- Email: [email protected]
Flotation scale up: use of separability curves
Minerals Engineering 16 (2003) 347–352 This article is also available online at: www.elsevier.com/locate/mineng
Flotation scale up: use of separability curves q J.B. Yianatos a
a,*
, L.G. Bergh a, J. Aguilera
b
Department of Chemical Engineering, Santa Marıa University, Valparaıso, Chile b Divisi on Salvador, Codelco-Chile, El Salvador, Chile Received 31 October 2002; accepted 17 January 2003
Abstract Separability curves (mineral recovery versus yield) have been used to characterize the copper flotation process both at batch laboratory scale and industrial plant scale (rougher banks). Then, to approach the scale-up problem the rougher bank operation and the batch were compared using the corresponding separability curves. Comparison was made at the maximum separation efficiency point in both operations. Thus, a time factor was established for optimal technical separation. The time factor can then be used for kinetic scale-up models, together with the ratio between minerals recovery in both operating scales. Experience from several tests recorded over a period of 10 months in an industrial concentrator showed a good consistency for scaling-up the rougher flotation recovery from batch tests within a 1% absolute error range. The effect of particle size and air flowrate in laboratory batch tests was evaluated in the space of separability curves, regarding their effect on recovery at the optimum separability point. Also, the effect of pulp level and particle size on the bank flotation kinetics was evaluated in an industrial flotation circuit. Thus, estimation of recovery changes due to variations in mineral characteristics and operating conditions was explored. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Flotation; Scale-up; Particle size; Optimal separability
1. Introduction The flotation scale-up problem is complex because the mineral characteristics (grade, size, mineralogy), cell characteristics (geometry, power consumption, energy dissipation, bubble and particle size distribution), reagent conditioning and operating conditions (air flowrate, pulp level, froth transport and discharge facilities) are different and variable in batch and plant operation. Time scale up factors for flotation kinetics prediction are generally derived by comparison of industrial flotation banks and laboratory batch cell recovery. However, in plant practice it is common to find very low mineral recoveries in the last cells of the rougher banks. Thus, a direct time comparison between the overall bank performance and the batch operation, at the same recovery, can introduce large errors. A better approach was to simulate the bank performance in order to estimate the q Presented at Minerals Engineering Õ02, Perth, Australia, September 2002. * Corresponding author. E-mail addresses: [email protected], [email protected] (J.B. Yianatos).
flotation rate constant and recovery at infinite times, and then to compare these parameters with those estimated from batch flotation (Yianatos et al., 2000). Even so, there is a lack of standard reference for batch tests and results are strongly dependent not only on mineral characteristics, such as particle size and grade, but also on flotation operating conditions such as air rate and pulp level. An alternative way to approach this problem is to compare the rougher bank operation and the batch flotation using the corresponding separability curves. 1.1. Separability curves Separability curves represent the evolution of the mineral separation of a particular flotation process in terms of the concentrate mineral recovery and the process yield defined as the ratio between concentrate and feed mass flowrates. Also, considering the x-axis as the ratio between process yield and feed grade, it is possible to estimate the average concentrate grade by the slope of the straight line resulting from connection of any recovery point of the curve with the origin. In addition, any straight line tangent to the curve represents the incremental concentrate grade at that point. According to
0892-6875/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0892-6875(03)00024-4
J.B. Yianatos et al. / Minerals Engineering 16 (2003) 347–352
AgarÕs principle (Agar et al., 1980), this property can be used to estimate the optimal separability point, when the concentrate incremental grade equals the feed grade. Separability curves depend on feed characteristics and mineral conditioning as well as on characteristics and operation of flotation cells. Thus, assuming a standard batch test gives the best flotation separation for a non-perfectly liberated mineral, the batch separability curve can be used as an ideal target for plant operation. In this approach the combined effect of the concentrate grade and recovery can be observed at the optimal separability point. 2. Flotation process modelling The particle collection rate is based on fundamental particle-bubble collision and/or cavitation and adhesion processes (Schulze, 2002). However, from a practical point of view, the overall flotation process is generally well represented by a first order kinetic model (Polat and Chander, 2000). Thus, mineral species recovery in continuous industrial flotation equipment can be described by the general equation, Z 1Z 1 rðtÞ ¼ r1 ð1 ekt ÞF ðkÞEðtÞ dk dt ð1Þ 0
0
where r1 represents the maximum flotation recovery at infinite time. The term ð1 ekt Þ represents the mineral recovery of a first order process with invariant kinetic rate constant k, as a time function. F ðkÞ is the kinetic constant distribution function for mineral species with different flotation rates, and EðtÞ is the residence time distribution function for continuous processes with different mixing characteristics. The simplest F ðkÞ distribution is the rectangular distribution which allows accounting for different kinetic properties of complex minerals, while maintaining the parsimony principle of using a reduced number of parameters. The rectangular distribution model is described as follows, 1 F ðkÞ ¼ for 0 < k < kmax ð2Þ kmax F ðkÞ ¼ 0 for 1 > k > kmax 2.1. Batch flotation modelling The mineral recovery in a batch flotation test can be estimated from Eqs. (1) and (2), with EðtÞ ¼ dðtÞ by, 1 ½1 ekmax t rðtÞ ¼ r1 kmax t
2.2. Rougher flotation modelling For N continuous perfect mixers-in-series, with a total residence time s, Eq. (4) has shown a good agreement to represent the residence time distribution of the rougher plant (Yianatos et al., 2002). tN 1 eð s Þ EðtÞ ¼ N s CðN Þ N N t
ð4Þ
Thus, the following Eq. (5) can be derived from Eqs. (1), (2) and (4) for mineral recovery, s 1N 1 1 1 þ kmax N RðsÞ ¼ R1 ð5Þ kmax s ðN 1Þ N
3. Experimental Experimental work was developed at laboratory and plant scale at Divisi on Salvador, Codelco-Chile. Batch flotation was developed at the Metallurgical Laboratory, using two standard Wemco cells of 2.7 (L) and 5.3 (L). Two kinds of tests were considered: (a) predictive monthly tests using ore samples, and (b) special tests to study the effect of different variables, such as particle size and air rate on batch performance. Plant testing was developed in the rougher flotation circuit, consisting of five parallel flotation banks. Each bank provided with nine self-aerated Wemco cells of 42.5 m3 (1500 ft3 ) in arrangement 3–3–3. Rougher flotation performance was evaluated on the basis of daily overall sampling (three shifts), and also special tests for kinetic characterization of the rougher bank were developed. 3.1. Batch flotation characterization Fig. 1 shows an example of the data over a monthly predictive batch test using Eq. (3).
100
80
Cu Recovery, %
348
60
40
Data
ð3Þ
where rðtÞ and r1 are the mineral recovery at time t and the maximum recovery at an infinite time, kmax is the maximum rate constant of a rectangular F ðkÞ distribution and t is the effective residence time.
20
Model
0 0
5
10
15
20
Time, min
Fig. 1. Batch flotation data fitting.
25
30
J.B. Yianatos et al. / Minerals Engineering 16 (2003) 347–352
349
16
Cumul. Grade
14
Increm. Grade
12
Cu Grade, %
Feed Grade 10 8 6 4 2 0 60
65
70
75
80
85
90
95
100
Cu Recovery, %
Fig. 4. Effect of air flowrate on batch separability curves.
Fig. 2. Grade or incremental grade versus recovery in batch flotation.
Data from the same experience in Fig. 1, can be represented in a grade-recovery space, or an incremental grade-recovery space, in order to visualize the optimal separability point where the incremental grade equals the feed grade, as it is shown in Fig. 2. An alternative way of representing the batch process is the separability curve. In this approach the maximum technical separability point corresponds to the point of tangency of the feed grade line, as it is shown in Fig. 3. 3.2. Effect of air rate on batch separability curves The change of air flowrate was evaluated regarding their effect on recovery for the optimum separability point. Thus, estimation of recovery changes due to variations in mineral characteristics and operating conditions was explored. Fig. 4 shows the comparison of batch separability curves at two air flowrates, low and high, corresponding to 6 and 10 l/min. From Fig. 4 it is shown that at higher air flowrate the final copper recovery and the final yield were both higher than for the
lower air flowrate. Similarly, for the same recovery, the concentrate grade decreased at higher air flowrates. In both conditions optimal separation was achieved at similar recoveries, however the time was lower for the higher air flowrate. This result shows how sensitive the ‘‘ideal’’ separability is in terms of the operating conditions. 3.3. Effect of grinding level on batch separability curves Among other variables, separability curves strongly depend on particle size, or otherwise on mineral liberation. For example, Fig. 5 shows a series of batch tests developed at the same flotation conditions but varying the grinding level from 5% to 30% þ 212 lm. Here, it can be seen that the grinding effect became significant at recoveries higher than 50% where the separability curves start to deviate more rapidly from the dash line representing the copper grade of the pure mineral. In this case, copper recovery for optimal separation varied from 70% to 85%, whereas the coarse particles content decreased from 30% to 5% þ 212 lm. The dash line
100 100
90
80
80
Recovery of Cu, %
Cu Recovery, %
90
70
60
Batch 50
Feed
70 5% +212 um 60
15% +212 um
50
20% +212 um 25% +212 um
40
30% +212 um 30
Min. Grade
20
Feed Grade
10
40
0
0
5
10
15
Yield / feed grade Fig. 3. Separability curve in batch flotation.
20
0
5
10
15
Yield / feed grade
Fig. 5. Effect of grinding on batch separability curves.
20
J.B. Yianatos et al. / Minerals Engineering 16 (2003) 347–352
represents the maximum ideal separability, while the continuous straight line corresponds to the feed grade and represents the case of a perfect sampling without separation. 3.4. Effect of pulp level on rougher flotation operation The effect of pulp level was observed from a kinetic study performed in two parallel rougher flotation banks. Sampling and overall mass balances per size class were developed by local sampling (around three cells) along the bank. The pulp level was increased in one rougher bank and the performance was compared with the rougher bank operating in parallel under normal conditions. Results showed a moderate increase of 2.7% in the final copper recovery, as it is shown in Fig. 6. However, comparison of separability curves of both operations, in Fig. 7, showed a critical effect in the middle section of the bank operating at high pulp level, where the concentrate overflow increased dramatically, thus generating a significant entrainment and an in-
100
Recovery of copper, %
90 80
90 80 70 60 50
Size: + 212 um
40
Size: +75-212 um
30
Size: +45-75 um
20
Size: -45 um
10
Feed grades
0 0
5
10
15
20
Yield / feed grade
Fig. 8. Separability curves for different particle size classes in rougher flotation.
crease in the overall yield above normal ranges. Also, the final concentrate grade showed a strong decrease while the overall pulp residence time increased. The significance of this experience is that sometimes a small modification in operating conditions, i.e. pulp level, can significantly destabilize the overall circuit performance, despite the expected result of achieving an increase in recovery. This problem arose because of an improper operation of the level control system in the middle of the bank. 3.5. Effect of particle size on rougher plant operation
70 60 50
High level Low level
40 30 0
3
6
9
12
Cell number
Fig. 6. Effect of pulp level in two parallel flotation banks.
100
90
Recovery of copper, %
100
Recovery of copper
350
80
70
Fig. 8 shows the separability curves for four particle size classes in a rougher flotation bank operating under normal conditions. Maximum recovery of 95.2% was achieved in the medium size class, +45–75 lm, and a minimum recovery of 30% was obtained for the coarser mineral, +212 lm. In both cases the final separability was very good. However, the finest size class, )45 lm, only reached an 80.3% final recovery, with an overall yield significantly higher than other classes. The reason is that the finest particle size class has a significant entrainment, particularly in the first three flotation cells of the bank, where the cumulative concentrate grade (slope of the curve) was the lowest despite the finest mineral being better liberated. In summary, feed characteristics and their conditioning as well as experimental operating conditions, both at laboratory and plant scale, can significantly affect the comparison for scale up purposes.
60
Feed Grade Low level
50
4. Scale-up factors
High level
40 0
5
10
15
20
25
30
Yield/ feed grade
Fig. 7. Effect of increasing pulp level in rougher flotation banks.
35
The following two dimensionless variables, from Eqs. (3) and (5), were found to be reasonably constant while comparing the batch laboratory and rougher plant operations,
J.B. Yianatos et al. / Minerals Engineering 16 (2003) 347–352
½Kmax sPlant ¼ ½kmax tLab RðsÞ rðtÞ ¼ R1 Plant r1 Lab
ð6Þ ð7Þ
Then, the following scale-up factors were selected at the optimum separability point, s kmax ¼ t Kmax RðsÞ R1 ¼ rðtÞ r1
ð8Þ ð9Þ
The parameters to evaluate are the flotation times s and t, as well as recoveries RðsÞ and rðtÞ, for plant and laboratory flotation at the optimal separability point. The proposed method was tested by comparing the average monthly rougher recovery with the recovery of monthly batch tests. Both operations were firstly characterized by their corresponding separability curves and then compared at the optimal separability point. Here, optimal technical separation refers to the point where the concentrate incremental grade, tangent to the curve, is equal to the feed grade. Fig. 9 shows an example of this approach where data from batch and plant rougher operation was compared using separability curves. Separability curves for the rougher flotation circuit was based on the average recovery calculated from daily recorded data (three shifts) on feed, concentrate and tailings grade, as well as average feed tonnage and pulp density. The data was processed in a rougher flotation simulator to generate the corresponding separability 100
351
curves. The simulator was previously validated from kinetic flotation sampling developed on the same rougher banks. An example of average monthly data and their standard deviation is presented in Table 1. Fig. 10 shows the results for the scale-up factor corresponding to the ratio between plant ðs ¼ NT Þ and laboratory ðtÞ flotation times, evaluated at the optimal separability point, considering repeats in the monthly batch flotation predictions. The average result over a period of 10 months was, sPlant ¼ 2:26 0:35 ð10Þ tlab On the other hand, it was found that the scale-up factor corresponding to the ratio between plant and laboratory recoveries, Eq. (9), was strongly dependent on the % of soluble copper in plant operation. Fig. 11 shows the effect of soluble copper content (%) on the ratio between plant and laboratory flotation recovery, both evaluated at the optimal separability point. This relation was correlated by the following equation, considering the maximum (R=r) ratio as a function of the soluble copper content, RðsÞ ¼ 1:045 0:00945 ½% soluble copper rðtÞ
ð11Þ
In summary, using Eqs. (8)–(11) the parameters for plant simulation, Kmax and R1 , can be derived from batch flotation characterization by kmax and r1 . Fig. 12 shows the comparison between the actual rougher recovery and the rougher recovery estimated from batch tests, using scale-up factors and simulation of the rougher circuit operation for the same conditions. From Fig. 12 it can be seen that for the testing period of
(NT/ t) at optimal separability
Recovery of Cu, %
90
80
70
Batch Lab.
60
Rougher Plant 50
Feed Grade
5
4
3
2
1
0
40
0
0
5
10
15
1
2
3
20
4
5
6
7
8
9
10
11
Month
Yield / feed grade
Fig. 9. Separability curves for batch and rougher plant operation.
Fig. 10. Comparison of flotation time between plant and laboratory at optimal separability.
Table 1 Rougher operating conditions, monthly average Month
Feed %Cu
Soluble Cu (%)
% þ212 lm
Throughput TPD
Cu recovery (%)
Solid (%)
November December January
0.715 0.033 0.697 0.028 0.722 0.005
9.16 1.68 7.52 0.86 8.03 1.94
24.46 1.56 22.92 1.61 22.35 0.27
34,590 2368 32,680 4015 31,567 486
81.38 1.31 83.71 1.35 83.79 0.39
35.96 0.57 35.24 0.61 35.05 0.31
352
J.B. Yianatos et al. / Minerals Engineering 16 (2003) 347–352
(R /r) at optimal separability
1
data model
0.98
0.96
0.94
0.92 0.9
0.88 4
6
8
10
12
14
16
Soluble copper, % Fig. 11. Effect of soluble copper on the ratio between plant and batch recovery at optimum separation.
88
mance, based on separability curves, was developed and evaluated in order to estimate scale-up factors. This approach is more robust and less sensitive to the laboratory and rougher flotation operation, particularly the last cells in the rougher bank. Experience from several tests recorded over a period of 10 months in an industrial concentrator showed a good consistency for scaling-up the rougher flotation recovery from batch tests within a 1% absolute error range. The significant effect of changing operation variables such as particle size and air flowrate at laboratory scale was evaluated for predictive purposes. It was also found that maximization of the rougher flotation recovery, by increasing pulp level, is critically limited by the quality of the pulp level control system.
Acknowledgements
Plant copper recovery
86
The authors are grateful to El Salvador Division of Codelco-Chile for providing access to their plant and for valuable assistance in the experimental work. Funding for process modeling and control research is provided by CONICYT, project Fondecyt 1020215, and Santa Marıa University, project 270122.
84 82 80 78 76
References
74 74
76
78
80
82
84
86
88
Estimated copper recovery Fig. 12. Estimated versus plant recovery from scale-up model fitting.
10 months the scale-up procedure shows a reasonable good result with a maximum deviation of about 1% in plant copper recovery.
5. Conclusions A standard comparison between laboratory batch flotation tests and industrial rougher flotation perfor-
Agar, G.E., Stratton-Crawley, R., Bruce, T.J., 1980. Optimizing the design of flotation circuits. CIM Bulletin 73 (824), 173–181. Polat, M., Chander, S., 2000. First-order flotation kinetics models and methods for estimation of the true distribution of flotation rate constants. International Journal of Mineral Processing 58, 145– 166. Schulze, H.J., 2002. Stability and rupture of thin aqueous films and flotation. In: Strategic Conference on Flotation and Flocculation: From Fundamentals to Applications, Hawaii, USA, 28 July–1 August 2002. Yianatos, J.B., Bergh, L.G., Aguilera, J., 2000. The effect of grinding on mill performance at Divisi on Salvador, Codelco-Chile. Minerals Engineering 13 (5), 485–495. Yianatos, J.B., Dıaz, F., Rodrıguez, J., 2002. Industrial flotation process modeling: RTD measurement by radioactive tracer technique. In: 15th IFAC World Congress, Barcelona, Spain, 21–26 July 2002.
Flotation scale up: use of separability curves q J.B. Yianatos a
a,*
, L.G. Bergh a, J. Aguilera
b
Department of Chemical Engineering, Santa Marıa University, Valparaıso, Chile b Divisi on Salvador, Codelco-Chile, El Salvador, Chile Received 31 October 2002; accepted 17 January 2003
Abstract Separability curves (mineral recovery versus yield) have been used to characterize the copper flotation process both at batch laboratory scale and industrial plant scale (rougher banks). Then, to approach the scale-up problem the rougher bank operation and the batch were compared using the corresponding separability curves. Comparison was made at the maximum separation efficiency point in both operations. Thus, a time factor was established for optimal technical separation. The time factor can then be used for kinetic scale-up models, together with the ratio between minerals recovery in both operating scales. Experience from several tests recorded over a period of 10 months in an industrial concentrator showed a good consistency for scaling-up the rougher flotation recovery from batch tests within a 1% absolute error range. The effect of particle size and air flowrate in laboratory batch tests was evaluated in the space of separability curves, regarding their effect on recovery at the optimum separability point. Also, the effect of pulp level and particle size on the bank flotation kinetics was evaluated in an industrial flotation circuit. Thus, estimation of recovery changes due to variations in mineral characteristics and operating conditions was explored. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Flotation; Scale-up; Particle size; Optimal separability
1. Introduction The flotation scale-up problem is complex because the mineral characteristics (grade, size, mineralogy), cell characteristics (geometry, power consumption, energy dissipation, bubble and particle size distribution), reagent conditioning and operating conditions (air flowrate, pulp level, froth transport and discharge facilities) are different and variable in batch and plant operation. Time scale up factors for flotation kinetics prediction are generally derived by comparison of industrial flotation banks and laboratory batch cell recovery. However, in plant practice it is common to find very low mineral recoveries in the last cells of the rougher banks. Thus, a direct time comparison between the overall bank performance and the batch operation, at the same recovery, can introduce large errors. A better approach was to simulate the bank performance in order to estimate the q Presented at Minerals Engineering Õ02, Perth, Australia, September 2002. * Corresponding author. E-mail addresses: [email protected], [email protected] (J.B. Yianatos).
flotation rate constant and recovery at infinite times, and then to compare these parameters with those estimated from batch flotation (Yianatos et al., 2000). Even so, there is a lack of standard reference for batch tests and results are strongly dependent not only on mineral characteristics, such as particle size and grade, but also on flotation operating conditions such as air rate and pulp level. An alternative way to approach this problem is to compare the rougher bank operation and the batch flotation using the corresponding separability curves. 1.1. Separability curves Separability curves represent the evolution of the mineral separation of a particular flotation process in terms of the concentrate mineral recovery and the process yield defined as the ratio between concentrate and feed mass flowrates. Also, considering the x-axis as the ratio between process yield and feed grade, it is possible to estimate the average concentrate grade by the slope of the straight line resulting from connection of any recovery point of the curve with the origin. In addition, any straight line tangent to the curve represents the incremental concentrate grade at that point. According to
0892-6875/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0892-6875(03)00024-4
J.B. Yianatos et al. / Minerals Engineering 16 (2003) 347–352
AgarÕs principle (Agar et al., 1980), this property can be used to estimate the optimal separability point, when the concentrate incremental grade equals the feed grade. Separability curves depend on feed characteristics and mineral conditioning as well as on characteristics and operation of flotation cells. Thus, assuming a standard batch test gives the best flotation separation for a non-perfectly liberated mineral, the batch separability curve can be used as an ideal target for plant operation. In this approach the combined effect of the concentrate grade and recovery can be observed at the optimal separability point. 2. Flotation process modelling The particle collection rate is based on fundamental particle-bubble collision and/or cavitation and adhesion processes (Schulze, 2002). However, from a practical point of view, the overall flotation process is generally well represented by a first order kinetic model (Polat and Chander, 2000). Thus, mineral species recovery in continuous industrial flotation equipment can be described by the general equation, Z 1Z 1 rðtÞ ¼ r1 ð1 ekt ÞF ðkÞEðtÞ dk dt ð1Þ 0
0
where r1 represents the maximum flotation recovery at infinite time. The term ð1 ekt Þ represents the mineral recovery of a first order process with invariant kinetic rate constant k, as a time function. F ðkÞ is the kinetic constant distribution function for mineral species with different flotation rates, and EðtÞ is the residence time distribution function for continuous processes with different mixing characteristics. The simplest F ðkÞ distribution is the rectangular distribution which allows accounting for different kinetic properties of complex minerals, while maintaining the parsimony principle of using a reduced number of parameters. The rectangular distribution model is described as follows, 1 F ðkÞ ¼ for 0 < k < kmax ð2Þ kmax F ðkÞ ¼ 0 for 1 > k > kmax 2.1. Batch flotation modelling The mineral recovery in a batch flotation test can be estimated from Eqs. (1) and (2), with EðtÞ ¼ dðtÞ by, 1 ½1 ekmax t rðtÞ ¼ r1 kmax t
2.2. Rougher flotation modelling For N continuous perfect mixers-in-series, with a total residence time s, Eq. (4) has shown a good agreement to represent the residence time distribution of the rougher plant (Yianatos et al., 2002). tN 1 eð s Þ EðtÞ ¼ N s CðN Þ N N t
ð4Þ
Thus, the following Eq. (5) can be derived from Eqs. (1), (2) and (4) for mineral recovery, s 1N 1 1 1 þ kmax N RðsÞ ¼ R1 ð5Þ kmax s ðN 1Þ N
3. Experimental Experimental work was developed at laboratory and plant scale at Divisi on Salvador, Codelco-Chile. Batch flotation was developed at the Metallurgical Laboratory, using two standard Wemco cells of 2.7 (L) and 5.3 (L). Two kinds of tests were considered: (a) predictive monthly tests using ore samples, and (b) special tests to study the effect of different variables, such as particle size and air rate on batch performance. Plant testing was developed in the rougher flotation circuit, consisting of five parallel flotation banks. Each bank provided with nine self-aerated Wemco cells of 42.5 m3 (1500 ft3 ) in arrangement 3–3–3. Rougher flotation performance was evaluated on the basis of daily overall sampling (three shifts), and also special tests for kinetic characterization of the rougher bank were developed. 3.1. Batch flotation characterization Fig. 1 shows an example of the data over a monthly predictive batch test using Eq. (3).
100
80
Cu Recovery, %
348
60
40
Data
ð3Þ
where rðtÞ and r1 are the mineral recovery at time t and the maximum recovery at an infinite time, kmax is the maximum rate constant of a rectangular F ðkÞ distribution and t is the effective residence time.
20
Model
0 0
5
10
15
20
Time, min
Fig. 1. Batch flotation data fitting.
25
30
J.B. Yianatos et al. / Minerals Engineering 16 (2003) 347–352
349
16
Cumul. Grade
14
Increm. Grade
12
Cu Grade, %
Feed Grade 10 8 6 4 2 0 60
65
70
75
80
85
90
95
100
Cu Recovery, %
Fig. 4. Effect of air flowrate on batch separability curves.
Fig. 2. Grade or incremental grade versus recovery in batch flotation.
Data from the same experience in Fig. 1, can be represented in a grade-recovery space, or an incremental grade-recovery space, in order to visualize the optimal separability point where the incremental grade equals the feed grade, as it is shown in Fig. 2. An alternative way of representing the batch process is the separability curve. In this approach the maximum technical separability point corresponds to the point of tangency of the feed grade line, as it is shown in Fig. 3. 3.2. Effect of air rate on batch separability curves The change of air flowrate was evaluated regarding their effect on recovery for the optimum separability point. Thus, estimation of recovery changes due to variations in mineral characteristics and operating conditions was explored. Fig. 4 shows the comparison of batch separability curves at two air flowrates, low and high, corresponding to 6 and 10 l/min. From Fig. 4 it is shown that at higher air flowrate the final copper recovery and the final yield were both higher than for the
lower air flowrate. Similarly, for the same recovery, the concentrate grade decreased at higher air flowrates. In both conditions optimal separation was achieved at similar recoveries, however the time was lower for the higher air flowrate. This result shows how sensitive the ‘‘ideal’’ separability is in terms of the operating conditions. 3.3. Effect of grinding level on batch separability curves Among other variables, separability curves strongly depend on particle size, or otherwise on mineral liberation. For example, Fig. 5 shows a series of batch tests developed at the same flotation conditions but varying the grinding level from 5% to 30% þ 212 lm. Here, it can be seen that the grinding effect became significant at recoveries higher than 50% where the separability curves start to deviate more rapidly from the dash line representing the copper grade of the pure mineral. In this case, copper recovery for optimal separation varied from 70% to 85%, whereas the coarse particles content decreased from 30% to 5% þ 212 lm. The dash line
100 100
90
80
80
Recovery of Cu, %
Cu Recovery, %
90
70
60
Batch 50
Feed
70 5% +212 um 60
15% +212 um
50
20% +212 um 25% +212 um
40
30% +212 um 30
Min. Grade
20
Feed Grade
10
40
0
0
5
10
15
Yield / feed grade Fig. 3. Separability curve in batch flotation.
20
0
5
10
15
Yield / feed grade
Fig. 5. Effect of grinding on batch separability curves.
20
J.B. Yianatos et al. / Minerals Engineering 16 (2003) 347–352
represents the maximum ideal separability, while the continuous straight line corresponds to the feed grade and represents the case of a perfect sampling without separation. 3.4. Effect of pulp level on rougher flotation operation The effect of pulp level was observed from a kinetic study performed in two parallel rougher flotation banks. Sampling and overall mass balances per size class were developed by local sampling (around three cells) along the bank. The pulp level was increased in one rougher bank and the performance was compared with the rougher bank operating in parallel under normal conditions. Results showed a moderate increase of 2.7% in the final copper recovery, as it is shown in Fig. 6. However, comparison of separability curves of both operations, in Fig. 7, showed a critical effect in the middle section of the bank operating at high pulp level, where the concentrate overflow increased dramatically, thus generating a significant entrainment and an in-
100
Recovery of copper, %
90 80
90 80 70 60 50
Size: + 212 um
40
Size: +75-212 um
30
Size: +45-75 um
20
Size: -45 um
10
Feed grades
0 0
5
10
15
20
Yield / feed grade
Fig. 8. Separability curves for different particle size classes in rougher flotation.
crease in the overall yield above normal ranges. Also, the final concentrate grade showed a strong decrease while the overall pulp residence time increased. The significance of this experience is that sometimes a small modification in operating conditions, i.e. pulp level, can significantly destabilize the overall circuit performance, despite the expected result of achieving an increase in recovery. This problem arose because of an improper operation of the level control system in the middle of the bank. 3.5. Effect of particle size on rougher plant operation
70 60 50
High level Low level
40 30 0
3
6
9
12
Cell number
Fig. 6. Effect of pulp level in two parallel flotation banks.
100
90
Recovery of copper, %
100
Recovery of copper
350
80
70
Fig. 8 shows the separability curves for four particle size classes in a rougher flotation bank operating under normal conditions. Maximum recovery of 95.2% was achieved in the medium size class, +45–75 lm, and a minimum recovery of 30% was obtained for the coarser mineral, +212 lm. In both cases the final separability was very good. However, the finest size class, )45 lm, only reached an 80.3% final recovery, with an overall yield significantly higher than other classes. The reason is that the finest particle size class has a significant entrainment, particularly in the first three flotation cells of the bank, where the cumulative concentrate grade (slope of the curve) was the lowest despite the finest mineral being better liberated. In summary, feed characteristics and their conditioning as well as experimental operating conditions, both at laboratory and plant scale, can significantly affect the comparison for scale up purposes.
60
Feed Grade Low level
50
4. Scale-up factors
High level
40 0
5
10
15
20
25
30
Yield/ feed grade
Fig. 7. Effect of increasing pulp level in rougher flotation banks.
35
The following two dimensionless variables, from Eqs. (3) and (5), were found to be reasonably constant while comparing the batch laboratory and rougher plant operations,
J.B. Yianatos et al. / Minerals Engineering 16 (2003) 347–352
½Kmax sPlant ¼ ½kmax tLab RðsÞ rðtÞ ¼ R1 Plant r1 Lab
ð6Þ ð7Þ
Then, the following scale-up factors were selected at the optimum separability point, s kmax ¼ t Kmax RðsÞ R1 ¼ rðtÞ r1
ð8Þ ð9Þ
The parameters to evaluate are the flotation times s and t, as well as recoveries RðsÞ and rðtÞ, for plant and laboratory flotation at the optimal separability point. The proposed method was tested by comparing the average monthly rougher recovery with the recovery of monthly batch tests. Both operations were firstly characterized by their corresponding separability curves and then compared at the optimal separability point. Here, optimal technical separation refers to the point where the concentrate incremental grade, tangent to the curve, is equal to the feed grade. Fig. 9 shows an example of this approach where data from batch and plant rougher operation was compared using separability curves. Separability curves for the rougher flotation circuit was based on the average recovery calculated from daily recorded data (three shifts) on feed, concentrate and tailings grade, as well as average feed tonnage and pulp density. The data was processed in a rougher flotation simulator to generate the corresponding separability 100
351
curves. The simulator was previously validated from kinetic flotation sampling developed on the same rougher banks. An example of average monthly data and their standard deviation is presented in Table 1. Fig. 10 shows the results for the scale-up factor corresponding to the ratio between plant ðs ¼ NT Þ and laboratory ðtÞ flotation times, evaluated at the optimal separability point, considering repeats in the monthly batch flotation predictions. The average result over a period of 10 months was, sPlant ¼ 2:26 0:35 ð10Þ tlab On the other hand, it was found that the scale-up factor corresponding to the ratio between plant and laboratory recoveries, Eq. (9), was strongly dependent on the % of soluble copper in plant operation. Fig. 11 shows the effect of soluble copper content (%) on the ratio between plant and laboratory flotation recovery, both evaluated at the optimal separability point. This relation was correlated by the following equation, considering the maximum (R=r) ratio as a function of the soluble copper content, RðsÞ ¼ 1:045 0:00945 ½% soluble copper rðtÞ
ð11Þ
In summary, using Eqs. (8)–(11) the parameters for plant simulation, Kmax and R1 , can be derived from batch flotation characterization by kmax and r1 . Fig. 12 shows the comparison between the actual rougher recovery and the rougher recovery estimated from batch tests, using scale-up factors and simulation of the rougher circuit operation for the same conditions. From Fig. 12 it can be seen that for the testing period of
(NT/ t) at optimal separability
Recovery of Cu, %
90
80
70
Batch Lab.
60
Rougher Plant 50
Feed Grade
5
4
3
2
1
0
40
0
0
5
10
15
1
2
3
20
4
5
6
7
8
9
10
11
Month
Yield / feed grade
Fig. 9. Separability curves for batch and rougher plant operation.
Fig. 10. Comparison of flotation time between plant and laboratory at optimal separability.
Table 1 Rougher operating conditions, monthly average Month
Feed %Cu
Soluble Cu (%)
% þ212 lm
Throughput TPD
Cu recovery (%)
Solid (%)
November December January
0.715 0.033 0.697 0.028 0.722 0.005
9.16 1.68 7.52 0.86 8.03 1.94
24.46 1.56 22.92 1.61 22.35 0.27
34,590 2368 32,680 4015 31,567 486
81.38 1.31 83.71 1.35 83.79 0.39
35.96 0.57 35.24 0.61 35.05 0.31
352
J.B. Yianatos et al. / Minerals Engineering 16 (2003) 347–352
(R /r) at optimal separability
1
data model
0.98
0.96
0.94
0.92 0.9
0.88 4
6
8
10
12
14
16
Soluble copper, % Fig. 11. Effect of soluble copper on the ratio between plant and batch recovery at optimum separation.
88
mance, based on separability curves, was developed and evaluated in order to estimate scale-up factors. This approach is more robust and less sensitive to the laboratory and rougher flotation operation, particularly the last cells in the rougher bank. Experience from several tests recorded over a period of 10 months in an industrial concentrator showed a good consistency for scaling-up the rougher flotation recovery from batch tests within a 1% absolute error range. The significant effect of changing operation variables such as particle size and air flowrate at laboratory scale was evaluated for predictive purposes. It was also found that maximization of the rougher flotation recovery, by increasing pulp level, is critically limited by the quality of the pulp level control system.
Acknowledgements
Plant copper recovery
86
The authors are grateful to El Salvador Division of Codelco-Chile for providing access to their plant and for valuable assistance in the experimental work. Funding for process modeling and control research is provided by CONICYT, project Fondecyt 1020215, and Santa Marıa University, project 270122.
84 82 80 78 76
References
74 74
76
78
80
82
84
86
88
Estimated copper recovery Fig. 12. Estimated versus plant recovery from scale-up model fitting.
10 months the scale-up procedure shows a reasonable good result with a maximum deviation of about 1% in plant copper recovery.
5. Conclusions A standard comparison between laboratory batch flotation tests and industrial rougher flotation perfor-
Agar, G.E., Stratton-Crawley, R., Bruce, T.J., 1980. Optimizing the design of flotation circuits. CIM Bulletin 73 (824), 173–181. Polat, M., Chander, S., 2000. First-order flotation kinetics models and methods for estimation of the true distribution of flotation rate constants. International Journal of Mineral Processing 58, 145– 166. Schulze, H.J., 2002. Stability and rupture of thin aqueous films and flotation. In: Strategic Conference on Flotation and Flocculation: From Fundamentals to Applications, Hawaii, USA, 28 July–1 August 2002. Yianatos, J.B., Bergh, L.G., Aguilera, J., 2000. The effect of grinding on mill performance at Divisi on Salvador, Codelco-Chile. Minerals Engineering 13 (5), 485–495. Yianatos, J.B., Dıaz, F., Rodrıguez, J., 2002. Industrial flotation process modeling: RTD measurement by radioactive tracer technique. In: 15th IFAC World Congress, Barcelona, Spain, 21–26 July 2002.