Circulating Load Calculations

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!


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!


100% Efficiency

++


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!


100% Efficiency

++


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!


100% Efficiency

++


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!


100% Efficiency

++


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!


100% Efficiency

++


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!


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


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


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


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!


4th Pass: t = 4t = 4thth hour hour70% Undersize


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!




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!




10 GC

Vibrating Screen

++

--70+(49.79x0.7) –(149.79x0.033)

= 99.8699.86 Mt

Re-circulate to GC!


30+(49.79x0.3)+(149.79x0.033) = 49.9349.93 Mt



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!




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!




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!




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!


Wait now! Going back…

• 1st Pass → 11stst hour hour

100 Mt100 Mt


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!


++

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!


++


(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!


++


(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!


++


(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!


++


(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!


++


(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!


++


(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!


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

Circulating Load Calculations

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