kWh/t (metric) . For grinding finer than 70µm Bond proposed a fine grinding correction factor, calculated from:
⎛ 10.3 + P80 FP = ⎜⎜ ⎝ 1.145 • P80
⎞ ⎟⎟ ⎠
The Bond equation can also be used for benchmarking existing mills in conjunction with actual mill shaft power consumption (WSA kWh/t) to compute the Bond factor:
FB =
WSA ⎛ 10 10 ⎞⎟ − 1.102 • Wi • ⎜ •F ⎜ P 80 ⎟ P F 80 ⎠ ⎝
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)
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Values of less than 1.3 would normally indicate an efficient mill. Typical values determined for specific mill types grinding cement raw materials are: 1. 2. 3. 4.
Bucket elevator ball mill Tandem Hammer / Airswept mill Airswept Mill Double Rotator Mill (Central discharge)
1.2 – 1.3 1.4 – 1.5 1.4 – 1.55 1.2 – 1.3
The Bond equation is also useful to assess the potential impact of changes to mill feed or product size.
7.
Separator
7.1.
Circulating Load (CL)
Junction with Three Streams • A, R, F are the feed, rejects and fines of the separator A ai , ri , f i are the cumulated % passing at a defined sieve(i).
F
R
-
da, dr, df are the % retained corresponding to the sieve interval dx.
-
A=R+F A da = Rdr + Fdf
With:
da = a i + 1 − ai ,
R df − da = , A df − dr
Drawing • Plot ( f i − a ) vs ( f i − ri ) If the mill circuit is steady, the graph has to be a straight line:
( f − a) = α + β( f − r )
-
α should be close to 0
-
β is the most probable value of
-
The circulating load is defined as:
7.2.
CL calculation • Using the least square line calculations, with α = 0 Quick CL calculation • With one set of results of sieving: R f −a = F a−r
β R = F 1− β
Tromp Curve
a) •
R A
F dr − da = A dr − df
Creating the Tromp Curve On the Gauss-logarithmic paper, let's plot the probability for a given particle of a certain size entering the separator to go to the rejects =
dr( x )* R with: da( x )* A
n
∑
( f i − ai )( f i − ri ) R i =0 = n A ( f i − ri ) 2
∑
i =0
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
The Tromp curve can be divided into two straight lines The higher sieve fractions have a slope which is representative of the separator efficiency (a perfect one would be vertical).
•
Tromp Curve Representation
OSEPA N1500
99.8 99.5 99 98 95 % Probability of Rejection
•
90 80 70 60 50 40 30 20 10 5
1.0
10.0
100.0
1000.0
Particle Size
b) •
Imperfection d 75 − d 25 I= 2 * d 50
where: - d25 is the size of the particle which has 25 % chance of going to rejects - d50 is the size of the particle which has 50 % chance of going to rejects - d75 is the size of the particle which has 75 % chance of going to rejects
Imperfection vs Circulation Load 0.44 Imperfection 0.42 0.40 0.38 0.36 0
c) • •
d)
100
200 300 Circ. load (%)
400
Acuity Limit AL is the abscissa of the intersection of the two Tromp curve lines. It’s the size at which selection is initiated
Bypass
Definition: • By-pass is the ordinate of the intersection of the two Tromp curve lines. • The bypass is the lowest percentage of feed that will go to the separator rejects.
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BALL MILLING incl. SEPARATORS – Page 18/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
Bypass vs. feed rate – Sturtevant • The following graph shows the Bypass of an 18’Sturtevant versus its feed rate.
Bypass vs. feed rate O’Sepa/Sturtevant 80
100
70 Bypass (%)
Bypass (%)
Sturtevant
60
80 60 40
50 40 30 20
O-Sepa
10
20
0 1.0
100 150 200 250 Feedrate to Separator (t/h)
QF/Qa vs. bypass • If Qf is the separator feed rate (kg/h) and Qa the separator ventilation (m3/h), • Qf/Qa is an important ratio for the separator efficiency.
•
⎛ Qf ⎞ ⎜⎜ − f1 ⎟ Qa ⎟⎠ ⎝
•
•
2.0
2.5
3.0
3.5
40 30 20 10
Bypass = 1 + e - f1: coefficient for the separator
7.3.
1.5
Qf/Qa (kg feed/m3 separator sweep)
300
Rosin Rammler Number (RR#)
The steeper the particle size distribution (RR# high) the more efficient the grinding and separating process. Raw mix RR# are usually lower than those for cement grinding
0 0
1
2 Qf/Qa (kg/m3)
3
4
RRnumber vs. Feed to Air Ratio 1.20 Rosin-Ramler Number (n)
50
Bypass (%)
0
1.15 1.10 1.05 1.00 1.0
1.5
2.0
2.5
3.0
3.5
4.0
Qf/Qa (kg/m3)
Separator Performance • Rate of recuperation in the fines of particles smaller than a given dimension.
r=
7.4.
F f * A a
Indicators for Cement Milling and Typical Values
Slope Rosin Rammler fines: % recovery, 45 μm: Acuity: Imperfection:
Bypass: Circulating load: HES Qf/Qa: % Passing 45 μm:
1.1 – 1.4 for HES 0.85 – 1.0 for 1st generation separators (Sturtevant, Raymond) 1.2 for second generation separators 45 to 55% for Sturtevant and >65% for HES 20 – 30μm for Sturtevant and <0.30μm for HES <0.35 for HES 0.45 – 0.6 for Raymond separators 0.6 –0.7 for Sturtevant separators 5 – 10% range for HES 150 –200 % with HES 1.5 – 2.0 range 93% minimum (45 μm = 325 mesh)
© Copyright 1990-2010, Lafarge SA. All rights reserved. INTERNAL USE ONLY
BALL MILLING incl. SEPARATORS – Page 19/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
7.5.
Recommended Sizing for a HES Parameter
Recommended
Possible (Min/Max)
Industrial Range
Cage loading
20-23 t/h/m2
less than 30
11-36 t/h/m2
Qf/Qa
2 kg/m3
less than 2,2
0,7-3,0 kg/m3
Radial velocity at the inlet of the cage
3,6-4,3 m/s
x
2,9-4,5 m/s
Ratio Am3/h/m2 Gas volume / Cage Area
14 000 Am3/h/m2
13000-15000 Am3/h/m2
10500-16300 Am3/h/m2
Circulating load
100%-250%
x
45%-270%
1,0 m/min Pulse jet H.P.
less than 1,2 m/min
Filtration Velocity or Air to cloth ratio
a) • • • • •
•
0,8-1,3 m/min 1,1 m/min Pulse jet L.P.
less than 1,2 m/min
Fan and Bag House Sizing Use the production rate (T/h), Qf/Qa (kg/ Am3) and circulating load (%) to specify the air flow. Most separators can operate at +/- 20% of nominal. Only a margin of 5 - 8% above the separator airflow is recommended for the BH. Margin of 5-10% is recommended on top of the BH for the fan. Correctly specifying the static pressure: - Pressure drop can be estimated by the dP of the separator (2.5 – 3 kPa), Dust Collector (2 – 2.5 kPa), ducting. (1-1.5 kPa) and if present, silencer (250 – 500 Pa). - The recommendation is 6.5 kPa with a minimum of 600 kPa. Include in the circuit design, the possibility for recirculation of up to 80% of the separator airflow.
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
8.
Grinding Aid
Type of Products • Surface active agents tend to saturate the free valence and inhibit the pack-set. Typical surfaceactive agents are: - ligno-sulphonates - polyoils - amines - organic acids • Polar compounds (water, ammonia) are known to have some action on such bonds through their polar moment. However, their practical use as surface agents is limited by their other impacts on the cement properties. • Other agents, particularly coal dust, have been used in the past. • Commercial products available as grinding aids are essentially (60-800 g/t ck): - Triethanolamine - Polypropylene glycols and polyethylene • HEA2, DDA& and other products cause a definite reduction of pack-set but do not prevent agglomeration or lump-formation problems that are caused by: - Alkalis ( K 2 SO4 ) - Moisture The effect of grinding aid on milling process: - Enhances the flowability and prevents agglomeration - Prevents coating on liners and grinding media - Lower effect on coarser product (below 320 m2/kg) - Reduces contraction - Increased production (5-7%)
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
9. 9.1.
Other Data Sieve Sizes
Sieve Screen #400 #325 #270 #230 #200 #170 #140 #120 #100 #80 #70 #60 #50 #45 #40 #35 #30 #25 #20 #18 #16
9.2.
Micron 37 44 53 63 74 88 105 125 149 177 210 250 297 354 420 500 595 707 1000
Iso alter 38 45 53 63 75 90 106 125 150 180 212 250 300 355 425 500 600 710 850 1000 1180
Screen #14 #12 #10 #8 #7 #6 #5 #4 #3.5 1/4" 5/16" 3/8" 7/16" 1/2" 5/8" 3/4" 7/8" 1" 1"1/4 1"1/2 2"
Micron 2000
6350 8000 9510 11200 12700 16000 19000 22600 25400 32000 38100 50800
Iso alter 1400 1700 2000 2360 2800 3350 4000 4750 5600 6300 8000 9500 11200 12500 16000 19000 22400 25000 31500 38100 50000
Bulk Densities Bulk density Sand Sand Iron Bauxite Brick Gypsum Fluid coke Limestone (crushed) Silica fume Bottom Ash Cement T I-II T 10 T III Clinker Clinker (underburnt) Raw mix
© Copyright 1990-2010, Lafarge SA. All rights reserved. INTERNAL USE ONLY
kg/m3 1387 1679 2629 1980 1502 1677 926 1803 1024 1241 1234 1207 1054 1575 1400 1041
BALL MILLING incl. SEPARATORS – Page 22/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
9.3.
Residue Conversion Chart CONVERSION OF SIEVE RESIDUES
% residue at 90μm 70
50 40
30
355 μm 20
250 μm 12.0% 10 200 μm 7
5
180 μm
150 μm
4
3 125 μm 2
106 μm 1
0.7
0.5
90 μm
0.4 80 μm 14.22%
63 μm 0.2
75 μm
56 μm
% residue
0.3
12.0%
50 μm 25 μm
45 μm 0.1
0.7
1
2
3
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4
5
7
10
20
30
40
50
BALL MILLING incl. SEPARATORS – Page 23/25 Version September 2010
CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
10. References ¾
Cement Portal Grinding Domain How to manage the ball charge level How to check the airflow through the mill How to do a routine stop inspection How to do a mill crash stop inspection How to optimise a ball charge How to manage liner wear in a ball mill How to conduct a ball mill audit How to remove scrap from a ball mill circuit How to check the separator efficiency Procedure for audit of Ball Mill Circuits Global mixing grinding media recommendations Technical agenda study – formalisation of knowledge on grinding aids Guide – ball mill optimisation Post Sevilla module 5 Priority study cement grinding workshop Priority study – separators
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CEMENT PROCESS ENGINEERING VADE-MECUM CHAPTER 1-1 – BALL MILLING INCLUDING SEPARATORS
My notes:
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