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Circulating Load Calculations
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Circulating Load Calculations
Screen Efficiency Factors
Circulating Load
- Amount of material deemedAmount of material deemed insufficiently processedinsufficiently processed
• Considered for closed-circuit comminution– Wide particle size distribution
• Computed for:– Equipment sizing– Feed control
ProblemProblem #1 #1
• Given:– 100 Mt/h ROM feed– Primary Gyratory Crusher
• Product particle size analysis: – 70% - ½” – 30% + ½”
– Single-deck Vibrating Screen• ½” aperture• Screen Efficiency: 100%100%
1st Pass: t = 1t = 1stst hour hour
100 Mt100 Mt70% Undersize
30% Oversize100% Efficiency
10 GC
Vibrating Screen
++
--70 Mt –½“
30 Mt +½“
Re-circulate to GC!
30%30%
70%70%
++
2nd Pass: t = 2t = 2ndnd hour hourNew feed:New feed: (100+30) (100+30) ==130130 Mt Mt
10 GC
Vibrating Screen
--70 + (0.7x30) = 9191 Mt
30 + (0.3x30) = 3939 Mt
Re-circulate to GC!
70% Undersize30% Oversize
100% Efficiency
30%30%
70%70%
++
3rd Pass: t = 3t = 3rdrd hour hourNew feed:New feed: (100+39) (100+39) ==139139 Mt Mt
10 GC
Vibrating Screen
--70 + (0.7x39) = 97.3097.30 Mt
30 + (0.3x39) = 41.7041.70 Mt
Re-circulate to GC!
70% Undersize30% Oversize
100% Efficiency
++
4th Pass: t = 4t = 4thth hour hourNew feed:New feed: (100+41.70) (100+41.70) ==141.70141.70 Mt Mt
10 GC
Vibrating Screen
--70 + (0.7x41.70) = 99.1999.19 Mt
30 + (0.3x41.70) = 42.5142.51 Mt
Re-circulate to GC!
70% Undersize30% Oversize
100% Efficiency
++
5th Pass: t = 5t = 5thth hour hourNew feed:New feed: (100+42.51) (100+42.51) ==142.51142.51 Mt Mt
10 GC
Vibrating Screen
--70 + (0.7x42.51) = 99.7699.76 Mt
30 + (0.3x42.51) = 42.75 42.75 Mt
Re-circulate to GC!
70% Undersize30% Oversize
100% Efficiency
++
6th Pass: t = 6t = 6thth hour hourNew feed:New feed: (100+42.75) (100+42.75) ==142.75142.75 Mt Mt
10 GC
Vibrating Screen
--70 + (0.7x42.75) = 99.9399.93 Mt
30 + (0.3x42.75) = 42.83 42.83 Mt
Re-circulate to GC!
70% Undersize30% Oversize
100% Efficiency
++
7th Pass: t = 7t = 7thth hour hourNew feed:New feed: (100+42.83) (100+42.83) ==142.83142.83 Mt Mt
10 GC
Vibrating Screen
--70 + (0.7x42.83) = 99.9899.98 Mt
30 + (0.3x42.83) = 42.85 42.85 Mt
Re-circulate to GC!
70% Undersize30% Oversize
100% Efficiency
++
8th Pass: t = 8t = 8thth hour hourNew feed:New feed: (100+42.85) (100+42.85) ==142.85142.85 Mt Mt
10 GC
Vibrating Screen
--70 + (0.7x42.85) = 99.9999.99 Mt
30 + (0.3x42.85) = 42.85 42.85 Mt
Re-circulate to GC!
70% Undersize30% Oversize
100% Efficiency
++
9th Pass: t = 9t = 9thth hour hourNew feed:New feed: (100+42.85) (100+42.85) ==142.85142.85 Mt Mt
10 GC
Vibrating Screen
--70 + (0.7x42.85) = 99.9999.99 Mt
30 + (0.3x42.85) = 42.86 42.86 Mt
Re-circulate to GC!
70% Undersize30% Oversize
100% Efficiency
++
10th Pass: t = 10t = 10thth hour hourNew feed:New feed: (100+42.85) (100+42.85) ==142.85142.85 Mt Mt
10 GC
Vibrating Screen
--70 + (0.7x42.85) = 99.9999.99 Mt
30 + (0.3x42.85) = 42.86 42.86 Mt
Re-circulate to GC!
70% Undersize30% Oversize
100% Efficiency
Total Feed
• Total feed is now computed as:
Mt.
MtMt
86142
86.42100
Load gCirculatin FeedFresh Feed Total
Total Feed
• May also be computed using the formula:
Where: F = Initial Feed
Ri = %Oversize of Crusher Product
iR-1
F Feed Total
Total Feed
• Using the formula, total feed may be computed as:
Mt
MtMt
86.142
7.0
100
3.01
100
R-1
F Feed Total
i
ProblemProblem #2 #2
• Given:– 100 Mt/h ROM feed– Primary Gyratory Crusher
• Product particle size analysis: – 70% - ½” – 30% + ½”
– Single-deck Vibrating Screen• ½” aperture• Screen Efficiency: 90%90%
Take Note:
• Screen Efficiency → affected by blinding – at lower efficiencies, there are particles,
supposedly undersize, that report to the oversize fraction!
• Formula:
– Where: %Eff = %Screen Efficiency
OSt = True GC OS fraction
OSa = Actual Screen OS fraction
a
t
OS
OS %Eff
Take Note:
• To determine the amount of US that reported to OS, we use:
• For the given problem, we get:
x
t
t
OS
OS %Eff
xMt
Mt
03
30 0.90
Feed of %33.333.3
300.9
30Mtx
Mt
Mt
Now, consider:
• 1st Pass → 11stst hour hour
100 Mt100 Mt
70% Undersize30% Oversize
90% Efficiency
10 GC
Vibrating Screen
++
--(70–3.33) =
66.6766.67 Mt
(30+3.33) = 33.33 33.33 Mt
Re-circulate to GC!
2nd Pass: t = 2t = 2ndnd hour hour70% Undersize
30% Oversize90% Efficiency
10 GC
Vibrating Screen
++
--70+(33.33x0.7) –(133.33x0.033)
= 88.8988.89 Mt
30+(33.33x0.3)+(133.33x0.033) = 44.4444.44 Mt
Re-circulate to GC!
New feedNew feed:: (100+33.33) (100+33.33) ==133.33133.33 Mt Mt
3rd Pass: t = 3t = 3rdrd hour hour70% Undersize
30% Oversize90% Efficiency
10 GC
Vibrating Screen
++
--70+(44.44x0.7) –(144.44x0.033)
= 96.3096.30 Mt
30+(44.44x0.3)+(144.44x0.033) = 48.1548.15 Mt
Re-circulate to GC!
New feedNew feed:: (100+44.44) (100+44.44) ==144.44144.44 Mt Mt
4th Pass: t = 4t = 4thth hour hour70% Undersize
30% Oversize90% Efficiency
10 GC
Vibrating Screen
++
--70+(48.15x0.7) –(148.15x0.033)
= 98.7798.77 Mt
30+(48.15x0.3)+(148.15x0.033) = 49.38 49.38 Mt
Re-circulate to GC!
New feedNew feed:: (100+48.15) (100+48.15) ==148.15148.15 Mt Mt
5th Pass: t = 5t = 5thth hour hour70% Undersize
30% Oversize90% Efficiency
10 GC
Vibrating Screen
++
--70+(49.38x0.7) –(149.38x0.033)
= 99.5999.59 Mt
30+(49.38x0.3)+(149.38x0.033) = 49.7949.79 Mt
Re-circulate to GC!
New feedNew feed:: (100+49.38) (100+49.38) ==149.38149.38 Mt Mt
6th Pass: t = 6t = 6thth hour hour70% Undersize
30% Oversize90% Efficiency
10 GC
Vibrating Screen
++
--70+(49.79x0.7) –(149.79x0.033)
= 99.8699.86 Mt
Re-circulate to GC!
New feedNew feed:: (100+49.79) (100+49.79) ==149.79149.79 Mt Mt
30+(49.79x0.3)+(149.79x0.033) = 49.9349.93 Mt
7th Pass: t = 7t = 7thth hour hour70% Undersize
30% Oversize90% Efficiency
10 GC
Vibrating Screen
++
--70+(49.93x0.7) –(149.93x0.033)
= 99.9599.95 Mt
30+(49.93x0.3)+(149.93x0.033) = 49.9849.98 Mt
Re-circulate to GC!
New feedNew feed:: (100+49.93) (100+49.93) ==149.93149.93 Mt Mt
8th Pass: t = 8t = 8thth hour hour70% Undersize
30% Oversize90% Efficiency
10 GC
Vibrating Screen
++
--70+(49.98x0.7) –(149.98x0.033)
= 99.9899.98 Mt
30+(49.98x0.3)+(149.98x0.033) = 49.9949.99 Mt
Re-circulate to GC!
New feedNew feed:: (100+49.98) (100+49.98) ==149.98149.98 Mt Mt
9th Pass: t = 9t = 9thth hour hour70% Undersize
30% Oversize90% Efficiency
10 GC
Vibrating Screen
++
--70+(49.99x0.7) –(149.99x0.033)
= 99.9999.99 Mt
30+(49.99x0.3)+(149.99x0.033) = 50.0050.00 Mt
Re-circulate to GC!
New feedNew feed:: (100+49.99) (100+49.99) ==149.99149.99 Mt Mt
10th Pass: t = 10t = 10thth hour hour70% Undersize
30% Oversize90% Efficiency
10 GC
Vibrating Screen
++
--70+(50.00x0.7) –(150.00x0.033)
= 100.00 100.00 Mt
30+(50.00x0.3)+(150.00x0.033) = 50.0050.00 Mt
Re-circulate to GC!
New feedNew feed:: (100+50.00) (100+50.00) ==150.00150.00 Mt Mt
Wait now! Going back…
• 1st Pass → 11stst hour hour
100 Mt100 Mt
70% Undersize30% Oversize
90% Efficiency
10 GC
Vibrating Screen
++
--(70–3.33) =
66.6766.67 Mt
(30+3.33) = 33.33 33.33 Mt
Re-circulate to GC!
Observations:
• Based on the 1st Pass, we determine:– 33.33%33.33% of the Feed reports to Oversize– 66.67%66.67% of the Feed reports to Undersize
• Thus, we can see that:– We use the OS/US cut-off of [33.33%33.33% : 66.67%66.67%]
instead of the original [30%30% : 70%70%]– We may “perceive” the screen efficiency to be
100%100% again!
1st Pass: t = 1t = 1stst hour hour
100 Mt100 Mt66.67% Undersize
33.33% Oversize100% Efficiency
10 GC
Vibrating Screen
++
--
Re-circulate to GC!
(70–3.33) = 66.6766.67 Mt
(30+3.33) = 33.33 33.33 Mt
33.33%33.33%
66.67%66.67%
++
2nd Pass: t = 2t = 2ndnd hour hourNew feed:New feed:
(100+33.33) (100+33.33) ==133.33133.33 Mt Mt
10 GC
Vibrating Screen
--133.33x0.67= 88.8988.89 Mt
133.33x0.33 = 44.4444.44 Mt
Re-circulate to GC!
66.67% Undersize33.33% Oversize100% Efficiency
33.33%33.33%
66.67%66.67%
++
3rd Pass: t = 3t = 3rdrd hour hourNew feed:New feed:
(100+44.44) (100+44.44) ==144.44144.44 Mt Mt
10 GC
Vibrating Screen
--144.44x0.67= 96.3096.30 Mt
144.44x0.33 = 48.1548.15 Mt
Re-circulate to GC!
66.67% Undersize33.33% Oversize100% Efficiency
++
4th Pass: t = 4t = 4thth hour hourNew feed:New feed:
(100+48.15) (100+48.15) ==148.15148.15 Mt Mt
10 GC
Vibrating Screen
--148.15x0.67= 98.7798.77 Mt
148.15x0.33 = 49.3849.38 Mt
Re-circulate to GC!
66.67% Undersize33.33% Oversize100% Efficiency
++
5th Pass: t = 5t = 5thth hour hourNew feed:New feed:
(100+49.38) (100+49.38) ==149.38149.38 Mt Mt
10 GC
Vibrating Screen
--149.38x0.67= 99.5999.59 Mt
149.38x0.33 = 49.7949.79 Mt
Re-circulate to GC!
66.67% Undersize33.33% Oversize100% Efficiency
++
6th Pass: t = 6t = 6thth hour hourNew feed:New feed:
(100+49.79) (100+49.79) ==149.79149.79 Mt Mt
10 GC
Vibrating Screen
--149.79x0.67= 99.8699.86 Mt
149.79x0.33 = 49.9349.93 Mt
Re-circulate to GC!
66.67% Undersize33.33% Oversize100% Efficiency
++
7th Pass: t = 7t = 7thth hour hourNew feed:New feed:
(100+49.93) (100+49.93) ==149.93149.93 Mt Mt
10 GC
Vibrating Screen
--149.93x0.67= 99.9599.95 Mt
149.93x0.33 = 49.9849.98 Mt
Re-circulate to GC!
66.67% Undersize33.33% Oversize100% Efficiency
++
8th Pass: t = 8t = 8thth hour hourNew feed:New feed:
(100+49.98) (100+49.98) ==149.98149.98 Mt Mt
10 GC
Vibrating Screen
--149.98x0.67= 99.9899.98 Mt
149.98x0.33 = 49.9949.99 Mt
Re-circulate to GC!
66.67% Undersize33.33% Oversize100% Efficiency
++
9th Pass: t = 9t = 9thth hour hourNew feed:New feed:
(100+49.99) (100+49.99) ==149.99149.99 Mt Mt
10 GC
Vibrating Screen
--133.33x0.67= 99.9999.99 Mt
149.99x0.33 = 50.0050.00 Mt
Re-circulate to GC!
66.67% Undersize33.33% Oversize100% Efficiency
++
10th Pass: t = 10t = 10thth hour hourNew feed:New feed:
(100+50.00) (100+50.00) ==150.00150.00 Mt Mt
10 GC
Vibrating Screen
--150.00x0.67= 100.00100.00 Mt
150.00x0.33 = 50.0050.00 Mt
Re-circulate to GC!
66.67% Undersize33.33% Oversize100% Efficiency
Total Feed
• Total feed is now computed as:
Mt
MtMt
501
50100
Load gCirculatin FeedFresh Feed Total
Total Feed
• May also be computed using the formula:
Where: F = Initial Feed
Ri = %Oversize of Crusher Product
%Eff = % Screen Efficiency
Rj = Ri / %Eff
jR-1
F
%
R-1
F Feed Total
Effi
Total Feed
• Using the formula, total feed may be computed as:
Mt
MtMt
150
67.0
100
9.03.0
1
100
%EffR
-1
F
R-1
F Feed Total
ij