The optimization and mathematical models determination of copper recovery – the precondition for improvement of recovery in Bucim copper mine

Abstract

The improvement in the chalcopyrite copper Bucim mine are gone forward to renewed reagent regime, including and involving new reagents for increase d recovery of copper and gold. The optimization and mathematical linear models using gradient method Box and Wilson are good example for improvement of industrial recoveries in flotation circuit. In this paper is shown optimization techniques, formatting the mathematical model and adequate model for carried out investigations. Tables and figures will show the optimal quantity in reagent regime (collectors), particle size, flotation time I rougher flotation, conditioning time etc.

Full text

Proceedings of the XV Balkan Mineral Processing Congress, Sozopol, Bulgaria, June 12 – 16, 2013
713
THE OPTIMIZATION AND MATHEMATICAL MODELS DETERMINATION OF COPPER
RECOVERY – THE PRECONDITION FOR IMPROVEMENT OF RECOVERY IN BUCIM COPPER
MINE
A. Krstev, B. Krstev, Z. Zdravev, Zivko Gocev, J. Zivanovic, D. Krstev
1University “Goce Delchev”, Faculty of Natural and Technical Sciences, Shtip, R. of Macedonia
2Mine BUCIM, Radovis, R. of Macedonia
3University “Goce Delchev”, Faculty of Computer Science, Shtip, R. of Macedonia
ABSTRACT. The improvement in the chalc opyrite copper Bu cim mine are gone forward to renewed reagent regime, including and involving new reagents for increase d
recovery of copper and gold. The optimization and mathematical linear mo dels using gradient method Box and Wil son are good example for improvement of industrial
recoveries in flotation circuit. In this paper is shown optimization techniques, formatting the mathematical model and adequate model for carried out investigations. Tabl es
and figures will show the optimal quantity in reagent regime (collectors), particle size, flotation time I rougher flotation, conditioning time etc.
KEYWORDS: investigation, mathematical, model, recovery, flotation, Bucim
INTRODUCTION
The previous carried out laboratory investigations with application
of the new collectors CYTEC and frothers confirmed that there is
possibility for significantly improvement of the gold recovery with
same copper quality and decreasing of the CaO consumption. The
investigations with reagents Aerophine 3404, Aero XD 5002 and
frother ОР-F49 in the previous period (2010) were very short because
of the low quality and variations of th e ores. Variations of the ore
from 0.15-0.22%Cu, instability of the flotation and other problems in
the flotation process. The combination of the Aerophine 3404,
KEX:KBX= 1:1, NaIPX, SKIK Bz 2000, in the different points of the
flotation process gave significantly better results that early. The
process was prolonged with pH=10.5 and the point of addition of
CaO was at the hydro cyclone (70%) and 30% in the flotation
process. The conclusions of these in vestigations were very heavy for
sure confirmation, bur the obtained results were close to the previous
results by standard conditions (specially for Au), may be better but
not significantly. The Au content in the ore was од 0,19-0,29 gr/t, in
the concentrate 8-12,3 gr/t, with Au recovery from 45-55% (some
appearances up to 60%), but the copper recovery in the standard
interval. Considering these investigations in laboratory and indust rial
real conditions may be concluded that:
 The instability and relative short period of investigations in the
real conditions have contributed for obtaining the technological
parameters closed to the standard conditions,
 As a result of the good regrinding, it was very heavy to clean
the rough concentrate Cu/Au,
 Using higher pH, highe r than standard in the rougher flotation
(elimination of pyrite flotation) by Aerophine 3404, it will be
expected higher quality and content of Cu/Au,
 In the existing real co nditions of flotation at рН 11,0-11,6 and
consumption of Aerophine 3404 (АР3404) from 18-22 гр/т,
together with change of adaptive changeable reagent regime by
different collectors (the combination from Aerophine 3404,
KEX:KBX, NaIPX),
 The prolonged changes of the reagent regime with
contemporary ad dition of new reagents (Bz 2000 = 4-8 gr/t +
KEX:KBX=1:1 = 8-4 gr/t, total 12 gr/t) in the grinding cycle,
together with addition of NaIPX in the condiotioner with 8-10
gr/t, in the flotation process (rougher and controlled flotation)
with 2-4 gr/t, or total addition of 14 gr/t NaIPX,
Full Factorial Plan of experiments for three factors in Bucim
mine
The plan of experiments is carried out for existing regent regime in
the flotation plant in Bucim mine. The obtained result are given in the
following table 1 and table 2:
Tabl. 1 Tests with a plan experiments
Опит
X
o
X
1
X
2
X
3
I
1
I
2
I
Cu
%
sr
1
+
15
10
5
90,13
89,05
89.59
2
+
15
6
5
90,52
87,90
89.21
3
+
9
10
5
89,18
88,80
88.99
4
+
9
6
5
86,66
87,22
86.94
5
+
15
10
3
89,10
87,22
88.16
6
+
15
6
3
88,60
90,48
89.54
7
+
9
10
3
88,90
89,62
89.26
8
+
9
6
3
88,00
87,08
87.54
Tabl. 2 Tests with a plan experiments
Considering the obtained results will be carried out analysis of the
obtained linear model, establishing his adequate. As the model is
obtained on the basis of the mean values of recoveries, then the
productivity error for the mean values will be:








       
64
08,8700,8862,8990,8848,9060,8822,8710,89
22,8766,8680,8818,8990,8752,9005,8913,90
2222
2222
2
.











rIsr
S
0,264
2
.
rIsr
S; 514,00,264
.
rIsr
S

Proceedings of the XV Balkan Mineral Processing Congress, Sozopol, Bulgaria, June 12 – 16, 2013
714
Adequate model checking
After the estimation of the investigated model, it’s needed to
calculate the mean result of each test, and instead xj in the
mentioned model we’ll put appropriate conditioned units of the test
(1):
Ipres.1 = 88,65 +0,346 (+1) + 0,47 (+1) – 0,596 (+1) = 88,87
Ipres.2 = 88,65 +0,346 (+1) + 0,47 (-1) – 0,596 (+1) = 87,93
Ipres.3 = 88,65 +0,346 (-1) + 0,47 (+1) – 0,596 (+1) = 88,18
Ipres.4 = 88,65 +0,346 (-1) + 0,47 (-1) – 0,596 (+1) = 87,24
Ipres.5 = 88,65 +0,346 (+1) + 0,47 (+1) – 0,596 (-1) = 90,06
Ipres.6 = 88,65 +0,346 (+1) + 0,47 (-1) – 0,596 (-1) = 89,12
Ipres.7 = 88,65 +0,346 (-1) + 0,47 (+1) – 0,596 (-1) = 89,37
Ipres.8 = 88,65 +0,346 (-1) + 0,47 (-1) – 0,596 (-1) = 88,43
In the above t able are gi ven errors I = Isr.Ipres., and the model
adequate may be checked by Fischer criteria:
 
.
1 0
22
.
1rIsr
N
i
k
i
iisr
SkN
bNI
F






 
 
Where: k – number of linear members in the mentioned model. In
our case we’ll have:
F = [89,592 + 89,212 + 88,992 + 86,942 + 88,162 + 89,542 + 89,262
+ 87,542]  8[88,652 + (0,346)2 + 0,472 + (0,03)2 + (-0,596)2 + 0,262
+ 0,242 + 0,182] / 5 * 0,514 ;
F = 2,157
For fb = 821 = 5 and fr = 8(21) = 8, fo r confidential level p =
95%=3,69, andStudent = 2,306, Fischer criteria:
F* = fr + p + t = 8 + 3,69 + 2,306 = 13,996.
As F  F*, the model is adequate. It means that investigated
process is correct described by means of the first order pollinom and
the difference which is appeared between experimented and
estimated results is accidental
The determination of the obtained linear model gradient for
reagent regime in the flotation plant in Bucim mine
The gradient method is based on the fact that biggest degree of
improvement for a function is achieved if the progressive by the
length of the gradient. As this direction is direction of the steeper
gradient, then we’re talking about for maximum, or the direction of
the steeper fall. In fact, the gradient is vector for a point of the n-
dimensional space. This one is determined by th e determination of
the first derivations of the aim function in the relationship of their
changeable factors. It’s important to note that the gradient direction
is a local, not a global property. If we suppose that the function y(x1,
x2,) which has had continuous partial derivations, then there is the
point (x1, x2), around which for a little small change in the every one
direction will be obtained the following estimation.

 ,  = (88.65 + 0.346 +0.47−0.596)
= −4,422

 ,  =(88 .65 + 0.346 +0.47−0.596)
= − 6,682
= 
 ( ,)
(()
)+(()
)=−4,422
8,012 = −0.55
= 
 ( ,)
(()
)+(()
)=−6,682
8,012 = −0,83
The moving direction will be shown as a vector φ marked with n
numbers (m1, m2 . . . mn).
Fig. 1. Direction of search

= −0,55
−0,83 = 0,663
∙∆= −0,55 ∙ 3= −1,65
∙∆= −0,83 ∙ 2 = −1,66
It’s evident that gradient direction is exact, andx1andx2has had to
be adjuste, because the coefficient of interaction b12with his sign
show this action. Standard deviation σ = ∑∆
 = 1.03.
By the analysis of the linear model of the first order polinom for
copper recovery from the chalcopyrite ore, above mentioned
equations for carried out investigations by decreasing of the collector
(x1–NaIPX) and with increasing of the (x2–KEX:KBX=1:1), we’ll be
obtained following results in table 4.
Tabl. 3 Tests with a plan experiments
I
1
I
2
I
Cu
%
sr
I
pres
∆I ∆I
2
∆I
2
/7
90,13 89,05 89.59 88,87 0,72 0,52
90,52 87,90 89.21 87,93 1,28 1,64
89,18 88,80 88.99 88,18 0,81 0,65
86,66 87,22 86.94 87,24 -0,30 0,09 1,07
89,10 87,22 88.16 90,06 -1,90 3,61
88,60 90,48 89.54 89,12 0,42 0,17
88,90 89,62 89.26 89,37 -0,11 0,01
88,00 87,08 87,54 88,43 -0,89 0,79
Tabl.4 Tests with a plan experiments
Опит X1 X2 I1 I2 ICu%sr
1 11.5 10.5 90.0 89.2 89.6
2 11.5 9.5 90.4 90.0 90.2
3 9.5 10.5 90.1 89.3 89.7
4 9.5 9.5 89.7 89.3 89.5
5 11.5 10.5 89.2 89.2 89.2
6 11.5 9.5 89.2 90.0 89.6
7 10 10.5 90.4 90.2 90.2
8 9.5 9.5 88.7 88.3 88.5

Proceedings of the XV Balkan Mineral Processing Congress, Sozopol, Bulgaria, June 12 – 16, 2013
715
The other working parameters (рН=11.72, 55÷60% - 0,074 mm,
flotation time 12 min and time of conditioning 6 min and X3 = 4÷6
gr/t) are standard as in the real industrial conditions. The copper
recovery in the ICu%sr is optimal or need minimum decreasing of
collector consumption of NaIPX = 10-11.5, and increasing of
KBX:KEX=1:1 = 9.5 ÷10.5 gr/t, according to the influence of the feed
ore quality, bigger content of copper in the feed, bigger consumption
of the collectors.
CONCLUSION
In this paper is shown optimization te chniques with formatting the
mathematical model and adequate model for carried out
investigations. Obtained tabular results and figures will show the
optimal quantity in reagent regime (collectors), pa rticle size, flotation
time for rougher flotation, conditioning time etc.
REFERENCES
Mular, A. L., (1980). “Empirical modeling and aptinusation of mineral
processes”, Mineral Science and Engineering, 4, No 3. Pp 30-42.
Napier-Munn, T. J., Morrell, S., Morrison, R. D., and Kojovic, T.,
(1996).
“
Mineral co mminution circuits: their operation and
optimization
”.
JKMRC., pp. 413.
Plitt, L. R., (December, 1976). “A mathematical model of the
hydrocyclone classifier”,
CIM Bull.
69, 114.
Povarov A. I., (1978). “Gridrocikloninaobogatitel’nyhfabrikah”,
“Nedra”. Moskva, Russia.
Renner, V. G., and Cohen, H. E., (June, 1978). “Measurement and
interpretation of size distribution of particles within a
hydrocyclone”,
Trans. IMM.,
Sec. C, 87,139.
Rowland C. A., (1986). “Ball Mill Scale-up-Diameter Factors.,
Advances in Mineral Processing”, P. Somasundaran Editor Society
of Mining Engineers/AIME, 34, 605.
Svarovsky, L., (1984). “Hydrocyclones”
,
Holt, Rinehart & Winston Ltd,
Eastbourne.
Wiegel R. L., and Li K. A., (1986). “Random Model for Mineral
Liberation by Size Reduction”, Trans. AIME, 238, 179.
Wills, B. A. (1988). “Mineral Processing Technology”, 4th edition