pump. froth selection warman

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Froth Pump Power Estimation According Weir [1] Qp = 454 m³/h Mineral froth correcti H = 18.3 m From Weir diagram 1.15 - PAV = 20% 9.14 m FVF = 1 / ( 1 - PAV) PAV = 20% FVF = 1.25 - Volume flow rate with froth Qf = FVF * Qd FVF = 1.25 - Qd = 454 m³/h Qf = 568 m³/h for the Froth Volume F Specifiv gravity with froth FVF = 1.25 Find the Mineral froth 1.15 efficiency corrections FVF = 1.25 HRf = 0.95 0.92 - ERf = 0.95 Constant of system curve "C" Required water head H = Hw = Hf/HRf C = (H - Hstat ) / Q^2 Hf = 23.43 H = 18.3 m HRf = 0.95 9.14 m Hw = 24.7 Q = 454 m³/h C = 4.43E-05 Efficiency on water From the selected pump Froht heigth Qf = 568 Height for q = Qf Hw = 24.7 Hf = find the efficiency on 9.14 m Let the efficiency on C = 4.43E-05 Ew = 0.68 Qf = 568 m³/h Hf = 23.43 m.p.c. SP = Hstat = SF = SP/FVF SP = SF = Hstat + C*Q^2 Hstat = Hstat + C*Qf^2 Hstat = S i = ρ i ρ w S F = ρ F ρ w ρ p = m P V

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Page 1: Pump. Froth Selection Warman

Froth Pump Power Estimation According Weir [1]

Qp = 454 m³/h Mineral froth correctionsH = 18.3 m From Weir diagram

1.15 -PAV = 20%

9.14 m

FVF = 1 / ( 1 - PAV)PAV = 20%

FVF = 1.25 -

Volume flow rate with frothQf = FVF * Qd

FVF = 1.25 -Qd = 454 m³/hQf = 568 m³/h

for the Froth Volume FactorSpecifiv gravity with froth FVF = 1.25 -

Find the Mineral froth height and

1.15 efficiency corrections FVF = 1.25 HRf = 0.95

0.92 - ERf = 0.95

Constant of system curve "C" Required water head

H = Hw = Hf/HRfC = (H - Hstat ) / Q^2 Hf = 23.43

H = 18.3 m HRf = 0.95

9.14 m Hw = 24.7 m.w.c.Q = 454 m³/hC = 4.43E-05 Efficiency on water

From the selected pump curve, forFroht heigth Qf = 568 m³/hHeight for q = Qf Hw = 24.7 m.w.c.

Hf = find the efficiency on water

9.14 m Let the efficiency on water beC = 4.43E-05 Ew = 0.68Qf = 568 m³/hHf = 23.43 m.p.c.

SP =

Hstat =

SF = SP/FVF

SP =

SF =

Hstat + C*Q^2

Hstat =

Hstat + C*Qf^2

Hstat =

Si=ρiρw

SF=ρFρw

ρp=mPV P

ρF=mP +mairV F

mair≈0

ρF=mP +0V F

ρF=mPV F

V F=V p⋅FVF

ρF=mPV p⋅FVF

ρF=mPV p

⋅1FVF

ρF=ρp⋅1FVF

ρF=ρpFVF

SF=ρFρw

SF=

ρ pFVFρw

SF=ρ pρw

1FVF1

SF=ρ pρw

1FVF

SF=S p1FVF

SF=S pFVF

Page 2: Pump. Froth Selection Warman

Si=ρiρw

SF=ρFρw

ρp=mPV P

ρF=mP +mairV F

mair≈0

ρF=mP +0V F

ρF=mPV F

V F=V p⋅FVF

ρF=mPV p⋅FVF

ρF=mPV p

⋅1FVF

ρF=ρp⋅1FVF

ρF=ρpFVF

SF=ρFρw

SF=

ρ pFVFρw

SF=ρ pρw

1FVF1

SF=ρ pρw

1FVF

SF=S p1FVF

SF=S pFVF

Page 3: Pump. Froth Selection Warman

Pump efficiency on frothThe pump efficiency on froth is

Ef = ERf * EwERf = 0.95

Ew = 0.68Ef = 0.646

Pump powerP = Qf * Sf* Hf / (367 * Ef)Qf = 567.81Sf = 0.920 - Hf = 23.4 m.p.c.Ef = 0.646 - P = 51.6 kWP = 69.15 hp

Security factor on power

SFP = 1.2

considering fluctuations in duty due to variations in air content.

Thus, the power requirement will be

SFP * HP

SFP = 1.2HP = 69.1

83.0 hp

HP = 100 hp

m3/h

HPreq =

HPreq =

The next comercial size [3]

Staic head Hstat = 9.14 m = 30 ft

Pulp head Hp = 18.3 m = 60 ft(without froth

Pulp head Hf = 23.43 m = 75 ft(with froth)

Required water head Hw = 23.7 m = 79 ft

Page 4: Pump. Froth Selection Warman

Microsoft Editor de ecuaciones 3.0

Microsoft Editor de ecuaciones 3.0

Efficiency on waterEw = 0.68 and pump speedN = 640 rpm

Page 5: Pump. Froth Selection Warman

Calculation of aereated flow "Qf"

Slurry design flow Qd = 454 m³/hSlurry design head (Note 1) H = 18.3 m

Specific gravity of slurry 1.15 -Percentage of air volume PAV = 20% Static height Hstat = 9.14 m

Flow volume factorFVF = 1 / ( 1 - PAV)PAV = 20%FVF = 1.25 -

Uncompressed (aereated) flowFroth flow Qf = FVF * Qd

FVF = 1.25 -Qd = 454 m³/hQf = 568 m³/h

Froth pump selection

Pump selectionSelect froth pump such that:Froth duty point is to the left of BEP lineand NPSHr < 3.7 mGo to the next size pump if in doubt. Add the froth system curve to the selected pump curve.Keep discharge pipe diameters large,pipe velocities less than 2 to 2.5 m/sand static head low to mantain totalhead below 30 m.

The design slurry duty point corresponds toQd = 454 m³/hHd = 18.3 m

Note 1. Calculate de design head of the slurry by themethod defined in the Proyect Design Criteria.

0.22712471

Plot system curve with static headHstat = 9.14 m 30 ft

and design flow and headQd = 454 m³/h 2000 gpmHd = 18.3 m 60 ft

System curve calculation

Froth pump selection (SI) [1]

SP =

The BEP line for the selected pump is the line for h = 74.5 %

Page 6: Pump. Froth Selection Warman

H = Hstat + C * Q²C = (Hd-Hstat)/Qd²

Hd = 18 mHstat = 9.14 mQd = 454 m³/hC = 0.000044

Froth height calculated from systemcurve, for froth flow rate Qf

Hf = Hstat + C*Qf^2Hstat = 9.14 m

C = 0.000044Qf = 568 m³/hHf = 23.4 m.p.c. 77 ft

(This is the calculated value)

System duty point at froth flowQf = 568 m³/h 2500 gpm

The estimated value from graphic isHf = 22.86 m 75 ft

This estimated value will be adopted inthe further calculation to mantain the Warman values.

Hf: froth height calculated from systemcurve, for froth flow rate Qf (page 2)

Hf = 23.4 m.p.c.(this is not the estimated Warman value)

Mineral froth head and eficiency corrections

Froth head corrección "HRf"

HRf = Hf / HwwithHd : Head on frothHw : Head on water

Froth efficiency corrección "ERf"

ERf = Ef / EwwithEd : Efficiency on frothEw : Efficiency on water

NoteOnly QU1 flow inducer impellersare used now

Page 7: Pump. Froth Selection Warman

From figures, determine the correction factors

ForFVF = 1.25

one obtainsHRF = 0.95ERF = 0.95

Required water head

FromHRf = Hf / Hw

The weater head isHw = Hf / HRf

withHf = 22.86 m

HRf = 0.95Hw = 24 m

The operation point in the pump diagram is defined by

Qf = 568 m³/hHw = 24 m

orQf = 2500 gpmHw = 79 ft

The required speed and efficiency on water

at this condition is read from the diagramN = 640 rpm

Ew = 68.0%

Froth heightHf = 75 ft.p.c.Hf = 22.9 m.p.c.

Height on waterHw = 79 ft.w.c.Hw = 24.1 m.w.c.

Page 8: Pump. Froth Selection Warman

Selected pumpQf = 568 m³/hHw = 24.1 m.w.c.N = 640 rpm

Ew = 68 %

Slurry efficiency Power

FromERf = Ef / Ew

The slurry efficiency isEf = ERf * Ew

withERf = 0.95 Q: Flow rate without froth

Ew = 68.0%

Ef = 64.6% Hf = TDH : Total dynamid head of pulp with froth

Ef = ERf * EwErf : Correction factor from figureEw : Water equivalent efficiencyfrom pump diagram, for

Q = 454 m³/hHf = 22.9 msc

Qp: slurry flow rate witout frothSp: specific gracity witout frothHf: froth height calculated from system P = Qp * Sp* Hf / (367 * Ef)

curve, for froth flow rate Qf (page 2) Qp = 454.25 (without froth)

Hf = 22.9 m.p.c. Sp = 1.150 - (without froth)

Ef: efficiency on slurry with froth Hf = 22.9 m.p.c. (syst. c.@Qf)

Ef = ERf * Ew Ef = 0.646 - (with froth)

ERf: froth correction factor P = 50.3 kWEw: efficiency on water, from P = 67.46 hppump diagram, @ Qf and Hw(page 4)

Hw = Hf / HRfHRf: froth correction factor

Pump power [1]Pump power P = Qp * Sp* Hf / (367 * Ef)

Pulp flow rate without froth Qp = 454.25Pulp specific gravity without froth Sp = 1.150 - Heigth from system curve, for the Hf = 22.9 m.p.c.pulp flow rate with froth (Qf)Efficiency oh froth Ef = Ew*ERf Ef = 0.646 -

P = 50.3 kW

SP : Specifuc gravity of pulp without froth

hf = Ef : Pump efficiency on pulp with froth

m3/h

m3/h

P=Q [m3h ]⋅SP⋅Hf [msc ]

3 .672⋅η f [% ][kW ]

Page 9: Pump. Froth Selection Warman

P = 67.46 hp

Froth pump selection, according Weir 5.- Froth height calculated from systemcurve, for froth flow rate Qf

In this example, Hf = Hstat + C*Qf^2Qp = 454 m³/h Hstat = 9.14 mHp = 18.3 m.p.c. C = 0.000044

Hstat = 9.14 m Qf = 568 m³/hFVF = 1.25 - Hf = 23.4 m.p.c.Sp = 1.150 - (Se note 1)

1.- Calculate de pulp system pressure 6.- Froth correction factors fromloss "Hp" for maximum flow "Qp". Weir figureFor the froht pump selection, this flow

and the heigt are input data.Qp = 454 m³/hHp = 18.3 m.p.c.

2.- Known points of system curve

2a.- Zero flow pointQ = 0 m³/h

Hstat = 9.14 m

For a froth volume factor2b.- Duty point without froth FVF = 1.25Design pulp flow rate (Qp = Qd) HRf = 0.95

Qp = 454 m³/h ERf = 0.95Design pulp height (Hp = Hd)

Hp = 18.3 m.p.c. 7.- Required water head Hw

3.- Constant of system curve Hw = Hf / HRFHp = Hstat + C * Q² Head on frothC = (Hp-Hstat)/Qd² Hf = 23.4 m.p.c.

Hp = 18 m Head correction for heightHstat = 9.14 m HRf = 0.95Qp = 454 m³/h Water headC = 0.000044 Hw = 24.7 m.w.c.

4.- Froth flow 8.- Efficiency on waterQf = FVF * Qp From selected pump curve, find the

FVF = 1.25 - eficiency on water @Qp = 454 m³/hQf = 568 m³/h Note 1. This is thecalculated value. The

Weir estimated value from system curve is Hf = 22.86 m.p.c.

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Rev. cjc. 28.06.2013

1

2

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5

Security factor on powerSFP = 1.2

considering fluctuations in duty due to variations in air content.

REf. 2Thus, the power requirement will be

SFP * HP Warman horizontal froth pump selection procedureSFP = 1.2

HP = 67.5 1.- Determine type of froth

81.0 hp Brittle 1.1 <0 FVF <= 1.25

Tenaciuos 1.5 <0 FVF <= 1.8Medium 1.25 <0 FVF <= 1.5

HP = 100 hp2.- Qs = De-aereated slurry flow (L/s)Use maximum reated design flowCheck for maximum duty slurry flow

8.- Slurry density Sf = Sm / FVF3.- Qf = Aereated froth flow

9.- Calculate froth power Qf = FVF * QsPf (kW) = Qf * Hf * Sf * 0.98 / EF

4.- Calculated froth system head Hf (m)Froth flow at aereated flow (Qf) for concentration of

Qf = FVF * Qs (L/s) solids in slurry, disregarding froth.Slurry density Keep dischatge pipe dismeters large

Sf = Sp / FVF5.- Hw = Hf/HRf

Qf * Sf = FVF * Qs * Sp / FVFQf * Sf = Qs * Sp 6.- Select froth pump with duty point is

to the left of BEP. Q >= 25% QBEPPf (kW) = Qs * Hf * Sp* 0.98 / EF NPSHreq >= 3.5 m

7.- At the duty point, select the pump Pump power [2] speed Nf /rpm) and the water efficiency

P = Qp * Sp* Hf / (367 * Ef) Ew (%). Ef =P = Qf/FVF * Sf*FVF* Hf / (367 * Ef)

P = Qf * Sf* Hf / (367 * Ef) 8.- Slurry density Sf = Sp / FVFQf = 567.81 Sp = 1.15Sf = 0.920 - FVF = 1.25Hf = 22.9 m.p.c. Sf = 0.92Ef = 0.646 - P = 50.3 kW 9.- Calculate froth power

HPreq =

HPreq =

The next comercial size [3]

m3/h

Microsoft Editor de ecuaciones 3.0

Page 14: Pump. Froth Selection Warman

P = 67.46 hp Pf (kW) = Qf * Hf * Sf * 0.98 / EF

10.- Check power

11.- Select motor size with 20% margin

Qf = 568 m³/hHw = 24.7 m.w.c.

For the selected pumpEw = 0.68

9.- Efficiency on frothEf = ERf * Ew

ERf = 0.95Ew = 0.68 Ef = 0.646

10.- Pump velocityFrom selected pump curve, find thepump velocity @

Qf = 568 m³/hHw = 24.7 m.w.c.

For the selected pump N = 640 rpm

11. Power [1]P = Qp * Sp* Hf / (367 * Ef)Qp = 454.25Sp = 1.150 - Hf = 23.4 m.p.c. (Note 1)Ef = 0.646 - P = 51.6 kWP = 69.15 hp

12.- MotorMargin for the motor selection

marg = 0.2Motor power with margin

Pmarg = P * (1 + marg)P = 69.15 hp

marg = 0.2Pmarg = 83.0 hp

13.- Selected motorFrom sheet Ref. 3 Motors table

Pmotor = 100 hp

Weir estimated value from system curve

m3/h

Page 15: Pump. Froth Selection Warman

Warman horizontal froth pump selection procedure

1.1 <0 FVF <= 1.25

1.5 <0 FVF <= 1.81.25 <0 FVF <= 1.5

2.- Qs = De-aereated slurry flow (L/s)Use maximum reated design flowCheck for maximum duty slurry flow

3.- Qf = Aereated froth flow(L/s)

4.- Calculated froth system head Hf (m)at aereated flow (Qf) for concentration ofsolids in slurry, disregarding froth.Keep dischatge pipe dismeters large

6.- Select froth pump with duty point isto the left of BEP. Q >= 25% QBEP

7.- At the duty point, select the pump speed Nf /rpm) and the water efficiency

Ew * ERf

8.- Slurry density Sf = Sp / FVF

Page 16: Pump. Froth Selection Warman

Qf * Hf * Sf * 0.98 / EF

11.- Select motor size with 20% margin

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Required water head Hw

Microsoft Editor de ecuaciones 3.0

Page 20: Pump. Froth Selection Warman

Hw = Hf / HRF

[1]HP =Sf =Sp =

FVF =Sf =

Qf =Hf =Sf =Ef =HP =

P = Qf =Hf =Sf =Ef =P =P =

The used Hf-value is from the Weir example, not the calculated value

Microsoft Editor de ecuaciones 3.0

HP=Q f⋅H f⋅( SG p

FVF )3960⋅Ef

SGf=SGpFVF

HP=Q f⋅H f⋅SGf3960⋅Ef

Page 21: Pump. Froth Selection Warman

Microsoft Editor de ecuaciones 3.0

Page 22: Pump. Froth Selection Warman

( Qf * Hf * Sf ) / (3960 * Ef)Sp/FVF

1.151.250.92

2500 gpm75 ft

0.92 -0.646 -67.43 BHP

Qf * Hf *Sf* / (367 * Ef)568 m³/h22.9 m.p.c.

0.920 - 0.646 - 50.3 kW

67.46 hpThe used Hf-value is from the Weir example, not the calculated value

Microsoft Editor de ecuaciones 3.0

Page 23: Pump. Froth Selection Warman

Weir technical bulletin Nº 28. Ver. 3http://www.weirminerals.com/pdf/Technical%20Bulletin%2028v.2%20-%20082109.pdf

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Kevin BurgesWarman Pump Thechnology Centre

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ArtarmonAustralia

2.- HRf & ERf also include effects of fine solids

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Kevin BurgesWarman Pump Thechnology Centre

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2.- HRf & ERf also include effects of fine solids (Wath about heterogeneous flows?)

REf. 2

Warman horizontal froth pump selection procedure

1.- Determine type of frothBrittle 1.1 <0 FVF <= 1.25Tenaciuos 1.5 <0 FVF <= 1.8Medium 1.25 <0 FVF <= 1.5

2.- Qs = De-aereated slurry flow (L/s)Use maximum reated design flowCheck for maximum duty slurry flow

3.- Qf = Aereated froth flowQf = FVF * Qs (L/s)

4.- Calculated froth system head Hf (m)at aereated flow (Qf) for concentration ofsolids in slurry, disregarding froth.Keep dischatge pipe dismeters large

Page 34: Pump. Froth Selection Warman

5.- Hw = Hf/HRf

6.- Select froth pump with duty point isto the left of BEP. Q >= 25% QBEPNPSHreq >= 3.5 m

7.- At the duty point, select the pump speed Nf /rpm) and the water efficiencyEw (%). Ef = Ew * ERf

8.- Slurry density Sf = Sm / FVF

9.- Calculate froth powerPf (kW) = Qf * Hf * Sf * 0.98 / EF

10.- Check power

11.- Select motor size with 20% margin

Vertical pump type

Use mainly for brittle type frothd eg copper

Use 2.0 <= FVF <= 2.5

Select a duty flowrate 30% to 85% of maximum flow shown on vertical froth pump curve

Use HR = ER = 0.9 (Conical hooper)

Select head and spedd as for horizontal froth pump

Ensure a good vortex in the hopper

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http://www.calgarypumpsymposium.ca/archives/Presentations/2007/Froth-Presentation.pdf[1]

[2] Warman Technical Bulletin No 28, version 2

[3] Standard motorshttp://oee.nrcan.gc.ca/regulations/products/14297

http://www.calgarypumpsymposium.ca/Froth-Presentation.pdf

http://www.weirminerals.com/pdf/Technical%20Bulletin%2028v.2%20-%20082109.pdf

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Microsoft Editor de ecuaciones 3.0