1. CHAPTER 10_ PRACTICAL FLOTATION MACHINES

2. Contents Residence time Mixing Columns New types of cells.
Mean residence time
Distribution of residence time
Mixing
Unit cells
Flotation banks
Columns
New types of cells.

3. Introduction
Flotation is a rate process - measure flotation rates in the laboratory, but need to know equipment characteristics to translate results to full scale plant
Mixing characteristics of the pulp in the flotation machines is particularly important
How long does it spend in cell (mean residence time)?
Does it all spend the same time there or does some pass quickly (by pass) & some stay a long time (dead space)?
This distribution of residence time is used to describe the mixing pattern within the equipment

4. Residence Time Distribution
A full description of the residence time distribution requires a detailed knowledge of the path of each element of pulp through the vessel
This is generally not practicable or necessary. All we need to know is how long different elements stay within the cell
The particles will be floating for this length of time so that we can calculate how much floats in this time
By integrating over all the elements in the pulp we can estimate the combined behaviour.

5. Residence Time Distribution
Definitions
V = volume of cell or tank (m3)
v = volumetric feed flow rate (m3 / s)
τ    = mean residence time (s) = V / v
E(t) = distribution of residence time
Et = the fraction of material in the exit stream with an ‘age’ between t and t + t

6. Residence Time Distribution
The fraction of material in the exit stream which has spent time less than t1 in the cell (i.e. younger than t1) is given by t1 0 E(t)dt

7. Residence Time Distribution
The fraction of material in the exit stream which has spent time more than t1 in the cell (i.e. older than t1) is given by  t1 t1 E(t)dt = 1 - 0 E(t)dt  The total area under the curve = 1 = 0 E(t)dt

8. Residence Time Distribution

9. Ideal Flow Cases Plug Flow
This is the ideal case where all material spends the same time in the cell, eg flow in a pipe. It is the same as a batch operation.

10. Ideal Flow Cases
2.    Perfectly Stirred Cell or CSTR (Continuous stirred tank reactor)
This is the opposite ideal case. Mixing is perfect so that all material in the cell is equally likely to leave, ie. fresh feed that has just entered is just as likely to leave as material that has been in cell for a long time

11. Ideal Flow Cases
2 CSTR’s in series Arranging CSTRs in series enables other (more realistic) situations to be modelled By connecting many CSTR’s together in series behaviour tends towards plug flow

12. Ideal Flow Cases Short Circuiting and Dead Space
These can be modelled by two regions in parallel
If τ1 << τ2
We say that material “short circuits” the vessel
If τ2 → ∞
We say we have “dead space” in the vessel, eg a flotation cell may be poorly mixed and “sanding-up”. T 1 2

14. Measurement of Residence Time
To measure the actual residence time distribution of a cell, tank or other item of equipment tracer techniques are used
The tracer which is added should be easily detected and measured, but should otherwise behave in exactly the same manner as the material that is being studied
For liquids – as tracer use some easily analysed solute which is not present in the plant water – fluorescene, lithium chloride, potasium bromide, etc
Solids are much more difficult. The best possible way is to irradiate the solids and measure radioactivity.

15. Measurement of Residence Time
It is quite common to trace the liquid and assume that the liquid response is also true for solids. This may or may not be true, depending on the size of the solids and the flow regime.
In principle it is possible to measure the response of the tracer to any input signal – cyclic, random, impulse. In practice the impulse test is the most convenient to do and to analyse.

16. Measurement of Residence Time
Impulse Test
At time 0 a quantity of tracer G (kgm) is added rapidly to the feed to the vessel
Samples are then taken of the outlet stream at particular subsequent times and analysed for the level of tracer.

17. Measurement of Residence Time
 G = 0 vcdt where c is tracer concentration - thus  G/v = 0 cdt = Area under the curve (v constant) But τ = V/v & c0 = G/V Thus area under curve = c0τ This enables the tracer concentration curve to be scaled to the E curve

18. Measurement of Residence Time

19. Measurement of Residence Time
Mean Residence Time τ
May be measured from the c curve
 
τ = 0 ctdt / 0 cdt
Integrals can be estimated from an experimental curve taking special care with the tail of the curve

20. Notes on Measurement of RTD
Important to carryout a mass balance on the tracer to ensure that it is all accounted for, ie estimate v then check that G = v.Area under c curve.
Steady state conditions have been assumed
We have assumed only one outlet. OK for a ball mill or conditioner, but care must be taken with flotation cells
Watch out for recycles. Can lead to tracer returning to the feed & upsetting simple approach
Residence times of solids, particularly coarse solids, can differ significantly from liquids

21. Mixing Models
Generally hard to incorporate an experimental RTD curve into a mathematical model. It is better to choose an ideal flow model that approximates the real situation, then carry out calculations using the flow model

22. Flotation Cells
A single flotation cell is an approximation to a perfectly stirred tank (CSTR)
Important that mixing is good & solids suspended
There should be a calmer region at top of cell for froth drainage, but pulp flow should be well mixed
Problems can arise with inadequate mixing
Solids can settle out providing dead regions of the cell
This will reduce the effective cell volume and the pulp residence time
Residence distribution tests can establish whether mixing in the cell is satisfactory

23. Recovery from a Unit Cell

24. Recovery from a Unit Cell
A total mass balance and component balance of flows around the cell gives
F = C + T (1)
F . cf = C . cc + T . ct (2)
Mean residence time for the cell τ is
τ = V/T (3)

25. Recovery from a Unit Cell
If the flotation rate constant of the mineral species is k (min-1)
C . cc = k . V . ct (4)
The recovery of mineral (R) is given by
R = C . cc / F . cf (5)
Using (1), (2), (3), (4) and (5) gives
R = /(1 + k τ) = k τ /(1 + k τ) (6)

26. Recovery from a Unit Cell
The equivalent result for a batch flotation cell is
R = exp(-k τ)
The following table indicates the “inefficiency” of a stirred cell. The problem is most important for the fast floating material (high k τ). Easily recovered material is lost as it passes rapidly from feed to tailing.

27. Recovery from a Bank of Cells
The general way to overcome this problem is to connect cells in series to make a flotation bank
Using (6) above we can estimate the recovery for the bank - assume that the single cell volume is distributed into n equal cells arranged in series
R = (1/(1 + k τ/n))n
As n → ∞, R → exp(-k τ) the recovery for a batch cell or plug flow reactor.

28. Recovery from a Bank of Cells
It can be seen that there is a recovery advantage in arranging cells in series and that this is more marked with the faster floating materials
A few cells in series is generally sufficient to gain most of the advantage of the ideal plug flow reactor.
It can be seen that there is a recovery advantage in arranging cells in series and that this is more marked with the faster floating materials. A few cells in series is generally sufficient to gain most of the advantage of the ideal plug flow reactor.

29. Concentrate Grade from a Bank of Cells
A similar small advantage in concentrate grade is expected from a series of cells
Consider the flotation to be separating values from gangue. Assume that the feed is 10% values and 90% gangue. Take the case with recovery of 50% values, ie k τ = 1 for values
The stage concentrate can be calculated as follows for a range of rate differences between values (kv) & gangue (kg)

30. Concentrate Grade from a Bank of Cells
This simplified case suggests some advantage in arranging the cells in series, but most of the advantage is achieved by the first few cells.

31. Different Types of Flotation Banks
At one extreme the cells are quite separate so that pulp can only flow forward, for example by overflowing a weir. This is closest to CSTR’s (unit cells) but
most complex to build and operate
bank volume is “wasted” between the cells
At the other extreme there may be no dividers between the cells
The bank is a trough – sometimes called a “hog trough”
It has several agitators along the length
Back mixing can occur so that the bank mixing tends to revert to a single CSTR
Very simple to build & operate but will be less efficient
In between there may be partial divisions – “skirts” – between the cells that prevent most but not all of the back mixing. This is the more usual compromise

32. Flotation Banks
Residence time measurements can show the mixing patterns in any particular bank. They may also show whether agitation is adequate or whether there is dead space in the bank.
Minor design changes have been made to the basic cells over the years aimed at increasing efficiency. Improvements are claimed for mixing, air dispersion, maintenance, controllability, etc.

33. Large Cells
The major trend in recent years is the scale-up of flotation cells to cope with the massive tonnages possible in SAG mills
Sizes are now up to about 200m3
To cope with the size there are some changes to the froth collection systems
Discharge is sometimes from both sides of the cell
Sometimes anular launders are used to increase the available lip length and reduce distance that froth flows
Major cost adavantages result from these big units
Partly from economies of scale in cell manufacture
Also lower installation and maintenance costs
Easier control

34. Flotation Columns
Flotation columns were originally considered in the 60’s but did not achieve acceptance until about 15 years ago
The arrangement aims at a true countercurrent separation
High froth depths are also possible making columns particularly suitable for cleaning duties

35. Flotation Column Arrangement

36. Flotation Columns Columns are typically about 10m high
Applications were originally in base metals, but they are now very widely used for both metallic and industrial minerals
Effective froth washing and process control were important aspects in the development
There are a number of options to improve the plug flow behaviour in the column with internal packing and baffles
Residence time distribution and flow patterns of bubbles and particles are critical to the efficient operation of these units.

37. Microcell
Bubble generation sometimes done outside the column, eg in the Microcell column
Designed to generate very small bubbles (0.1 – 0.6mm) particularly targeted at the flotation of fine particles

38. Jameson Cell

39. Jameson Cell
A novel system that has gained considerable acceptance in a wide range of applications
Air and feed slurry are pumped to the cell in a vertical jet that entrains air and generates a froth
This provides a good environment for both particle capture and separation
The equipment is much smaller than a full column
Is claimed to be cheaper to install and operate

40. EKOF The different tasks of
particle suspension
pulp transport
production of small air bubbles
done in external units connected to the cell
As the unit gets larger more of these “aerators” are needed around the cell

41. EKOF