This document summarizes a methodology for modeling and simulating rougher flotation circuits based on operating variables and parameters fitted from plant data. It describes modeling single flotation cells using two zones - the collection zone where particle-bubble aggregates are formed, and the cleaning zone (froth) where particles drop back. The methodology characterizes residence time distribution, flotation rate distribution, and models recovery, water recovery, and gangue recovery to simulate performance of individual cells and entire banks. The simulator was validated using data from a concentrator and can be applied to model other flotation circuits.

1. FLOATATION
Modelling and simulation of rougher flotation circuits
Mayank Shubham 150397
Mohammad Imran 150417
Navneet Kumar 150439
Meddhnash Pratap Shahi 150399

2. Introduction and Abstract
In this work, a procedure for modelling and simulating rougher
flotation banks that is based on operating variables and parameters
fitted by empirical data from plant measurements is presented.
A new methodology, consists of using a new apparatus for direct
bubble load measurement below the pulp–froth interface in industrial cells.
Self-aspirated Cells Forced-air flotation cells
Two types of mechanical flotation cells are employed in industrial
applications:
The minimum number of cells per bank can be estimated from a
hydrodynamic analysis assuming perfectly mixed cells

3. Single-cell characterization:
Pulp and froth model
 For modelling, scale-up and analysis purposes, two zones are distinguished in the
flotation cell:
 The collection zone
where the particle-bubble aggregate is formed and carried to the pulp–froth
interface (true flotation)
 The cleaning zone (froth)
located between the pulp–froth interface and the concentrate overflow, where
entrained particles have the chance to drop back to the collection zone.
𝑅 𝐺 =
𝑅 𝐶 𝑅 𝐹
1 − 𝑅 𝐶(1 − 𝑅 𝐹)
modelling
The global cell recovery 𝑅 𝐺 is related to the collection zone recovery 𝑅 𝐶with equation

4. Collection Zone 𝑅 𝐶
 The mineral recovery RC in the collection zone can be described by the general expression
𝑅 𝐶 = 𝑅 𝑚𝑎𝑥
0
∞
0
∞
1 − 𝑒−𝑘𝑡
𝐸 𝑡 𝐹 𝑘 𝑑𝑡𝑑𝑘
Where,
 E(t) is the residence time distribution function for continuous processes with different
mixing characteristics
 F(k) is the flotation rate distribution for mineral species with different flotation rates
 𝑅 𝑚𝑎𝑥 represents the maximum flotation recovery at infinite time.
 The term 𝟏 − 𝒆−𝒌𝒕
represents the mineral recovery of a first-order process with invariant
kinetic constant k, as a time function

5. Residence time distribution E(t)
The hydrodynamic of flotation cells can be
characterized by means of the residence
time distribution function, E(t).
Flotation rate distribution F(k)
 The rectangular model for 𝑖 𝑡ℎ
size
class(+100#,−100+325#,−325#,where
#means mesh) and and for the n-th cell,
given by Eq.
To characterise the decrease of the
flotation rate distribution of mineral
class i along the rougher bank given by
Eq:

6. Cleaning Zone
 The cleaning zone was characterised by means of the froth recovery, which can be estimated from bubble
load measurement along with a mass balance around the cell. Thus, the froth recovery, 𝑅 𝐹, was calculated
by Eq.
where λB is the bubble load, JG is the superficial gas rate, AC the cross-
sectional area of the cell, C is the solid mass flow in the concentrate and XC
and XB are the concentrate and bubble load grade.
 where α is the maximum recovery in the froth, βn is the froth stability
 factor for the n-th cell and τF, n is the gas mean residence time in the froth of the
n-th cell, which is given by Eq.

where HF,n is the froth height and εG is the mean gas concentration (hold-up) in
the froth.

7. The water recovery, RW, is defined as the fraction of
feed water reported to the concentrate stream and is
given by Eq.
where 𝑊𝐶corresponds to the water mass flow rate in
the concentrate and 𝑊𝐹is the feed water mass flow
rate to each cell. 𝑅 𝑤 =
𝑊𝐶
𝑊𝐹
where 𝑊𝐶corresponds to the water mass flow rate in
the concentrate and 𝑊𝐹is the feed water mass flow
rate to each cell.
For simulation purposes, the water recovery was
modelled as a function of the froth height, the froth
stability factor and the superficial gas rate for each
cell is given by:
where ξ is the maximum water recovery, and γ and η
are fit parameters.
Water RecoveryGangue recovery
The gangue is recovered into the concentrate by
entrainment caused by the water reported to the
concentrate stream. The gangue recovered
per size class in the n-th cell, RG,I n ,was
estimated by means of Eq.
where EFi is the entrainment factor per size class.
The gangue recovery per size class can then be
obtained from RW measurements and
empirical EFi values.

8. Single Cell Simulation
 In order to evaluate the contribution of each individual cell in the flotation bank recovery, the
collection zone recovery by true flotation ,𝑅 𝑐, the froth recovery of floatable minerals, RF, the water
recovery, 𝑅 𝑤, and the gangue recovery,𝑅 𝑐,, were calculated for each cell. In addition, the mass flow
rate of water and solids per size class in the tailings of each cell were obtained by means of a mass
balance. The global recovery of mineral m, size class i, in cell n is given by:
 Also, the concentrate grade X of mineral m, size class i, in
cell n is
where the supra-indices C and F refer to the concentrate and feed streams.
Notice from Eq. above, that three size classes, i, were considered:
coarse (+100#), intermediate (−100+325#) and fine (−325#) in order to take into account different
liberation grades.
In addition, two types of minerals were included for the simulation:
valuable mineral – e.g., chalcopyrite and molybdenite – and gangue.

9. Conclusion
 The model parameters were calibrated from plant operating data using a flotation rate
evaluation based on the short-cut method, adjusted mass balances and a new approach to
evaluate bubble load and froth recovery.
 The simulator was validated using experimental data from the rougher operation at El
Teniente concentrator, which consists of flotation banks of seven 130 m3 cells in series. The
simulation allowed the evaluation of the industrial rougher flotation bank as a function of
the main operating variables, including particle size distribution, mass flow rate, solid
percentage, pulp level and feed grade.
 This methodology can be applied to other flotation operations, such as cleaner and
scavenger circuits, that use mechanical flotation cells.