Pergamon 0892--6875(98)00046-6

Minerals Engineering, Vol. 11, No. 7, pp. 615-626, 1998 1998 Published by Elsevier Science Ltd

All fights reserved. Printed in Great Britain 0892--6875/98 $19.00~.00

STUDIES ON IMPELLER TYPE, IMPELLER SPEED AND AIR FLOW RATE IN AN INDUSTRIAL SCALE FLOTATION CELL. PART 5:

VALIDATION OF k-S b RELATIONSHIP AND EFFECT OF FROTH DEPTH

B.K. GORAIN, T.J. NAPIER-MUNN, J.-P. FRANZIDIS and E.V. MANLAPIG

Julius Kruttschnitt Mineral Research Centre, University of Queensland, Isles Rd., Indooroopilly, Queensland 4068, Australia. E-Mall: j.franzidis@mallbox.uq.oz.an

(Received 6 February 1998; accepted 13 March 1998)

ABSTRACT

A previous investigation carried out by the authors at the Hellyer concentrator, using a 3 m 3 cellfitted with four different impellers treating plant zinc cleaner feed ore, suggested a linear correlation betweenflotation rate constant k and bubble surface areaflux Sir The relationship between k and S b was found to be independent of impeller type. This paper describes an investigation at the Scuddles concentrator in Western Australia to validate the findings at Hellyer for a different ore. Unlike the HeUyer work for which only one froth depth was used, the Scuddles work was carried out at different froth depths using the same 3 m 3 cell fitted in turn with three different impellers viz. Batequip, Dorr-Oliver and Outokumpu. The results confirmed the strong correlation between k and S b at three different froth depths used for the study. Moreover, this relationship was found to be practically independent of impeller type. However, at shallow froth depth the k-S b relationship was found to be linear, whereas at intermediate and deep froth depths the relationship was found to be non-linear with the froth playing an important role in the overall kinetics. 1998 Published by Elsevier Science Ltd. All rights reserved

Keywords Flotation bubbles, Flotation kinetics, Froth flotation, Flotation machines

INTRODUCTION

The authors have previously reported the findings of a study conducted in a 3 m 3 portable sub-aeration flotation cell fitted in turn with four different impellers viz. Agitalr Chile-X, Agitair Pipsa, Dorr-Oliver and Outokumpu, treating zinc cleaner feed at the Hellyer Concentrator in Tasmania [1,2,3,4]. In this investigation, the three different indicators of gas dispersion in the cell, viz. bubble size, gas holdup and superficial gas velocity, were measured at different operating conditions (various combinations of impeller speed and air flow rate), along with the metallurgical performance.

It was found that metallurgical performance expressed in terms of a kinetic rate constant k could not easily be related to these indicators individually, but when taken together, these properties determine the bubble surface area flux (Sb) in the cell, which could be related to flotation rate constant extremely well. A linear relationship between k and S b was found for all the four different impellers investigated. Moreover, and

615

616 B.K. Gorain et al.

importantly, the relationship was found to be independent of the type of impeller used. The k-S b relationship can be represented mathematically as:

k--P,s (1)

where P is a parameter which is dependent on ore floatability.

These findings suggest that S b is an important criterion for characterising the metallurgical performance of mechanical flotation cells. S b could potentially be useful for cell optimisation and impeller comparison, selection and design, and the k-S b relationship could have important implications in flotation modelling and scale-up.

This paper presents the results of a second investigation, carried out to confirm the results obtained previously and to investigate the effects of froth depth on the k-S b relationship. This investigation was conducted at the Scuddles concentrator, Normandy Golden Grove Operations in Western Australia, using a zinc cleaner feed ore. As in the previous work, the 3 m 3 pilot plant cell was operated with several impellers, to test the finding that the k--S b relationship is independent of impeller type. Unlike the Hellyer test work, this investigation was carried out at different froth depths to study the effect of this variable.

It should be emphasised that these experiments were not conducted to compare the performance or characteristics of the different impellers used, The impellers were not always operated under optimum (recommended) conditions, or in a cell of optimum design, and were utilised solely to provide a range of hydrodynamic conditions for the study.

EXPERIMENTAL DETAILS

Test feed

The feed used for the Scuddles tests was the plant zinc cleaner feed. The flotation cell used in this investigation was the same continuously operated 3 m 3 cell as used at Hellyer [1]. The cell and other ancilliaries were located on the ground floor of the concentrator where the feed to the test cell could be taken easily from the feed pipe to the plant zinc cleaner bank and the concentrates and tailings of the test cell could be recycled easily back to the same circuit. During the test work, the slurry feed rate to the cell was kept constant to maintain an average residence time of about 9 minutes. As far as possible the chemical conditions in the test cell were kept identical to the plant circuit, i.e. no additional chemicals were added to the test feed during any of the experiments.

Test cells, impellers and cell operating conditions

The pilot cell had the facility to be fitted with different impellers. Batequip, Dorr-Oliver and Outokumpu impellers were used during this test program.

To generate a wide range of hydrodynamic conditions the cell was operated at different impeller speeds and air flow rates as shown in Table 1. The impeller speeds investigated for each impeller were selected

TABLE 1 Operating conditions for the 3 m 3 cell for the Scuddles testwork

Impeller type Cell volume Air flow rates Impeller speeds Froth Depths

(m e) (LJsec) (rpm) (cm)

Outokumpu 3 21.2, 32.9 and 49.4 185, 205" and 225 7, 30 & 45

Dorr-Oliver 3 21.2, 32.9 and 49.4 2:35, 255" and 275 7, 30 & 45

Batequip 3 21.2, 32.9 and 49.4 215, 235" and 255 7, 30

represents manufacturers' recommended impeller speed

Studies on an industrial scale flotation ceil. Part 5 617

around the values recommended by each respective manufacturer for the particular cell size and application.

Variation in froth depth

To investigate the effect of froth depth on the k-S b relationship, the tests described above were repeated at a number of different froth depths. Three froth depths were investigated with respect to the Outokumpu and Dorr-Oliver impellers, and two with respect to the Batequip impeller. The froth depths selected can be classified as shallow, intermediate and deep.

The shallow froth depth was selected as the minimum height such that no pulp discharged into the product launder at any air flow rate selected for the study. Typically the pulp-froth interface was maintained at about 7 cm below the height of cell lip at this condition. The intermediate and deep froth depths selected for the study were 30 cm and 45 cm, respectively.

Experimental procedure

Tests were conducted with each impeller in turn over a period of two weeks. The procedure adopted involved setting a froth depth by adjusting the weir. Then, with the impeller speed kept fixed, the air flow rate was set to the desired value, and conditions in the cell were allowed to stabilise, after which bubble size, gas holdup and superficial gas velocity were measured 1 and samples of the feed, concentrate and tailings were taken. The air flow rate was then set to a new value and the process repeated. After measurements had been made at all three air flow rates, the impeller speed was changed to the new desired value and the whole procedure repeated from the beginning. Once measurements at nine operating conditions (a combination of three air flow rates and three impeller speeds) had been conducted, the froth depth was changed to a new value and all the measurements were repeated.

The whole process was repeated three times, during which the cell was fitted alternately with the Outokumpu, Dorr-Oliver and Batequip mechanisms.

During the testwork care was taken to ensure as far as possible that the test feed was consistent with respect to its composition and feed flow rate. Replicates of some tests were conducted to check the reproducibility of the results with regards to grade and recovery.

In the discussion below, tests will be named as either Outokumpu (OK) tests or Dorr-Oliver (DO) tests or Batequip (BQ) tests depending on the type of impeller fitted in the 3 m 3 cell during a test.

RESULTS AND DISCUSSION

The k-S b relationship is a powerful tool for the quantification and modelling of flotation performance, and the factors which control it The analysis of the present data considers four aspects of the relationship:

A validation of the linear correlation itself, over the range of the data collected

The effect of froth depth on the relationship.

The effect of impeller type on the relationship.

The threshold bubble surface area flux, Sb*

1The procedures for measuring bubble size, gas hold up and superficial gas velocity can be found in Gorain et al [1,2,3].

618 B.K. Gorain et al.

This is done principally through a statistical analysis of the individual k-S b regression lines, including a comparison of the regression lines for different froth depths and impellers, using a method based on that suggested by Hald [5].

Validation of the k-S b relationship

Tables 2a-2c show the measured values of Sauter mean bubble diameter d32, gas holdup eg, superficial gas velocity Jg and calculated values of flotation rate constant 2 k and bubble surface area flux S b for each set of operating conditions for the OK, DO and BQ tests respectively. Figure I shows a plot of k against S b at different froth depths for each of the OK, DO and BQ tests.

TABLE 2 Physical measurements and metallurgical results for the 3 m 3 cell fitted with different impellers/stators

Q = volumetric air flow rate, L/sec; N = impeller speed, rpm; d32 = Sauter mean bubble diameter, mm; eg = gas holdup, %; Jg = superficial gas velocity, cm/sec; kl = k for 7 cm froth depth, 1/min;

k2 = k for 30 cm froth depth, 1/min; k3 = k for 45 cm froth depth, 1/min; S b = bubble surface area flux, m2/m 2 sec

(a) Outokumpu impe l le r / s ta tor (OK tests)

Q N d~ e~ J~ k l k2 k3 S= 21.2 185 1.26 8.62 0.78 0.1135 0.0818 0.0650 37.14 21.2 205 1.15 8,87 0.76 0.1245 0.0735 0.0619 39.65 21.2 225 1.23 10.85 0.75 0.1077 0.0893 0.0560 36.59 32.9 185 1.50 10.97 1.25 0.1820 0.1361 0,0970 50.00 32.9 205 1.26 12.55 1.22 0.2025 0.1326 0.1091 58.1G 32.9 225 1.45 12.65 1.18 0.1923 0.1131 0.1021 48.83 49,4 185 1.57 11,58 1.69 0.2278 0.1666 0.1411 64.59 49,4 205 1.42 13.79 1.68 0.2921 0.1909 0.1729 70.99 49.4 225 1.39 14.53 1.65 0.2801 0.2107 0.1626 71.22

(b) Dorr-Oliver impelleffstator (DO tests)

Q N d~ e= J= k l k2 k3 S b 21.2 235 1.24 5,59 0.78 0.1014 0.0653 0.0413 37.74 21,2 255 1.17 6.25 0.77 0.1096 0.0832 0.0486 39.49 21.2 275 1.16 8.35 0.75 0.1021 0.0697 0.0481 38.79 32.9 235 1.45 7.53 1.25 0.1412 0.0959 0.0842 51.72 32.9 255 1.26 10.17 1,23 0.1632 0.1178 0.0987 58.57 32,9 275 1.31 11.17 1.19 0.1742 0.1220 0.1010 54.50 49.4 235 1.53 7.97 1.52 0.1764 0.1277 0.1236 59.61 49.4 255 1.40 11.1 1.67 0.1977 0.1828 0.1394 71.57 49.4 275 1.35 13.8 1.68 0.2502 0.2174 0.1635 74.67

(c) Batequip impeller/stator (BQ tests) Q

21.2 21.2 21.2 32.9 32.9 32.9 49.4 49.4 49.4

215 235 255 215 235 255 215 235 255

dl= 1.47 1.36 1.13 1.64 1.41 1.16 1.85 1.55 1.29

8.87 9.38 11.17 11.15 14.86 17.22 12.28 15.97 18.87

gl~ 0.76 0.76 0.75 1.20 1.19 1.20 1.67 1.66 1.65

k l 0.0967 0.0877 0.1106 0.1451 0.1841 0.2282 0.2294 0.2267 0.2719

k2 0.0591 0.0818 0.1050 0.1110 0.1411 0.2012 0.1807 0.1945 0.2406

S b 31.02 33.53 39.82, 43.90 50.64 61.02 54.16 64.26 76.74

2The procedures for determining k and calculating St~ may be found in Gorain et al [4].

Studies on an industrial scale flotation cell. Pan 5 619

~

d

O

d o

O

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 ' 0

0.4

0.35

0.3

0.25

0.2

Outokumpu impe l le r

] ','-~ " /em froth depth I i . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . . . . . ! . . . . . . . . . . . . . . . . _~

I ra 30 cm froth depth I ! -~

I ,Se . ,~thd,~th I ! . . . . . . . . . . . . . . . . . . : . . . . . . . . . ~ . . . . . . :: . . . . . . . . . . . . . . . .

i ! a g i : .................................. :.. ........ g ....... ~.~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . o , ~

............................... .,,~..: ...... ~> ...... .o.i ................. , ...............

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . : . . . . . . . . . . . . . . . .

2 4

20 40 60 80 100

Bubble surface area f lux (m~/m ~ sec)

Batequip impe l le r " ' 7- "~-~r - - -~-~- -~- - r " - -~ . . . . . . . . . ~- -7 . . . . . . . . ~ . . . . . .

1 ..,,.h I i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . . . . . . . . ; i l / : ; . . . . . . . . . . ~ i . . . . . . . . . . . . . . . . .

0.15 ................................... ~":~'"-~ ....... : ................. ! ................ --

0.1 ................................... ~--~ ............. :. ...................................

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0 20 40 60 80 100

Bubble surface area f lux (m2/m 2 sec)

.~I 0.4

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g: 0.3

0.25

0.2

0.15

O .~ ,, 0.1

O 005

0

Dorr-Oliver im )eller ' I

~[ O 7 cm froth depth .................................................... 30 em froth depth

O 45 em froth depth q

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ ~ . . . . . . . . . . . . ~ i . . . . . . . . . . . . . . . . : "-~ O 2

.... ~ ~

20 40 60 80 100

Bubble surface area f lux (m2/m 2 sec)

Fig. 1 Variation of k with S b at different froth depths for the 3 m 3 cell fitted with different impellers.

The analysis which follows assumes that the k-S b correlation can be modelled by a straight l ine over the range of the data collected. Figure 1 suggests that this is a reasonable assumption for a given impeller and froth depth. The l inear correlation coefficient was calculated for each line in Figure 1, and its significance tested using a t-test. The results are shown in Table 3. All correlation coefficients are significant at a confidence level greater than 99%, and it is therefore concluded that the assumption of l inearity is justified.

620 B.K. Gorain et aL

The questions which now arise are:

Do the lines differ between froth depths for a given impeller? Do the lines differ between impellers for a given froth depth? Do the lines pass through the origin, or are their intercepts significant?

TABLE 3 Significance of linear correlation coefficient R for k-S b tests for the 3 m 3 cell (Figure 1)

Impeller type Froth Depth Correlation t Coeff icient R (significance of R)

Outokumpu 7 cm 0.983 14.15

Dorr- Oliver

Batequip

30 cm 45 cm

0.969 0.986

10.33 15.59

7 cm 0.967 10.03 30 cm 0.962 9.33 45 cm 0.987 16.03

0.965 0.800

7 cm 30 cm

9.77 3.53

Critical t values

t0.05 = 2.36 t0.01 =

(n-2 = 7 degrees of freedom)

3.50

Effect of froth depth

Figure 1 suggests that the k-S b correlation varies with froth depth for a given impeller, k decreasing as froth depth increases. This may be tested statistically by comparing the regression lines for different froth depths within each impeller. Differences in gradient are assessed by an F-test and differences in the mean separation of the lines by a t-test. The results are shown in Table 4. With the exception of the OK cell tests, for which the gradient of the 7 cm froth depth line is significantly greater than that of the 30 cm depth, the gradients of the regression lines are essentially the same. This suggests that the floatability of the material under these conditions (P in eqn 1) is largely unaffected by froth depth or impeller. However the separation of the lines (ie differences in k with froth depth) reaches significance at the 99% level of confidence in all cases, except in that of the Batequip impeller in which the difference does not quite reach significance at the 95% level. It can therefore be concluded that the k-S b relationship does indeed vary with froth depth, k being greater for lower froth depths.

Laplante et al [6] have found that at low froth depth and very high air flow rates, the overall flotation rate constant k is equal to the collection zone rate constant k c. Hence the k values obtained for the shallow froth depth (7 cm) in the present work can be considered equal to the value of k c. Therefore equation 1 can be modified for shallow froth depth to:

k=k~=P*S~ (2)

At intermediate froth depths of 30 cm, the values of k are smaller than for shallow froths at the same values of S b (see Table 2). The k values become even smaller when the froth depth is further increased to 45 cm. This suggests that the effect of the froth is becoming more significant with increase in froth depth. In the literature [7] the effect of froth depth is generally represented by a froth recovery factor (Rf) which is defined as the ratio of the overall rate constant (k) and the collection zone rate constant (kc) and can be represented mathematically as:

Studies on an industrial scale flotation cell. Part 5 621

(3)

Combining equations 2 and 3, the effect of froth depth on the k-S b relationship can be represented as:

k=P,Sb ,R/ (4)

TABLE 4 Comparison of k--S b regression lines for different froth depths

k- S b

parameter

I Gradient

F-value

Separation of lines

t-value

OK

9.00

0.0587

7 cm 30 cm 45 cm

0.0048 0.0034 0.0031

0.664

0.0252

9.46 5.01

DO 7 cm 30 cm 45 cm

0.0035 0.0036 0.0031

0.0342 1.284

0.0371 0.0259

5.53 4.66

BQ 7 cm 30 cm

0.0043 0.0033

1.11

0.0295

2.03

Note: The tests are:

1. Between the gradients of pairs of lines (F-test: 1, 14 degrees of freedom,)

2. Between the mean separation of pairs of lines (2-sided t-test : 14 degrees

of freedom)

Critical values of F and t

F0.10 = 3.10 t0.10 = 1.76 F0.01 = 8.86 t0.05 = 2.14

t0.01 = 2.98

Effect of the impeller

Figure 2 shows that the k-S b points cluster quite well around single lines for each of the froth depths, suggesting that the relationship is independent of impeller type. Such an assumption may be an adequate approximation for many practical situations. A rigorous statistical analysis along the lines described earlier confirms the assumption in general but also reveals some interesting differences.

Apart from the OK and DO tests, in which the OK impeller exhibits a significantly larger gradient than the DO at 7 cm froth depth (F = 7.35), the gradients of the k-S b correlation are the same (not significantly different) for each froth depth (see Table 4). However some of the separations of the lines are significantly different, as shown in Table 5.

It is clear that both the OK and BQ impellers produce greater values of k than the DO impeller at a given froth depth. The differences are small--about 0.03 min-~--but may indicate an effect worth investigating. The OK and BQ impellers produce essentially the same k; there is a small difference at the largest froth depth, but no significant difference at the other two.

It may therefore be concluded that the k-S b correlation is independent of impeller type for the OK and BQ impellers, but the DO unit shows a small difference. For some practical purposes this difference may be ignored.

622 B .K . Gora in et al.

]

@ e~

@

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0 . I$

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O Batequ Jp

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ! . . . . . . . ~ ; .o .~ .o . . . . . . . . . . . . . ! . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . i -~ ,---=. . . . . . . . :: . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . ~ .~.~.~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 : , :

................. ! ................. i ................. ! ................. ! ................

0 20 40 60 80 I00

Bubble surface area flux (~/m z see)

" 0.4

0.3$

0 .3

@

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P ~ 0 .1

~@ 0.05

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30 cm froth depth

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -: . . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . . .

i e, tJ i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~. . . . . .

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. . . . . . . . . . . . . . . . i . . . . . . . . . . . . . -~-~-.?--- :--.o ~- -~- . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . . . .

L ~ i ;

i J I i i i I , i i 1 i i i l i I r

0 20 40 60 80 100

Bubble surface area flux (m2/m 2 see)

. 0.4

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i 0.~ 0.2 lPl 0 .15

0.1

i 0 .05

45 cm froth depth I ! J

i : !

ii iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii iiiiii iiiiiiiiiiiiiiiiiiiiiiiiiiiiill iiiiiiiii i i ~n i

................. ? ................................... i " '~t5 ...... ~ ................ : {3 :

. . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . ~ . . . . . . %-~- .~ i - . . . . . . . . . . . . . . . . . ! . . . . . . . . . . . . . . . . .

................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i ................. i ................ t I i [ I i I I t I [ I I t i ~ J

20 40 60 80 100

Bubb le sur face area f lux (m2hn 2 see)

Fig.2 Variation of k with S b for different impellers at each of the three different froth depths.

Threshold bubble surface area flux Sb*

Statistical t-tests for the intermediate and deep froth depths showed that the best straight lines through the data points are very likely (greater than 99.5% confidence level) to intersect the x-axis and therefore do not pass through the origin (see Figure 2). This suggests that, for the intermediate and deep froth depths, there are non zero (positive) values for S b for which the overall flotation rate constant k is zero. The value of S b which is intercepted by the fitted line on the x-axis will be referred to as Sb . Table 6 shows the values of Sb* for the line (k = P'* S b + c) fitted through the data points for the intermediate and deep froth depths. The fitted Sb* values range from 16 to 21 m2/m 2 see.

Studies on an industrial scale flotation cell. Part 5

TABLE 5 Effect of impeller type on the k-S b relationship

623

Comparison

OK1 vs DO1

OK2 vs DO2

OK3 vs DO3

OK1 vs BQ1

OK2 vs BQ2

BQ1 vs DO1

BQ2 vs DO2

Mean Separation

of lines

0.0385

0.0162

0.0165

-0.022

0.0046

0.032

0.038

t-value

(14 d. f.)

6.06

2.47

4.59

1.55

0.60

4.11

2.68

Significance

> 99%

95%

99%

Not signilicant

Not significant

99%

98%

Key: OK = Outokumpu 1 = Froth depth 7 cm

DO = Doff-Oliver 2 = Froth depth 30 cm

BQ = Batequip 3 = Froth depth 45 cm

TABLE 6 Observed and fitted values of Sb* at different froth depths for the 3 m 3 cell

Froth depth Sb* (fitted) S~* (observed) Impeller type 4.50 Outokumpu

Intermediate 16.22 5.30 Doff-Oliver {30 cm) 4.32 Batequip

Deep 21.00 7.65 Outokumpu (45 cm) 8.04 Dorr-Oliver

The physical significance of the parameter Sb* is that it represents the threshold value of bubble surface area flux in a cell, above which the froth which builds up in the cell is discharged into the launder. Below this threshold value of Sb* the froth will not be discharged into the launder: the overall cell recovery and k will be zero even though particle collection is occurring in the pulp phase or collection zone.

The fact that there is a threshold value of S b was confirmed experimentally by operating the cells at very low air flow rates. The froth did not discharge over the lip even though mineral loaded bubbles were found to cover the pulp in the cell slowly until a very thin froth layer was formed. A further increase in air flow rate resulted in a gradual build up of froth, but it was not until a superficial gas velocity (Jg) of about 0.1 to 0.2 cm/sec (depending on froth depth) was reached that the froth build up was sufficient to reach the overflow lip, at which point froth started to drip into the launder.

At the air flow rate when the froth was just able to discharge into the launder, bubble size was measured to determine the Sb* for the different impellers at the intermediate and deep froth depth. The values of S b so obtained are shown in Table 6 ("observed" values) and were in the range from 4 to 8 m2/m 2 sec, depending on froth depth and impeller type, although the effect of impeller type on the values of Sb* is practically insignificant.

A comparison of the fitted and the observed values values of S b shows that the observed values are 3 to 4 times smaller than the fitted values obtained using a straight line k = P' * S b + c. This suggests that the data points at intermediate and deep froth depths may represent a curve at the lower end rather than a straight line (see Figure 3). The data points were fitted using a non-linear relationship proposed by Harris [8], which takes into account the effect of the froth on the overall flotation kinetics:

624 B.K. Gorain et al.

k o

= P ,Sb ,

1 +o *(S~-S;) (5)

where

P t~

Sb

= ore floatability = froth related constant = threshold bubble surface area flux

0.4

0.35 pm

~ 0.3

~ o.~ o ,~ 0.2

~ 0.15

O ~ o.1

O 0.05

0

i . / /

. . / -

! i / " j ,"~ . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . . . . . ! ; , " ~ . J : : : - -

, , , f~ . ,4~1J "

. . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . i" . . . . . . . ~">; i . . . . . . . . . . . . . . . -

. . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . :~ . . . . . . . . . . . . . . . . . L ,~c : . . . . . . . . . i . . . . . . . . . . . . . . . : ~b . observed i. --_.-. ~,, /, ~,~.s- : ! : _i

. . . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

/ : ~ :~ ' j~- - -~ S fitted: : . - - t - - - ' - x "~ , I . ,~ ~ , I I ,h t I I I I t I L i L

O 20 40 60 80 100

Bubble surface area flux (m2/m 2 see)

Fig.3 Variation of k with S b for the 3 m 3 Dorr-Oliver impeller operated at 30 cm froth depth; illustrating the probability of a curve rather than a straight line.

The statistical values of R 2 and Chi square (Z 2) obtained from fitting equation 5 are shown in Table 7. As can be seen from Table 7, equation 5 was able to fit the experimental data points very well. This supports the hypothesis that the relationship between k and S b is non-linear for intermediate and deep froth depths. The non-linear relationship between k and S b indicates that both the collection zone and the froth zone have an effect on the overall flotation kinetics for intermediate and deep froth depths.

TABLE 7 Values of R z and X z values obtained from fitting equation 5 through the data points at intermediate and deep froth depths

Froth depth R = X = Impeller type

0.94 0.0011

Intermediate

(30 cm)

Deep

(45 cm)

0.88 0.0024

0.95 0.0015 Batequip

0.97

0.94

0.0004

0.0008

Outokumpu

Dorr-Oliver

Outokumpu

Dorr-Oliver

Studies on an industrial scale flotation cell. Part 5 625

The relationship between k and S b, therefore, transforms from a linear one at a shallow froth depth to a non- linear one at intermediate and deep froth.

The effect of froth depth on flotation kinetics is being investigated by the authors at other mine sites as part of the AMIRA P9 project. The results of these investigations will be reported at a later date in this journal.

CONCLUSIONS

Investigations at the Scuddles concentrator have confirmed a strong correlation between the flotation rate constant k and bubble surface area flux S b at three different froth depths. The correlation is linear over the range of data collected. The correlation was found to be relatively independent of impeller type, a finding similar to that obtained previously by the authors, although small differences were identified in some cases; the reasons for these need to be studied further.

At shallow froth depth the relationship between k and S b can be mathematically represented as:

k = k c =P*S b

where k c = collection zone rate constant and P is the floatability of the ore.

At intermediate and deep froth depths, when froth plays an important role in determining the overall kinetics, the relationship between k and S b can be suitably represented using a froth recovery factor Rf as shown below:

k -- P*Sb*R f

Rf in turn can be represented mathematically as [8]:

o .(sb-s;)

1 + o "(S b -s ; )

where (I

S b * = froth related constant = threshold bubble surface area flux which can be defined as the value of S b above which the froth which builds up in the cell is discharged into the launder.

ACKNOWLEDGEMENTS

The authors would like to acknowledge gratefully the full support and co-operation received from the staff at Scuddles Mine, Normandy Golden Grove Operations in Western Australia, during the period of the test work, especially Roy Francis, Ashley Kidd and other metallurgical, electrical and mechanical staff.

Thanks are also due to Martin Harris and Dave Deglon of the Department of Chemical Engineering, University of Cape Town for their useful discussions and help during the test work.

Finally the authors would like to thank the Australian Research Council (ARC) and the sponsors of the Australian Mineral Industries Research Association (AMIRA) P9K and P9L projects for their financial support.

626 B.K. Gorain et al.

REFERENCES

1.

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.

.

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6.

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8.

Gorain, B.K., Franzidis, J.-P. & Manlapig, E.V., Studies on impeller type, impeller speed and air flow rate in an industrial scale flotation cell. Part 1. Effect on bubble size distribution", Minerals Engineering, 8(6), 615-635 (1995). Gorain, B.K., Franzidis, J.-P. & Manlapig, E.V., Studies on impeller type, impeller speed and air flow rate in an industrial scale flotation cell. Part 2. Effect on gas holdup. Minerals Engineering, 8(12), 1557-1570 (1995). Gorain, B.K., Franzidis, J.-P. & Manlapig, E.V., Studies on impeller type, impeller speed and air flow rate in an industrial scale flotation cell. Part 3. Effect on superficial gas velocity. Minerals Engineering, 9(6), 615-635 (1996). Gorain, B.K., Franzidis, J.-P. & Manlapig, E.V., Studies on impeller type, impeller speed and air flow rate in an industrial scale flotation cell--Part 4 : Effect of bubble surface area flux on flotation kinetics, Minerals Engineering, 10(4), 367-379 (1997). Hald, A., Statistical theory with engineering applications, John Wiley and Sons, (1952). Laplante, A.R., Kaya, M. & Smith, H.W., The effect of froth on flotation kinetics--A mass transfer approach, Min. Proc. and Extr. Met. Rev., 5, 147-168 (1989). Finch, J.A. & Dobby, G.S., Column Flotation, Pergamon Press, (1990). Harris, M.C., Department of Chemical Engineering, University of Cape Town, Personal Communication, (1996).

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