Froth Pump Power Estimation According Weir [1]
Froth Pump Power Estimation According Weir [1]
Q
Qp
p
=
=
4
45
54
4
m
m³³//h
h
M
Miin
ne
erra
al
l
ffrro
otth
h
c
co
orrrre
ec
cttiio
on
ns
s
H
H
=
=
1
18
8..3
3
m
m
F
Frro
om
m
We
W
eiir
r
d
diia
ag
grra
am
m
S
S
PP=
=
1
1..1
15
5
--P
PA
AV
V
=
=
2
20
0%
%
H
H
statstat=
=
9
9..1
14
4
m
m
F
FV
VF
F =
=
1
1 /
/ (
( 1
1 -
- P
PA
AV
V))
P
PA
AV
V
=
=
2
20
0%
%
F
FV
VF
F
=
=
1
1..2
25
5
--Volume flow rate with froth
Volume flow rate with froth
Q
Qf
f =
=
F
FV
VF
F *
* Q
Qd
d
F
FV
VF
F
=
=
1
1..2
25
5
--Q
Qd
d
=
=
4
45
54
4
m
m³³//h
h
Q
Qf
f
=
=
5
56
68
8
m
m³³//h
h
for the Froth Volume Factor
for the Froth Volume Factor
S
Sp
pe
ec
ciiffiiv
v
g
grra
av
viitty
y
w
wiitth
h
ffrro
otth
h
F
FV
VF
F
=
=
1
1..2
25
5
S
S
FF=
=
S
S
PP/FVF
/FVF
Find the Mineral froth height
Find the Mineral froth height
S
S
PP=
=
1
1..1
15
5
e
effffiic
ciie
en
nc
cy
y
c
co
orrrre
ec
cttiio
on
ns
s
F
FV
VF
F
=
=
1
1..2
25
5
H
HR
Rf
f
=
=
0
0..9
95
5
S
S
FF=
=
0
0..9
92
2
--
E
ER
Rf
f
=
=
0
0..9
95
5
C
Co
on
ns
stta
an
nt
t o
of
f s
sy
ys
stte
em
m c
cu
urrv
ve
e ""C
C""
R
Re
eq
qu
uiirre
ed
d w
wa
atte
er
r h
he
ea
ad
d
H =
H =
H
H
statstat+ C*Q^2
+ C*Q^2
H
Hw
w =
=
H
Hff//H
HR
Rf
f
C
C
=
=
((H
H
-
-
H
Hs
stta
at
t
)
)
/
/
Q
Q^^2
2
H
Hf
f
=
=
2
23
3..4
43
3
H
H
=
=
1
18
8..3
3
m
m
H
HR
Rf
f
=
=
0
0..9
95
5
H
H
statstat=
=
9
9..1
14
4
m
m
H
Hw
w
=
=
2
24
4..7
7
Q
Q
=
=
4
45
54
4
m
m³³//h
h
C
C
=
=
4
4..4
43
3E
E--0
05
5
E
Effffiic
ciie
en
nc
cy
y
o
on
n
w
wa
atte
er
r
Fr
From t
om the
he se
sele
lect
cted
ed pu
pump c
mp cur
ur
F
Frro
oh
ht
t
h
he
eiig
gtth
h
Q
Qf
f
=
=
5
56
68
8
H
He
eiig
gh
ht
t
ffo
or
r
q
q
=
=
Q
Qff
H
Hw
w
=
=
2
24
4..7
7
Hf =
Hf =
H
H
statstat+ C*Qf^2
+ C*Qf^2
find the efficiency on water
find the efficiency on water
H
H
statstat=
=
9
9..1
14
4
m
m
L
Le
et
t tth
he
e
e
effffiic
ciie
en
nc
cy
y
o
on
n
w
wa
atte
er
r b
b
C
C
=
=
4
4..4
43
3E
E--0
05
5
E
Ew
w
=
=
0
0..6
68
8
Q
Qf
f
=
=
5
56
68
8
m
m³³//h
h
H
Hf
f =
=
2
23
3..4
43
3
m
m..p
p..c
c..
S S S S F F F F w w ii ii
FVF FVF S S S S FVF FVF S S S S FVF FVF S S FVF FVF S S FVF FVF S S S S FVF FVF FVF FVF FVF FVF V V m m FVF FVF V V m m FVF FVF V V V V V V m m V V m m m m V V m m m m V V m m p p F F p p F F w w p p F F w w p p F F w w p p F F w w F F F F p p F F p p F F p p P P F F p p P P F F p p F F F F P P F F F F P P F F air air F F air air P P F F P P P P p p w w
1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 Pump efficiency on froth
Pump efficiency on froth
The pump efficiency on froth is
The pump efficiency on froth is
E
Ef
f =
=
E
ER
Rf
f *
* E
Ew
w
E
ER
Rf
f
=
=
0
0..9
95
5
E
Ew
w
=
=
0
0..6
68
8
E
Ef
f
=
=
0
0..6
64
46
6
Pump power
Pump power
P
P
=
=
Qf
Qf
*
*
Sf*
Sf*
Hf
Hf
/
/
(367
(367
*
*
Ef)
Ef)
Qf =
Qf =
567.81
567.81
m
m
33/h
/h
Sf =
Sf =
0
0..9
92
20
0
--Hf =
Hf =
2
23
3..4
4
m
m..p
p..c
c..
Ef =
Ef =
0
0..6
64
46
6
--P =
P =
5
51
1..6
6
k
kW
W
P =
P =
6
69
9..1
15
5
h
hp
p
- -
Se
S
ec
cu
urriitty
y
ffa
ac
ctto
or
r
o
on
n
p
po
ow
we
er
r
a
an
nd
d
S
SF
FP
P =
=
1
1..2
2
considering fluctuations in duty due to
considering fluctuations in duty due to
variations in air content.
variations in air content.
Thus, the power requirement will be
Thus, the power requirement will be
HP
HP
reqreq=
=
SFP * HP
SFP * HP
S
SF
FP
P
=
=
1
1..2
2
H
HP
P
=
=
6
69
9..1
1
HP
HP
reqreq=
=
8
83
3..0
0
h
hp
p
m.w.c.
m.w.c.
The
The n
next comercial size [3]
ext comercial size [3]
H
HP
P
=
=
1
10
00
0
h
hp
p
e,
e, for
for
m³/h
m³/h
m.w.c.
m.w.c.
Staic head
Staic head Hstat =
Hstat = 9.14
9.14
= 30 ft
= 30 ft
Pulp
Pulp head Hp
head Hp =
= 18.3
18.3 m
m
= 60 ft
= 60 ft
(without froth
(without froth
Pulp
Pulp head Hf
head Hf =
= 23.43
23.43
= 75 ft
= 75 ft
(with froth)
(with froth)
Required
Required water
water head
head
Hw
Hw =
= 23.7
23.7 m
m
= 79 ft
= 79 ft
m
Efficiency on water
Ew = 0.68
Froth pump selection (SI) [1]
Calculation of aereated flow "Qf"
Slurry design flow Qd = 454 m³/h
Slurry design head (Note 1) H = 18.3 m
Specific gravity of slurry SP = 1.15
-Percentage of air volume PAV = 20%
Static height Hstat = 9.14 m
Flow volume factor
FVF = 1 / ( 1 - PAV)
PAV = 20%
FVF= 1.25
-Uncompressed (aereated) flow
Froth flow Qf = FVF * Qd
FVF = 1.25
-Qd = 454 m³/h
Qf = 568 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 30 ft
and design flow and head
Qd = 454 m³/h 2000 gpm
Hd= 18.3 m 60 ft
System curve calculation H = Hstat + C * Q²
Hd= 18 m
Hstat = 9.14 m
Qd = 454 m³/h
C = 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. 77 ft
(This is the calculated value)
System duty point at froth flow
Qf= 568 m³/h 2500 gpm
The estimated value from graphic is
Hf= 22.86 m 75 ft
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
For
FVF = 1.25
one obtains
HRF = 0.95
ERF = 0.95
Required water head From
HRf = Hf / Hw
The weater head is
Hw = Hf / HRf
with
Hf = 22.86 m
HRf = 0.95
Hw= 24 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= 640 rpm Ew = 68.0% Froth height Hf = 75 ft.p.c. Hf = 22.9 m.p.c. Height on water Hw = 79 ft.w.c. Hw = 24.1 m.w.c. Selected pump Qf = 568 m³/h Hw = 24.1 m.w.c. N= 640 rpm Ew= 68 %
Slurry efficiency Power
From
ERf = Ef / Ew
The slurry efficiency is
Ef = ERf * Ew
with
ERf = 0.95 Q: Flow rate without froth
Ew = 68.0% SP: Specifuc gravity of pulp without froth
Ef = 64.6% 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
Qp: slurry flow rate witout froth Sp: specific gracity witout froth
Hf: froth height calculated from system P = Qp * Sp* Hf / (367 * Ef)
curve, for froth flow rate Qf (page 2) Qp = 454.25 m3/h (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 kW
Ew: efficiency on water, from P = 67.46 hp
pump diagram, @ Qf and Hw (page 4)
Hw = Hf / HRf
HRf: froth correction factor
Pump power [1]
Pump power P = Qp * Sp* Hf / (367 * Ef)
Pulp flow rate without froth Qp = 454.25 m3/h
Pulp 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 P = 67.46 hp
kW msc Hf S h m Q P f P % 672 . 3 3 h
Froth pump selection, according Weir 5.- Froth height calculated from system curve, for froth flow rate Qf
In this example, Hf = Hstat + C*Qf^2
Qp= 454 m³/h Hstat= 9.14 m
Hp= 18.3 m.p.c. C= 0.000044
Hstat= 9.14 m Qf= 568 m³/h
FVF= 1.25 - Hf= 23.4 m.p.c.
Sp = 1.150 - (Se note 1)
1.- Calculate de pulp system pressure 6.- Froth correction factors from
loss "Hp" for maximum flow "Qp". Weir figure For the froht pump selection, this flow
and the heigt are input data.
Qp = 454 m³/h
Hp = 18.3 m.p.c.
2.- Known points of system curve 2a.- Zero flow point
Q = 0 m³/h
Hstat = 9.14 m
For a froth volume factor
2b.- Duty point without froth FVF = 1.25
Design pulp flow rate (Qp = Qd) HRf = 0.95
Qp= 454 m³/h ERf= 0.95
Design pulp height (Hp = Hd)
Hp = 18.3 m.p.c. 7.- Required water head Hw
3.- Constant of system curve Hw = Hf / HRF
Hp = Hstat + C * Q² Head on froth
C = (Hp-Hstat)/Qd² Hf = 23.4 m.p.c.
Hp = 18 m Head correction for height
Hstat= 9.14 m HRf = 0.95
Qp= 454 m³/h Waterhead
C= 0.000044 Hw= 24.7 m.w.c.
4.- Froth flow 8.- Efficiency on water
Qf = FVF * Qp From selected pump curve, find the
FVF = 1.25 - eficiency on water @
Qp = 454 m³/h
Qf = 568 m³/h Note 1. This is thecalculated value. The
Weir estimated value from system curve
Rev. cjc. 28.06.2013
1
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 Warmanhoriz
SFP = 1.2
HP= 67.5 1.-Determine
HPreq = 81.0 hp Brittle
Tenaciuos
The next comercial size [3] Medium
HP= 100 hp 2.- Qs = De-a Use maximu Check for ma 8.- Slurry density Sf = Sm / FVF 3.- Qf = Aere
9.- Calculate froth power Qf =
Pf (kW) = Qf * Hf * Sf * 0.98 / EF
4.- Calculate
Froth flow ataereatedfl
Qf = FVF * Qs (L/s) solids in slurr
Slurry density Keep dischat
Sf = Sp / FVF 5.- Hw = Qf * Sf = FVF * Qs * Sp / FVF Qf*Sf= Qs*Sp 6.-Selectfrot to the left of B Pf (kW) = Qs * Hf * Sp* 0.98 / EF NPSHreq >= 7.- At the duty
Pump power[2] speedNf/rpm
P = Qp * Sp* Hf / (367 * Ef) Ew (%).
P = Qf/FVF * Sf*FVF* Hf / (367 * Ef)
P = Qf * Sf* Hf / (367 * Ef) 8.- Slurry den
Qf = 567.81 m3/h Sp = Sf = 0.920 - FVF = Hf = 22.9 m.p.c. Sf= Ef = 0.646 -P = 50.3 kW 9.-Calculatef P = 67.46 hp Pf(kW)= 10.- Check po 11.- Select m
Qf = 568 m³/h
Hw = 24.7 m.w.c.
For the selected pump
Ew = 0.68 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 = 454.25 m3/h 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
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
Required water Hw =
[1] f p f f E FVF SG H Q HP
3960 f f f f p fE
SG
H
Q
HP
FVF
SG
SG
3960head Hw Hf / HRF
HP = ( Qf * Hf * Sf ) / (3960 * Ef) Sf = Sp/FVF Sp = 1.15 FVF = 1.25 Sf = 0.92 Qf = 2500 gpm Hf= 75 ft Sf = 0.92 -Ef = 0.646 -HP = 67.43 BHP P = Qf * Hf *Sf* / (367 * Ef) Qf = 568 m³/h Hf = 22.9 m.p.c. Sf = 0.920 -Ef = 0.646 -P = 50.3 kW P = 67.46 hp
The used Hf-value is from the Weir example, not the calculated value
