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On-line bias estimation using conductivity measurements
Minerals Engineering 21 (2008) 851–855
Contents lists available at ScienceDirect
Minerals Engineering journal homepage: www.elsevier.com/locate/mineng
On-line bias estimation using conductivity measurements M. Maldonado a,*, A. Desbiens a, R. del Villar b, J. Chirinos b a b
Department of Electrical and Computer Engineering, LOOP (Laboratoire d’observation et d’optimisation des procédés), Université Laval, Quebéc City, Canada G1V 0A6 Department of Mining, Metallurgical and Materials Engineering, LOOP (Laboratoire d’observation et d’optimisation des procédés), Université Laval, Quebéc City, Canada G1V 0A6
a r t i c l e
i n f o
Article history: Received 4 December 2007 Accepted 30 May 2008 Available online 17 July 2008 Keywords: Column flotation Process instrumentation Process control Mineral processing
a b s t r a c t Bias is an important variable in column flotation operation: negative values will deteriorate the concentrate grade due to mechanical entrainment of gangue, whereas excessive bias will reduce the particle residence-time in the collection zone as well as dilute the tails stream. Its estimation is usually made, at a high instrumentation cost, through a water mass-balance in the collection zone, nonetheless providing unreliable estimates. This paper presents a new method based on the measurement of the volumetric fraction of wash-water underneath the pulp–froth interface, using electrical-conductivity sensors. The method has been evaluated in a pilot flotation column, with a two-phase system. The results obtained indicate that it can be directly used for supervision and control of flotation column operation. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Perhaps the most characteristic feature of flotation columns is the addition of a fine spray of water, called wash water, at the top of the device or a few inches underneath the froth surface. Besides helping the stabilization of the froth and facilitating the removal of the bubble–particle aggregates to the concentrate launder, this stream washes back to the pulp zone the hydrophilic particles that might have been entrained with these aggregates. This washing action can only take place if a proper water mass-balance is assured in the lower part of the column, below the feed port, namely in the collection zone, so that part of this wash water can make its way down through the froth zone. This downward water stream, also called bias rate, is said to be positive if it goes down the column, and negative otherwise. When this latter case occurs, the concentrate could become contaminated with entrained hydrophilic particles and grade would decrease; a non desirable situation. While some authors claim that a slight, but positive, bias value ensures an adequate cleaning action (Finch and Dobby, 1990; Clingan and McGregor, 1987), others have established that small values do not contribute to reducing the entrainment of gangue. On the other hand, high bias values (above 0.4 cm/s) are detrimental since they might generate increased froth mixing and thus, dropback of collected particles (Yianatos et al., 1987). During column operation, bias can become negative as a result of an excessive gas flow rate, entraining most of the wash-water over the top of the column, diminishing the cleaning action of the froth zone. On the other hand, increasing bias would affect * Corresponding author. E-mail address: [email protected] (M. Maldonado). 0892-6875/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2008.05.011
the residence-time of ascending bubbles and that of settling particles in the collection zone, thus altering the recovery. Its action may also reflect on the froth zone recovery. Unfortunately, all these observations are mostly qualitative since bias measurements, particularly in three-phase systems, are not very reliable. Bias rate evaluation, as a difference between the rate of water going out in the tailing stream (Jwt) and that coming in through the feed stream (Jwf), implies a steady-state column operation, which is unlikely. Therefore, this method can only be used for sensor calibration or for auditing purposes, and only under carefully maintained steady-state conditions. 2. Background Two different approaches have been proposed so far for estimating bias rate. The first one considers some sort of water mass-balance on either zone of the column, above or below the interface, and makes use of measurements of external flow rates to estimate an internal variable, the bias rate. The second approach uses column internal variables, measured near the interface, for estimating the bias rate. The focus of this method is a change in some internal variable within the variation of the water content in the upper part of the column (above the interface), resulting from a change in the bias rate. In the following paragraphs, these two approaches are detailed and their advantages and problems are discussed. 2.1. Water mass-balance method Assuming a steady-state column operation, bias rate can be estimated by a water mass-balance in a column section below the feed port as
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M. Maldonado et al. / Minerals Engineering 21 (2008) 851–855
J b ¼ J wt J wf
ð1Þ
or above it
J b ¼ J ww J wc
ð2Þ
where Jwt, Jwf, Jww, Jwc and Jb are the superficial velocity (volumetric flow rate divided by column cross-sectional area) of the liquid component of tails, feed, wash-water, concentrate and bias streams, respectively, as shown in Fig. 1. Since the concentrate stream usually contains a large proportion of air bubbles, the flow rate and pulp density measurements required to evaluate the water component of this stream are unreliable. Consequently, the first definition, Eq. (1), was originally retained in industrial practice to estimate the bias. To implement this measurement method, four relatively expensive instruments are required: two magnetic flow meters and two c-ray density meters, one of each type installed in the feed and tailings streams of the column. Using these four measurements, bias is estimated as follows:
J b ¼ J t ð1 /st Þ J f ð1 /sf Þ
ð3Þ
where J represents a superficial velocity and /s a solid percent; subscripts t and f stand for tailings and feed pulp-streams. The variance of the estimate V Jb is given by the following equation, where V Ji and V /si respectively represents the error level of flow and density meters:
V Jb ¼ ð1 /st Þ2 V Jt þ J 2t V /st þ ð1 /sf Þ2 V Jf þ J 2f V /sf
ð4Þ
Despite this costly set-up, the accuracy of this estimate is very poor since bias is a very small value calculated from two large quantities (Jt, Jf), and subjected to an important error propagation (four instruments each having its own degree of uncertainty). Assuming a 3% error on each instrument reading, Eq. (4) leads to a 75% relative error on bias estimates, which is completely unacceptable (Finch and Dobby, 1990). As a result of this unreliable estimation and the high cost associated, to our knowledge not a single concentrator is presently using a bias control loop for the operation of their flotation columns. 2.2. Conductivity based methods To improve the accuracy of the bias estimation through the mass-balance approach, Uribe-Salas proposed to include the liquid-phase conductivity of the tails, concentrate, feed and washwater streams (Uribe-Salas et al., 1991). This is done through the so-called ‘‘additivity rule”, stating that the conductivity of a mixture is a weighed average of the component conductivities:
jAB ¼ xA jA þ xB jB
ð5Þ
where j represents a conductivity and x the composition of components A and B, respectively. The concentrate water-component Jwc
Jww Jwc Jwwc Jwwt Jwfc Jb
can be considered made of a wash-water short-circuiting stream Jwwc and a water feed-entrainment stream Jwfc (Fig. 1). Applying Eq. (5) to this ‘‘mixture”, the following expression can be obtained:
jwc ¼
J wfc J jwf þ wwc jww J wc J wc
ð6Þ
Similarly, the tails water component Jwt can be assumed as composed of a wash-water downward stream Jwwt and a water-feed downward stream Jwft. Applying Eq. (5) to this ‘‘mixture”, the following expression can be obtained:
jwt ¼
J wft J jwf þ wwt jww J wt J wt
ð7Þ
Since bias can be related to Jwt and Jwf by a water-balance in the lower part of the column (Jb = Jwt Jwf), its value can be obtained by
J b ¼ J wt
jwf jwt jwc jww J wc jwf jww jwf jww
ð8Þ
Uribe-Salas claimed that this approach would in principle improve the precision of the bias estimate as compared to that obtained through the traditional form (Jb = Jwt Jwf). However, it still requires steady-state conditions, otherwise the problem of time-synchronization of the various conductivity and flow rate values will reduce its reliability. The situation is particularly critical for low jf/jw ratio values. The extensive instrumentation required, the need for the conductivity of the liquid component of some streams and above all, the requirement of a steady-state operation limit the practical application of this method to laboratory set-up mostly working with two-phase systems in well controlled steady-state operation. While conducting experiments to validate the use of temperature or conductivity profiles in the upper part of the column for froth-depth evaluation, Moys observed that the shape of this profile changed with wash-water rate variations (Moys and Finch, 1988). A similar pattern was later reported by Uribe-Salas for the conductivity profile (Uribe-Salas et al., 1991). None of these phenomena were practically implemented, lacking of a mathematical tool for their modelling. Based on these observations, Pérez-Garibay managed to successfully relate the conductivity-profile change to the prevailing bias rate using an artificial neural network (ANN) (Perez and del Villar, 1998). Vermette also did a similar work using the temperature profile (Vermette, 1997). These methods though, require the existence of an important difference between wash water and feed-water conductivities or temperatures. Reported experimental results (laboratory scale) are very good for two-phase and three-phase systems. The conductivity profile is obtained using the same sensor designed for froth-depth sensing (Maldonado et al., 2008). The method has yet to be tested in industrial columns. Fig. 2 shows some validation results on a threephase system, the solids being a synthetic mixture of hematite and silica. The observed scatter is the result of an ANN training with two-phase data. It is reasonable to believe that a neural network trained with three-phase data would have given even better predictions. The drawbacks of the method are as follows:
Jwf Jwft
Jwt Fig. 1. Flotation column internal water-streams.
(1) Extensive experimentation to create the robust data-base required for both learning and validation steps of the ANN. (2) An independent and reliable method of measuring bias rate is necessary for the ANN training data-base; this can easily be done at the laboratory scale by a steady-state water balance, but has not yet been implemented in an industrial scale.
M. Maldonado et al. / Minerals Engineering 21 (2008) 851–855
4. Experimental set up
0.6 0.8
JB predicted value
0.4
0.2
two-phase, 12”
0.6
0.4
0
0.2
-0.2
three-phase, 2”
-0.2
0
0.2
0.4
0.6
0 0.8
JB measured value Fig. 2. Static evaluation of bias rate (ANN).
(3) As a result of the above mentioned procedure, i.e. ANN training using steady-state bias values (see Fig. 2) will learn nothing about dynamic behavior. More recently, Aubé (2003) used a simple multi-linear regression technique to replace the ANN algorithm for modelling the bias rate to the conductivity profile. Results were satisfactory, eliminating at least some of the drawbacks outlined above. Both the ANN and multi-linear regression approaches have been successfully used for automatic control of bias in a laboratory-scale column at various occasions (del Villar et al., 1999; Bouchard et al., 2005; Desbiens et al., 1998). In order to eliminate the remaining concerns, the following method combines the positive features of each: process phenomenology and some empirical correlations. 3. Bias estimation method
The pilot column flotation used for the validation of this method is located at the COREM (Mineral Processing Research Consortium) pilot plant in Québec City. The column is made of 5.1 cm internal diameter polycarbonate tubes, for a total height of 800 cm. A cylindrical 5 lm porous stainless-steel sparger (38 cm2 area) is located at the bottom of the column to provide a constant air flow rate controlled through a local PID loop (Fig. 3). To measure the froth-depth, the uppermost section of the pilot flotation column is implemented with stainless-steel conductivity electrodes, 5.1 cm external diameter by 1.5 cm height rings, flush-mounted inside the column wall at 10 cm intervals. Local control loops are implemented to regulate all flow rates (feed, tails, wash-water and air). Slurry and water pumping is done via variable-speed MasterflexTM peristaltic pumps. All flow rates are measured using appropriate flow meters (magnetic, turbine, etc). The tests described in this paper were performed with a twophase system (air-water). The conductivity of the feed and washwater were carefully set at 1500 and 500 lS/cm (25 °C) respectively using sodium chloride. Dow froth 250 C at 30 ppm was used. A ‘‘factorial” experimentation using superficial gas velocities (Jg) of 1, 1.3, 1.6 cm/s and superficial wash-water rate Jww of 0.16, 0.24, 0.3 cm/s under different conditions of froth-depth and feed rate was completed to generate the necessary data for the validation of this method. Data acquisition was performed by a SCADA software (iFIXTM) working under WindowsTM operating system. 5. Experimental results Fig. 4 shows the static relation between the bias rate obtained from the application of the ‘‘additivity rule” method (Uribe-Salas et al., 1991), here considered as a reliable reference given the con-
The proposed method has been developed for a water-air mixture only. Work is underway for its extension to three-phase systems. It is based on the estimation of the volumetric fraction of wash-water (eww) below the interface, i.e. where bias is defined. Using the ‘‘additivity rule”, the volumetric fraction of washwater below the interface is given by
eww ð%Þ ¼ 100
jwf j jwf jww
ð9Þ
where j* is the conductivity of the liquid phase underneath the interface, estimated from the conductivity of the water-air mixture and then compensated through a gas hold-up (eg) measurement near the interface derived from the Maxwell’s equation that relates conductivity to concentration of a dispersed non-conducting phase (i.e. air bubbles) in a continuous liquid phase (water in this case) (Maxwell, 1954).
j ¼ ji
853
jl 0:5eg þ 1 ¼ ji 1 eg jlg
ð10Þ
where ji is the conductivity of the water-air mixture underneath the interface (conductivity cell i) and jl and jlg the water-only and water-air conductivities, both measured for gas hold-up estimation, using the McGill’s method based on the so-called ‘‘flow cells”, namely, syphon and open cells (Uribe-Salas et al., 1994; Gomez et al., 2003). An empirical linear relation between bias rate and the volumetric wash-water fraction underneath the interface is proposed for the final bias rate estimation:
J b ¼ a eww þ b
ð11Þ
Fig. 3. Pilot column flotation set-up.
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M. Maldonado et al. / Minerals Engineering 21 (2008) 851–855
0.25
0.15 0.1 0.05
0.3
B
JB (cm/s)
0.2
J measured (cm/s)
0.2
0.15
0.1
0.05
validation data linear fitting R2=0.93
0.25
1.6 1.4
0
0.2
1.2 1
J (cm/s)
J
ww
g
(cm/s) 0.05
0
0.05
0.1
0.15
0.2
J estimated (cm/s)
Fig. 4. Effect of Jg and Jww on bias rate (estimated by additivity rule).
B
Fig. 6. Relation between measured and estimated bias rates.
bias rate (cm/s)
0.25
0.15
Jb = Jwt − Jwf Jb = aεww+b
0.4 0.3 0.2 0.1 0 −0.1 0
0.1
20
40
60
80 time (min)
100
120
140
B
J measured (cm/s)
0.2
0
20
30
ε
ww
40
50
60
(%)
Fig. 5. Relationship between bias rate and volumetric fraction of wash-water.
trolled steady-state conditions maintained throughout the tests, and both wash-water and gas superficial rates. These data were used to determine the parameters a and b in Eq. (11). Fig. 5 shows the relation between the bias rate measured using the ‘‘additivity rule” method and the volumetric fraction of wash-water (eww) below the interface (Eq. (11)). Parameters a = 0.003966 ± 0.000377 and b = 0.03409 ± 0.01556 were obtained by least-square curve fit. Fig. 6 presents the validation of the method using a different data set from that used for the rest of the development. It can be seen that very good estimates are obtained using the proposed method. One important advantage of this method is the fact that it can dynamically estimate the bias rate independently of the existence of steady-state conditions. Fig. 7 shows the dynamic bias estimates (solid line), during step-changes in wash-water rate (the variable used to control bias rate), and bias values obtained from a waterbalance in the collection zone. During this test, feed rate was regulated at a constant value using a local PI controller and the froth-depth was maintained at a fixed value also using a PI controller, by manipulation of tailings flow rate. Despite the fact that bias rate estimation is based on a steadystate water mass-balance in the collection zone, it is intentionally plotted as a dynamic variable to emphasize the effect of the frothdepth control-loop on the estimation.
0.3
bias rate (cm/s)
data linear fitting 2 R =0.94
0.05
0.2 0.1 Jb = Jwt − Jwf
0
Jb = aεww+b
−0.1 0
20
40
60
80 100 time (min)
120
140
160
180
Fig. 7. Dynamic bias estimation.
This bias estimation has been successfully implemented in different control applications at the pilot scale (Maldonado et al., 2007a; Maldonado et al., 2007b). The method proposed improved the stability of the system as compared to those control strategies using bias rate estimates obtained as the difference between tails and feed rates water-components (e.g. Carvalho and Durao, 2002, 2004). 6. Conclusions This work has presented a new method for the dynamic estimation of bias rate based on conductivity measurements. In contrast to those methods based on external (water- component) flow rate balances, this one obtains information directly below the interface, where the bias rate is defined. More precisely, it uses a linear relationship between the bias rate and the volumetric fraction of wash-water below the interface, estimated from conductivity measurements. The proposed method is particularly interesting for control and optimization purposes because it is not constrained to steady-state conditions as was the case of most algorithms reported so far. In addition, the estimation reduces the system coupling as compared to those estimations based on flow mass-balances.
M. Maldonado et al. / Minerals Engineering 21 (2008) 851–855
Evaluation of this method in an industrial flotation column is an ongoing project. Acknowledgement The authors would like to acknowledge the Natural Sciences and Engineering Research Council of Canada, Algosys Inc. and Société Minière Raglan du Québec for providing the necessary funding for this project. References Aubé, V., 2003. Validation semi-industrielle des capteurs de profondeur d’écume et de différentiel d’eau dans une colonne de flottation. Master’s Thesis, Department of Metallurgy and Material Engineering. Université Laval. Bouchard, J., Desbiens, A., del Villar, R., 2005. Recent advances in bias and froth depth control in flotation columns. Minerals Engineering 18, 709–720. Carvalho, M.T., Durao, F., 2002. Control of a flotation column using fuzzy logic inference. Fuzzy Sets and Systems 125, 121–133. Clingan, B.V., McGregor, D.R., 1987. Column flotation experience at magma copper co. Minerals and Metallurgical Processing 3 (3), 121–125. del Villar, R., Grégoire, M., Pomerleau, A., 1999. Automatic control of a laboratory flotation column. Minerals Engineering 33 (2), 291–308. Desbiens, A., Milot, M., del Villar, R., 1998. Identification and gain-scheduled control of a pilot flotation column. In: Proceeding of the 9th IFAC Symposium on Automation in Mining, Mineral and Metal Processing. Cologne, Germany, pp. 337–342. Finch, J.A., Dobby, G., 1990. Column Flotation. Pergamon Press, Oxford. Gomez, C.O., Cortés-Lopéz, F., Finch, J.A., 2003. Industrial testing of a gas holdup sensor for flotation systems. Minerals Engineering 16, 493–501.
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Maldonado, M., Desbiens, A., del Villar, R., 2007a. Control of a pilot flotation column: A 33 system. In: del Villar, R., Nesset, J.E., Gomez, C.O., Stradling, A.W. (Eds.), Proceeeding of the Sixth International Copper-Cobre Conference. August 25–30, vol. 2, Toronto, Canada, pp. 261–275. Maldonado, M., Desbiens, A., del Villar, R., Quispe, R., 2007b. Towards the optimization of flotation columns using predictive control. In: Bazin, C., Duchesne, C., Poulin, E. (Eds.), Proceeeding of the 12th IFAC Symposium on Automation in Mining, Mineral and Metal Processing, August 21–23, Québec City, Canada, pp. 75–80. Maldonado, M., Desbiens, A., del Villar, R., 2008. An update on the estimation of the froth depth using conductivity measurements. Minerals Engineering doi:10.1016/j.mineng.2008.02.018. Maxwell, J.C., 1954. A Treatise of Electricity and Magnetism, vol. 1. Oxford University Press, London. (Part 11). Moys, M.H., Finch, J.A., 1988. The measurement and control of level in flotation columns. In: K.V.S. Sastry, (Ed.), Proceedings of the column flotation’ 88, SME Annual Meeting, AZ, USA, pp. 103–112 (chapter 12). Perez, R., del Villar, R., 1998. Estimation of bias and entrainment in flotation columns using conductivity measurements. Canadian Metallurgical Quarterly 36 (5), 299–307. Persechini, M.A.M., Jota, F.G., Peres, A.E.C., Gontalves, F., 2004. Control strategy for a column flotation process. Control Engineering Practice 12, 963–976. Uribe-Salas, A., Gomez, C.O., Finch, J.A., 1991. Bias detection in flotation columns. In: the Proceeeding of Column’91, pp. 391–407. Uribe-Salas, A., Gomez, C.O., Finch, J.A., 1994. A conductivity technique for gas and solilds holdup determination in three-phase reactors. Chemical Engineering Science 49 (1), 1–10. Vermette, H., 1997. Mesure du biais dans une colonne de flottation par profils de température et conductivité. Master’s Thesis, Department of Metallurgy and Material Engineering. Université Laval. Yianatos, J.B., Finch, J.A., Laplante, A.R., 1987. The cleaning action in column flotation froths. Transactions of the Institution of Mining and Metallurgy Section C 96, C199–C205.
Contents lists available at ScienceDirect
Minerals Engineering journal homepage: www.elsevier.com/locate/mineng
On-line bias estimation using conductivity measurements M. Maldonado a,*, A. Desbiens a, R. del Villar b, J. Chirinos b a b
Department of Electrical and Computer Engineering, LOOP (Laboratoire d’observation et d’optimisation des procédés), Université Laval, Quebéc City, Canada G1V 0A6 Department of Mining, Metallurgical and Materials Engineering, LOOP (Laboratoire d’observation et d’optimisation des procédés), Université Laval, Quebéc City, Canada G1V 0A6
a r t i c l e
i n f o
Article history: Received 4 December 2007 Accepted 30 May 2008 Available online 17 July 2008 Keywords: Column flotation Process instrumentation Process control Mineral processing
a b s t r a c t Bias is an important variable in column flotation operation: negative values will deteriorate the concentrate grade due to mechanical entrainment of gangue, whereas excessive bias will reduce the particle residence-time in the collection zone as well as dilute the tails stream. Its estimation is usually made, at a high instrumentation cost, through a water mass-balance in the collection zone, nonetheless providing unreliable estimates. This paper presents a new method based on the measurement of the volumetric fraction of wash-water underneath the pulp–froth interface, using electrical-conductivity sensors. The method has been evaluated in a pilot flotation column, with a two-phase system. The results obtained indicate that it can be directly used for supervision and control of flotation column operation. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Perhaps the most characteristic feature of flotation columns is the addition of a fine spray of water, called wash water, at the top of the device or a few inches underneath the froth surface. Besides helping the stabilization of the froth and facilitating the removal of the bubble–particle aggregates to the concentrate launder, this stream washes back to the pulp zone the hydrophilic particles that might have been entrained with these aggregates. This washing action can only take place if a proper water mass-balance is assured in the lower part of the column, below the feed port, namely in the collection zone, so that part of this wash water can make its way down through the froth zone. This downward water stream, also called bias rate, is said to be positive if it goes down the column, and negative otherwise. When this latter case occurs, the concentrate could become contaminated with entrained hydrophilic particles and grade would decrease; a non desirable situation. While some authors claim that a slight, but positive, bias value ensures an adequate cleaning action (Finch and Dobby, 1990; Clingan and McGregor, 1987), others have established that small values do not contribute to reducing the entrainment of gangue. On the other hand, high bias values (above 0.4 cm/s) are detrimental since they might generate increased froth mixing and thus, dropback of collected particles (Yianatos et al., 1987). During column operation, bias can become negative as a result of an excessive gas flow rate, entraining most of the wash-water over the top of the column, diminishing the cleaning action of the froth zone. On the other hand, increasing bias would affect * Corresponding author. E-mail address: [email protected] (M. Maldonado). 0892-6875/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2008.05.011
the residence-time of ascending bubbles and that of settling particles in the collection zone, thus altering the recovery. Its action may also reflect on the froth zone recovery. Unfortunately, all these observations are mostly qualitative since bias measurements, particularly in three-phase systems, are not very reliable. Bias rate evaluation, as a difference between the rate of water going out in the tailing stream (Jwt) and that coming in through the feed stream (Jwf), implies a steady-state column operation, which is unlikely. Therefore, this method can only be used for sensor calibration or for auditing purposes, and only under carefully maintained steady-state conditions. 2. Background Two different approaches have been proposed so far for estimating bias rate. The first one considers some sort of water mass-balance on either zone of the column, above or below the interface, and makes use of measurements of external flow rates to estimate an internal variable, the bias rate. The second approach uses column internal variables, measured near the interface, for estimating the bias rate. The focus of this method is a change in some internal variable within the variation of the water content in the upper part of the column (above the interface), resulting from a change in the bias rate. In the following paragraphs, these two approaches are detailed and their advantages and problems are discussed. 2.1. Water mass-balance method Assuming a steady-state column operation, bias rate can be estimated by a water mass-balance in a column section below the feed port as
852
M. Maldonado et al. / Minerals Engineering 21 (2008) 851–855
J b ¼ J wt J wf
ð1Þ
or above it
J b ¼ J ww J wc
ð2Þ
where Jwt, Jwf, Jww, Jwc and Jb are the superficial velocity (volumetric flow rate divided by column cross-sectional area) of the liquid component of tails, feed, wash-water, concentrate and bias streams, respectively, as shown in Fig. 1. Since the concentrate stream usually contains a large proportion of air bubbles, the flow rate and pulp density measurements required to evaluate the water component of this stream are unreliable. Consequently, the first definition, Eq. (1), was originally retained in industrial practice to estimate the bias. To implement this measurement method, four relatively expensive instruments are required: two magnetic flow meters and two c-ray density meters, one of each type installed in the feed and tailings streams of the column. Using these four measurements, bias is estimated as follows:
J b ¼ J t ð1 /st Þ J f ð1 /sf Þ
ð3Þ
where J represents a superficial velocity and /s a solid percent; subscripts t and f stand for tailings and feed pulp-streams. The variance of the estimate V Jb is given by the following equation, where V Ji and V /si respectively represents the error level of flow and density meters:
V Jb ¼ ð1 /st Þ2 V Jt þ J 2t V /st þ ð1 /sf Þ2 V Jf þ J 2f V /sf
ð4Þ
Despite this costly set-up, the accuracy of this estimate is very poor since bias is a very small value calculated from two large quantities (Jt, Jf), and subjected to an important error propagation (four instruments each having its own degree of uncertainty). Assuming a 3% error on each instrument reading, Eq. (4) leads to a 75% relative error on bias estimates, which is completely unacceptable (Finch and Dobby, 1990). As a result of this unreliable estimation and the high cost associated, to our knowledge not a single concentrator is presently using a bias control loop for the operation of their flotation columns. 2.2. Conductivity based methods To improve the accuracy of the bias estimation through the mass-balance approach, Uribe-Salas proposed to include the liquid-phase conductivity of the tails, concentrate, feed and washwater streams (Uribe-Salas et al., 1991). This is done through the so-called ‘‘additivity rule”, stating that the conductivity of a mixture is a weighed average of the component conductivities:
jAB ¼ xA jA þ xB jB
ð5Þ
where j represents a conductivity and x the composition of components A and B, respectively. The concentrate water-component Jwc
Jww Jwc Jwwc Jwwt Jwfc Jb
can be considered made of a wash-water short-circuiting stream Jwwc and a water feed-entrainment stream Jwfc (Fig. 1). Applying Eq. (5) to this ‘‘mixture”, the following expression can be obtained:
jwc ¼
J wfc J jwf þ wwc jww J wc J wc
ð6Þ
Similarly, the tails water component Jwt can be assumed as composed of a wash-water downward stream Jwwt and a water-feed downward stream Jwft. Applying Eq. (5) to this ‘‘mixture”, the following expression can be obtained:
jwt ¼
J wft J jwf þ wwt jww J wt J wt
ð7Þ
Since bias can be related to Jwt and Jwf by a water-balance in the lower part of the column (Jb = Jwt Jwf), its value can be obtained by
J b ¼ J wt
jwf jwt jwc jww J wc jwf jww jwf jww
ð8Þ
Uribe-Salas claimed that this approach would in principle improve the precision of the bias estimate as compared to that obtained through the traditional form (Jb = Jwt Jwf). However, it still requires steady-state conditions, otherwise the problem of time-synchronization of the various conductivity and flow rate values will reduce its reliability. The situation is particularly critical for low jf/jw ratio values. The extensive instrumentation required, the need for the conductivity of the liquid component of some streams and above all, the requirement of a steady-state operation limit the practical application of this method to laboratory set-up mostly working with two-phase systems in well controlled steady-state operation. While conducting experiments to validate the use of temperature or conductivity profiles in the upper part of the column for froth-depth evaluation, Moys observed that the shape of this profile changed with wash-water rate variations (Moys and Finch, 1988). A similar pattern was later reported by Uribe-Salas for the conductivity profile (Uribe-Salas et al., 1991). None of these phenomena were practically implemented, lacking of a mathematical tool for their modelling. Based on these observations, Pérez-Garibay managed to successfully relate the conductivity-profile change to the prevailing bias rate using an artificial neural network (ANN) (Perez and del Villar, 1998). Vermette also did a similar work using the temperature profile (Vermette, 1997). These methods though, require the existence of an important difference between wash water and feed-water conductivities or temperatures. Reported experimental results (laboratory scale) are very good for two-phase and three-phase systems. The conductivity profile is obtained using the same sensor designed for froth-depth sensing (Maldonado et al., 2008). The method has yet to be tested in industrial columns. Fig. 2 shows some validation results on a threephase system, the solids being a synthetic mixture of hematite and silica. The observed scatter is the result of an ANN training with two-phase data. It is reasonable to believe that a neural network trained with three-phase data would have given even better predictions. The drawbacks of the method are as follows:
Jwf Jwft
Jwt Fig. 1. Flotation column internal water-streams.
(1) Extensive experimentation to create the robust data-base required for both learning and validation steps of the ANN. (2) An independent and reliable method of measuring bias rate is necessary for the ANN training data-base; this can easily be done at the laboratory scale by a steady-state water balance, but has not yet been implemented in an industrial scale.
M. Maldonado et al. / Minerals Engineering 21 (2008) 851–855
4. Experimental set up
0.6 0.8
JB predicted value
0.4
0.2
two-phase, 12”
0.6
0.4
0
0.2
-0.2
three-phase, 2”
-0.2
0
0.2
0.4
0.6
0 0.8
JB measured value Fig. 2. Static evaluation of bias rate (ANN).
(3) As a result of the above mentioned procedure, i.e. ANN training using steady-state bias values (see Fig. 2) will learn nothing about dynamic behavior. More recently, Aubé (2003) used a simple multi-linear regression technique to replace the ANN algorithm for modelling the bias rate to the conductivity profile. Results were satisfactory, eliminating at least some of the drawbacks outlined above. Both the ANN and multi-linear regression approaches have been successfully used for automatic control of bias in a laboratory-scale column at various occasions (del Villar et al., 1999; Bouchard et al., 2005; Desbiens et al., 1998). In order to eliminate the remaining concerns, the following method combines the positive features of each: process phenomenology and some empirical correlations. 3. Bias estimation method
The pilot column flotation used for the validation of this method is located at the COREM (Mineral Processing Research Consortium) pilot plant in Québec City. The column is made of 5.1 cm internal diameter polycarbonate tubes, for a total height of 800 cm. A cylindrical 5 lm porous stainless-steel sparger (38 cm2 area) is located at the bottom of the column to provide a constant air flow rate controlled through a local PID loop (Fig. 3). To measure the froth-depth, the uppermost section of the pilot flotation column is implemented with stainless-steel conductivity electrodes, 5.1 cm external diameter by 1.5 cm height rings, flush-mounted inside the column wall at 10 cm intervals. Local control loops are implemented to regulate all flow rates (feed, tails, wash-water and air). Slurry and water pumping is done via variable-speed MasterflexTM peristaltic pumps. All flow rates are measured using appropriate flow meters (magnetic, turbine, etc). The tests described in this paper were performed with a twophase system (air-water). The conductivity of the feed and washwater were carefully set at 1500 and 500 lS/cm (25 °C) respectively using sodium chloride. Dow froth 250 C at 30 ppm was used. A ‘‘factorial” experimentation using superficial gas velocities (Jg) of 1, 1.3, 1.6 cm/s and superficial wash-water rate Jww of 0.16, 0.24, 0.3 cm/s under different conditions of froth-depth and feed rate was completed to generate the necessary data for the validation of this method. Data acquisition was performed by a SCADA software (iFIXTM) working under WindowsTM operating system. 5. Experimental results Fig. 4 shows the static relation between the bias rate obtained from the application of the ‘‘additivity rule” method (Uribe-Salas et al., 1991), here considered as a reliable reference given the con-
The proposed method has been developed for a water-air mixture only. Work is underway for its extension to three-phase systems. It is based on the estimation of the volumetric fraction of wash-water (eww) below the interface, i.e. where bias is defined. Using the ‘‘additivity rule”, the volumetric fraction of washwater below the interface is given by
eww ð%Þ ¼ 100
jwf j jwf jww
ð9Þ
where j* is the conductivity of the liquid phase underneath the interface, estimated from the conductivity of the water-air mixture and then compensated through a gas hold-up (eg) measurement near the interface derived from the Maxwell’s equation that relates conductivity to concentration of a dispersed non-conducting phase (i.e. air bubbles) in a continuous liquid phase (water in this case) (Maxwell, 1954).
j ¼ ji
853
jl 0:5eg þ 1 ¼ ji 1 eg jlg
ð10Þ
where ji is the conductivity of the water-air mixture underneath the interface (conductivity cell i) and jl and jlg the water-only and water-air conductivities, both measured for gas hold-up estimation, using the McGill’s method based on the so-called ‘‘flow cells”, namely, syphon and open cells (Uribe-Salas et al., 1994; Gomez et al., 2003). An empirical linear relation between bias rate and the volumetric wash-water fraction underneath the interface is proposed for the final bias rate estimation:
J b ¼ a eww þ b
ð11Þ
Fig. 3. Pilot column flotation set-up.
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M. Maldonado et al. / Minerals Engineering 21 (2008) 851–855
0.25
0.15 0.1 0.05
0.3
B
JB (cm/s)
0.2
J measured (cm/s)
0.2
0.15
0.1
0.05
validation data linear fitting R2=0.93
0.25
1.6 1.4
0
0.2
1.2 1
J (cm/s)
J
ww
g
(cm/s) 0.05
0
0.05
0.1
0.15
0.2
J estimated (cm/s)
Fig. 4. Effect of Jg and Jww on bias rate (estimated by additivity rule).
B
Fig. 6. Relation between measured and estimated bias rates.
bias rate (cm/s)
0.25
0.15
Jb = Jwt − Jwf Jb = aεww+b
0.4 0.3 0.2 0.1 0 −0.1 0
0.1
20
40
60
80 time (min)
100
120
140
B
J measured (cm/s)
0.2
0
20
30
ε
ww
40
50
60
(%)
Fig. 5. Relationship between bias rate and volumetric fraction of wash-water.
trolled steady-state conditions maintained throughout the tests, and both wash-water and gas superficial rates. These data were used to determine the parameters a and b in Eq. (11). Fig. 5 shows the relation between the bias rate measured using the ‘‘additivity rule” method and the volumetric fraction of wash-water (eww) below the interface (Eq. (11)). Parameters a = 0.003966 ± 0.000377 and b = 0.03409 ± 0.01556 were obtained by least-square curve fit. Fig. 6 presents the validation of the method using a different data set from that used for the rest of the development. It can be seen that very good estimates are obtained using the proposed method. One important advantage of this method is the fact that it can dynamically estimate the bias rate independently of the existence of steady-state conditions. Fig. 7 shows the dynamic bias estimates (solid line), during step-changes in wash-water rate (the variable used to control bias rate), and bias values obtained from a waterbalance in the collection zone. During this test, feed rate was regulated at a constant value using a local PI controller and the froth-depth was maintained at a fixed value also using a PI controller, by manipulation of tailings flow rate. Despite the fact that bias rate estimation is based on a steadystate water mass-balance in the collection zone, it is intentionally plotted as a dynamic variable to emphasize the effect of the frothdepth control-loop on the estimation.
0.3
bias rate (cm/s)
data linear fitting 2 R =0.94
0.05
0.2 0.1 Jb = Jwt − Jwf
0
Jb = aεww+b
−0.1 0
20
40
60
80 100 time (min)
120
140
160
180
Fig. 7. Dynamic bias estimation.
This bias estimation has been successfully implemented in different control applications at the pilot scale (Maldonado et al., 2007a; Maldonado et al., 2007b). The method proposed improved the stability of the system as compared to those control strategies using bias rate estimates obtained as the difference between tails and feed rates water-components (e.g. Carvalho and Durao, 2002, 2004). 6. Conclusions This work has presented a new method for the dynamic estimation of bias rate based on conductivity measurements. In contrast to those methods based on external (water- component) flow rate balances, this one obtains information directly below the interface, where the bias rate is defined. More precisely, it uses a linear relationship between the bias rate and the volumetric fraction of wash-water below the interface, estimated from conductivity measurements. The proposed method is particularly interesting for control and optimization purposes because it is not constrained to steady-state conditions as was the case of most algorithms reported so far. In addition, the estimation reduces the system coupling as compared to those estimations based on flow mass-balances.
M. Maldonado et al. / Minerals Engineering 21 (2008) 851–855
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