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A flotation bank is a serial arrangement of cells. How to optimally operate a bank remains a challenge. This article reviews three reported strategies: air profiling, mass-pull (froth velocity) profiling and Peak Air Recovery (PAR) profiling. These are all ways of manipulating the recovery profile down a bank, which may be the property being exploited. Mathematical analysis has shown that a flat cell-by-cell recovery profile maximizes the separation of two floatable minerals for a given target bank recovery when the relative floatability is constant down the bank. Available bank survey data are analyzed with respect to recovery profiling. Possible variations on recovery profile to minimize entrainment are discussed.

Flotation is used to separate valuable minerals from each other and from gangue. To reach a target metallurgical performance, usually assessed in terms of concentrate grade and recovery, feed is passed through stages such as roughing, cleaning and scavenging. All these stages comprise serial arrangements of flotation cells known as banks, lines or rows.

Although a bank is the simplest interconnection of cells in a circuit,

Due to their localized impact, gas rate and/or froth depth are usually used to modify the operating point of a cell in a bank. The problem then becomes to find the optimal profile (e.g., gas rate profile) that achieves the target bank metallurgical objective. This solution is not obvious and a brute force approach based on a trial-and-error search rapidly becomes intractable even for simulation. To exemplify this point, consider a bank of 9 cells and assume that only the froth depth in each cell can be manipulated, then for 10 discrete froth depth values in each cell the number of possible froth depth profiles rises to 10^{9}!

Attempts to solve this optimization problem have been proposed [

This paper reviews three operational strategies to improve bank performance that have been successfully implemented in several industrial operations: air rate profiling, mass-pull (froth velocity) profiling, and Peak Air Recovery (PAR) air profiling. Although different in concept they are all ways of manipulating the recovery profile down a bank, which may be the property being exploited. Mathematical analysis has shown that a flat cell-by-cell recovery profile maximizes the separation of two floatable minerals for a given target bank recovery when the relative floatability is constant down the bank [

The air rate profiling strategy consists of distributing air to each cell to achieve a set pattern (profile) down the bank. Xstrata Brunswick Division pioneered this strategy on the final Zn cleaner bank of seven DR100 Denver cells [

Analysis concluded the following: that operating with reduced air rate in the first cells improved selectivity against entrainment by reducing water recovery and that this high starting grade aided increasing grade at target bank recovery. The need to increase air down the bank, it was argued, was to compensate for reduced floatability, but more directly it was necessary to provide the total bank air required to meet the target recovery. The analysis included recovery profiles and it was observed that the relative floatability of sphalerite to pyrite (S = k_{sp}/k_{py}) was independent of the air profiling and fairly constant down the bank (S≈2). Other operations have subsequently implemented the increasing air profile with significant performance benefits [

‘Down-the-bank’ Zn grade-recovery curve showing best and worst performances of the three air rate profiles: increasing, balance and decreasing.

Air recovery (α) was first proposed by Woodburn _{g }is the total air flowrate into the cell, _{f} the overflowing froth velocity, _{f}) using image processing techniques.

Studies found there was a gas rate that produces the maximum air recovery and that operating at this gas rate flotation performance, particularly mineral recovery, can be improved [_{g} is the superficial gas velocity.

Application of the PAR strategy in a platinum concentrator produced a significant increase in platinum recovery for a given concentrate grade when operating each cell of a bank of 4 cells at the PAR air rate [

PAR air profiling strategy applied to a bank of N cells.

This method profiles the solid mass overflow (concentrate) rate. It is usually implemented by controlling the froth velocity. This strategy has been used in several operations having the attraction that measurement of froth velocity using image analysis (machine vision) is non-invasive [

Supomo

Illustration of the froth velocity set-point profile targeted by PT Freeport [

A similar study was conducted at Los Colorados concentrator at BHP Escondida [^{TM} system was installed in the copper rougher circuit of 8 parallel banks of 10 cells. Based on tonnage and copper feed grade an expert control system continuously selects between three predetermined froth velocity profiles labeled as low-velocity, medium-velocity and high-velocity for each of the rougher banks (

Average froth velocity profiles implemented at Los Colorados concentrator, Escondida Mine [

Although different in concept and roots the strategies described above are all ways of manipulating the recovery down the bank. In this section a strategy for optimizing banks based on cell-by-cell recovery profiling is argued. For the sake of simplicity two floatable minerals A and B are considered. _{i} is the recovery of cell i.

Flotation bank composed of N cells.

Making the common assumption of first-order flotation kinetics and fully mixed transport, recovery of mineral A and B in an isolated cell is given by:
_{A} and k_{B} are the flotation rate constants for mineral A and B and

The relative floatability provides an indication about how difficult the separation is: when S = 1 (R_{A} = R_{B}) no separation is possible. Notice that for a given relative floatability the recovery of mineral B is completely determined by the recovery of mineral A. The operational objective of a bank can be expressed as finding the recovery of A in each cell (recovery profile) such that for a target bank recovery of mineral A the bank recovery of mineral B is minimized. Taking as a measure of separation efficiency for two floatable minerals as E = R_{A}− R_{B }[

The optimal strategy that solves this problem was found to be a flat cell-by-cell recovery profile,

This is the result for separating two floatable minerals, which is our focus. In this case the optimum flat cell-by-cell recovery profile result is independent of changes in rate constant along the bank provided the relative rate constant is unchanged. If we allow for the moment that the rate constant is unchanged then an additional interesting property emerges relevant when recovery of a single floatable mineral is the concern (e.g., bitumen). The flat cell-by-cell recovery profile produces the maximum cumulative bank recovery for a given installed volume. This is illustrated in _{1}/V_{2} = 1) at 75%, we note that all other volume combinations give less than 75%. Most banks are constructed with cells of the same size and

Optimal operation for two floatable minerals (flat recovery profile,

Separation efficiency

Optimal flat cell-by-cell recovery profile for a target bank recovery of 90% giving R_{i} = 22.57%; and recovery profile based on bank feed.

Two-cell bank recovery relative to bank recovery when cells are equal volume (V1/V2 = 1).

There are few studies in which grade-recovery down a bank has been reported under different operating conditions. This is not surprising given the effort that these surveys entail. We have found three that give sufficient data to compare with the ‘recovery profile’ theory.

Cell-by-cell Zn recovery profiles resulting from implementing an increasing, balance and decreasing air rate profiling, and optimal theoretical flat cell-by-cell recovery for a Zn bank recovery of 72%.

The increasing profile represents slowing down flotation in the first cells and re-distributing recovery (mass) down the bank. The corresponding cell-by-cell recovery is not the flat profile from theory but rather trends upwards along the bank. (The profiles probably reveal that cell 5 is over-pulling.) The high initial recoveries seen with the decreasing and balanced air profiles proved detrimental while the low recovery in the first cells of the bank with the increasing profile produced the increase in grade that was maintained down the bank. Recovery profiling was not the initial ambition but it does provide a new way to consider what was achieved. There is no way of knowing if the increasing air profile used gives the true optimum. An argument for reducing recovery in the first cells below the balanced value may be that it benefits entrainment rejection. The original analysis emphasized rejection of entrained particles in the first cells as the mechanism of grade enhancement [

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There appears to be no agreed method of operating a bank of cells to achieve optimal performance, however defined. Three strategies to search for the optimum have been described in recent literature: air rate profiling, air recovery profiling, and mass-pull profiling. We introduce the notion that the feature common to these strategies is the way recovery is distributed down the bank, the cell-by-cell recovery profile. Defining optimal as maximizing separation efficiency at a target bank recovery, what has emerged is the potential benefit of a flat cell-by-cell recovery profile. While plant data are limited, the three cases examined lend some support to this conclusion.

The mathematical analysis assumed constant relative floatability, S. The Brunswick Mine data supported this assumption and it is a more defendable than assuming a constant floatability (rate constant) [

The optimal flat cell-by-cell recovery profile is independent of how the total volume is allocated in the bank; for instance, if one cell in a bank is of different volume (size), the flat cell-by-cell recovery profile is still optimal. This is due to the fact that separation of two minerals is not related to cell volume. As noted, having equal-sized cells gives the highest ratio of bank recovery to bank cell volume. From these points, plants seeking to increase bank volume would be advised to add cells of the same volume, not larger as might be the temptation.

Air profiling is a low cost approach to improve performance of flotation banks which is encouraging its growing application. For cells provided with gas flowrate sensors it can be implemented without capital investment. In their absence, as was the case at Brunswick Mine, use was made of a gas velocity sensor [

PAR air profiling translates the problem of optimizing a bank of cells to a local problem of optimizing each cell. The total bank air flowrate in this case is completely determined and corresponds to the sum of the gas rate that produces PAR in each cell (J_{gT} = J_{g1} + J_{g2} + … + J_{gN}, see

A limitation in implementing the PAR strategy is the extensive measurement effort and instrumentation required on each cell to calculate air recovery. It may be possible to find a surrogate for air recovery such as equilibrium froth height which is another measure of froth stability.

A component in the calculation of air recovery is froth velocity and that may be used independently as in the third strategy, mass-pull control. This now requires a search for the froth velocity profile to achieve the target bank performance. An exponentially decreasing froth velocity profile is usually selected [

The analysis considers only separation between floatable minerals, not entrainment. The evidence at Brunswick Mine is that probably both are affected by air profiling and by extension recovery profiling. The increasing air rate profile reduces air and mass-pull rate in the first cells both of which benefit entrainment rejection [

Three strategies for optimizing flotation bank performance have been reviewed: air profiling, peak air recovery profiling, and mass-pull (froth velocity) profiling. PAR profiling translates the problem of optimizing a bank of cells to a local problem of finding the gas rate (and froth depth) that maximizes air recovery in each cell. Consequently the optimal total air rate is completely determined. A downside of this strategy is the extensive instrumentation required to calculate air recovery which is prone to error propagation. Mass pull profiling strategy uses a vision system to calculate the froth velocity in each cell and then change gas rate and/or froth depth to achieve a target froth velocity. A monotonically decreasing froth velocity profile has been successfully implemented in industrial operations. However it is not clear how to select the froth velocity set point to achieve a target metallurgical performance. Gas rate profiling is the simplest optimizing strategy requiring no capital investment for cells equipped with air flow meters. An increasing air rate profile has been reported to improve metallurgical bank performance. The total air rate is not directly determined as opposed to the PAR profiling but must be manipulated to provide a target bank recovery.

The possibility that the property underlining these strategies is the way recovery is distributed down the bank (recovery profiling) is discussed. It is shown that a flat cell-by-cell recovery profile maximizes separation efficiency for a target bank recovery and for any relative floatability larger than one as long as it is invariant down the bank. A feature of a flat recovery profile is that it is independent of how the total volume is allocated in the bank,

Although the flat cell-by-cell recovery profile is mathematically proven for true floating minerals and changes to this profile may be necessary to compensate for entrainment, it offers a starting point towards bank optimization. The three case studies lend support to this strategy.

Funding of this work is under the Chair in Mineral Processing co-sponsored by Vale, Teck, Xstrata Process Support, Agnico-Eagle, Shell Canada, Barrick Gold, SGS Lakefield Research, COREM and Flottec under the CRD (Collaborative Research and Development Program) of NSERC (Natural Sciences and Engineering Research Council of Canada) and through the AMIRA P9O project also under an NSERC-CRD. M. Maldonado would also like to acknowledge the Chilean Council of Science and Technology (CONICYT) for financial support. This article was originally presented at the Canadian Mineral Processor (CMP) conference, Ottawa, Canada, January 2012 and it has been accepted for presentation at the International Mineral Processing Conference (IMPC) that will take place in New Delhi, India, September 2012.