R. del Villar

Automatic control of a laboratory flotation column

Abstract The operation of industrial flotation columns requires the control of at least two variables, the interface position and the bias rate, by manipulation of some appropriate operating variables. Problems arise due to the reliability of existing methods of measuring the bias (i.e bias = tailings water - feed water), a situation which has often forced the industry to disregard this control loop. Moreover, when using such a measuring approach, the identification of the process dynamics is impossible. A second problem arises from the possible interaction between both control loops that might call for the use of a more complex multivariable control strategy. Recent work done at Laval University has demonstrated the feasibility of an independent sensor for bias, which models the relation between the conductivity profile across the interface and the bias value using a neural network algorithm. A 250 cm height, 5.25 cm diameter Plexiglas laboratory column was equipped with a series of conductivity electrodes in its uppermost part (across the interface) to measure both interface position and bias rate. Using such equipment, the flotation column dynamics was identified. The results thus obtained permitted the design and implementation of a distributed PI control strategy, where bias was associated to wash water rate and froth depth to tails rate. Both PI controllers were tuned using a frequency-response tuning method. Results of both identification and process control are presented and discussed.

Modelling the cyclone performance with a size dependent entertainment factor

Abstract Conventional cyclone models use a particle size independent correction factor assumed equal to water recovery, R £ . Thus R £ is the minimum predicted recovery to the cyclone underflow, at an infinitely small particle size. Ample industrial and laboratory data suggest that at a size range between 5 and 40 μm, recovery to the underflow is slightly below R £ . In this paper, a mathematical model that accounts for this phenomenon is proposed. The proposed and conventional models are compared for laboratory and industrial data. Possible mechanisms are discussed.

Development of a softsensor for particle size monitoring

Abstract Some key control variables of industrial processes, associated with product quality, often cannot be measured directly or frequently enough to establish adequate control. In such cases, it is possible to use available measurements to provide a prediction for these process variables and use them in a control strategy, thereby giving rise to what is now commonly called a softsensor. In some industrial grinding circuits, the on-line particle size analyzer is shared between various sampling points. Therefore, for a given location, the actual measurement is only available every 10 to 20 minutes, a delay which is unacceptable for automatic control purposes. To alleviate this problem, a softsensor based on an artificial neural network has been investigated. First, the structure of the neural network and different schemes for the training process are analyzed. Then, the performance of the neural network softsensor is compared with other inferential methods such as ARMA models and Kalman filters.

Identification and Gain-Scheduled Control of a Pilot Flotation Column

Abstract Since measurements of recovery and grade are often complex and inaccurate, flotation columns are controlled using secondary variables, such as froth depth, bias and gas hold-up. This paper describes the control of the froth depth of a pilot flotation column by manipulating the tails flow rate. Using a virtual froth depth sensor, it is shown that the model explaining the variations of the interface position with the tails flow rate is more precise when the air flow rate is taken into account. Therefore, the parameters of the proposed controller are functions of the air flow rate.

Flotation column amenability and scale-up parameter estimation tests

Abstract A preliminary step in the decision to install flotation columns in an existing separation circuit is the so-called amenability testing. This testing consists of comparing metallurgical results from laboratory columns with, for example the performance of the existing circuit or with laboratory mechanical cells. The following step is to select the size and number of columns required for the duty. One way this is achieved is by using a computer simulator based on a scale-up model. This model requires, among other parameters, the flotation rate constants and the solids removal froth capacity, which have to be experimentally determined. This paper describes the apparatus and methodology used to conduct flotation column amenability and scale-up tests and discusses problems encountered during experience at a number of different concentrators. Amenability tests and scale-up procedure are illustrated using examples from two particular case studies: Mount Isa Mines and Falcombridge Ltd.

Parameterization of Bubble Size Distribution in Flotation Columns

Abstract A bubble detection technique based on Circular Hough Transform (CHT) has been implemented for bubble size distribution (BSD) determination in two-phase (gas-liquid) systems. This technique allows overcoming issues related to the detection of large single bubbles as well as clusters. A high resolution CCD camera is used to capture bubble images. The obtained digital images are automatically pre-conditioned to eliminate the background, eventual noises, and to enhance the contrast. Tests were carried out in a laboratory flotation column using different concentrations of frother and air flow-rates. Results were compared against manual (visual) counting, as well as a commonly used bubble detection method based on circular particle detection (CPD). The CHT-based technique allows proper detection and measurement of bubble clusters, large bubbles, and also incomplete bubbles in the image frame. Results obtained are very similar to those resulting from manual counts. Compared to CPD algorithms, the CHT approach significantly improves D 32 estimation (error of ~3% instead of ~18%) with a comparable processing time. Different methods to represent the resulting BSD are explained. In this paper, the BSD is estimated as a function of a lognormal distribution. Results are compared with manual estimation, showing a good representation of the distribution.

TOWARDS THE OPTIMIZATION OF FLOTATION COLUMNS USING PREDICTIVE CONTROL

Abstract This work details the application of a predictive control strategy to a pilot flotation column working with a two-phase system (water-air). All controlled variables are estimated using electrical-conductivity based techniques. In particular, the results of a new method for estimating the bias rate, based on the measurement of the volumetric fraction of wash water under the interface, is presented. The froth depth is controlled using a PI controller manipulating the set-point of a local tailing flow controller as it is often done in industry. The bias rate and gas hold-up are controlled using a multivariable predictive controller which manipulates the set-point of local flow controllers of wash-water and air. Several operational constraints are considered. Experimental results show that column flotation operation could advantageously optimized using a MPC strategy.

Self-optimization of an autogenous grinding circuit

Abstract This paper deals with the optimization of an autogenous grinding circuit using a random search technique. This technique is based on a hierarchical structure of learning automata operating in a random environment constituted by the autogenous circuit to be optimized. The ore feed rate to the mill is considered as the control variable while the mass flow rate of the concentrate of the subsequent separation process constitutes the controlled variable. The variation domain of the manipulated variables is discretized into a set of regions which are associated to the actions of the automata of the last level of the hierarchical learning system. A probability is associated to each action (region). The learning system selects one of the available actions and, based on the response of the environment, modifies the strategy (the probabilities associated to the set of actions) using an adaptation procedure called reinforcement scheme. Numerical results illustrate the feasibility and the performance of this self-adjusting optimization algorithm.

Nonlinear control of bubble size in a laboratory flotation column

Abstract Gas dispersion properties have proven to be key variables of the flotation process. Among them, bubble surface area flux (BSAF) has been reported to linearly correlate with the flotation rate constant; therefore, it is a potential variable to achieve a desired metallurgical performance. BSAF can be represented as a combination of two other gas dispersion properties: superficial gas velocity and Sauter mean bubble diameter. Thus, controlling BSAF implies controlling bubble size and superficial gas velocity. This work focuses on the nonlinear control of the Sauter mean bubble diameter. Sauter bubble mean diameter was indirectly calculated from the bubble size distribution, estimated by using a Gaussian mixture model. To improve controllability, a so-called frit-and-sleeve sparger was installed to regulate bubble size independently from superficial gas velocity. With this device, the bubble size can be modified by manipulating the water flow rate circulating through the sleeve that surrounds the porous ring. A Wiener model is used to represent the dynamic relationship between the sleeve water flow rate and Sauter mean diameter. Wiener models consist of a linear system in series with a memory-less (static) nonlinear element. An IMC controller based on the identified Wiener model was implemented in a laboratory flotation column. Tracking performance and rejection of gas velocity and unmeasured frother concentration variations were then successfully evaluated.

Flotation column amenablity and scale-up parameter estimation tests

A preliminary step in the decision to install flotation columns in an existing separation circuit is the so-called amenability testing. This testing consists of comparing metallurgical results from laboratory columns with the performance of the existing circuit or with laboratory mechanical cells. The following step is sizing the columns required for the duty. This is achieved by using a computer simulator based on a well established scale-up model. This model requires, among other parameters, the flotation rate constants and the solids removal froth capacity, which have to be experimentally determined. This paper describes the apparatus and methodology used to conduct flotation column amenability and scale-up tests and discusses problems encountered during experience at a number of different concentrators.