FLOWSHEETS
Zinc Plant Flowsheet (SOMINCOR)
http://www.sec.gov/Archives/edgar/containers/fix270/1377085/000120445907001642/lundintechrep.htm
Analysis of flowsheets
SIMPLE CASE
Feed
semiproduct P1
1
2
concentrate C1 concentrate C2
final concentrate
semiproduct P2
3
concentrate C3
tailing O
final tailing
Balance of each node
GRADE
 – content of a component in feed %,
 – content of a component in concentrate, %,
 – content of a component in combined products, %,
 – content of a component in tailing, %
semiproduct P1
feed
α
Input data
input parameters: α, , 


concetrate
calculated parameteres: , , r, a…
tailing
concentrate C1
concentrate C2
concentrate C3
 – yield of a product , %
 – recovery of a considered component in a product, %
r – recovery of other than considered components
in another product, %
feed
Node #
1
2
3
Grade
concentrate
α

%
1.421
15.250
0.219
%
15.25
29.00
0.60
tailing
Concentrate *
yield
recovery
ν
γ
ε
%
0.2185
7.0000
0.1500
%
8.00
37.50
15.22
%
85.85
71.31
41.80
*, and r calculated from α, , 
Tail*
recovery
Selectivity
εr
a
%
93.122
68.584
84.836
101.232
122.591
133.133
EQUATIONS
  100(   ) /(   )
  ( ) / 
(%)
(%)
 r  100 (100  ) /(100  ) (%)
a   r  r /( r    100)
a = 100 ideal separation , a ~ 1000 no separation
(-)
Flowsheet with balances of nodes (local balances)
feed
F
1.421
100.0 100.0
product
grade ,%
yield,%
recov., %
1
P1 15.25
8.00 85.85
P2
0.2185
92.00 14.15
2
C1 29.00
37.50 71.31
concentrate C1
3
C2
7.000
62.50 28.69
concentrate C2
C3 0.60
15.22 41.80
concentrate C3
T
0.150
84.84 58.20
tailing T
Upgrading curves for nodes using local balances
conclusion: separation is best in node 1 (a=101.30 and worse in nodes 2 and 3, a=~125)
Best flotation results upgrading curve
Product
C1
C2
C3
T
F

29.00
7.00
0.60
0.15
1.42

29.00
15.25
5.93
1.42

3.00
5.00
14.00
78.00

0.00
3.00
8.00
22.00
100.00

100.00
61.22
24.63
5.91
8.23
EQUATIONS
weighted average
for instance for products C1+C2
 (   )   C1C1   C 2C 2
   C1   C 2

0.00
61.22
85.86
91.77
100.00
r
r
100.00
97.84
95.28
85.88
20.99
100.00
97.84
93.12
79.01
0.00
Global balance of flowsheet
α
1


concetrate
2
local
,
 2,c,  2,c,
tailing
α
,
 2,T,  2,T
global
 G = 1-2,c=  1,c  2,c/100
 G = 1-2,T=  1,T  2,T/100
 G = 1-2,c=  1,c  2,c/100
 G = 1-2,T=  1,T  2,T/100
concetrate
tailing
Global balance of flowsheet
Options of industrial flowsheet
Feed
semiproduct P1
concentrate C1
1
semiproduct P2
2
3
concentrate C2
tailing T
concentrate C3
4
final concentrate Cf
final tailing Tf
Cf=C1
Option 1


C1
Cf
29.00
29.00
3.00
3.00
C2
C3
T
Tf
7.00
0.60
0.15
0.57
5.00
14.00
78.00
97.00
F
1.42
100.00


Final concentrate, C f
3.00
29.00
3.00
29.00
Final tailing, T f
8.00
15.25
22.00
5.93
100.00
1.42
100.00
0.57
Feed, F
100.00
1.42


 r
61.22
61.22
61.22
61.22
97.84
97.84
24.63
5.91
8.23
38.78
85.86
91.77
100.00
100.00
93.12
79.01
0.00
0.00
100.00
100.00
0.00
Feed
concentrate C1
1
Feed
semiproduct P2
2
semiproduct P1
=
semiproduct P1
3
=
concentrate C2
tailing T
concentrate C3
5
semiproduct P2
2
3
final concentrate C
4
final concentrate C f
1
final tailing T
f
final tailing T f
Cf=C1+C2
Option 2


C1
C2
Cf
29.00
7.00
15.25
3.00
5.00
8.00
C3
T
Tf
0.60
0.15
0.22
14.00
78.00
92.00
F
1.421
100.00


Final concentrate, C f
3.00
29.00
8.00
15.25
8.00
15.25
Final tailing, T f
22.00
5.93
100.00
1.42
100.00
0.22
Feed, F
100.00
1.42


 r
61.22
24.63
85.86
61.22
85.86
85.86
97.84
93.12
93.12
5.91
8.23
14.14
91.77
100.00
100.00
79.01
0.00
0.00
100.00
100.00
0.00
f
Feed
semiproduct P1
1
semiproduct P2
concentrate C1
2
3
concentrate C2
concentrate C3 tailing T
4
final concentrate
C
f
final tailing
T
f
Cf=C1+C2+C3
Option 4


C1
C2
C3
Cf
29.00
7.00
0.60
5.93
3.00
5.00
14.00
22.00
T
Tf
0.15
0.15
78.00
78.00
F
1.421
100.00


Final concentrate, C f
3.00
29.00
8.00
15.25
22.00
5.93
22.00
5.93
Final tailing, T f
78.00
1.42
100.00
0.15
Feed, F
78.00
1.42


 r
61.22
24.63
5.91
91.77
61.22
85.86
91.77
91.77
97.84
93.12
79.01
79.01
8.23
8.23
8.23
100.00
0.00
0.00
100.00
100.00
0.00
Feed
1
semiproduct P1
concentrate C1
semiproduct P2
2
3
concentrate C2
tailing T
concentrate C3
5
4
final concentrate C f
final tailing T f
Cf=C1+C3
Option 3


C1
C3
Cf
29.00
0.60
5.61
3.00
14.00
17.00
C2
T
Tf
7.00
0.15
0.56
5.00
78.00
83.00
F
1.421
100.00


Final concentrate, C f
3.00
29.00
17.00
5.61
17.00
5.61
Final tailing, T f
22.00
5.93
100.00
1.42
100.00
0.56
Feed, F
100.00
1.42


 r
61.22
5.91
67.14
61.22
67.14
67.14
97.84
83.72
83.72
24.63
8.23
32.86
91.77
100.00
100.00
79.01
0.00
0.00
100.00
100.00
0.00
Feed
1
semiproduct P1
concentrate C1
semiproduct P2
2
3
concentrate C2
concentrate C3
tailing T
4
final concentrate Cf
final tailing T f
Cf=C2
Option 8


C2
Cf
7.00
7.00
5.00
5.00
C1
C3
T
Tf
29.00
0.60
0.15
1.13
3.00
14.00
78.00
95.00
F
1.421
100.00


Final concentrate, C f
5.00
7.00
5.00
7.00
Final tailing, T f
8.00
15.25
22.00
5.93
100.00
1.42
100.00
1.13
Feed, F
100.00
1.42


 r
24.63
24.63
24.63
24.63
95.28
95.28
61.22
5.91
8.23
75.37
85.86
91.77
100.00
100.00
93.12
79.01
0.00
0.00
100.00
100.00
0.00
Selectivity of separation for different options of composition of final flotation
products
Feed
1
semiproduct P1
concentrate C1
semiproduct P2
2
concentrate C2
4
final concentrate Cf
final tailing T f
Feed
ideal upgrading
C1
C2
90
C1+C2
1
semiproduct P1
semiproduct P2
3
80
C1+C3
C2+C3
4
concentrate C3
tailing T
C1+C2+C3
70
final concentrate Cf
60
a=101.3
50
40
30
C1+C2+O
20
10
=
0
0
10
20
30
40
50
60
70
80
useful component recovery in concentrate, , %
90
ideal remixing
other than useful comp.recovery in tailing , r, %
100
100
final tailing T f
Selection of optimum point of process
ideal upgrading
90
80
C1+C2
C1
C2
common sense optimum point
of separation
C1+C3
C2+C3
C1+C2+C3
70
example of point of optimum
separation based on
economics
60
a=101.3
50
40
30
C1+C2+O
20
10
ideal remixing
other than useful comp.recovery in tailing , r, %
100
0
0
10
20
30
40
50
60
70
80
90
100
useful component recovery in concentrate, , %
Final decision: Cf=C1+C2 + something depending on criterion of upgrading optimal point
100 (  a )

1002   (100   )  100a
100
90
80
70
ideal upgrading
C2
C2+C3
C1
C1+C
C1+C
C1+C2+C
60
50
a=101.3
40
30
20
C1+C2+
10
ideal remixing
(100   r )
 a
(a   r )
other than useful comp.recovery in
tailing , r, %
Transformation of the Fuerstenau(recovery-recovery or -) upgrading curve into
Halbich (grade-recovery or β- ) upgrading curve
0
0 10 20 30 40 50 60 70 80 90 100
useful component recovery in
concentrate, , %
the Fuerstenau (- ) is alfa -insensitive equivalent of the Halbich ( β- ) upgrading curve
FLOWSHEET WITH A RECYCLE STREAM
feed 1
1
feed 2
semiproduct P2
semiproduct P1
3
2
semiproduct P3
concentrate C1
concentrate C2
4
5
concentrate C3
tailing T
final concentrate Cf
final tailing T f
Flowsheet with balance of nodes (local balances)
input parameters: α, , 
Feed 1
F1
21.95
P1
0.89
C2
88.23
, %
, %
C3
78.05
0.60
60.04
1.42
39.96
1
F2
100.00
Product
, %
0.78
100.00
2
25.00
28.40
3.00
88.23
P1
11.77
25.00
11.77
P3
100.00
5.59
100.00
25.00
52.63
Concentrate 1=P1
0.57
71.60
P2
100.00
0.57
100.00
3
4
C1
11.76
P2
99.11
5
C2
88.24
3.00
47.37
C3
78.48
0.60
83.30
T
21.52
Tailing
0.44
16.70
EQUATIONS
Recycle node (1)
100 F 2   F 1 F 1  (100   F 1 )C 3

 F1F1
 F1 
100F 2
Separating nodes
  100(   ) /(   )
(%)
  ( ) / 
(%)
 r  100 (100  ) /(100  ) (%)
a   r  r /( r    100)
a = 100 ideal separation , a ~ 1000 no separation
(-)
node
2
4
5


25,00
0,57
0,78
0,89
99,11


25,00
3,00
5,59
11,76
88,24


0,60
0,44
0,57
78,48
21,52

0,00
0,89
100,00

0,00
11,76
100,00

0,00
78,48
100,00

28,40
71,60

52,63
47,37

83,30
16,70

0,00
28,40
100,00

0,00
52,63
100,00

0,00
83,30
100,00
r
100,00
99,33
0,00
r
100,00
90,65
0,00
r
100,00
21,55
0,00
Upgrading curves for nodes using local balances
feed 1
feed 1
1
1
feed 2
feed 2
semiproduct P1
semiproduct P1
semiproduct P2
2
semiproduct P2
2
5
5
concentrate C3
concentrate C3
tailing T
final concentrate Cf
final tailing T f
tailing T
final concentrate Cf
final tailing T f
node 5 is not efficient
Global balance of flowsheet (feed F2 is 100%)
Eqs for recycling nodes
 F 2   C 3   F1
FEED 1
F2
0.78
450.00 247.78
C2
30.00
3.00
63.34
25.00
70.37
Concentrate
C3
0.60
350.00 147.78
2
25.00
70.37
P2
0.57
446.00 177.41
3
4
C1
4.00
 F 2   C 3   F1
F1
1.42
100.00 100.00
1
P1
4.00
known parameters: α, , 
P3
5.59
34.00 133.71
C2
30.00
5
3.00
63.34
C3
0.60
350.00 147.78
T
96.00
0.44
29.63
Tailing
1
Calculations
Feed 1: grades are known, 
G and
n
 are equal to 100%
G
2
β
Node 1
Grades are known, local  and  for F1 are known (=21.95%) (for C3 is
100- 21.95 =78.05%) or can be calculated from grades of products
100   11  (100   1 ) 2
Calculation of global  for F2
Q) How large is  for C3 when for F1 is 100%?
A) When  F1=100%,  C3 =(100/21.95)x 78.05= 350%. Then  F2=  F1+ C3
= 100+350=450%
100 F 2   F 1 F 1  (100   F 1 )C 3

G
F1
 100%

G
C3
 C3
 100
 F1
F1
C3
1
F2
Calculation of  for recycling node (here F2):
 FG1  100%
F1
C3

G
C3


G
F2
100 C 3

 F1
100 F 2
 F1
 FG2   CG3  100%
1
F2
Calculation for (normal) separation nodes
P2

G
C3

G
C3


 P 2 C 3
100
 P 2 C 3
100
5
P2
C3
T
C3
T
Graphical representation of separation data (not very useful, recoveries greater than 100%)
Grade –recovery curve for Pb, Cu and Zn circuits within the Eureka Concentrator
(based on Ch. Greet, Spectrum Series, 2010)
Some flowsheets can be complex
100.000
t/h
 L%
 % Cu
 bb %
 BI %
281.466
 BII %
0.011
100.000
0.851
0.005
0.006
3
0.0091
366.536
19.636
6.680
0.075
50.184
45.655
0.005
0.129
0.022
0.002
0.092
2.435
100.0783
0.0020
0.003
0.260
0.007
9.840
0.021
20.3013
0.0070
32.372
0.260
172.665
81.281
0.007
0.216
143.687
143.687
158.795
0.011
0.075
0.643
7.130
0.096
68.274
62.842
50.017
70.319
0.007
Balast II
2
3.779
0.071
69.8499
62.712
0.335
8.865
0.0085
57.579
0.113
3a
91.577
242.515
100.000
282.018
12.298
26.770
0.005
21.901
89.347
13.361
45.972
55.120
0.011
1
1
5
100.000
0.028
0.028
2.928
0.006
1.595
177.865
62.712
215.770
Flotacja Główna a b
0.260
65.9125
0.0104
0.0066
0.004
0.004
54.333
0.358
10.680
15.745
6.050
28.006
0.091
0.314
0.205
54.913
188.937
50.543
90.011
226.535
0.01786
2
1.595
1.595
0.824
3.352
88.701
0.011
0.034
30.014
0.010
0.310
0.755
23.3027
0.0138
0.0023
0.004
0.003
Flotacja Główna c
1.230
0.081
0.277
9.874
33.974
2.177
0.230
72.727
0.490
11.231
0.967
0.246
22.339
50.017
45.503
89.320
66.289
13.090
0.038
172.093
81.011
0.910
72.865
4.260
118.017
0.172
0.591
0.205
72.865
250.703
86.857
Flot. Czyszcząca II
6
0.132
0.046
59.622
0.216
155.503
0.471
0.910
10.653
3
1.595
2.597
80.1767
0.0081
37.158
178.004
0.0280
66.092
2.994
4a
89.320
21.413
38.086
Hydrocyklon
1.687
38.642
17.909
13.428
4b
23.303
37.158
0.200
0.674
13.428
100.078
2.320
46.203
178.004
4
Balast I
5
6
1.595
178.427
7
31.854
100.000
2.177
49.873
49.763
0.967
8
100.000
100.000
2.928
0.751
77.661
0.133
22.847
20.785
1.720
0.751
0.459
78.610
37.005
0.817
27.273
82.091
0.850
0.610
2.928
177.865
178.585
0.751
0.159
27.235
71.032
0.751
128.554
70.763
7
9
8
2.598
0.017
2.928
2.608
68.274
201.923
0.034
5.212
0.740
0.851
100.000
2.550
0.075
19.1569
0.0019
0.002
30.548
111.912
0.920
0.476
0.609
94.788
5a
1.836
0.010
68.274
1.067
90.639
62.920
62.842
0.216
153.367
281.655
1.836
0.643
0.331
234.909
111.912
Flot. Czyszcząca I
1.180
100.000
1a
2.928
0.010
0.551
0.851
100.000
9.758
0.120
0.184
0.817
2.197
3.504
0.633
9.758
7.560
9.758
6.232
9.736
0.00273
The Eureka Mine – An Example of How to Identify and Solve Problems in a Flotation Plant
Christopher Greet
Useful literature
Publications : Spectrum Series
Flotation Plant Optimisation: A Metallurgical Guide to Identifying and Solving Problems in Flotation Plants
Spectrum Series 16
Published in 2010
The Eureka Mine – An Example of How to Identify and Solve Problems in a Flotation Plant
Christopher Greet
Homework
Create your own flowsheet and calculate local and global balanses as well as plot graphs
which will help you to evaluate the plant performance