Froth flotation is a common method to extract a certain type of mineral from ore while depressing the amount of undesired minerals in the extracted concentrate. It is done by adding certain chemical reagents to selectively render the desired mineral hydrophobic.
In a flotation cell, air bubbles then lift the mineral. The resulting froth layer is then skimmed to produce the concentrate. Normally a flotation process consists of several flotation cells together with cyclones, mills, and mixing tanks. For poly-metallic ore, different flotation circuits and a grinding circuit can be combined in order to form a concentrator used for extracting several mineral types from the same ore. This is the case for the Garpenberg concentrator, although our focus here is zinc.
Due to the strong interaction between recovery (ratio between the quantity of valuable mineral in the concentrate and its original quantity in the ore), the economically best way to operate the concentrator is typically a trade off between these variables. Disturbances acting on the flotation circuit will have a negative impact on the performance and consequently on the economical result.
The Garpenberg concentrator, which is owned and operated by Boliden, processes a polymetallic ore extracted from an underground mine. The concentrator is composed of three flotation circuits and has a capacity of roughly 1 400 000 metric tons of ore per year. It yields three concentrates − a copper concentrate (chalcopyrite), a lead concentrate (galena), and a zinc concentrate (sphalerite). Gravity separation is also used in order to extract gold.
Measured variables
A flotation circuit typically comprises a variety of sensors installed in the zinc flotation circuit in Garpenberg. Volume flows are measured at three positions in the circuit. An on-line X-ray analyser taking samples from different locations in the circuit is used to determine the mass content of different metals (zinc, iron, copper, lead, etc.) as well as the overall solid fraction. Most of the flotation cells are equipped with sensors for measuring froth level thickness and air rate.
Automatic low-level control is used for the regulation of the froth levels using the froth level sensors and the valves at the tailings ports. However, manual control of the plant is still state of the art for optimising flotation performance. This means that a human operator has to observe the behaviour of the circuit using the various sensor outputs and determine appropriate set-points for the above mentioned manipulated variables.
This situation is suboptimal for the following reasons:
- Due to the aforementioned feed variations, the process is usually not in a steady state
- The dynamic interactions inside a flotation circuit are intricate and pose a challenge for humans
- Operator shift changes, in combination with the operators’ different philosophies concerning how the process should be controlled, upset the process
- The dynamic variations inside the process may lead to an excess of the design limits of the equipment, and reduce its lifetime
It must also be noted that, among others, one precondition for the success of the controller described in this article is the ability to tightly control the pulp levels of the flotation cells. Although simple PID loops are most often implemented, level control is a multivariable control problem due to the interactions between the cells. Furthermore, the existence of operating constraints suggests the use of advanced process control techniques in the form of an additional control strategy inside Expert Optimizer.
Given the above mentioned issues, automatic control is expected to lead to significant improvement in terms of flotation performance. In the remainder of this contribution, we will present a solution to the problem of controlling the zinc flotation circuit in Garpenberg based on model predictive control (MPC). To our knowledge, various approaches resorting to expert systems exist, but so far, no MPC-based solution has been applied successfully to a complete flotation circuit.
Our aim is twofold. Firstly, we would like to stabilise the process in spite of external disturbances. Secondly, the zinc concentrate production should be maximised while guaranteeing a minimum concentrate quality (i.e. zinc grade). This means that we try to push the process to an operating point closer to the upper limit. In order to fulfil this, optimal set-points should automatically be chosen by the controller.
A secondary objective concerns the tailoring of an efficient engineering process for the solution. It should be possible for a commissioning engineer to apply the control strategy to a different flotation circuit, with a reasonable amount of effort.
Model predictive control
The core of our solution is model predictive control. MPC is inherently multivariable, and its fundamental principle is to predict the process behaviour during a finite horizon in the future, using a discrete-time model.
Based on this prediction (continuous line), a sequence of future control moves (dashed line) is computed using mathematical optimisation. This sequence must comply with operational constraints and optimises a revenue function that maps goals such as set-point deviation and use of actuators. The underlying optimisation problem is solved at each sampling time, but only the first control move is carried out (circle), thus yielding closed-loop control.
The optimisation horizon should be long enough in order to cover the time constant of the process. Since a flotation circuit is a rather slow process, the sampling time of the controller can be chosen to allow enough time to perform the computations for solving the optimisation problem.
The future behaviour of the process must be predicted using a reliable dynamical model of the flotation circuit. There are two fundamental approaches for how the model for the MPC is obtained, commonly named using the terminology ‘grey box models’ and ‘first principles models’. In real applications though, the methods are blended in one way or another.
Findings
In total there were 25 days with the MPC controlling the flotation circuit and there were 31 days where the existing control strategy was used. By only considering achievements for the last day, the results for the ‘on/off two days’ are assumed to be less influenced by the other strategy, and therefore probably slightly more credible.
No particular difference can be seen in the zinc product concentrates in column three. The zinc concentrates in the tailings are slightly lower for the periods when MPC is used. The important difference is that the recovery for the zinc is at least one percentage unit higher when MPC is used compared with the existing manual control strategy.
Michael Lundh, Henrik Lindvall, Eduardo Gallestey and Sebastian Gaulocher
PULL QUOTE: A flotation circuit typically comprises a variety of sensors installed in the zinc flotation circuit
PULL QUOTE: The future behaviour of the process must be predicted using a reliable dynamical model of the flotation circuit
BOX: Did you know?
Without the flotation process, today's society, with its copper wires for electrical conduction and electrical motors, would not have happened. Copper would be too expensive. Historically froth flotation was first used in the mining industry, where it was one of the great enabling technologies of the 20th century. It has been described as "the single most important operation used for the recovery and upgrading of sulphide ores". The development of froth flotation improved the recovery of valuable minerals, such as copper- and lead-bearing minerals. Along with mechanised mining, it allowed the economic recovery of valuable metals from much lower grade ore than before.
