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Modelling and simulation of rougher flotation circuits
International Journal of Mineral Processing 112–113 (2012) 63–70
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International Journal of Mineral Processing journal homepage: www.elsevier.com/locate/ijminpro
Modelling and simulation of rougher flotation circuits J. Yianatos a,⁎, C. Carrasco a, L. Bergh a, L. Vinnett a, C. Torres b a b
Automation and Supervision Centre for the Mining Industry, CASIM, Chemical and Environmental Engineering Department, Federico Santa María Technical University, Valparaíso, Chile División El Teniente, Codelco, Rancagua, Chile
a r t i c l e
i n f o
Article history: Received 7 June 2011 Received in revised form 9 June 2012 Accepted 14 June 2012 Available online 21 June 2012 Keywords: Flotation Modelling Simulation Rougher cells
a b s t r a c t At present, large mechanical flotation cells of 100 to 300 m3 are used in rougher operation in different industrial flotation plants around the world. However, in spite of the advances in fundamental research and the notable growth in equipment size, there is still a lack of reliable data for industrial flotation modelling and simulation. In this work, a procedure for modelling and simulating rougher flotation banks that is based on operating variables and parameters fitted by empirical data from plant measurements is presented. Recently, a new methodology for describing industrial flotation by separating the collection and froth zones has been developed. This approach consists of using a new apparatus for direct bubble load measurement below the pulp–froth interface in industrial cells. The procedure allows independently estimating the froth recovery and the collection zone recovery. Metallurgical characterisation is developed by plant sampling, mass balance adjustment and applying a short-cut method for kinetic characterisation of flotation banks. In addition, the effect of grinding is characterised using flotation models with distributed flotation rates (for each particle size class) and a low number of parameters. From the experimental data, a non-linear distributed model to simulate rougher flotation banks was developed, which allows describing the industrial operation as a function of the main operating variables (e.g., mass flow rate, solid percentage, grinding degree, pulp level and superficial air rate). The simulator was calibrated and validated using experimental data from the rougher operation at El Teniente Division, Codelco-Chile. The new approach is a practical tool that is useful for flotation operation diagnosis, for robust design and analysis of new control and optimisation strategies and for evaluation of the effect that design and operating variables have upon the collection and froth zone performance in large flotation cells. This methodology can be applied to other flotation operations, such as cleaner and scavenger circuits that use mechanical flotation cells. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Two types of mechanical flotation cells are employed in industrial applications: self-aspirated and forced-air flotation cells. The main differences between the cells are the type and location of the rotor and the mechanism used for the air input. In self-aspirated cells, the rotor is located near the top of the cell, whereas in forced-air cells, the rotor is located near the bottom. Mechanical cell designs have included some modifications, such as the use of froth-crowders and internal radial launders. These modifications have been focused on improving the froth transport and consequently the mineral recovery. The minimum number of cells per bank can be estimated from a hydrodynamic analysis assuming perfectly mixed cells. For example, it has been observed that when using four or more cells in series,
⁎ Corresponding author. E-mail address: [email protected] (J. Yianatos). 0301-7516/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.minpro.2012.06.005
the time scale-up factor required to reach the same recovery of a plug flow operation (batch) with the same flotation rate constant is close to 1.15 (Arbiter, 2000; Yianatos et al., 2006). Thus, the mixing effect can be compensated by increasing the bank mean residence time, e.g., increasing the number of cells or the cell size. Bourke (2002) noted an important aspect related to the minimum number of control points for proper bank operation. For instance, in a ten-cell arrangement, 2-2-3-3, only four level control points are available, whereas a five-cell arrangement, 1-1-1-1-1, has five level control points. In plant practice, a minimum of 4–6 cells in series, including at least four control points, is recommended. The behaviour of a flotation bank has been typically modelled as a set of tanks in series with the same properties, i.e., the same residence time distribution, flotation rate and froth characteristics in each cell. At present, important efforts have been made to characterise flotation circuits as distributed systems in order to obtain a more realistic description of the process. Maldonado et al. (2007) discussed a control strategy to improve the grade of the concentrate using the froth depth along a rougher flotation bank as the manipulated variable.
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Tsatouhas et al. (2005) reported a decrease in the froth recovery along a rougher bank in two industrial rougher circuits. Dobby and Savassi (2005) reported a change of flotation rate in the collection zone along a bank of cells based on the results of batch tests. The distributed character of a flotation rougher bank requires mass balances around each cell for solid and liquid phases in order to describe the operating conditions downward the bank, i.e. mean residence time per cell, froth depth, entrainment, and solid liberation, among others. In addition, the performance of each flotation cell in terms of mineral recovery and concentrate grade depends on the flotation rates in the collection zone and the cleaning effect controlled by the froth depth. On this subject, Finch and Dobby (1990) described industrial flotation equipment separating the collection and froth zone to identify the effects independently in order to estimate the overall flotation performance. Reviews on the collection and froth zone modelling have been reported in literature by Finch and Dobby (1990), Mathe et al. (1998) and Yianatos (2007), where detailed hydrodynamic characterisation of the collection zone and summaries of the froth transport modelling are presented. Several approaches for flotation process simulation have been proposed in literature which typically simplify or remove the froth phase. For example, Sosa-Blanco et al. (1999) developed a simulator to integrate the grinding and flotation process, where the flotation cells were modelled as a perfect mixer with entrainment in the froth phase; Ferreira and Loveday (2000) described the collection zone as a perfect mixer and the froth phase in terms of the froth recovery for a flotation circuit with 3 nodes; Casali et al. (2002) proposed a dynamic rougher simulator without considering the froth zone due to the close to plug flow behaviour; Maldonado et al. (2007) considered that the volumetric concentrate flowrate depends on the froth depth linearly; among others. Currently, several commercial simulators exist: the JK Simfloat mineral processing simulator (Schwarz and Alexander, 2009), which includes operational variables such as superficial gas rate, bubble surface area flux, froth recovery, entrainment, water recovery, solids per size class, mean residence times, overall flotation rate constants and mineral recovery per size class; the FloatStar mineral processing simulator (MinTek, 2012), which uses advanced process control to overcome design-related limitations and maximise the flotation circuit performance; the UsimPac mineral processing simulator (Metso, 2012), which considers the raw materials, products, water and waste for equipment dimensioning, carrying out mass balances, energy consumption evaluation, among other results; and the MetSim simulator (MetSim, 2009), which allows mass and energy balance development in complex flotation plants while taking into account chemical, control and equipment dimensioning aspects as well as capital cost estimations, among others. In spite of the wide commercial application of the aforementioned simulators, in general the software is closed for the user, with limited information about the process modelling. An exception is the JK Simfloat (Schwarz and Alexander, 2009), in which the collection and froth zones are separately modelled. The collection zone hydrodynamic is modelled by a perfect mixing regime whereas the froth zone is represented by a probability of detachment as a function of the froth residence time. On the other hand, the concept of using an overall flotation rate, accounting for the collection and froth zones together, is still employed. The overall rate constant depends on the bubble surface area flux, the mineral floatability and the froth recovery. The simulator reported in this paper is focused on providing a detailed phenomenological description of the flotation process in which a rougher bank has been modelled as a distributed system, i.e., each cell is an independent unit that consists of two different zones: collection and froth, which are linked by mass balance and not hindered by an overall rate constant. Moreover, the different liberation grades for the mineralogical species were taken into account. In order to obtain a representative description of the actual flotation process, the
variations in the collection flotation rates and residence time, as well as the froth transport characteristics and the froth recovery downstream from the bank of cells were considered. The simulator has been successfully tested in the rougher flotation SAG plant of El Teniente, Codelco-Chile, which consists of four banks of seven selfaspirated Wemco cells of 130 m 3 (array 1-2-2-2). 2. Single-cell characterisation: pulp and froth model For modelling, scale-up and analysis purposes, two zones are distinguished in the flotation cell: (a) the collection zone, where the particle-bubble aggregate is formed and carried to the pulp–froth interface (true flotation) and (b) the cleaning zone (froth), located between the pulp–froth interface and the concentrate overflow, where entrained particles have the chance to drop back to the collection zone. This zone is now described by the froth recovery. The global cell recovery RG is related to the collection zone recovery RC and the froth recovery RF, taking into account the overall mass balance around the cell (Eq. (1)) (Finch and Dobby, 1990; Finch et al., 2008). RG ¼
RC ⋅RF 1−RC ⋅ð1−RF Þ
ð1Þ
This approach is used for both (a) kinetic parameter estimation in the collection zone based on industrial mass balance measurements, which allow obtaining RG and RF, and (b) evaluation of the overall mineral recovery in each cell using the previously calibrated simulator, i.e., using hydrodynamic, flotation rate, granulometric and froth zone parameters as input. 2.1. Collection zone, RC The mineral recovery RC in the collection zone can be described by the general expression Eq. (2) (Polat and Chander, 2000; Yianatos, 2007). ∞ ∞ −k⋅t ⋅Eðt Þ⋅F ðkÞ dt dk RC ¼ RMAX ⋅ ∫ ∫ 1−e
ð2Þ
0 0
where E(t) is the residence time distribution function for continuous processes with different mixing characteristics, F(k) is the flotation rate distribution for mineral species with different flotation rates and RMAX represents the maximum flotation recovery at infinite time. The term (1-e − kt) represents the mineral recovery of a firstorder process with invariant kinetic constant k, as a time function. 2.1.1. Residence time distribution, E(t) The hydrodynamic of flotation cells can be characterised by means of the residence time distribution function, E(t). The mixing regime of mechanical cells arranged in banks has been typically represented by a model of N perfect mixers in series (Yianatos et al., 2001). However, for describing the E(t) of single large cells, the perfect mixing condition is not valid based on the empirical evidence. At present, better fits for industrial data can be obtained using alternative approaches (Lelinski et al., 2002; Yianatos et al., 2008a). For example, the hydrodynamic of a flotation cell has been well represented by means of the large and small (LSTS) tanks in series model given by Eq. (3) (Yianatos et al., 2008a). Eðt Þ ¼
exp½−ðt−τP Þ=τS − exp½−ðt−τP Þ=τ L ðτ S −τP Þ
ð3Þ
where τL is the mean residence time of the large tank, τS is the mean residence time of the small tank and τp is the dead time. In addition, the ratio τS/τL is usually close to 0.1 in mechanical cells (Yianatos et al., 2005). Eq. (3) was considered for the simulator implementation.
J. Yianatos et al. / International Journal of Mineral Processing 112–113 (2012) 63–70
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Fig. 1 shows good agreement between the LSTS model and the experimental data recorded in a Wemco cell of 130 m 3. 2.1.2. Flotation rate distribution, F(k) Several models have been proposed in order to evaluate the flotation rate distribution in flotation cells. The Dirac delta function, δ(k − kB), and rectangular models correspond to single parameter models, where δ(k − kB) represents a single flotation rate constant, kB. The rectangular model for the i-th size class (+100#, −100+ 325#, −325#, where # means mesh) and for the n-th cell, given by Eq. (4), was used for simulating the flotation rate distribution in a distributed manner n because of its flexibility and low number of parameters, kmax,i . n F i ðkÞ
¼
8 <
1 knmax;i : 0
; if
0bkbknmax;i
; if
k > knmax;i
ð4Þ Fig. 2. Recovery prediction model for batch tests.
Then, the mineral recovery in the collection zone of class i and cell n n,RCi , was calculated by means of Eq. (5): n
n
RC;i ¼ RC
MAX;i
∞ ∞ −k⋅t n ⋅Eðt Þ⋅F i ðkÞdt dk ⋅ ∫ ∫ 1−e
ð5Þ
0 0
where RnC MAX,i is the maximum collection zone recovery of the i-th class in the n-th cell. Notice that because of the amount of valuable mineral decreases along the flotation bank, the maximum recovery value in each size class (i.e., fine, intermediate and coarse) also decreases. If this change is not taken into account, the flotation rate distribution in each cell will be hindered by the variation of RnC MAX,i. Therefore, the valuable mineral was described by a fraction with a probability (> 0) of being floated and a non-floatable fraction. Thus, the amount of floatable, valuable and non-valuable material feeding a single cell in a bank was obtained from a mass balance in the previous cell, where the recoveries were known. To estimate the maximum recovery of the raw material entering the rougher circuit, batch tests for each size class were carried out using the same feed samples from the mass balance measurements. Fig. 2 shows a batch test result along with the RMAX estimation per size class. The same residence time distribution was considered in Eq. (5) for each size class because the empirical data showed no significant differences in the mean residence time and the distribution shape. Samples for the mass balances per size class were obtained for a complete description of the first 3 cells and the overall bank. The results for the global and froth recovery in each cell allowed estimating
Fig. 1. Model fit to industrial data (non-floatable tracer), τL = 5.5 min, τS = 0.5 min, τp = 0.8 min.
the kinetic parameters in cells 1, 2 and 3 and to extrapolate the results for the bank. Additionally, the air flow rate, the froth height and the bubble load were measured during the same sampling campaign in order to characterise the rougher circuit. To characterise the decrease of the flotation rate distribution of mineral class i along the rougher bank, Eq. (6) was used. The parameters were fitted by regression. The model variables (δ and n) were chosen considering the significant dependence of the flotation rate on the particle size and the cell number. kratio ¼
knmax;i k1max;i
n−1 χ ¼ exp − δi
ð6Þ
Eq. (6) allows obtaining the rectangular model parameters for the n-th cell as a function of the first one. The δi parameter depends on the characteristic size of the i-th size class, and χ is a fit parameter. Fig. 3 shows a comparison between the proposed model and the plant data in three size classes for a chalcopyrite mineral. 2.2. Cleaning zone, RF The cleaning zone was characterised by means of the froth recovery, which can be estimated from bubble load measurement along
Fig. 3. Plant data and model describing changes in the collection rate along the flotation bank.
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with a mass balance around the cell. Thus, the froth recovery, RF, was calculated by Eq. (7) (Yianatos et al., 2008b): C ⋅X C RF ¼ λB ⋅J G ⋅AC ⋅X B
ð7Þ
ð8Þ
where α is the maximum recovery in the froth, βn is the froth stability factor for the n-th cell and τF, n is the gas mean residence time in the froth of the n-th cell, which is given by Eq. (9) (Yianatos et al., 2008b): τF;n ¼
H F;n ⋅εG JG
ð9Þ
where HF,n is the froth height and εG is the mean gas concentration (hold-up) in the froth. The empirical evidence showed that the froth stability of each cell downstream from the bank is reduced, i.e., the froth selectivity increases along the cells arrangement. Therefore, the βn parameter in Eq. (8) was modelled as follows: βn ¼ ψ⋅Mn ⋅RC;n :
The water recovery, RW, is defined as the fraction of feed water reported to the concentrate stream and is given by Eq. (11): RW ¼
where λB is the bubble load, JG is the superficial gas rate, AC the crosssectional area of the cell, C is the solid mass flow in the concentrate and XC and XB are the concentrate and bubble load grade, respectively. It has been shown that Eq. (7) is useful for calculating the froth recovery and the valuable minerals collected by true flotation from experimental data (Yianatos et al., 2008b). In addition, Eq. (8) is usually employed for modelling the froth zone (Gorain et al., 1998; Mathe et al., 1998; Zheng et al., 2004). RF;n ¼ α ⋅ exp −βn ⋅τF;n
2.3. Water recovery
ð10Þ
where Mn is the amount of valuable mineral entering the n-th cell, RC, n is the overall recovery of the collection zone and ψ is a fit parameter. Notice that Mn·RC, n corresponds to the overall amount of valuable mineral entering the froth zone by true flotation. Fig. 4 shows the Cu grade of the bubble load and at the top of froth in a single cell, for different size classes. Based on these results, a rather non-selective froth was observed, which is consistent with the results reported by Yianatos et al., 2008b. Therefore, the same froth recovery per size class was assumed.
WC WF
ð11Þ
where WC corresponds to the water mass flow rate in the concentrate and WF is the feed water mass flow rate to each cell. The calculation of RW was carried out from solid percentage data and mass balance results. For simulation purposes, the water recovery was modelled as a function of the froth height, the froth stability factor and the superficial gas rate for each cell (Eq. (12)): RW;n ¼ ξ⋅ exp −
H
γ η F;n ⋅β n
!
JG
ð12Þ
where ξ is the maximum water recovery, and γ and η are fit parameters. Notice that Eq. (12) is similar to the froth recovery relationship in Eq. (8). In addition, this equation considers the influence of the froth behaviour in the water recovery as a distributed system. 2.4. Gangue recovery The gangue is recovered into the concentrate by entrainment caused by the water reported to the concentrate stream. The gangue ren covered per size class in the n-th cell, RG,i , was estimated by means of Eq. (13) (Yianatos and Contreras, 2010). n
RG;i ¼ EF i ⋅RW;n
ð13Þ
where EFi is the entrainment factor per size class. The gangue recovery per size class can then be obtained from RW measurements and empirical EFi values. 3. Single-cell simulation In order to evaluate the contribution of each individual cell in the flotation bank recovery, the collection zone recovery by true flotation, RC, the froth recovery of floatable minerals, RF, the water recovery, RW, and the gangue recovery, RG, were calculated for each cell. In addition, the mass flow rate of water and solids per size class in the tailings of each cell were obtained by means of a mass balance. The global recovery of mineral m, size class i, in cell n is given by m
Ri;n ¼
RC;i :RF;i 1−RC;i þ RC;i :RF;i
ð14Þ
Also, the concentrate grade X of mineral m, size class i, in cell n is m F i;n ⋅X F;m i;n ⋅Ri;n
C;m
X i;n ¼
2 P
3 P
m¼1 i¼1
Fig. 4. Comparison between Cu grade in the bubble load (CB) and at the top of froth (TOF).
ð15Þ
m F i;n ⋅X F;m i;n ⋅Ri;n
where the supra-indices C and F refer to the concentrate and feed streams. Notice from Eq. (15) that three size classes, i, were considered: coarse (+100#), intermediate (−100 + 325#) and fine (− 325#) in order to take into account different liberation grades. In addition, two types of minerals were included for the simulation: valuable mineral – e.g., chalcopyrite and molybdenite – and gangue. The overall recovery and concentrate grade of the flotation bank were calculated by integrating the distributed result of each cell, which were determined by Eqs. (14) and (15).
J. Yianatos et al. / International Journal of Mineral Processing 112–113 (2012) 63–70 Table 1 Simulation results for the rougher flotation bank. Feed Flow rate Froth depth Solid percentage Froth recovery, Cu Collection recovery, Cu Overall recovery, Cu
Cell 1 Cell 2 Cell 3 Cell 4 Cell 5 Cell 6 Cell 7 tph 900 803.9 790.4 782.1 775.7 770.7 765.6 cm 5 12 12 8 8 8 8 % 42.0 43.1 43.8 44.8 45.7 46.6 47.6 % 83.4 63.5 56.8 63.1 48.1 27.7 6.0 % 70.4 64.5 59.1 53.8 45.7 38.8 31.5 % 66.5 53.6 45.1 42.4 28.8 14.9 2.7
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Therefore, the simulation requires a set of test and previously measured variables to calibrate the flotation models, including: mass balances, feed particle size distribution, batch tests, bubble load, superficial gas rate, residence time distribution and froth recovery. 5. Results 5.1. Case of study
4. Summary The general procedure for developing and calibration of the simulator includes the following steps: i) Sampling the first, second and third cells of the bank together with sampling the flotation bank as a whole. ii) Characterise the streams in terms of solid percentage by weight, and mass and grades (Cu, Mo and Fe) per size class. iii) Carry out mass balance adjustment per size class and estimate mineral recoveries. iv) Using the feed sample, conduct batch test to determine the RMAX values per size class. v) Estimate froth recovery, Eq. (7), using the measured values of XC, XB, λB and JG. The adjusted value of concentrate C and the cross sectional area is also required. vi) Using results from steps iii) and v), obtain the collection zone recovery per size class from Eq. (1). vii) Estimate the flotation rate parameters per size classes from Eq. (5) based on the RTD model, the distributed RMAX,i n along the bank per size class and the collection zone recovery results from step vi). viii) Characterise the decrease of the flotation rate distribution per size class along the rougher bank using Eq. (6). ix) From Eqs. (8), (9) and (10) and results from step v), determine the froth recovery parameter ψ using HF, n, εG and JG data along the bank together with the amount of valuable mineral entering the froth by true flotation. An α value of 92% was assumed in Eq. (8). x) Estimate gangue recovery from water recovery. First, obtain water recovery using the mass balance results together with the solid percentage by weight. Second, estimate parameters of Eq. (12) using the JG, and HF, n, and βn values along the bank. Determine gangue recovery from mass balances and bubble load measurements (Yianatos and Contreras, 2010) and estimate EFi factors per size class. xi) Based on the previously adjusted parameters (by regression), Eqs. (3) to (13), the overall mineral recovery and the concentrate grade can be computed from Eqs. (14) and (15), respectively.
The rougher flotation circuit (SAG plant) at El Teniente, CodelcoChile, was considered. The rougher circuit consists of four banks with seven self-aspirated Wemco cells (130 m 3) in series, in a 1-22-2 array. For the simulator calibration, measurements of feed, tail and concentrate grades per size class, superficial gas rate, bubble load, solid percentage, gas hold-up, residence time distribution and froth depth profiles along the rougher bank were carried out in the rougher flotation SAG plant (Carrasco, 2010). These results allowed obtaining the simulator parameters as well as to validate them. Table 1 shows the simulation results for Cu performance corresponding to a feed tonnage of 900 tph, a feed grade of 1%, a solid percentage by weight of 42% and 18% particle size (% + 100#) in a rougher bank. Table 2 presents a comparison between the simulator outputs based on operational parameters and plant results for two tests conducted in the rougher bank. The operational parameters of Test 1 were as follows: feed tonnage 790 tph, Cu feed grade 0.99%, Mo feed grade 0.021%, Fe feed grade 5.0%, percentage + 100# 19.8%, solids percentage by weight 41.5% and froth height (first cell) 5 cm. For Test 2, the operational parameters were: feed tonnage 650 tph, Cu feed grade 0.95%, Mo feed grade 0.020%, Fe feed grade 5.5%, percentage +100# 22.0%, solids percentage by weight 40.0% and froth height (first cell) 3 cm. A reasonable agreement between the simulated data and the plant performance was observed. 5.2. Sensitivity analysis For visualisation of the simulation responses, a sensitivity analysis for different operating conditions was carried out. The main variables for this analysis were particle size distribution (PSD), froth depth in the first cell of the bank, feed tonnage, feed grade and solid percentage. These variables are interesting for control purposes because of the economic impact in terms of mineral recovery and concentrate grade in industrial flotation banks. 5.2.1. Effect of particle size distribution (PSD) The effect of changes in the PSD on the cumulative Cu recovery and the incremental grade along the flotation bank was studied. The
Table 2 Comparison between plant performance and simulation results. Test 1
Rougher recovery %
Final concentrate
07/12/2009
Cu
Mo
Cu grade %
Mo grade %
Solid %
Cu/Fe ratio
% − 325 #
Plant data Simulation % Error
90.8 91.0 0.2
80.00 83.76 4.7
5.5 5.3 3.6
0.09 0.084 6.7
27.2 27.1 0.4
0.63 0.64 1.6
69.8 69.2 0.9
Test 2
Rougher recovery %
Final concentrate
14/12/2009
Cu
Mo
Cu grade %
Mo grade %
Solid %
Cu/Fe ratio
% − 325 #
Plant data Simulation Error (%)
91.2 91.6 0.4
81.0 83.4 3.0
5.00 5.03 0.6
0.071 0.070 1.4
24.5 25.3 3.3
0.61 0.60 1.6
67.4 66.9 0.7
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Fig. 5. Comparison of (a) the cumulative Cu recovery and (b) the incremental Cu grade as a function of the coarser feed content.
following variables were assumed constant for the simulation: feed tonnage 800 tph, feed copper grade 0.98%, solid percentage by weight 40% and 8 cm froth depth along the bank. The increment in particle size was represented by increasing the +100# fraction in the mineral feed by 18% to 25%. Fig. 5(a) shows a 1% decrease in the cumulative mineral recovery when the particle size was increased by increasing the coarse material in the flotation bank. From laboratory and plant experiments, the finer classes (− 100#) showed a higher collection probability; therefore, a coarser feed decreases the global recovery of the flotation bank (Carrasco, 2010). In addition, an increase in the incremental concentrate grade was observed for the coarser feed (Fig. 5(b)) because of the decrease in the liberated fine gangue entrainment to the concentrate.
5.2.2. Effect of froth depth A change in the froth height of the first cell, from 5 to 25 cm, was considered in order to evaluate its impact on the mineral recovery and concentrate grade of the flotation bank. The rest of the operating variables was kept constant, i.e., feed tonnage 800 tph, 0.98% feed copper grade, 40% solid percentage by weight, 8 cm froth depth in all of the other cells and 20% + 100# in the mineral feed size.
Fig. 6. Effect of froth depth change in the first cell on (a) the cumulative Cu recovery and (b) the incremental Cu grade.
Fig. 6(a) shows a 3% decrease in the cumulative mineral recovery when the froth depth was increased from 5 to 25 cm, while Fig. 6(b) shows the significant impact that the froth depth had on the concentrate grade obtained in the first cell. Also, a strong decrease in the incremental grade was observed downstream the rougher bank when the first cell was operated with froth depth of 25 cm. Finally, an increase of 1% in the rougher concentrate grade was obtained. Adequate level control in the first cell of a rougher bank is necessary to control the entrainment of non-floatable material and the overall concentrate grade in self-aerated cells. Otherwise, the grade of the first cell constrains the maximum grade achievable along the whole flotation bank. 5.2.3. Effect of feed tonnage The feed tonnage is relatively constant in the rougher flotation SAG plant because the four rougher banks are fed by two SAG mills, reducing the variations in the feed flow rate. An increase in feed tonnage from 600 to 800 tph was analysed. Again, the following variables were kept constant: feed copper grade 0.98%, solid percentage by weight 40%, 8 cm froth depth along the bank and 20% +100# mineral feed size. Fig. 7(a) shows a decrease of 1%–2% in mineral recovery from increasing the feed tonnage. In addition, a negligible effect of this change on the incremental concentrate grade was observed (Fig. 7(b)). The effect shown in the cumulative recovery is mainly due to variation of the mineral residence time in the bank of cells.
J. Yianatos et al. / International Journal of Mineral Processing 112–113 (2012) 63–70
Fig. 7. Effect of feed tonnage change on (a) the cumulative Cu recovery and (b) the incremental Cu grade.
5.2.4. Effect of feed grade The effect of increasing the copper feed grade from 0.9% to 1.1% was evaluated. In this case, the following variables were kept constant: feed tonnage 800 tph, 40% solid percentage by weight, 8 cm froth depth along the bank and 20% + 100# mineral feed size. A negligible effect on the cumulative recovery was observed when the feed grade increased from 0.9% to 1.1%, as shown in Fig. 8(a). However, a significant impact on the incremental concentrate grade was observed (Fig. 8(b)) because of the higher quality of the fresh material entering the rougher bank. Based on the models described in the previous sections, the key parameter related with the feed grade is the froth stability factor, β, which affects the froth and water recoveries. 5.2.5. Effect of solid percentage The solid percentage determines the mean residence time in flotation cells (rheological effects were not considered). An increase in solid percentage by weight from 30% to 40% was analysed while keeping the rest of the operating variables constant: feed tonnage 800 tph, 0.98% feed copper grade, 8 cm froth depth along the bank, and 20% +100# mineral feed size. Fig. 9(a) shows an increase in the cumulative recovery by changing the solid percentage from 30 to 40%, due to the longer residence time of minerals in the flotation cells. Also, a slight increase in the concentrate grade was observed in Fig. 9(b), because the water recovery to the concentrate was slightly lower which reduced the gangue entrainment relative to the valuable solid recovered into the concentrate.
69
Fig. 8. Comparison of (a) the cumulative Cu recovery and (b) the incremental Cu grade as a function of the feed grade.
The modelling of the flotation cells by separating the collection and froth zones, without using an apparent rate constant, allows for a better identification of the true flotation process (collection efficiency) as well as the froth separation process (product quality). Changes in the main operating variables yield to the expected mineral recovery and concentrate grade trends, while the effects on the mineral collection and the froth separation were clearly identified. In addition, the distributed approach for the rougher bank modelling involves the decrease of mean residence time (from actual RTD), froth stability and flotation rates, together with the increase of particle size, along the bank. All these information was obtained from plant measurements. The model does not consider reagents as manipulated variables explicitly, but they are partially represented by the flotation rate profile (per size class) along the bank, Fig. 3. Bigger efforts must be made to describe the rougher circuit performance as a function of the collector and frother dosage downward the bank. 6. Conclusions A procedure for modelling and simulating rougher flotation banks as a distributed process was developed. The model parameters were calibrated from plant operating data using a flotation rate evaluation based on the short-cut method, adjusted mass balances and a new approach to evaluate bubble load and froth recovery. The simulator was validated using experimental data from the rougher operation at El Teniente concentrator, which consists of flotation banks of seven 130 m 3 cells in series. The simulation allowed
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References
Fig. 9. Comparison of (a) the cumulative Cu recovery and (b) the incremental Cu grade as a function of feed solid percentage.
the evaluation of the industrial rougher flotation bank as a function of the main operating variables, including particle size distribution, mass flow rate, solid percentage, pulp level and feed grade. The new approach is a practical tool that is useful for flotation operation diagnosis, for robust design and analysis of new control and optimisation strategies, and for evaluating the effect that design and operating variables have upon the metallurgical performance in large flotation cells. This methodology can be applied to other flotation operations, such as cleaner and scavenger circuits, that use mechanical flotation cells. Acknowledgements Funding for process modelling and control research was provided by CONICYT, project Fondecyt 1100854, NEIM, Project P07-087-F, ICM-MINECON, Santa Maria University, project 270522.
Arbiter, N., 2000. Development and scale-up of large flotation cells. Miner. Eng. 52 (3), 28–33. Bourke, P., 2002. Selecting flotation cells: how many and what size? MEI on-line, www. min-eng.com2002. Carrasco, C., 2010. Modelación Zona de Colección y Espuma para Supervisión y Control Industrial, Master Thesis, Chemical Engineering Department, Santa María University, Chile, 2010. Casali, A., Gonzalez, G., Agusto, H., Vallebuona, G., 2002. Dynamic simulator of a rougher flotation circuit for a copper sulphide ore. Miner. Eng. 15 (4), 253–262. Dobby, G., Savassi, O., 2005. An advanced modeling technique for scale-up of batch flotation results to plant metallurgical performance. Proceedings of the Centenary of Flotation Symposium, Brisbane, Australia (June), pp. 99–103. Ferreira, J.P., Loveday, B.K., 2000. An improved model for simulation of flotation circuits. Miner. Eng. 13 (14–15), 1441–1453. Finch, J.A., Dobby, G.S., 1990. Column Flotation. Pergamon Press. Finch, J., Nesset, J., Acuña, C., 2008. Role of frother on bubble production and behaviour in flotation. Miner. Eng. 21 (12–14), 949–957 (November). Gorain, B., Harris, M., Franzidis, J.-P., Manlapig, E., 1998. The effect of froth residence time on kinetics of flotation. Miner. Eng. 11 (7), 627–638. Lelinski, D., Allen, J., Redden, L., Weber, A., 2002. Analysis of the residence time distribution in large flotation machines. Miner. Eng. 15 (7), 499–505. Maldonado, M., Sbarbaro, D., Lizama, E., 2007. Optimal control of a rougher flotation process based on dynamic programming. Miner. Eng. 20, 221–232. Mathe, Z.T., Harris, M.C., O'Connor, C.T., Franzidis, J.-P., 1998. Review of froth modelling in steady state flotation system. Miner. Eng. 11 (5), 397–421. MetSim, 2009. The Premier Process Simulator for WindowsRetrieved September 2009 from , http://www.metsim.com/2009. Metso, 2012. USIM PAC© simulatorRetrieved March 2012 from , http://www.metso. com/2012. MinTek, 2012. FloatStar Dynamic SimulatorRetrieved March 2012 from , http://www. mintek.com.au/2012. Polat, J., Chander, S., 2000. First order flotation kinetics models and methods for estimation of the true distribution of flotation rate constants. Int. J. Miner. Process. 58, 145–166. Schwarz, S., Alexander, D., 2009. JKSimFloat v6.1plus: improving flotation circuit performance by simulationRetrieved September 2009 from , http://www.jktech.com.au/ 2009. Sosa-Blanco, C., Hodouin, D., Bazin, C., Lara-Valenzuela, C., Salazar, J., 1999. Integrated simulation of grinding and flotation application to a lead–silver ore. Miner. Eng. 12 (8), 949–967. Tsatouhas, G., Grano, S.R., Vera, M., 2005. Case studies on the performance and characterization of the froth phase in industrial flotation circuits. Miner. Eng. 19, 774–783. Yianatos, J., 2007. Fluid flow and kinetic modelling in flotation related processes: columns and mechanically agitated cells — a review. Chem. Eng. Res. Des. 85 (2007), 1591–1603. Yianatos, J., Contreras, F., 2010. Particle entrainment model for industrial flotation cells. Powder Technol. 197 (3), 260–267. Yianatos, J.B., Bergh, L., Condori, P., Aguilera, J., 2001. Hydrodynamic and metallurgical characterization of industrial flotation banks for control purposes. Miner. Eng. 14 (9), 1033–1046. Yianatos, J.B., Bergh, L.G., Díaz, F., Rodríguez, J., 2005. Mixing characteristics of industrial flotation equipment. Chem. Eng. Sci. 60, 2273–2282. Yianatos, J., Henriquez, F., Oroz, A., 2006. Characterization of large size flotation cells. Miner. Eng. 19, 531–538. Yianatos, J., Bergh, L., Tello, K., Díaz, F., Villanueva, A., 2008a. Residence time distribution in single big industrial flotation cells. Miner. Metall. Process. 25 (1), 46–52. Yianatos, J.B., Moys, M.H., Contreras, F., Villanueva, A., 2008b. Froth recovery of industrial flotation cells. Miner. Eng. 21 (12–14), 817–825 (Selected Papers from Flotation '07). Zheng, X., Franzidis, J.-P., Manlapig, E., 2004. Modelling of froth transportation in industrial flotation cells, part I. Development of froth transportation models for attached particles. Miner. Eng. 17, 981–988.
Contents lists available at SciVerse ScienceDirect
International Journal of Mineral Processing journal homepage: www.elsevier.com/locate/ijminpro
Modelling and simulation of rougher flotation circuits J. Yianatos a,⁎, C. Carrasco a, L. Bergh a, L. Vinnett a, C. Torres b a b
Automation and Supervision Centre for the Mining Industry, CASIM, Chemical and Environmental Engineering Department, Federico Santa María Technical University, Valparaíso, Chile División El Teniente, Codelco, Rancagua, Chile
a r t i c l e
i n f o
Article history: Received 7 June 2011 Received in revised form 9 June 2012 Accepted 14 June 2012 Available online 21 June 2012 Keywords: Flotation Modelling Simulation Rougher cells
a b s t r a c t At present, large mechanical flotation cells of 100 to 300 m3 are used in rougher operation in different industrial flotation plants around the world. However, in spite of the advances in fundamental research and the notable growth in equipment size, there is still a lack of reliable data for industrial flotation modelling and simulation. In this work, a procedure for modelling and simulating rougher flotation banks that is based on operating variables and parameters fitted by empirical data from plant measurements is presented. Recently, a new methodology for describing industrial flotation by separating the collection and froth zones has been developed. This approach consists of using a new apparatus for direct bubble load measurement below the pulp–froth interface in industrial cells. The procedure allows independently estimating the froth recovery and the collection zone recovery. Metallurgical characterisation is developed by plant sampling, mass balance adjustment and applying a short-cut method for kinetic characterisation of flotation banks. In addition, the effect of grinding is characterised using flotation models with distributed flotation rates (for each particle size class) and a low number of parameters. From the experimental data, a non-linear distributed model to simulate rougher flotation banks was developed, which allows describing the industrial operation as a function of the main operating variables (e.g., mass flow rate, solid percentage, grinding degree, pulp level and superficial air rate). The simulator was calibrated and validated using experimental data from the rougher operation at El Teniente Division, Codelco-Chile. The new approach is a practical tool that is useful for flotation operation diagnosis, for robust design and analysis of new control and optimisation strategies and for evaluation of the effect that design and operating variables have upon the collection and froth zone performance in large flotation cells. This methodology can be applied to other flotation operations, such as cleaner and scavenger circuits that use mechanical flotation cells. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Two types of mechanical flotation cells are employed in industrial applications: self-aspirated and forced-air flotation cells. The main differences between the cells are the type and location of the rotor and the mechanism used for the air input. In self-aspirated cells, the rotor is located near the top of the cell, whereas in forced-air cells, the rotor is located near the bottom. Mechanical cell designs have included some modifications, such as the use of froth-crowders and internal radial launders. These modifications have been focused on improving the froth transport and consequently the mineral recovery. The minimum number of cells per bank can be estimated from a hydrodynamic analysis assuming perfectly mixed cells. For example, it has been observed that when using four or more cells in series,
⁎ Corresponding author. E-mail address: [email protected] (J. Yianatos). 0301-7516/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.minpro.2012.06.005
the time scale-up factor required to reach the same recovery of a plug flow operation (batch) with the same flotation rate constant is close to 1.15 (Arbiter, 2000; Yianatos et al., 2006). Thus, the mixing effect can be compensated by increasing the bank mean residence time, e.g., increasing the number of cells or the cell size. Bourke (2002) noted an important aspect related to the minimum number of control points for proper bank operation. For instance, in a ten-cell arrangement, 2-2-3-3, only four level control points are available, whereas a five-cell arrangement, 1-1-1-1-1, has five level control points. In plant practice, a minimum of 4–6 cells in series, including at least four control points, is recommended. The behaviour of a flotation bank has been typically modelled as a set of tanks in series with the same properties, i.e., the same residence time distribution, flotation rate and froth characteristics in each cell. At present, important efforts have been made to characterise flotation circuits as distributed systems in order to obtain a more realistic description of the process. Maldonado et al. (2007) discussed a control strategy to improve the grade of the concentrate using the froth depth along a rougher flotation bank as the manipulated variable.
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Tsatouhas et al. (2005) reported a decrease in the froth recovery along a rougher bank in two industrial rougher circuits. Dobby and Savassi (2005) reported a change of flotation rate in the collection zone along a bank of cells based on the results of batch tests. The distributed character of a flotation rougher bank requires mass balances around each cell for solid and liquid phases in order to describe the operating conditions downward the bank, i.e. mean residence time per cell, froth depth, entrainment, and solid liberation, among others. In addition, the performance of each flotation cell in terms of mineral recovery and concentrate grade depends on the flotation rates in the collection zone and the cleaning effect controlled by the froth depth. On this subject, Finch and Dobby (1990) described industrial flotation equipment separating the collection and froth zone to identify the effects independently in order to estimate the overall flotation performance. Reviews on the collection and froth zone modelling have been reported in literature by Finch and Dobby (1990), Mathe et al. (1998) and Yianatos (2007), where detailed hydrodynamic characterisation of the collection zone and summaries of the froth transport modelling are presented. Several approaches for flotation process simulation have been proposed in literature which typically simplify or remove the froth phase. For example, Sosa-Blanco et al. (1999) developed a simulator to integrate the grinding and flotation process, where the flotation cells were modelled as a perfect mixer with entrainment in the froth phase; Ferreira and Loveday (2000) described the collection zone as a perfect mixer and the froth phase in terms of the froth recovery for a flotation circuit with 3 nodes; Casali et al. (2002) proposed a dynamic rougher simulator without considering the froth zone due to the close to plug flow behaviour; Maldonado et al. (2007) considered that the volumetric concentrate flowrate depends on the froth depth linearly; among others. Currently, several commercial simulators exist: the JK Simfloat mineral processing simulator (Schwarz and Alexander, 2009), which includes operational variables such as superficial gas rate, bubble surface area flux, froth recovery, entrainment, water recovery, solids per size class, mean residence times, overall flotation rate constants and mineral recovery per size class; the FloatStar mineral processing simulator (MinTek, 2012), which uses advanced process control to overcome design-related limitations and maximise the flotation circuit performance; the UsimPac mineral processing simulator (Metso, 2012), which considers the raw materials, products, water and waste for equipment dimensioning, carrying out mass balances, energy consumption evaluation, among other results; and the MetSim simulator (MetSim, 2009), which allows mass and energy balance development in complex flotation plants while taking into account chemical, control and equipment dimensioning aspects as well as capital cost estimations, among others. In spite of the wide commercial application of the aforementioned simulators, in general the software is closed for the user, with limited information about the process modelling. An exception is the JK Simfloat (Schwarz and Alexander, 2009), in which the collection and froth zones are separately modelled. The collection zone hydrodynamic is modelled by a perfect mixing regime whereas the froth zone is represented by a probability of detachment as a function of the froth residence time. On the other hand, the concept of using an overall flotation rate, accounting for the collection and froth zones together, is still employed. The overall rate constant depends on the bubble surface area flux, the mineral floatability and the froth recovery. The simulator reported in this paper is focused on providing a detailed phenomenological description of the flotation process in which a rougher bank has been modelled as a distributed system, i.e., each cell is an independent unit that consists of two different zones: collection and froth, which are linked by mass balance and not hindered by an overall rate constant. Moreover, the different liberation grades for the mineralogical species were taken into account. In order to obtain a representative description of the actual flotation process, the
variations in the collection flotation rates and residence time, as well as the froth transport characteristics and the froth recovery downstream from the bank of cells were considered. The simulator has been successfully tested in the rougher flotation SAG plant of El Teniente, Codelco-Chile, which consists of four banks of seven selfaspirated Wemco cells of 130 m 3 (array 1-2-2-2). 2. Single-cell characterisation: pulp and froth model For modelling, scale-up and analysis purposes, two zones are distinguished in the flotation cell: (a) the collection zone, where the particle-bubble aggregate is formed and carried to the pulp–froth interface (true flotation) and (b) the cleaning zone (froth), located between the pulp–froth interface and the concentrate overflow, where entrained particles have the chance to drop back to the collection zone. This zone is now described by the froth recovery. The global cell recovery RG is related to the collection zone recovery RC and the froth recovery RF, taking into account the overall mass balance around the cell (Eq. (1)) (Finch and Dobby, 1990; Finch et al., 2008). RG ¼
RC ⋅RF 1−RC ⋅ð1−RF Þ
ð1Þ
This approach is used for both (a) kinetic parameter estimation in the collection zone based on industrial mass balance measurements, which allow obtaining RG and RF, and (b) evaluation of the overall mineral recovery in each cell using the previously calibrated simulator, i.e., using hydrodynamic, flotation rate, granulometric and froth zone parameters as input. 2.1. Collection zone, RC The mineral recovery RC in the collection zone can be described by the general expression Eq. (2) (Polat and Chander, 2000; Yianatos, 2007). ∞ ∞ −k⋅t ⋅Eðt Þ⋅F ðkÞ dt dk RC ¼ RMAX ⋅ ∫ ∫ 1−e
ð2Þ
0 0
where E(t) is the residence time distribution function for continuous processes with different mixing characteristics, F(k) is the flotation rate distribution for mineral species with different flotation rates and RMAX represents the maximum flotation recovery at infinite time. The term (1-e − kt) represents the mineral recovery of a firstorder process with invariant kinetic constant k, as a time function. 2.1.1. Residence time distribution, E(t) The hydrodynamic of flotation cells can be characterised by means of the residence time distribution function, E(t). The mixing regime of mechanical cells arranged in banks has been typically represented by a model of N perfect mixers in series (Yianatos et al., 2001). However, for describing the E(t) of single large cells, the perfect mixing condition is not valid based on the empirical evidence. At present, better fits for industrial data can be obtained using alternative approaches (Lelinski et al., 2002; Yianatos et al., 2008a). For example, the hydrodynamic of a flotation cell has been well represented by means of the large and small (LSTS) tanks in series model given by Eq. (3) (Yianatos et al., 2008a). Eðt Þ ¼
exp½−ðt−τP Þ=τS − exp½−ðt−τP Þ=τ L ðτ S −τP Þ
ð3Þ
where τL is the mean residence time of the large tank, τS is the mean residence time of the small tank and τp is the dead time. In addition, the ratio τS/τL is usually close to 0.1 in mechanical cells (Yianatos et al., 2005). Eq. (3) was considered for the simulator implementation.
J. Yianatos et al. / International Journal of Mineral Processing 112–113 (2012) 63–70
65
Fig. 1 shows good agreement between the LSTS model and the experimental data recorded in a Wemco cell of 130 m 3. 2.1.2. Flotation rate distribution, F(k) Several models have been proposed in order to evaluate the flotation rate distribution in flotation cells. The Dirac delta function, δ(k − kB), and rectangular models correspond to single parameter models, where δ(k − kB) represents a single flotation rate constant, kB. The rectangular model for the i-th size class (+100#, −100+ 325#, −325#, where # means mesh) and for the n-th cell, given by Eq. (4), was used for simulating the flotation rate distribution in a distributed manner n because of its flexibility and low number of parameters, kmax,i . n F i ðkÞ
¼
8 <
1 knmax;i : 0
; if
0bkbknmax;i
; if
k > knmax;i
ð4Þ Fig. 2. Recovery prediction model for batch tests.
Then, the mineral recovery in the collection zone of class i and cell n n,RCi , was calculated by means of Eq. (5): n
n
RC;i ¼ RC
MAX;i
∞ ∞ −k⋅t n ⋅Eðt Þ⋅F i ðkÞdt dk ⋅ ∫ ∫ 1−e
ð5Þ
0 0
where RnC MAX,i is the maximum collection zone recovery of the i-th class in the n-th cell. Notice that because of the amount of valuable mineral decreases along the flotation bank, the maximum recovery value in each size class (i.e., fine, intermediate and coarse) also decreases. If this change is not taken into account, the flotation rate distribution in each cell will be hindered by the variation of RnC MAX,i. Therefore, the valuable mineral was described by a fraction with a probability (> 0) of being floated and a non-floatable fraction. Thus, the amount of floatable, valuable and non-valuable material feeding a single cell in a bank was obtained from a mass balance in the previous cell, where the recoveries were known. To estimate the maximum recovery of the raw material entering the rougher circuit, batch tests for each size class were carried out using the same feed samples from the mass balance measurements. Fig. 2 shows a batch test result along with the RMAX estimation per size class. The same residence time distribution was considered in Eq. (5) for each size class because the empirical data showed no significant differences in the mean residence time and the distribution shape. Samples for the mass balances per size class were obtained for a complete description of the first 3 cells and the overall bank. The results for the global and froth recovery in each cell allowed estimating
Fig. 1. Model fit to industrial data (non-floatable tracer), τL = 5.5 min, τS = 0.5 min, τp = 0.8 min.
the kinetic parameters in cells 1, 2 and 3 and to extrapolate the results for the bank. Additionally, the air flow rate, the froth height and the bubble load were measured during the same sampling campaign in order to characterise the rougher circuit. To characterise the decrease of the flotation rate distribution of mineral class i along the rougher bank, Eq. (6) was used. The parameters were fitted by regression. The model variables (δ and n) were chosen considering the significant dependence of the flotation rate on the particle size and the cell number. kratio ¼
knmax;i k1max;i
n−1 χ ¼ exp − δi
ð6Þ
Eq. (6) allows obtaining the rectangular model parameters for the n-th cell as a function of the first one. The δi parameter depends on the characteristic size of the i-th size class, and χ is a fit parameter. Fig. 3 shows a comparison between the proposed model and the plant data in three size classes for a chalcopyrite mineral. 2.2. Cleaning zone, RF The cleaning zone was characterised by means of the froth recovery, which can be estimated from bubble load measurement along
Fig. 3. Plant data and model describing changes in the collection rate along the flotation bank.
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with a mass balance around the cell. Thus, the froth recovery, RF, was calculated by Eq. (7) (Yianatos et al., 2008b): C ⋅X C RF ¼ λB ⋅J G ⋅AC ⋅X B
ð7Þ
ð8Þ
where α is the maximum recovery in the froth, βn is the froth stability factor for the n-th cell and τF, n is the gas mean residence time in the froth of the n-th cell, which is given by Eq. (9) (Yianatos et al., 2008b): τF;n ¼
H F;n ⋅εG JG
ð9Þ
where HF,n is the froth height and εG is the mean gas concentration (hold-up) in the froth. The empirical evidence showed that the froth stability of each cell downstream from the bank is reduced, i.e., the froth selectivity increases along the cells arrangement. Therefore, the βn parameter in Eq. (8) was modelled as follows: βn ¼ ψ⋅Mn ⋅RC;n :
The water recovery, RW, is defined as the fraction of feed water reported to the concentrate stream and is given by Eq. (11): RW ¼
where λB is the bubble load, JG is the superficial gas rate, AC the crosssectional area of the cell, C is the solid mass flow in the concentrate and XC and XB are the concentrate and bubble load grade, respectively. It has been shown that Eq. (7) is useful for calculating the froth recovery and the valuable minerals collected by true flotation from experimental data (Yianatos et al., 2008b). In addition, Eq. (8) is usually employed for modelling the froth zone (Gorain et al., 1998; Mathe et al., 1998; Zheng et al., 2004). RF;n ¼ α ⋅ exp −βn ⋅τF;n
2.3. Water recovery
ð10Þ
where Mn is the amount of valuable mineral entering the n-th cell, RC, n is the overall recovery of the collection zone and ψ is a fit parameter. Notice that Mn·RC, n corresponds to the overall amount of valuable mineral entering the froth zone by true flotation. Fig. 4 shows the Cu grade of the bubble load and at the top of froth in a single cell, for different size classes. Based on these results, a rather non-selective froth was observed, which is consistent with the results reported by Yianatos et al., 2008b. Therefore, the same froth recovery per size class was assumed.
WC WF
ð11Þ
where WC corresponds to the water mass flow rate in the concentrate and WF is the feed water mass flow rate to each cell. The calculation of RW was carried out from solid percentage data and mass balance results. For simulation purposes, the water recovery was modelled as a function of the froth height, the froth stability factor and the superficial gas rate for each cell (Eq. (12)): RW;n ¼ ξ⋅ exp −
H
γ η F;n ⋅β n
!
JG
ð12Þ
where ξ is the maximum water recovery, and γ and η are fit parameters. Notice that Eq. (12) is similar to the froth recovery relationship in Eq. (8). In addition, this equation considers the influence of the froth behaviour in the water recovery as a distributed system. 2.4. Gangue recovery The gangue is recovered into the concentrate by entrainment caused by the water reported to the concentrate stream. The gangue ren covered per size class in the n-th cell, RG,i , was estimated by means of Eq. (13) (Yianatos and Contreras, 2010). n
RG;i ¼ EF i ⋅RW;n
ð13Þ
where EFi is the entrainment factor per size class. The gangue recovery per size class can then be obtained from RW measurements and empirical EFi values. 3. Single-cell simulation In order to evaluate the contribution of each individual cell in the flotation bank recovery, the collection zone recovery by true flotation, RC, the froth recovery of floatable minerals, RF, the water recovery, RW, and the gangue recovery, RG, were calculated for each cell. In addition, the mass flow rate of water and solids per size class in the tailings of each cell were obtained by means of a mass balance. The global recovery of mineral m, size class i, in cell n is given by m
Ri;n ¼
RC;i :RF;i 1−RC;i þ RC;i :RF;i
ð14Þ
Also, the concentrate grade X of mineral m, size class i, in cell n is m F i;n ⋅X F;m i;n ⋅Ri;n
C;m
X i;n ¼
2 P
3 P
m¼1 i¼1
Fig. 4. Comparison between Cu grade in the bubble load (CB) and at the top of froth (TOF).
ð15Þ
m F i;n ⋅X F;m i;n ⋅Ri;n
where the supra-indices C and F refer to the concentrate and feed streams. Notice from Eq. (15) that three size classes, i, were considered: coarse (+100#), intermediate (−100 + 325#) and fine (− 325#) in order to take into account different liberation grades. In addition, two types of minerals were included for the simulation: valuable mineral – e.g., chalcopyrite and molybdenite – and gangue. The overall recovery and concentrate grade of the flotation bank were calculated by integrating the distributed result of each cell, which were determined by Eqs. (14) and (15).
J. Yianatos et al. / International Journal of Mineral Processing 112–113 (2012) 63–70 Table 1 Simulation results for the rougher flotation bank. Feed Flow rate Froth depth Solid percentage Froth recovery, Cu Collection recovery, Cu Overall recovery, Cu
Cell 1 Cell 2 Cell 3 Cell 4 Cell 5 Cell 6 Cell 7 tph 900 803.9 790.4 782.1 775.7 770.7 765.6 cm 5 12 12 8 8 8 8 % 42.0 43.1 43.8 44.8 45.7 46.6 47.6 % 83.4 63.5 56.8 63.1 48.1 27.7 6.0 % 70.4 64.5 59.1 53.8 45.7 38.8 31.5 % 66.5 53.6 45.1 42.4 28.8 14.9 2.7
67
Therefore, the simulation requires a set of test and previously measured variables to calibrate the flotation models, including: mass balances, feed particle size distribution, batch tests, bubble load, superficial gas rate, residence time distribution and froth recovery. 5. Results 5.1. Case of study
4. Summary The general procedure for developing and calibration of the simulator includes the following steps: i) Sampling the first, second and third cells of the bank together with sampling the flotation bank as a whole. ii) Characterise the streams in terms of solid percentage by weight, and mass and grades (Cu, Mo and Fe) per size class. iii) Carry out mass balance adjustment per size class and estimate mineral recoveries. iv) Using the feed sample, conduct batch test to determine the RMAX values per size class. v) Estimate froth recovery, Eq. (7), using the measured values of XC, XB, λB and JG. The adjusted value of concentrate C and the cross sectional area is also required. vi) Using results from steps iii) and v), obtain the collection zone recovery per size class from Eq. (1). vii) Estimate the flotation rate parameters per size classes from Eq. (5) based on the RTD model, the distributed RMAX,i n along the bank per size class and the collection zone recovery results from step vi). viii) Characterise the decrease of the flotation rate distribution per size class along the rougher bank using Eq. (6). ix) From Eqs. (8), (9) and (10) and results from step v), determine the froth recovery parameter ψ using HF, n, εG and JG data along the bank together with the amount of valuable mineral entering the froth by true flotation. An α value of 92% was assumed in Eq. (8). x) Estimate gangue recovery from water recovery. First, obtain water recovery using the mass balance results together with the solid percentage by weight. Second, estimate parameters of Eq. (12) using the JG, and HF, n, and βn values along the bank. Determine gangue recovery from mass balances and bubble load measurements (Yianatos and Contreras, 2010) and estimate EFi factors per size class. xi) Based on the previously adjusted parameters (by regression), Eqs. (3) to (13), the overall mineral recovery and the concentrate grade can be computed from Eqs. (14) and (15), respectively.
The rougher flotation circuit (SAG plant) at El Teniente, CodelcoChile, was considered. The rougher circuit consists of four banks with seven self-aspirated Wemco cells (130 m 3) in series, in a 1-22-2 array. For the simulator calibration, measurements of feed, tail and concentrate grades per size class, superficial gas rate, bubble load, solid percentage, gas hold-up, residence time distribution and froth depth profiles along the rougher bank were carried out in the rougher flotation SAG plant (Carrasco, 2010). These results allowed obtaining the simulator parameters as well as to validate them. Table 1 shows the simulation results for Cu performance corresponding to a feed tonnage of 900 tph, a feed grade of 1%, a solid percentage by weight of 42% and 18% particle size (% + 100#) in a rougher bank. Table 2 presents a comparison between the simulator outputs based on operational parameters and plant results for two tests conducted in the rougher bank. The operational parameters of Test 1 were as follows: feed tonnage 790 tph, Cu feed grade 0.99%, Mo feed grade 0.021%, Fe feed grade 5.0%, percentage + 100# 19.8%, solids percentage by weight 41.5% and froth height (first cell) 5 cm. For Test 2, the operational parameters were: feed tonnage 650 tph, Cu feed grade 0.95%, Mo feed grade 0.020%, Fe feed grade 5.5%, percentage +100# 22.0%, solids percentage by weight 40.0% and froth height (first cell) 3 cm. A reasonable agreement between the simulated data and the plant performance was observed. 5.2. Sensitivity analysis For visualisation of the simulation responses, a sensitivity analysis for different operating conditions was carried out. The main variables for this analysis were particle size distribution (PSD), froth depth in the first cell of the bank, feed tonnage, feed grade and solid percentage. These variables are interesting for control purposes because of the economic impact in terms of mineral recovery and concentrate grade in industrial flotation banks. 5.2.1. Effect of particle size distribution (PSD) The effect of changes in the PSD on the cumulative Cu recovery and the incremental grade along the flotation bank was studied. The
Table 2 Comparison between plant performance and simulation results. Test 1
Rougher recovery %
Final concentrate
07/12/2009
Cu
Mo
Cu grade %
Mo grade %
Solid %
Cu/Fe ratio
% − 325 #
Plant data Simulation % Error
90.8 91.0 0.2
80.00 83.76 4.7
5.5 5.3 3.6
0.09 0.084 6.7
27.2 27.1 0.4
0.63 0.64 1.6
69.8 69.2 0.9
Test 2
Rougher recovery %
Final concentrate
14/12/2009
Cu
Mo
Cu grade %
Mo grade %
Solid %
Cu/Fe ratio
% − 325 #
Plant data Simulation Error (%)
91.2 91.6 0.4
81.0 83.4 3.0
5.00 5.03 0.6
0.071 0.070 1.4
24.5 25.3 3.3
0.61 0.60 1.6
67.4 66.9 0.7
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Fig. 5. Comparison of (a) the cumulative Cu recovery and (b) the incremental Cu grade as a function of the coarser feed content.
following variables were assumed constant for the simulation: feed tonnage 800 tph, feed copper grade 0.98%, solid percentage by weight 40% and 8 cm froth depth along the bank. The increment in particle size was represented by increasing the +100# fraction in the mineral feed by 18% to 25%. Fig. 5(a) shows a 1% decrease in the cumulative mineral recovery when the particle size was increased by increasing the coarse material in the flotation bank. From laboratory and plant experiments, the finer classes (− 100#) showed a higher collection probability; therefore, a coarser feed decreases the global recovery of the flotation bank (Carrasco, 2010). In addition, an increase in the incremental concentrate grade was observed for the coarser feed (Fig. 5(b)) because of the decrease in the liberated fine gangue entrainment to the concentrate.
5.2.2. Effect of froth depth A change in the froth height of the first cell, from 5 to 25 cm, was considered in order to evaluate its impact on the mineral recovery and concentrate grade of the flotation bank. The rest of the operating variables was kept constant, i.e., feed tonnage 800 tph, 0.98% feed copper grade, 40% solid percentage by weight, 8 cm froth depth in all of the other cells and 20% + 100# in the mineral feed size.
Fig. 6. Effect of froth depth change in the first cell on (a) the cumulative Cu recovery and (b) the incremental Cu grade.
Fig. 6(a) shows a 3% decrease in the cumulative mineral recovery when the froth depth was increased from 5 to 25 cm, while Fig. 6(b) shows the significant impact that the froth depth had on the concentrate grade obtained in the first cell. Also, a strong decrease in the incremental grade was observed downstream the rougher bank when the first cell was operated with froth depth of 25 cm. Finally, an increase of 1% in the rougher concentrate grade was obtained. Adequate level control in the first cell of a rougher bank is necessary to control the entrainment of non-floatable material and the overall concentrate grade in self-aerated cells. Otherwise, the grade of the first cell constrains the maximum grade achievable along the whole flotation bank. 5.2.3. Effect of feed tonnage The feed tonnage is relatively constant in the rougher flotation SAG plant because the four rougher banks are fed by two SAG mills, reducing the variations in the feed flow rate. An increase in feed tonnage from 600 to 800 tph was analysed. Again, the following variables were kept constant: feed copper grade 0.98%, solid percentage by weight 40%, 8 cm froth depth along the bank and 20% +100# mineral feed size. Fig. 7(a) shows a decrease of 1%–2% in mineral recovery from increasing the feed tonnage. In addition, a negligible effect of this change on the incremental concentrate grade was observed (Fig. 7(b)). The effect shown in the cumulative recovery is mainly due to variation of the mineral residence time in the bank of cells.
J. Yianatos et al. / International Journal of Mineral Processing 112–113 (2012) 63–70
Fig. 7. Effect of feed tonnage change on (a) the cumulative Cu recovery and (b) the incremental Cu grade.
5.2.4. Effect of feed grade The effect of increasing the copper feed grade from 0.9% to 1.1% was evaluated. In this case, the following variables were kept constant: feed tonnage 800 tph, 40% solid percentage by weight, 8 cm froth depth along the bank and 20% + 100# mineral feed size. A negligible effect on the cumulative recovery was observed when the feed grade increased from 0.9% to 1.1%, as shown in Fig. 8(a). However, a significant impact on the incremental concentrate grade was observed (Fig. 8(b)) because of the higher quality of the fresh material entering the rougher bank. Based on the models described in the previous sections, the key parameter related with the feed grade is the froth stability factor, β, which affects the froth and water recoveries. 5.2.5. Effect of solid percentage The solid percentage determines the mean residence time in flotation cells (rheological effects were not considered). An increase in solid percentage by weight from 30% to 40% was analysed while keeping the rest of the operating variables constant: feed tonnage 800 tph, 0.98% feed copper grade, 8 cm froth depth along the bank, and 20% +100# mineral feed size. Fig. 9(a) shows an increase in the cumulative recovery by changing the solid percentage from 30 to 40%, due to the longer residence time of minerals in the flotation cells. Also, a slight increase in the concentrate grade was observed in Fig. 9(b), because the water recovery to the concentrate was slightly lower which reduced the gangue entrainment relative to the valuable solid recovered into the concentrate.
69
Fig. 8. Comparison of (a) the cumulative Cu recovery and (b) the incremental Cu grade as a function of the feed grade.
The modelling of the flotation cells by separating the collection and froth zones, without using an apparent rate constant, allows for a better identification of the true flotation process (collection efficiency) as well as the froth separation process (product quality). Changes in the main operating variables yield to the expected mineral recovery and concentrate grade trends, while the effects on the mineral collection and the froth separation were clearly identified. In addition, the distributed approach for the rougher bank modelling involves the decrease of mean residence time (from actual RTD), froth stability and flotation rates, together with the increase of particle size, along the bank. All these information was obtained from plant measurements. The model does not consider reagents as manipulated variables explicitly, but they are partially represented by the flotation rate profile (per size class) along the bank, Fig. 3. Bigger efforts must be made to describe the rougher circuit performance as a function of the collector and frother dosage downward the bank. 6. Conclusions A procedure for modelling and simulating rougher flotation banks as a distributed process was developed. The model parameters were calibrated from plant operating data using a flotation rate evaluation based on the short-cut method, adjusted mass balances and a new approach to evaluate bubble load and froth recovery. The simulator was validated using experimental data from the rougher operation at El Teniente concentrator, which consists of flotation banks of seven 130 m 3 cells in series. The simulation allowed
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References
Fig. 9. Comparison of (a) the cumulative Cu recovery and (b) the incremental Cu grade as a function of feed solid percentage.
the evaluation of the industrial rougher flotation bank as a function of the main operating variables, including particle size distribution, mass flow rate, solid percentage, pulp level and feed grade. The new approach is a practical tool that is useful for flotation operation diagnosis, for robust design and analysis of new control and optimisation strategies, and for evaluating the effect that design and operating variables have upon the metallurgical performance in large flotation cells. This methodology can be applied to other flotation operations, such as cleaner and scavenger circuits, that use mechanical flotation cells. Acknowledgements Funding for process modelling and control research was provided by CONICYT, project Fondecyt 1100854, NEIM, Project P07-087-F, ICM-MINECON, Santa Maria University, project 270522.
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