Evaluation of flotation performance using variance spectrum analysis

Minerals Engineering, Vol. 8, Nos 1/2, pp. 51--62, 1995

Pergamon

0892--6875(94)00102-2

El~vier Sciettce Ltd Printed in Great Britain 0892-6875/95 $934)+0.00

EVALUATION OF FLOTATION PERFORMANCE USING VARIANCE SPECTRUM ANALYSIS

R. AGNEW§, S.W. WILSON§ and R. STRATTON-CRAWLEYt § INCO Limited, Matte Separation, Copper Cliff, Ontario, P0M 1N0, Canada t INCO Limited, J.Roy Gordon Research Laboratory, 2060 Flavelle Boulevard, Sheridan Park, Mississauga, Ontario, L5K 1Z9, Canada (Received 22 July 1994; accepted 6 September 1994)

ABSTRACT The performance of Denver sub-A flotation cells in rougher and 1st cleaner service in lnco's Matte Separation plant was studied using the technique of Variance Spectrum Analysis. The procedure involves fitting a Fourier Series to real-time plant data and filtering out the lowfrequency disturbances on the assumption that performance would be enhanced with improved equipment installation - in this case Denver DR flotation cells. The resulting series is then recalculated to estimate the response of the process under improved control In the case ureter study, recovery of nickel to the high grade nickel sulfide product was projected to increase by 5 % as a result of implementing the equipment upgrade in the rougher circuit. In addition, it was projected that the quality specification target of ~ secondary nickel sulfide product could be met simultaneously with that of the copper sui'fide product, by upgrading the 1st cleaner cells. These targets had previously been difficult to achieve concurrently due to the strong inverse correlation between them. Based on this study an equipment upgrade was carried out. Subsequent operation of both circuits confirmed the projected results and the validity of the method as a basis for justifying ,capital investment based on improved metallurgical performance. Keywor&; INCO Lin~ted, Matte Separation, Flotation, Variance Spectrum Analysis

INTRODUCTION Since 1930, Inco ]Limited has been milling Sudbury basin ores to produce copper and nickel concentrates which were subsequently processed separately through the Copper Cliff Smelter. The separation efficiencies achievable in the milling operation necessitated a further copper-nickel separation step following the nickel converters. Through the first half of the century, this was performed by the now obsolete Orford process. During the 1940's, Inco developed the Matte Separation flowsheet [1] based on mineral processing techniques (Figure 1) and this became the process of choice for separating copper and nickel in nickel converter matte since that time. In the Matte Separation process, nickel converter matte is slow cooled which promotes coarse crystallization of a synthetic mineral system comprising copper sulfide (Cu2S, ehalcoeite), nickel sulfide (Ni3S2, heazlewotxlite) and a nickel-copper metallic alloy. The matte is crushed and ground to minus 200-mesh. The metallic phase is first separated by magnetic separation and thence becomes feed to the Copper Cliff Nickel Refinery. The copper and nickel sulfides are then separated by flotation using a copper sulfide selective collector, diphenylguanidine (an imine derivative of urea), in near-saturated lima environment. The resulting copper concentrate, assaying typically 76 %Cu 3 %Ni 20 %S is filtered, dried 51

52

R. AGNEWet

al.

and fed to the copper smelter. Two nickel concentrates are produced. The high-grade concentrate, assaying about 70 %Ni 1%Cu 26 %S, is roasted and shipped to Inco's nickel refinery in Clydach, Wales. The low grade concentrate, assaying about 67 %Ni 6 %Cu 25 %S, is roasted and distributed between the two nickel refineries on the basis of feed requirements. Cu-Ni Matte c .... IMallonconmnlme / / t .... notatm u ~ I I m.... ma0rml~ l

Grindlng and L. Classmc~ion F

Magnetic Separaion

Reoand I

-I Mq.S~. I

scav~

Regand

Flotation

Flotation

Cn (MY)

t~(~,2

conc

High Grade)

(MR)

1 ~

F t

-J nognnO [ -I

1

1°

I ~rN:lGlower t

Flotation

I

Fkxdo, I i c

t

- (LowGr~) (ME)

Fig. 1 Matte separation flowsheet In 1985, the Ontario government specified that annual SO2 emissions from the Copper Cliff Smelter be reduced to 265 kilotonnes by January 1994. The conceptual framework and technology developed to meet this target has been described elsewhere [2]. Fundamentally, Inco flash smelting technology was adapted and improved to allow smelting of a combined copper-nickel bulk concentrate, thus exploiting the principal technical feature of the process, that being the ability to efficiently capture high strength low volume SO2 gas. Concomitant with this philosophy was the cessation of copper-nickel separation in the Sudbury area mills and rationalization of the milling operations. As a consequence, the focus for coppernickel separation shifted entirely to the Matte Separation process. Prior to the change to the bulk smelting process in 1993, in order to maintain a high grade ( < 0 . 5 ~ N i ) chalcopyrite concentrate for oxygen flash smelting, approximately half the copper recovered in the millg was processed with the nickel concentrate. Subsequent separation was carried out, as previously

Evaluation of flotation performance

53

discussed, in Matte Separation. The decision to smelt a combined bulk concentrate obviously meant that the entire amount of copper recovered in the milling process would report, along with the nickel, to Matte Separation. The principal focus of effort from the late 1980's on with respect to Matte Separation was therefore expansion of the plant to accommodate the increased copper load that the plant would be required to separate. However, in addition to copper processing issues, it was also recognized that continuous improvement and upgrading of the matte separation process was necessary to avoid obsolescence in the plant that was to become the focal point for copper-nickel separation. At that time, consideration was given to replacing the flotation equipment then in use for rougher and 1st cleaner service (see flowsheet). The equipment in place was 50 ft3 Denver sub-A flotation cells. Each application comprised 6 flotation banks each 6 cells in length. The sub-A is a cell-to-cell device with metallurgical control being maintained by the use of manual weirs (inter-ceU) for level and regulating valves for (self-)aeration control. Intuitively, the aging (maintenance intensive) equipment with its manual (labour intensive) control philosophy was a high priority for replacement. Intuition, however, carries little weight in the pragnmtic world of capital appropriation justification on the basis of return on investment. While maintenance and operating man-hours savings resulting from equipment upgrading could be quantified, potential metallurgical benefits were also part of the equation. Consequently, the question arose as to how to project what metallurgical improvements might be possible in a system that, on cursory glance (Figure 2), varied randomly around a given setpoint.

8

7

6 ( 5

t

.c 4

3 •

2

g ROUGHER

h f I h , * J . . . l * , . I H * h . , I . * , J , . , r H , l * , . I , , , J , . , J * , , f . , , h , , J . . , J . , * h , , l * , . I , . . i , . . r , * . l , H J*,,I

tT.'00

11.'00

15:00

19.'00

23:00

03:00

07.'00

"nine

Fig.2 Plant data- %Cu in rougher tails

VARIANCE SPECTRUM ANALYSIS There are many approaches for transforming noisy data into a meaningful functional relationship. One of the most well known is the Fourier Transformation. In the early 19th century, Jean Baptiste Joseph Fourier showed that almost any function of a real variable is made up of sine and cosine waves of different frequencies. Fourier also showed that periodicity is not a necessity for analysis and application of the approach has since become an accepted tool in the statistical analysis of processes influenced by random variables. Further, although the approach has been primarily used as a statistical tool in the description of various phenomena, the spectrum of wavelengths obtained from data analysis can in itself be the object of meaningful study. Since, in effect, the original data is merely rearranged and presented in a different manner, viewed from a different perspective new insights can be obtained. In terms of data

54

R. AGNEWet

al.

manipulation, most examples of this approach in the literature use an algorithm, utilizing complex numbers, to compute the transform. The older method is considered to be less efficient. Since this latter concern is hardly a factor in todays PC-based spreadsheet environment, the traditional approach has been used in this study. In consideration for those who suffer anxiety attacks when confronted with papers full of greek symbols, the mathematical basis for the approach has been relegated (even then in summary) to the Appendix and only the key equation is found in the main text. In the time domain, the sum of the periodic functions of the type described in the Appendix for discrete equi-spaeed data, can be shown to be [3], --+a

Y, = ao

I

coJ 2 ~ i ~ + "t'-~

J

..... + a

keos(_~}

In the plant applications studied, 15 minute averages from the on-stream analyzer over a 24 hour period, were used. Thus, N kmax i k

= = = = =

95 (N-l)/2 47 0-'94 0-'47

As noted in the Appendix, in effect this approach separates the different harmonics in the data set and the contribution of each frequency to the overall variance can be assessed. The process is obviously reversible, that is the original data set can be recreated by treating the function in reverse. This is the crux of the analysis that follows.

ROUGHER FLOTATION The key parameter in determining the product quality of the final high-grade nickel concentrate (<0.8%Cu) at the time of the study was the rougher tailings grade %Cu (Figure 3). Figure 3 dearly highlights the difficulty the operator has in manual control in that it is obvious from the graph that the Denver sub-A control setpoints in the scavenger application are not adjusted, but that the target product grade is manipulated by changing the circuit feed grade. Consideration of the flowsheet (Figure 1) will indicate that nickel misdirected to the rougher concentrate has no possibility of reporting to the preferred, high-grade, nickel stream. Therefore, nickel losses to lower grade products is exacerbated by the operators' inability to operate the rougher circuit at (or at least close to) the target, 6.8%Cu, dictated by the ultimate scavenger product grade. It should be borne in mind that the ease being made for replacement of the rougher Denver sub-As also holds for the scavenger circuit and, indeed, a flotation column was constructed to replace the Denver sub-A cells in that case [4]. Rougher flotation data was analyzed following the procedure outlined above and the Fourier coefficients determined. An example calculation for the rougher tails data set shown in Figure 1 is shown in Table 1. Using these results the variance spectrum was obtained and plotted as a histogram in Figure 4. In this example, there is a significant contribution to the overall: variance from low frequency or long period disturbances. It has been suggested that improved control can remove those disturbances with a period greater than 1 hour [5]. Thus, for the purpose of this analysis, the replacement equipment's function was considered to act to bring the system under control. Therefore, the low frequency disturbances w e r e removed from the series and the function recalculated to provide an estimate of the process under improved control. The resulting simulation is plotted as the relative frequency of the projected rougher

E v a l u a t i o n o f flotation p e r f o r m a n c e

55

tails copper assay in Figure 5 and compared to the existing rougher performance. figure that a narrower range o f observed tails grades is projected.

It is clear from the

0.9 J 0.8

0.7

._= ..,

0.6

Sept. 4-14, 1990

0.5

SHIFTAVERAGES 0.4 3

__I..-,--,--,.---I 4

5

L 6

8

9

%Cu in Rougher Tails

Fig.3 M R product grade vesus rougher tails %Cu T A B L E 1 Calculation o f the F o u r i e r Coefficients, a k a n d b k OBSERVATION DATE

TIME

I [

# (i)

xicos(2xki/n), for k =

~C'u (xi)

0

1

2

...

47

ll-SEPT

07:00

0

6.15

6.15

6.15

6.16

...

6.15

ll-SEPT

07:15

1

5.80

5.80

5.79

5.75

...

-5.80

11-SEPT

07:30

2

5.75

5.75

5.70

5.55

...

5.74

11-SEPT

etc..,

i

. . . . . . . . . . . . . . .

94

4.24

4.24

4.21

4.17

...

-4.25

4.921*

-0.076

0.077

...

0.119

.

ak =

n-~X~

n J

* • stands alo~ as ~ e n w a n o f d ~ f u ~ o n I

2~ x ./2=+~ b~ =

"

-o.391

-0.196

0.005

56

R. AGNEW et al.

0.4

0.3

J 0.2

0.1

7.9 4.0 2.6 2.0 1.6 1.3 1.1 0.99 o.ml 0.7110.72 O.M 0.61 0.5"70.s3 Lower Limit on Period, h

Fig.4 Variance spectrum for rougher tails

70

li 10 0

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

Tails % Cu

Fig.5 Relative frequency of rougher tails copper assay Applying the relative frequency distributions shown in Figure 5 to the rougher grade-recovery relationship (Figure 6) results in a projected 5 % increase in nickel recovery over that presently achieved. This is likely to be a very conservative estimate of recovery gain as examination of the right side of the frequency distribution suggests that with the tighter control projected, the operator can push the median operating grade closer to the target level without fear of exceeding the product specification. This would result in an increase in the overall recovery as the grade-recovery relationship would suggest. Also, the graderecovery relationship (which has been assumed to remain constant in previous deliberations) would likely improve p e r s e through use of more efficient separation equipment. In 1992, two banks of Denver DR-300 ceils were installed in Matte Separation. Each bank comprised four 312 ft3 cells assembled as two pairs of cells with separate level and air flow control to each pair of

Evaluation of flotation performance

57

cells. Initial tesl:s were carried out to determine performance in 1st cleaner service (see below). Following that, th,~ cells were tested over a wide range of operating variables, level control, air flow rate and feed grade variation, in rougher application in March 1993. The results, along with Denver sub-A performance conducted in parallel, are shown in Figure 7.

10o

90

-

2:1Ni:OuM

a

~

80-

::/~I:INi:CuMatte 9.o

70-

l

60-

m

50-

400

I

I

2

I

I

I 12

I

4 6 8 10 %Cuin RougherTails

14

Fig.6 Matte separation rougher grade-recovery curves

I00

90

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

i.-=- r

". 0

.

10

20 30 NickelRecovery,%

4O

Fig.7 Denver DR-300: rougher performance

5O

58

R. AGNEW et al.

Obviously, an increased nickel recovery to tails (indicated by decreased nickel recovery to concentrate in the graph) in the order of 10-15 % at any given copper recovery has resulted from installation of the Denver DR-300 ceils. The graph suggests significant variation of data with the DR-300. This is, however, entirely attributable to operation of the equipment under diverse conditions during this commissioning period in order to establish the performance capabilities of the equipment. In fact, at any of the set-points studied, rougher tails copper could be readily controlled to 5- 1%Cu. These results confirm the projections made above.

1st CLEANER FLOTATION The performance of the 1st cleaners has a direct impact on the quality of two products, the low-grade nickel concentrate, ME, and the copper concentrate, MK. This relationship is presented in Figure 8.

~K %Ni

ME %Cu

4.5

12

10 s ~J

~

4

sJ

S

J

3,5 "

.Er

Q

3

2.5

•"

.OPEFIATINq -WINDOW J

•" 2

10

I

I

15

20

I

I

I

25

30

35

2

40

1st Cleaner Tails %Cu

Fig.8 Relationship between MK Ni/ME Cu and 1st cleaner tails %Cu In order to meet the specifications of both products concurrently, it is obvious there is only a narrow operating window, as indicated. Further, with the proposed changes that would result in increased copper units through the process, this window would shrink and, indeed, disappear due to pressure on the copper level in ME. Regardless of these considerations, the existing Denver sub-A cells could not consistently operate within the window shown (Figure 9). The same procedure for carrying out the Fourier transformation as that discussed above was applied to the data for 1st cleaner operation. The resulting plot of variance contributions of the various harmonic curves is shown in Figure 10. The function was filtered, as before, by removing low frequency disturbances (with periods > 1 hour) followed by recalculation. The result is again a projected relative frequency of tails copper assays for the process under improved control (Figure 11). In this example, where a narrow operating band is required, this procedure indicates that a 1st cleaner tails copper grade target can be met within a 1-2%Cu window. This was, indeed, confirmed when the DR-300 cells were installed and operated in Matte Separation.

Evaluation of flotation performance

59

4S 40 35 30 25 _¢ 2O

15

5opt.27/0o 10

I..,I...h..I,..h,.J...J...I.,.h..l*..h

10:00

14:00

,.h..h..h.,h.h,.h..I.,.h..lo..f.d.,h,,h,,

18.'00

22:00

02:00

I I

06:00

10:00

11me

Fig.9 Plant data- %Cu in 1st cleaner tails

40

30

J 20

10

0 ~

7.9 4.0 2.6 2.0 1.6 1.3 1.1 0.~ o.u 0.~ 0.72 o.u o.el o.57 o.53 Lower Limit on Period. h

Fig. 10 Variance spectrum for 1st cleaner tails As with the rougher cells, when first installed, the 1st cleaners operated under a wide variety of level, air flow, feed grade variation and target tails grade conditions in order to thoroughly acquaint the operators with the full performance capabilities of the equipment. The data obtained during this commissioning period are presented in Figure 12 as copper recovery to concentrate versus nickel recovery with lines of equal separation efficiency (defined as copper recovery minus nickel recovery) indicated. At any given point,, the equipment could be operated so as to control the tails to + 1%Cu, well within the window required for meeting product target grades. In addition, whereas separation effieieneies in the range 30-50 % were observed with the sub-A cells, the separation efficiencies achieved with the DR300 cells were in the range 50-70%. Thus, not only was target control achieved, but the improved separation resulted in a dramatic decrease in the circulating loads within the plant which in turn had further metallurgie~d benefits.

60

R. AGNEWet al.

100 80

i

60

1"-I="

.~ 40 2O

..,,tJ

~L.,..BB

182022242628

Tails % Cu

Fig. 11 Relative frequency of 1st cleaner tails assay

100

Sepa~ionElfidency

f.,/.YY'.7 []

10

20

30

40

50

60

70

Nickel Recovery, %

Fig. 12 Denver DR-300: 1st cleaner performance

CONCLUSIONS The application of variance spectrum analysis to noisy flotation process data has been shown to give insight into the nature of the process disturbances. Further, manipulation of the Fourier function can provide a basis for quantifying the metallurgical benefits that might be projected for an equipment upgrade or control system installation.

Evaluationof flotationperformance

61

In the cases studies, the improved control projected by the analysis was achieved in practice. The recovery predictions were, however, exceeded as the equipment upgrade resulted in an improvement to the grade-recovery relationship and consequently the separation efficiency in both cases improved over and above that which could be attributed to result from improved control alone.

REFERENCES Sproule, K., Harcourt, G.A. and Renzoni, L.S., Treatment of Nickel - Copper Matte, Journal of Metals, 3-8 (March 1960). Sopko, M.D. et al, Environmental Programs at Sudbury, Toronto '94, CIMM 96th. Annual General ldeeting, Toronto, 61-77 (May 1994). Rayner, LN., An Introduction to Spectral Analysis, Pion Ltd., London, 174 (1971). Wilson, S.W. and Stratton-Crawley, R., Design of Production Scale Flotation Columns Using a First Order Kinetic Model, Column '91, Sudbury, 165-180 (June 1991). Flintoff, B.C., Neale, A.J. and Hochstein, R.F., The Justification of Process Control Systems in Mineral and Coal Processing Applications, 22nd. CIM Canadian Mineral Processors Conference, Ottawa, 71-98 (Jan. 1990).

.

2. 3. 4. 5.

APPENDIX The Fourier Model In general, a cosine curve can be written,

(i)

Y = AkcosCkO - ~t)

where the curve has a frequency k cycles per basic interval, amplitude Ak, and phase angle ®kThis simplifies to, y

Akcos(~,~)cos(kO)

=

+

Aesin(¢~)sin(~)

(ii)

By defining the Fourier coefficients as, a k = Akeos(@t)

(iii)

bk

(iv)

=

A~in(~

Equation (ii) becomes, y = aFos(~)

+ b~sin(kO)

(v)

Ak and @k can obviously be calculated if ak and b k are known. The sum of squares of equations (iii) and (iv) and dividing equation (iv) by (iii) gives respectively, Ak ffi Ca] + b~ ''~

(vi)

~ t = arctan(bJa~)

(vii)

m

8-Z/Z-E

62

R. AGNEW et al.

The Fourier Series The sum of the functions of the type given in equation (v) above is known as the Fourier series,

y, = ~ [a~cos(kO) + bksin(~)]

(viii)

k=O

For continuous data, this is equivalent to,

(ix) k--0

where,

t T

= =

independent variable (units of distance or time) basic interval

And for discrete equi-spaced data, [a/2nki~

":

,.oE'

.

. [2xki~.

(x)

+

where, i n

= =

observation number number of data points

Calculating the Fourier Coefficients The Fourier coefficients, ak and bk, are easily found based on the relationships of orthogonal functions. For discrete equi-spaced data,

2 ~ ak =

bk

[2~ki'~

)

_

2 ~

. (2n~

(xi)

(xii)

The Variance Spectrum Clearly, Fourier analysis separates the different harmonics within a data set. The significance of each frequency can thus be evaluated in terms o f its contribution to the total variance. The variance of each curve can be shown to be given by half the square of its amplitude, o2 k

= A~/2 = Ca2÷ bb/2

(xiii)

The value of the individual variances plotted against the corresponding frequencies is known as the variance spectrum.