pump. froth selection warman
TRANSCRIPT
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
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
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
Microsoft Editor de ecuaciones 3.0
Microsoft Editor de ecuaciones 3.0
Efficiency on waterEw = 0.68 and pump speedN = 640 rpm
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 %
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
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.
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 ]
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.
Rev. cjc. 28.06.2013
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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
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
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
Qf * Hf * Sf * 0.98 / EF
11.- Select motor size with 20% margin
Required water head Hw
Microsoft Editor de ecuaciones 3.0
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
Microsoft Editor de ecuaciones 3.0
( 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
Weir technical bulletin Nº 28. Ver. 3http://www.weirminerals.com/pdf/Technical%20Bulletin%2028v.2%20-%20082109.pdf
Kevin BurgesWarman Pump Thechnology Centre
ArtarmonAustralia
2.- HRf & ERf also include effects of fine solids
Kevin BurgesWarman Pump Thechnology Centre
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
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
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
Microsoft Editor de ecuaciones 3.0