1. Ball Mill Energy and Mass Balance
Plant: Lyons Diamater 16 ft
Date: April 7, 2007 Absorbed Power Length 45 ft
Mill: Raw Mill 2005.57 kW Area 13571.68 ft2
m
Inputs cp t T Q Q
(lbm·min-1) (Btu·lb-1·°R-1) (°F) (°R) (Btu·min-1) (%)
Raw Feed (dry) 3964 0.190 139 598.67 46695.92 6.54%
Seperator Rej. (dry) 4503.09 1.190 177 636.67 535868.04 75.06%
Raw Feed Water 36.33 1.000 139 598.67 3886.98 0.54%
Seperator Rej. Water 7.23 1.000 177 636.67 1048.07 0.15%
Inlet Air (dry) 698.28 0.240 75 534.67 -335.17 -0.05%
False Air 2 14.55 0.240 75 534.67 -6.98 0.00%
Mill Power 126725.75 17.75%
Totals 9223.47 713882.61 100.00%
m
Out Puts cp t T Q Q
(lbm·min ) (Btu·lb ·°R )
-1 -1 -1
(°F) (°R) (Btu·min-1) (%)
Mill Discharge 8427.84 0.19 180 639.67 164932.73 56.73%
Mill Sweep 712.82 0.24 170 629.67 15910.25 5.47%
Water Heat Rise 43.56 1 212 671.67 5879.93 2.02%
Heat Vap Water 42264.9 14.54%
Water Sensible Heat 0.45 170 629.67 -823.19 -0.28%
Shell Losses 62542.83 21.51%
Totals 9184.22 290707.45 100.00%
Closure 39.26 423175.16 2.46%
Note:
Goal seek "Mill dust in Sweep' to 325M on 'Flw Dgrm' sheet to close mass balance.
Goal seek % false air to close Energy balance.
2. Ambient Temp. 75 Mill Sweep D/C exit
Air flow 13396.33
Temp. 150
Stat, Pres. -4
Nuisance D/C Mill sweep D/C
Dust collectors 2.47
200 mesh 93
Diff. Pres. 2.25 Diff. Pres. 4.5
Sep. Feed 252.84
200 mesh 56.5
Sep. Fines 117.53
200 mesh 73.6 Mill Sweep
Air flow 11375.03
Sep. Rej. 135.31 Temp. 170
200 mesh 41.3 Stat, Pres. -3.5
Moisture 0.16
Temp. 177
Final Prod 120
200 mesh 74 Raw Feed 120 Mill Discharge 252.84
Moisture 0.18 Moisture 0.9 Moisture 0.24
Temp. 139 Temp. 180
Air flow to mill
Temp.
Sep Eff. 61.30% Stat, Pres.
CL 2.13
C 1.13
CL=C+1 2.13
Total feed to mill 255.31 tph
Total feed in mill 21.28 tons
Retention time 5 min
Total steel in mill 208 tons
Steel:Material ratio 9.78
3. Plant: Lyons
Date: April 7, 2007
Discription: RM Mill sweep and Dust Collector
Mill Sweep
Mill Data
Effective Diameter 2nd compt 12.5 ft2
Volume Load Compt 2 29.68 %
Percent swell 5%
Mill Discharge gas flow 11375.03 acfm
Mill Sweep
Mill Open cross sectional area 80.12 ft2
Mill Sweep 141.97 fpm 0.72 m/s
Typical values:
Semi air-swept: 1.0-1.5 m·s-1
Fully air-swept: 3.5-6.0 m·s-1
Air to Cloth Ratio
Bag Data
Number of Bags 648
Bag Diameter 6 in
Bag Length 107 in
Air-to-Cloth Ratio Typical Values:
Pulse Jet: 4.0-4.5 acfm/ft2
Air Flow 11375.0 acfm Reverse <2.5 acfm/ft2
Unit bag Cloth Area 14.01 ft2 Shakerless2.0-2.5 acfm/ft2
Total Cloth Area 9076.06 ft2
A:C Ratio 1.25 acfm/ft2
Note:
Data gathered from gas flow mesurements
4. Gas Flow
Plant: Lyons
Date: April 7, 2007
Flue Description: RM Mill Sweep
Data Velocity Presure Measurements
Lapse Rate 0 °R/ft
Universal Gas Constant 1545.3 lbf·ft/lb-mol·°R 0.65
Molecular Weight (air dry) 28.96 lbm/lb-mol
Gravitation force 32.17 ft/s2
Gravitational conversion factor 32.17 ft·lbm/lbf·s2
Density air (STP) 0.08 lbm/ft3
Flue Elevation 0 ft Number of points measured 5
Ambient air Temp. 70 °F Average Velocity preasure 0.65
Barametric pressure 30.06 in Hg Pitot Coeffecient 1
Calculated atmospheric pressure and density
Pressure corrected to elevation 30.0600 in Hg
Density Air Calculated 0.0752 lbm/ft3
Temperature in Flue 192 °F
Static Pressure Flue -12.5 in H2O
Calculated pressure and density in flue
convert in H20 to in Hg -0.9194 in Hg Gas Velocity 3635.23 ft/min
Pressure absolute Flue 29.1406 in Hg Mass Flow 794.11 lbm/min
Density in Flue 0.0593 lbm/ft3 Volumetric Flow 13396.33 ft3/min
Standard gas flow 10555.34 ft3·std/min
Flue Dimension
Diameter 26 in
Length 0 in
Width 0 in
Area of Flue 530.66 in2
3.69 ft2
Notes: These equations are used to perform the
FM fresh feed 110 tph corresponding calculations (US customary units):
Seperator cage speed 175 rpm
Mill inlet plugged by material. Atmospheric pressure pb × [(T0 - 0.003566H) / T0]
patm = gM/0.003566R
Gas density ρ = M(pa / RT)
Avg velocity pressure{(Σ√pvi)/k}
pv = 2
Gas velocity v = Cv(2pv / ρ)½
Mass flow m = ρvA
Actual gas flow Qa = vA
Normal gas flow Qn = Qa(pa / pref)(Tref / T)
5. Square roots of p
0.65
0.81
in H2O Temperature in Flue 170 °F
Static Pressure Flue -4 in H2O
Calculated pressure and density in flue
convert in H20 to in Hg -0.2942 in Hg
Pressure absolute Flue 29.7658 in Hg
Density in Flue 0.0627 lbm/ft3
Energy Balance for air flow across D/C
3635.18
Mass D/C exit 794.11 lb/min Temp D/C Exit 150 F
Mass False 81.29 lb/min Temp False 75 F
Mass Mill exit 712.82 lb/min Temp Mill Exit 170 F
Mill Exit Density 0.06 lbm/ft3 Mill Exit Flow 11375.03 acfm
Q D/C exit 15246.95 Btu's
Q fase air 97.54 Btu's
Q Mill Exit 17107.80 Btu's
17205.34
Delta= -1958.39 False air 9.29 %
Note:
ustomary units): Goal seek false air to close energy balance.
6H) / T0]gM/0.003566R
6. Raw Mill Data Samples
Sample 200M Moisture
Sep Prod
Sep Feed
Sep Rej
Raw Feed
Mill Dischrg
Final Prod
Dust Collect.
7. Absorbed Power
Critical Speed Calculated rotation
Plant: Lyons 21.08 rpm 15.86 rpm
Date: April 7, 2007
Mill: Raw Mill Percent critical
75.24%
Equations (from FLSmidth)
πD 2 L n n
V =
4 N = C·F ·g·D·a·sinα·π ·
60 H D D
D
h =H −
2 h α a
q
F = ·w ·V
100
F
where: = arm of gravity in relation to mill diameter [---]
a see Table 1
C = conversion factor [1.0 in SI units]
D = effective diameter of compartment [m]
F = ball charge weight [Mg]
g = gravitational acceleration [9.80665 m·s-2]
h = center distance [m]
H = free height [m]
L = effective length of compartment [m]
µ = torque factor (= sinα) [---] see Table 2
N = power consumption by compartment at mill shell [kW]
n = rotational speed of mill [rev·min-1]
q = ball charge volume load (degree of filling) [%] see Table 1
V = compartment volume [m3]
w = ball charge bulk density [Mg·m-3]
Equations Volume Loading
2H − D
D 2 cos−1 − ( 4H − 2D) DH − H
2
D
Percent loading =
πD 2
πD2
Cross sectional area (A) =
4 (Note: use radians for trig calcs)
πD2
Volume (V) = L = AL
4
Mill Data and Calculations
Raw Mill
Effective diameter, D 4.102 m
Effective length, L 6.991 m
Effective volume, V 92.398 m3
Free height, H 2.718 m
Center distance, h 0.667 m
Distance:diameter ratio, h/D 0.163 --- Physical data
Gravity arm, a 0.596 --- 410
8. Ball charge vol loading, q 29.7 % 4208
0.97
Ball charge bulk density, w 4.50 Mg·m-3 1.05
Ball charge weight, F 123.4 Mg 111.94 tons ball Calculated
charge 3043.56
Torque factor, µ 0.73
Mill speed, n 17.20 rpm
Absorbed Power
Raw Mill Motor ratings
Average absorbed power 1,945 kW
Drive efficiency 97.0 %
Motor shaft power 2,006 kW
