**1. Introduction**

390 Radioisotopes – Applications in Physical Sciences

Wershofen, H., Aumann, D.C. (1989). Iodine-129 in the environment of a nuclear fuel

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### **1.1 Objective and organization of chapter**

In order to study the hydrodynamic behaviour of large flotation machines, the radioactive tracer technique has been used to measure a number of internal characteristics such as:


#### **1.2 Relevance to industrial flotation machines**

Industrial flotation cells need to accomplish several functions such as: air bubble dispersion, solid suspension as well as to provide the best conditions for bubble-particle collision, aggregate formation and froth transport. For this reason, cells are typically provided with mechanical agitation systems which generate well mixed conditions for the pulp and air bubbles. In an industrial mechanical cell, however, the mixing condition prevents that particles have the same opportunity to be collected because a significant fraction of them actually spent a very short time in the cell (in a well-mixed condition almost 40% of particles stay in the cell for less than a half of the mean residence time). Because of the large short circuit in single continuous cells, the industrial flotation operation considers the arrangement of cells in banks. Thus, banks of 5-10 cells in series are commonly used in plant practice. The largest flotation cells presently used in industrial flotation operation are 130, 160, 250 and 300 m3. Figure 1 show the main characteristics of a self-aerated mechanical flotation cell, where the feed pulp circulates upwards through a draft tube by the rotor. Also, the air is self-aspirated from the upper part of the cell by the rotor.

Hydrodynamic Characterization of Industrial Flotation Machines Using Radioisotopes 393

which describes the continuous operation of "N" perfect mixed tank in series. For description of the RTD of a single large flotation cell, the LSTS model (large and small tank in series) has been used. This model gives a better fit to the actual flotation process of a single cell, which consists of one large perfect mixer (residence time τL) and one small perfect mixer in series (residence time τS) represented by the following

> / / ( ) *<sup>S</sup> <sup>L</sup> <sup>t</sup> <sup>t</sup> S L*

τ

<sup>−</sup> <sup>−</sup> <sup>−</sup> <sup>=</sup> <sup>−</sup> (2)

= + (3)

*e e E t* τ

ττ

where the overall mean residence time τ is given by,

**1.4.2 RTD modelling of pneumatic flotation columns** 

*E t*

described by Yianatos et al. (2008c).

following equation (Yianatos et al., 2005b),

τ τ

*S L*

Both models can be normalized in terms of the dimensionless time (θ=t/τ), as it was

A typical approach to describe the mixing condition in column flotation operations is the use of the axial dispersion model (Dobby and Finch, 1985). Also, the liquid RTD of industrial flotation columns can be described using a model of less than two perfect mixers in series. However, a better fit has been obtained using a model of one large perfect mixer (residence time τL) and two small perfect mixers in series (residence time τS) represented by the

( ) / / / ( )

τ τ

 τ τ

The hydrodynamic characteristics of industrial flotation machines have been evaluated from residence time distribution RTD measurements using radioactive tracers. This technique allows for non-invasive tracer detection, and is also adaptable to different kinds of equipment (Goodall and O'Connor, 1991, Niemi, 1995). However, the application of the radioactive tracer technique for industrial flotation characterization is rather scarce (Yianatos and Bergh, 1992, Lelinski et al., 2002). The procedure consists of selecting a liquid or solid tracer that allows on-line RTD data acquisition. The way the tracer is injected into the feed is critical in order to generate a pulse signal (closer to impulse). For this purposes, a pneumatic system of high reliability has been developed in order to introduce a small amount of radioactive tracer (around 100 mL of liquid, pulp with solids, or gas) at the feed pulp entrance (Díaz and Yianatos, 2010). Then, the time response of the radioactive tracer was measured on-line using non-invasive sensors located directly in different points of the cell or cell discharge. Activity (cps) was measured by scintillating crystal sensors of NaI(Tl)

*L S t ee*

τ

*S*

ατ

τα

*<sup>S</sup> <sup>L</sup> t t*

 α τ

<sup>−</sup> <sup>−</sup> −− + <sup>=</sup> <sup>−</sup> (4)

= − *LLS* ( ) (5)

 τ

equation,

where

**1.5 Experimental method** 

Fig. 1. Large mechanical flotation cell.

In pneumatic columns the mixing is primarily due to convective pulp recirculation and dispersion due to the turbulence caused by bubble motion, as well as the pulp feed and air entrances near the top and bottom, respectively. Mixing characteristics are also a key aspect related to scale-up from laboratory batch flotation cells, or pilot columns, to large size continuous flotation operations. In the last decade a dramatic increase in cell and column sizes has been observed, while more than 2 billion tons per year of ore are presently treated by flotation processes in the world. Thus far, however, the design and scale-up of flotation devices are still mainly based on empirical rules (Yianatos, 2010a).

#### **1.3 Impulse response method**

In a multiphase system with segregation, estimation of the mean residence time of each phase is related to the effective volume occupied by each phase. In plant practice, the volume occupied by each phase (liquid, solid or gas) is unknown and varies with operational conditions. Alternatively, in order to evaluate the effective residence time of the liquid and solid in flotation machines, the impulse response method has been used. This method is a dynamic identification procedure which consists of introducing a small amount of tracer (close to an impulse) into the system operating at steady state, and to register the transient response (tracer concentration). The response corresponds to the transfer function of the system, and it is useful for hydrodynamic characterization, dynamic identification (order, noise) in control systems studies, as well as for dynamic modelling (short-circuiting, recirculation) (Yianatos and Bergh, 1992, Yianatos et al., 2002).

#### **1.4 Process modelling**

#### **1.4.1 RTD modelling of mechanical flotation cells**

In order to model a flotation bank of cells (Mavros, 1992; Yianatos et al., 2001, 2005a), the following equation has been used,

$$E(t) = \frac{\left(t\right)^{N-1} e^{-t/\left(\tau f N\right)}}{\left(\tau f N\right)^{N} \Gamma(N)}\tag{1}$$

which describes the continuous operation of "N" perfect mixed tank in series. For description of the RTD of a single large flotation cell, the LSTS model (large and small tank in series) has been used. This model gives a better fit to the actual flotation process of a single cell, which consists of one large perfect mixer (residence time τL) and one small perfect mixer in series (residence time τS) represented by the following equation,

$$E(t) = \frac{e^{-t/\tau\_S} - e^{-t/\tau\_L}}{\tau\_S - \tau\_L} \tag{2}$$

where the overall mean residence time τ is given by,

$$
\boldsymbol{\sigma} = \boldsymbol{\tau}\_S + \boldsymbol{\tau}\_L \tag{3}
$$

Both models can be normalized in terms of the dimensionless time (θ=t/τ), as it was described by Yianatos et al. (2008c).

#### **1.4.2 RTD modelling of pneumatic flotation columns**

A typical approach to describe the mixing condition in column flotation operations is the use of the axial dispersion model (Dobby and Finch, 1985). Also, the liquid RTD of industrial flotation columns can be described using a model of less than two perfect mixers in series. However, a better fit has been obtained using a model of one large perfect mixer (residence time τL) and two small perfect mixers in series (residence time τS) represented by the following equation (Yianatos et al., 2005b),

$$E(t) = \frac{(-t \;/\ \tau\_S - \alpha)e^{-t/\tau\_S} + \alpha e^{-t/\tau\_L}}{\tau\_L - \tau\_S} \tag{4}$$

where

392 Radioisotopes – Applications in Physical Sciences

ROTOR

CIRCULATION

PULP/FROTH INTERFACE

TAIL

CONCENTRATE

CROWDER

In pneumatic columns the mixing is primarily due to convective pulp recirculation and dispersion due to the turbulence caused by bubble motion, as well as the pulp feed and air entrances near the top and bottom, respectively. Mixing characteristics are also a key aspect related to scale-up from laboratory batch flotation cells, or pilot columns, to large size continuous flotation operations. In the last decade a dramatic increase in cell and column sizes has been observed, while more than 2 billion tons per year of ore are presently treated by flotation processes in the world. Thus far, however, the design and scale-up of flotation

In a multiphase system with segregation, estimation of the mean residence time of each phase is related to the effective volume occupied by each phase. In plant practice, the volume occupied by each phase (liquid, solid or gas) is unknown and varies with operational conditions. Alternatively, in order to evaluate the effective residence time of the liquid and solid in flotation machines, the impulse response method has been used. This method is a dynamic identification procedure which consists of introducing a small amount of tracer (close to an impulse) into the system operating at steady state, and to register the transient response (tracer concentration). The response corresponds to the transfer function of the system, and it is useful for hydrodynamic characterization, dynamic identification (order, noise) in control systems studies, as well as for dynamic modelling (short-circuiting,

In order to model a flotation bank of cells (Mavros, 1992; Yianatos et al., 2001, 2005a), the

τ

( )

=

*E t*

( ) ( ) ( ) ( )

− −

1 /

*N t N N t e*

τ

(1)

*N N*

Γ

devices are still mainly based on empirical rules (Yianatos, 2010a).

FEED PULP

AIR

recirculation) (Yianatos and Bergh, 1992, Yianatos et al., 2002).

**1.4.1 RTD modelling of mechanical flotation cells** 

Fig. 1. Large mechanical flotation cell.

FEED

**1.3 Impulse response method** 

**1.4 Process modelling** 

following equation has been used,

$$
\alpha = \pi\_L \Big| \left( \pi\_L - \pi\_S \right) \tag{5}
$$

#### **1.5 Experimental method**

The hydrodynamic characteristics of industrial flotation machines have been evaluated from residence time distribution RTD measurements using radioactive tracers. This technique allows for non-invasive tracer detection, and is also adaptable to different kinds of equipment (Goodall and O'Connor, 1991, Niemi, 1995). However, the application of the radioactive tracer technique for industrial flotation characterization is rather scarce (Yianatos and Bergh, 1992, Lelinski et al., 2002). The procedure consists of selecting a liquid or solid tracer that allows on-line RTD data acquisition. The way the tracer is injected into the feed is critical in order to generate a pulse signal (closer to impulse). For this purposes, a pneumatic system of high reliability has been developed in order to introduce a small amount of radioactive tracer (around 100 mL of liquid, pulp with solids, or gas) at the feed pulp entrance (Díaz and Yianatos, 2010). Then, the time response of the radioactive tracer was measured on-line using non-invasive sensors located directly in different points of the cell or cell discharge. Activity (cps) was measured by scintillating crystal sensors of NaI(Tl)

Hydrodynamic Characterization of Industrial Flotation Machines Using Radioisotopes 395

N=7

Fig. 2. Liquid RTD in a flotation bank after 1, 3, 5 and 7 cells of 130 m3 (Diaz and Yianatos,

Figure 3(a) shows the experimental results of the solid residence time distribution in a rougher flotation bank at El Salvador, Codelco-Chile, consisting of nine 42.5 m3 self-aerated mechanical cells in series (Yianatos et al., 2002). Activated mineral gangue (final tailing) was used as solid non-floatable tracer. For this operation the tank-in-series model, Eq. (1) in dimensionless form, considering N=9, showed a very good agreement with experimental

Figure 3(b) shows the effect of particle size on the RTD in a rougher flotation circuit, consisting of nine cells in series, 42.5 m3 each, at El Salvador, Codelco-Chile (Yianatos et al., 2003). It can be appreciated that mixing characteristics are similar for the different particle sizes. However, it was found that the mean residence time of solid was approximately 5% lower than liquid, thus showing a minor segregation mainly related with coarser particles

Fig. 3. (a) Solid RTD and (b) Effect of particle size classes in a flotation bank of nine cells

0 500 1000 1500 2000 2500 3000 3500 4000

Time, s

0,0000

0,0005

0,0010

0,0015

0,0020

RTD, E(t)

2010).

data.

(+100µm).

(Yianatos et al., 2002).

0,0025

0,0030

N=1

N=3

**2.1.1.2 Mineral segregation: Effect of particle size on RTD** 

(a) (b)

N=5

0,0035

of 1"x1.5", Saphymo Srat, thus allowing the simultaneous data acquisition of up to 12 control points, with a minimum period of 50 milliseconds. Br-82 in solution was used as liquid tracer, while mineral gangue was used as non-floatable irradiated solid tracer. The solid tracer was also tested at three size classes (coarse: +150, intermediate: -150+45 and, fine –45 microns) in order to evaluate solids transport and segregation in mechanical cells and pneumatic columns. Floatable irradiated solid tracer was used to evaluate the RTD of floatable minerals recovered into the concentrate. Also, Kripton-85 and Freon 13B1 have been used as gaseous tracers for industrial flotation columns and mechanical cells testing. Liquid, solid and gaseous tracers were irradiated at the nuclear reactor of the Chilean Commission of Nuclear Energy in Santiago, Chile. An advantage of using the radioactive tracer technique is the direct testing of the actual solid particles (similar physical and chemical properties, size distribution, shape, etc.). Tracer injection is almost instantaneous, because only a small amount of radioactive tracer is required. Another advantage is its capability for on-line measurements at various points inside the system without disturbances related to process sampling.
