Froth flotation is the single most important means by which valuable minerals are recovered, upgraded and separated from unwanted gangue in minerals processing. The process was patented in 1906, and while it has been employed in the mining industry for over a century, it remains to be a process with significant room for operational improvement and optimization.

The concentration takes place in a solids-water-air mixture, based on the different physico-chemical surface properties of the mineral particles. To be precise, the selective separation of different mineral particles with true flotation is achieved based on the differences in their hydrophobicity. Thus, a mineral can be categorized into either polar or nonpolar type; the latter being hydrophobic and having a naturally high floatability.

Reagents are used to aid the process. During the required conditioning time collectors adsorb to the surface of a particle, making it hydrophobic and thus more likely to attach to an air bubble. Regulators (activators and depressants) affect the attachment of certain minerals to the air, and are also used for the pH control of the pulp. Frothers are added to create a stable enough froth phase.

In addition to the reagent dosage, another important control variable of a flotation cell is pulp level, which has an impact on the froth height and the air feed rate. Also, in some cases, the impeller speed can be controlled too.

Flotation is a multiphase process involving complex chemical and physical phenomena both in terms of particle and fluid (gas and liquid) dynamics. Yet industrial flotation circuits are often fitted with instrumentation that only allows stabilising control of tank levels, and gas and slurry flows - with other fundamental physical and chemical parameters neither tracked nor responded to in real-time.

Pic. 1. A bubbles flow diagram of a mechanical flotation cell.

Mechanical flotation cells are the work-horses of the flotation industry and, despite competition from a large variety of alternative flotation technologies, are still responsible for the bulk of global flotation. A mechanical flotation cell typically consists of a square or round tank up to 630 m3 in volume, and agitated by an impeller incorporated in a rotor-stator assembly situated near the bottom of the cell. Air is introduced into the rotor-stator assembly, either by induced air suction (induced-air) or by an external blower (forced-air).

The level of agitation has a profound effect on flotation in mechanical flotation cells. Agitation is responsible for creating a suitable hydrodynamic environment in the cell for efficient gas dispersion, particle suspension and flotation.

Pic. 2. A schematic diagram of a mechanical flotation cell by Outotec.

Pic. 3. Schematic diagram of bubble-particles-droplets collisions

Pic. 4. The main variables in a froth flotation.

In flotation, there are different cell configurations and two basic types of cells which are:

This is the most common type of flotation equipment used in mineral processing. Each machine will have a rotating impeller installed inside the tank/cell.

In both cell and tank types, mixing of air and pulp occurs in injection nozzles. In the flotation column, countercurrent flow is established in the lower section of the column

The mechanical configuration of the equipment plays a major role in the flotation process. Let’s explore a few design considerations:

Pic. 5. Diagram of the flotation process (adapted from Wills et al., 2015)

Thus, it is evident that a mechanical flotation cell is an example of an intricate system with many interrelated components. Change in one design parameter has a knock-on effect on the whole system. Also, based on the importance of the physical characteristics of the equipment listed above, Virtual Sensors must take them into consideration.

Hydrodynamics is a vast branch of physics which describes the motion of fluids but for the purposes of the Application and this document we suggest narrowing the term down to the following definition: the bulk or macroscopic flow of fluid in a vessel. Much of the pioneering work in the field of flotation hydrodynamics was conducted by the researchers Arbiter (Arbiter and Harris, 1969; Arbiter et al., 1976; Arbiter, 1999) and Degner (1976, 1980, 1985). Their work has not become obsolete over time, and some of its elements have inspired the creators of the Flotation Application.

Flotation hydrodynamics is largely driven by the action of the impeller which establishes a flow pattern, or an average path of the bulk fluid flow. Flow patterns are governed by vessel characteristics, such as size and shape, and impeller properties, such as geometry and rotational speed. Fluid leaves the impeller in axial, radial and tangential fluid jets which carry kinetic energy, in the form of fluid flow, into the bulk cell where they ultimately decay into turbulence and circulate back to the impeller.

Historically, hydrodynamics in flotation has been described using a range of dimensionless numbers and key hydrodynamic parameters e.g. power intensity, impeller tip speed, Power number, Froude number, tank-turnover time, air flow number (Deglon et al., 2000). These quantities have been extensively used for flotation cell scale-up and to define regions of agitation where flotation cell hydrodynamics is suitable for effective gas dispersion, solids suspension and flotation. The Application focuses on the gas dispersion aspects of the flotation hydrodynamics because they provide insight into a cell’s performance and can help guide the optimization efforts.

Pic. 6. Typical flow of slurry, bubbles, froth of a mechanical cell.

Now, let’s consider Gas Dispersion in detail. The main parameters used to characterize gas dispersion in flotation equipment are:

These parameters can be used to estimate the surface flow of the bubble area - Sb [1/s]. This parameter is important because it is interlinked with the total air surface area and, hence, directly linked to the flotation performance.

This parameter corresponds to the relationship between the volumetric gas flow (Qg) and the cross-sectional area of the flotation equipment (Ac ).

This parameter is directly linked to the flotation kinetics, which influences the recovery, the surface area of the bubbles and the discharge of froth in said equipment.

Gas Hold-up is defined as the volumetric fraction of the slurry in a flotation cell that is displaced by the gas phase (Cortes-Lopez, 1998). Or, the volumetric fraction of gas bubbles in the flotation slurry. It is well-known that the kinetics and carrying capacity of a flotation cell - and therefore its overall performance - is a function of the Gas Hold-up.

This gas dispersion parameter affects the residence time of the particles and the collection of minerals within the flotation equipment. In particular, the gas hold-up is an indirect measure of the residence time and the size of the bubbles within the flotation equipment, since large bubbles tend to travel faster than smaller bubbles when inside the flotation equipment.

Similarly, the mean Gas Bubble Size in a flotation cell directly impacts not only the Gas Hold-up, but - along with it - the Bubble Surface Area Flux within the pulp phase. That is, the gas-liquid surface area moving up through the flotation cell. Gas Bubble Size is impacted by several parameters, including frother dosage, gas flow and bubble generation mechanism. Finer bubbles are generally preferred as they provide significantly more bubble surface area (per m3 of total gas flow) for the increased probability of particle contact. However, in some fast kinetic flotation duties, small bubbles can negatively impact froth mobility and hence mass pull and valuable mineral recovery. Therefore, the ability to measure this key flotation parameter, in real time using our Virtual Sensor, allows operations to target the ideal mean Gas Bubble Size for their specific needs by controlling the various parameters affecting this variable.

The ranges of these variables - Gas Hold-up and Gas Bubble Size - that lead to desirable performance can be determined, and thereafter they can be tracked in real-time to ensure that the flotation circuit is operated in such a way that they remain within these desired bands.

These two Virtual Sensors, delivered using a combination of computational fluid dynamics (CFD) and machine learning models, provide much-needed insight into the real-time performance of the cells/banks/columns in a flotation circuit. This not only enables better root cause analysis, but allows operators to make better decisions when performance is not what they want it to be.

Bubble size is generally measured by Sauter mean bubble diameter (d32). It is a ratio between volume of bubbles and their measured surface area

𝑑32 = 6∙𝑉𝑏 / 𝐴𝑏

where

Bubble size describes the surface area available for flotation (Gorain et al. 1995a). With the same volume of air smaller bubbles have greater relative surface area and increased probability to attach particles compared to larger ones. However, the bubble size must be aligned with particle size as the adhesion force between bubble and particle must be stronger than particle weight in order to a particle to float. The adhesion can be described by contact angle which is an angle between particle and bubble.

Typical industrial range of bubble diameter is 2-10 mm. Typically, the influence of impeller speed on bubble size diminishes with the increase of flotation cell size.

Sb corresponds to the surface area of the bubble per unit time per unit cross-sectional area. It is possible to determine the bubble area surface flow by the relationship of the gas surface velocity parameters and the bubble size (Sauter mean diameter or d32).

Sb is related to the flotation performance, since this is a superficial process and points directly to the surface area of the air.

It is correlated with the floating speed kinetics constant (k), and impacts metallurgical performance.

There is an approximation that allows to linearly relate the gas hold-up Eg with the Sb described by:

This relationship is applicable to mechanical cells and flotation columns, both on a laboratory and industrial scale, for a range of:

Pic. 7. The relationship between Sb and Recovery.

In mechanical agitation, the impeller physically imparts energy to the fluid and is the driving force for the subsequent flow which develops in the flotation cell.

Pic.8. Typical Stator and Rotor of a mechanical cell.

Two parameters are used to describe the effect of the rotor:

The shape of the rotor is designed for a rotational speed range to produce the greatest amount of bubble and particle collisions and to maintain their adhesion - stability and contribute to recovery.

Pic. 9. The relationship between Impeller Speed and Recovery.

The graph above shows that the recovery increases with the increase in the rotational speed, but this relationship is more prominent for shallow froth than for deep froth.

Significant progress has been made over the past few years on characterizing and understanding the hydrodynamic properties of frothers and collectors and their effect on flotation performance. This new understanding of the relationship between chemistry and hydrodynamics has dramatic implications for how flotation circuits should be controlled and optimized.

In addition, we know that collector chemistry will also influence hydrodynamic properties and needs to be taken into consideration. To achieve the desired outcome, the overall system of reagents and operating parameters must be considered.

Frothers perform various functions in flotation but the primary ones are control of bubble size in the pulp zone and stabilization of the froth zone.

Pic. 10. Examples of froth height versus gas hold-up for a variety of frothers showing the wide range in response

In most flotation circuits, keeping other variables (such as air rate and collector dosage) fixed, frother dosage (concentration) can be used to control the kinetics (mass removal rate). The fact that each frother type has a distinct relationship between froth stability (particle loading capability) and kinetics, means each frother will perform differently in a circuit. This implies that there is a specific frother (having a specific hydrodynamic characteristic) that will best balance mass pull (kinetics) and froth stability (loading). It is important to find the frother with the appropriate strength that will provide the optimum control in each flotation circuit across a useful range of dosages and ore conditions.

Understanding flotation cell hydrodynamics, how they can be affected by frothers and other operating parameters, and what hydrodynamic conditions exist in the circuit can assist greatly in making adjustments to improve metallurgical performance.

Pic. 11. How the bubble size distribution changes as frother concentration is increased (DF250)

Typical operating values obtained from Cu, Mo and Au big mining, for mechanical cells.

Gorain, Franzidis, and Manlapig (1998) developed an empirical prediction model of bubble surface area flux in mechanical flotation cells from cell design and operating data.

As discussed above, in a mechanical flotation cell the production of Sb may be assumed to be dependent on impeller rotational speed (Ns), air flow rate per unit cell cross-sectional area (Q/A), impeller aspect ratio (As) and 80% passing feed size (P80). This can be expressed mathematically as:

Where:

Physically Sb is the total surface area of bubbles moving through the cell per unit cell cross-sectional area per unit time.

Different forms of multiple regression models (both linear and nonlinear, with and without dimensionless groups representing the independent variables) were examined by comparing their statistical significance using the coefficient of multiple determination (R2), Chi-square statistic (Z2) and F-tests.

The form of the model which most adequately represents the relationship between Sb and the independent variables Ns, Q/A, As and P80 is shown below:

where a, b, c, d and e are the parameters for the model.

Standard units of the operating variables are used in the model, m/s for Ns, cm/sec for Q/A which in theory is equal to superficial gas velocity Jg, dimensionless for As and microns for P80 which is typically used to represent particle size in flotation operations.

The parameter values obtained from the fitting are:

Pic. 12. Predicted vs Experimental Sb values using the new model parameters.

With more operational data, laboratory test, pilot plant and CFD analysis, the flotation researchers in the last 10 years were able to improve the work started by Gorain, obtaining new relationships for gas hold-up and bubble surface area flux.

Gas dispersion properties include bubble size (d32), gas holdup (Eg) and bubble surface area flux (Sb) and input power (P) are effective parameters on flotation performance.

Pic. 13. Gas holdup Eg vs Jg & Ns

The most effective parameter on gas holdup Eg is Ns and the effect of Pd is insignificant, the ranges to apply this model are:

The gas holdup of this model must be: 3.04% < Eg < 22%.

Pic. 13. Bubble surface area flux Sb vs Jg & Ns

.

The most effective parameters on bubble surface area flux Sb are Jg and Ns respectively. The effect of Pd on bubble surface area flux is very low.

The bubble surface area flux of this model must be: 16.2 < Sb < 35.03 [1/s]

Flotation is a complex multifaceted process that is widely used for the separation of finely ground minerals. The theory of froth flotation is complex and is not completely understood yet. This fact has brought many monitoring challenges in a processing plant. To solve those challenges, it is important to understand the effect of different parameters on the fine particle separation, and control flotation performance for a particular system.

In the operation of mechanical flotation cells, the dispersion of gas into fine bubbles may be expressed by three indicators: bubble size, gas holdup and superficial gas velocity. Taken together, these properties determine the bubble surface area flux (Sb) in the cell, which has been found to have a strong correlation with the flotation rate constant (k). Therefore, the Hydrodynamic Virtual Sensors can be used in the optimization of the flotation process.