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• Juan Pablo Apaza

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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

m³/h m -

Mineral froth corrections From Weir diagram

m

-

Volume flow rate with froth Qf = FVF * Qd FVF = 1.25 Qd = 454 m³/h Qf = 568 m³/h for the Froth Volume Factor FVF = 1.25 Find the Mineral froth height and

Specifiv gravity with froth SF = SP/FVF SP = FVF = SF =

1.15 1.25 0.92

-

Constant of system curve "C" Hstat + C*Q^2 H= C= (H - Hstat ) / Q^2 H= 18.3 m Hstat = 9.14 m Q= 454 m³/h C= 4.43E-05 Froht heigth Height for q = Qf Hstat + C*Qf^2 Hf = Hstat = 9.14 m C= 4.43E-05 Qf = 568 m³/h Hf = 23.43 m.p.c.

i w  SF  F w Si 

p  F 

mP VP m P  mair

efficiency corrections HRf = 0.95 ERf = 0.95 Required water head Hw = Hf = HRf =

Hf/HRf 23.43 0.95

Hw =

24.7

Efficiency on water From the selected pump curve, for Qf = 568 Hw = 24.7 find the efficiency on water Let the efficiency on water be Ew = 0.68

i w  SF  F w Si 

p 

mP VP

F 

m P  mair VF

mair  0

F 

m P 0 VF

F 

mP VF

VF  V p  FVF

F 

mP V p  FVF

F 

mP 1  V p FVF

F   p  F 

SF 

p

1 FVF

FVF

F w p

S F  FVF

w

1

 S F  p FVF w 1  1 SF  p  w FVF SF  S p SF 

1 FVF

Sp 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) Qf = m3/h 567.81 Sf = 0.920 Hf = 23.4 m.p.c. Ef = 0.646 P= 51.6 kW P= 69.15 hp

froth height and

Required water head Hw = 23.7 m = 79 ft

Security factor on power SFP = 1.2 considering fluctuations in duty due to variations in air content. Thus, the power requirement will be HPreq = SFP * HP SFP = HP = HPreq =

1.2 69.1 83.0

hp

m.w.c.

ed pump curve, for m³/h m.w.c.

y on water be

The next comercial size [3] HP = 100 hp

Pulp head Hf = 23.43 m = 75 ft (with froth) Pulp head Hp = 18.3 m = 60 ft (without froth Staic head Hstat = 9.14 m = 30 ft

w = 23.7 m

f = 23.43 m

p = 18.3 m

Hstat = 9.14 m = 30 ft

Efficiency on water Ew = 0.68 and pump speed

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

FVF = PAV = FVF =

1 / ( 1 - PAV) 20% 1.25

Qf = FVF = Qd = Qf =

FVF * Qd 1.25 454 568

m³/h m 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%

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

 m3    S P  Hf msc Q  h  P 3.672 h f %

kW 

Q: Flow rate without froth SP : Specifuc gravity of pulp without froth Hf = TDH : Total dynamid head of pulp with froth hf = 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

P= Qp = Sp = Hf = Ef = P= P=

Qp * Sp* Hf / (367 * Ef) m3/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) m3/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

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.

For a froth volume factor FVF = 1.25 HRf = 0.95 ERf = 0.95 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 = 1.2 HP = 67.5 HPreq = 81.0 hp The next comercial size [3] HP = 100 hp

Warman horizontal froth pump selection proc 1.- Determine type of froth Brittle Tenaciuos Medium 2.- Qs = De-aereated slurry flow (L/s) Use maximum reated design flow Check for maximum duty slurry flow

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 = Aereated froth flow Qf = 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 =

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) Qf = m3/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 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 (%). 8.- Slurry density Sf = Sp / FVF Sp = FVF = Sf = 9.- Calculate froth power Pf (kW) = 10.- Check power 11.- Select motor size with 20% margin

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) Qp = m3/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

Warman horizontal froth pump selection procedure 1.- Determine type of froth 1.1