Froth Pump Power Estimation According Weir [1]
Qp = H= SP = PAV = Hstat =
454 18.3 1.15 20% 9.14
FVF = PAV = FVF =
1 / ( 1 - PAV) 20% 1.25
m ³ /h m -
Mineral froth corrections From W eir diagram
m
-
Volume flow rate with froth Qf = FVF * Qd FVF = 1.25 Qd = 454 m ³ /h Qf = 568 m ³ /h for the Froth Volume Factor FVF = 1.25 Find the Mineral froth height
Specifiv gravity with froth SF = SP/FVF SP = FVF = SF =
1.15 1.25 0.92
-
Constant of system curve "C" H= C= H= Hstat = Q= C=
Hstat + C*Q^2 (H - Hstat ) / Q^2 18.3 m 9.14 m 454 m ³ /h 4.43E-05
Froht heigth Height for q = Qf Hstat + C*Qf^2 Hf = Hstat = C= Qf = Hf =
S i
i w
S F
F
9.14 m 4.43E-05 568 m ³ /h 23.43 m.p.c.
efficiency corrections HRf = 0.95 ERf = 0.95 Required water head Hw = Hf = HRf = Hw =
Hf/HRf 23.43 0.95 24.7
Efficiency on water From From the the sele select cted ed pump pump cur cur Qf = 568 Hw = 24.7 find the efficiency on water Let the efficiency on water b Ew = 0.68
w p
m P
F
m P mair
V P V F
mair 0 F
m P 0
F
m P
V F V F
V F V p FVF m P
F
F
F
p
F
S F
V p FVF m P
1
V p FVF 1
FVF
p
FVF F w p
S F FVF w
1
S F S F
p
FVF
w
1
p
1
w
FVF
S F S p S F
1
FVF S p
FVF
Pump efficiency on froth The pump efficiency on froth is Ef = ERf * Ew ERf = 0.95 Ew = 0.68 Ef = 0.646 Pump power P= Qf * Sf* Hf / (367 * Ef) 3 Qf = m /h 567.81 Sf = 0.920 Hf = 23.4 m.p.c. Ef = 0.646 P= 51.6 kW P= 69.15 hp
and
Security factor on power SFP = 1.2
Required water head Hw = 23.7 m = 79 ft
considering fluctuations in duty due to variations in air content.
Pulp head Hf
Thus, the power requirement will be HPreq = SFP * HP SFP = HP = HPreq =
1.2 69.1 83.0
hp
m.w.c. The next comercial size [3] HP = 100 hp e, for m³/h m.w.c.
= 23.43 = 75 ft
(with froth) Pulp head Hp
= 18.3 m = 60 ft
(without froth Staic head Hstat = 9.14 = 30 ft
Efficiency on water Ew = 0.68 and pump speed
m
Froth pump selection (SI) [1] Calculation of aereated flow "Qf" Slurry design flow Slurry design head (Note 1) Specific gravity of slurry Percentage of air volume Static height
Qd = H= SP = PAV = Hstat =
454 18.3 1.15 20% 9.14
m³/h m -
FVF = PAV = FVF =
1 / ( 1 - PAV) 20% 1.25
Qf = FVF = Qd = Qf =
FVF * Qd 1.25 454 568
m
Flow volume factor
Uncompressed (aereated) flow Froth flow
-
m³/h m³/h
Froth pump selection Pump selection Select froth pump such that: Froth duty point is to the left of BEP line and NPSHr < 3.7 m Go 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/s and static head low to mantain total head below 30 m. The design slurry duty point corresponds to Qd = 454 m³/h Hd = 18.3 m The BEP line for the selected pump is the line for
h =
74.5 %
Note 1. Calculate de design head of the slurry by the method defined in the Proyect Design Criteria. 0.22712471
Plot system curve with static head Hstat = 9.14 m and design flow and head Qd = 454 Hd = 18.3
m³/h m
System curve calculation H= Hstat + C * Q² C= (Hd-Hstat)/Qd²
30
2000 60
ft
gpm ft
Hd = Hstat = Qd = C=
18 m 9.14 m 454 m³/h 0.000044
Froth height calculated from system curve, for froth flow rate Qf Hf = Hstat + C*Qf^2 Hstat = 9.14 m C= 0.000044 Qf = 568 m³/h Hf = 23.4 m.p.c. (This is the calculated value)
System duty point at froth flow Qf = 568 m³/h The estimated value from graphic is Hf = 22.86 m This estimated value will be adopted in the further calculation to mantain the Warman values.
Hf: froth height calculated from system curve, 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 / Hw with Hd : Head on froth Hw : Head on water
Froth efficiency corrección "ERf" ERf = Ef / Ew with Ed : Efficiency on froth Ew : Efficiency on water Note Only QU1 flow inducer impellers are used now
From figures, determine the correction factors
77
2500
75
ft
gpm
ft
For FVF = one obtains HRF = ERF =
1.25 0.95 0.95
Required water head From HRf = Hf / Hw The weater head is Hw = Hf / HRf with Hf = 22.86 HRf = 0.95 Hw = 24
m m
The operation point in the pump diagram is defined by Qf = 568 m³/h Hw = 24 m or Qf = 2500 gpm Hw = 79 ft The required speed and efficiency on water at this condition is read from the diagram
N= Ew =
640 68.0%
rpm
Froth height Hf = Hf =
75 22.9
ft.p.c. m.p.c.
Height on water Hw = Hw =
79 24.1
ft.w.c. m.w.c.
Selected pump Qf = Hw = N= Ew =
568 24.1 640 68
m³/h m.w.c. rpm %
Slurry efficiency
Power
From ERf = Ef / Ew The slurry efficiency is Ef = ERf * Ew with ERf = 0.95 Ew = 68.0% Ef =
64.6%
m3 S P Hf msc h 3.672 h f %
Q P
kW
Q: Flow rate without froth SP : Specifuc gravity of pulp without froth Hf = TDH : hf =
Total dynamid head of pulp with froth
Ef : Pump efficiency on pulp with froth
Ef = ERf * Ew Erf : Correction factor from figure Ew : Water equivalent efficiency from pump diagram, for Q= 454 m³/h Hf = 22.9 msc Qp: slurry flow rate witout froth Sp: specific gracity witout froth Hf: froth height calculated from system curve, for froth flow rate Qf (page 2) Hf = 22.9 m.p.c. Ef: efficiency on slurry with froth Ef = ERf * Ew ERf: froth correction factor Ew: efficiency on water, from pump diagram, @ Qf and Hw (page 4) Hw = Hf / HRf HRf: froth correction factor
Pump power [1] Pump power Pulp flow rate without froth Pulp specific gravity without froth Heigth from system curve, for the pulp flow rate with froth (Qf) Efficiency oh froth Ef = Ew*ERf
P= Qp = Sp = Hf = Ef = P= P=
Qp * Sp* Hf / (367 * Ef) 3 m /h 454.25 1.150 22.9 m.p.c. 0.646 50.3 kW 67.46 hp
P= Qp = Sp = Hf =
Qp * Sp* Hf / (367 * Ef) 3 m /h 454.25 1.150 22.9 m.p.c.
Ef = P= P=
0.646 50.3 67.46
kW hp
(without froth) (without froth) (syst. c.@Qf) (with froth)
Froth pump selection, according Weir In this example, Qp = Hp = Hstat = FVF = Sp =
454 18.3 9.14 1.25 1.150
m³/h m.p.c. m -
1.- Calculate de pulp system pressure loss "Hp" for maximum flow "Qp". For the froht pump selection, this flow and the heigt are input data. Qp = 454 m³/h Hp = 18.3 m.p.c.
5.- Froth height calculated from system curve, for froth flow rate Qf Hf = Hstat + C*Qf^2 Hstat = 9.14 m C= 0.000044 Qf = 568 m³/h Hf = 23.4 m.p.c. (Se note 1) 6.- Froth correction factors from Weir figure
2.- Known points of system curve 2a.- Zero flow point Q= 0 Hstat = 9.14
m³/h m For a froth volume factor FVF = 1.25 HRf = 0.95 ERf = 0.95
2b.- Duty point without froth Design pulp flow rate (Qp = Qd) Qp = 454 m³/h Design pulp height (Hp = Hd) Hp = 18.3 m.p.c.
7.- Required water head Hw
3.- Constant of system curve Hp = Hstat + C * Q² C= (Hp-Hstat)/Qd² Hp = 18 m Hstat = 9.14 m Qp = 454 m³/h C= 0.000044
Hw = Hf / HRF Head on froth Hf = 23.4 Head correction for height HRf = 0.95 Water head Hw = 24.7
4.- Froth flow Qf = FVF = Qp = Qf =
8.- Efficiency on water From selected pump curve, find the eficiency on water @
FVF * Qp 1.25 454 568
m³/h m³/h
m.p.c.
m.w.c.
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
1
2
3
4
5 Security factor on power SFP = 1.2 considering fluctuations in duty due to variations in air content. REf. 2 Thus, the power requirement will be HPreq = SFP * HP SFP = HP =
1.2 67.5
HPreq =
81.0
Warman horiz 1.- Determine
hp
The next comercial size [3] HP = 100 hp
Brittle Tenaciuos Medium 2.- Qs = De-a Use maximu Check for ma
8.- Slurry density Sf = Sm / FVF 9.- Calculate froth power Pf (kW) = Qf * Hf * Sf * 0.98 / EF Froth flow Qf = FVF * Qs Slurry density Sf = Sp / FVF
(L/s)
3.- Qf = Aere Qf = 4.- Calculate at aereated fl solids in slurr Keep dischat 5.- Hw =
Qf * Sf = Qf * Sf =
FVF * Qs * Sp / FVF Qs * Sp
Pf (kW) =
Qs * Hf * Sp* 0.98 / EF
Pump power [2] P= Qp * Sp* Hf / (367 * Ef) P= Qf/FVF * Sf*FVF* Hf / (367 * Ef) P= Qf * Sf* Hf / (367 * Ef) 3 Qf = m /h 567.81 Sf = 0.920 Hf = 22.9 m.p.c. Ef = 0.646 P= 50.3 kW P= 67.46 hp
6.- Select frot to the left of B NPSHreq >=
7.- At the duty speed Nf /rpm Ew (%). 8.- Slurry den Sp = FVF = Sf = 9.- Calculate f Pf (kW) = 10.- Check po 11.- Select m
Qf = 568 Hw = 24.7 For the selected pump Ew = 0.68
m³/h m.w.c.
9.- Efficiency on froth Ef = ERf * Ew ERf = 0.95 Ew = 0.68 Ef = 0.646 10.- Pump velocity From selected pump curve, find the pump velocity @ Qf = 568 m³/h Hw = 24.7 m.w.c. For the selected pump N= 640 rpm 11. Power [1] P= Qp * Sp* Hf / (367 * Ef) 3 Qp = m /h 454.25 Sp = 1.150 Hf = 23.4 m.p.c. (Note 1) Ef = 0.646 P= 51.6 kW P= 69.15 hp 12.- Motor Margin for the motor selection marg = 0.2 Motor power with margin Pmarg = P * (1 + marg) P= 69.15 hp marg = 0.2 Pmarg = 83.0 hp 13.- Selected motor From sheet Ref. 3 Motors table Pmotor = 100 hp
ontal froth pump selection procedure type of froth 1.1 <0 FVF <= 1.25 1.5 <0 FVF <= 1.8 1.25 <0 FVF <= 1.5 ereated slurry flow (L/s) reated design flow imum duty slurry flow ated froth flow FVF * Qs (L/s) froth system head Hf (m) w (Qf) for concentration of , disregarding froth. e pipe dismeters large Hf/HRf pump with duty point is EP. Q >= 25% QBEP .5 m
point, select the pump ) and the water efficiency Ef = Ew * ERf ity Sf = Sp / FVF 1.15 1.25 0.92 roth power Qf * Hf * Sf * 0.98 / EF wer tor size with 20% margin
Required water Hw =
[1]
SG p FVF 3960 E f
Q f H f HP
SG f HP
SG p
FVF Q f H f SG f 3960 E f
head Hw Hf / HRF
HP = Sf = Sp = FVF = Sf = Qf = Hf = Sf = Ef = HP = P= Qf = Hf = Sf = Ef = P= P=
( Qf * Hf * Sf ) / (3960 * Ef) Sp/FVF 1.15 1.25 0.92 2500 75 0.92 0.646 67.43
gpm ft BHP
Qf * Hf *Sf* / (367 * Ef) 568 m³/h 22.9 m.p.c. 0.920 0.646 50.3 kW 67.46 hp The used Hf-value is from the Weir example, not the calculated value
Weir technical bulletin Nº 28. Ver. 3 http://www.weirminerals.com/pdf/Technical%20Bulletin%2028v.2%20-%20082109.pdf
Kevin Burges Warman Pum Artarmon Australia
2.- HRf & ERf
p Thechnology Centre
also include effects of fine solids
(Wath about heterogeneous flows?)
REf. 2 Warman horizontal froth pump selection procedure 1.- Determine type of froth Brittle 1.1 <0 FVF <= 1.25 Tenaciuos 1.5 <0 FVF <= 1.8 Medium 1.25 <0 FVF <= 1.5 2.- Qs = De-aereated slurry flow (L/s)
Use maximum reated design flow Check for maximum duty slurry flow 3.- Qf = Aereated froth flow Qf = FVF * Qs (L/s) 4.- Calculated froth system head Hf (m) at aereated flow (Qf) for concentration of solids in slurry, disregarding froth. Keep dischatge pipe dismeters large 5.- Hw =
Hf/HRf
6.- Select froth pump with duty point is to the left of BEP. Q >= 25% QBEP NPSHreq >= 3.5 m
7.- At the duty point, select the pump speed Nf /rpm) and the water efficiency Ew (%). Ef = Ew * ERf 8.- Slurry density Sf = Sm / FVF 9.- Calculate froth power Pf (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
[1]
http://www.calgarypumpsymposium.ca/archives/Presentations/2007/Froth-Presentation.pdf http://www.calgarypumpsymposium.ca/Froth-Presentation.pdf
[2]
Warman Technical Bulletin No 28, version 2 http://www.weirminerals.com/pdf/Technical%20Bulletin%2028v.2%20-%20082109.pdf
[3]
Standard motors http://oee.nrcan.gc.ca/regulations/products/14297
