Mining, Metallurgy & Exploration

, Volume 36, Issue 1, pp 139–149 | Cite as

Grinding and Flotation Optimization Using Operational Intelligence

  • O. A. BascurEmail author
  • A. Soudek


In recent years, metal-producing companies have increased their investment in automation and technological innovation, embracing new opportunities to enable transformational change. Transformation to a digital plant can fundamentally revolutionize how industrial complexes operate. The abundant and growing quantity of real-time data and events collected in the grinding and flotation circuits in a mineral processing plant can be used to solve operational issues and optimize plant performance. A grade recovery model is used to identify the best operating conditions in real time. The strategy for increasing the value of instrumentation in current plants is reviewed. An optimal Gaudin size distribution model provides augmented information from traditional sensors to find the optimal grind cut size to reduce metal losses in the flotation circuits. Sensors in flotation circuits enable an estimate of the recovery and determination of the optimal froth depth and aeration using an air hold up flotation model. A strategy of classifying data for on-line generation of insights to using operational intelligence tools is described. The implementation of a recovery/grind strategy with industrial examples in non-ferrous mineral processing is presented.


Dynamic performance management Digital plant template Operational intelligence Machine learning Grind cut flotation optimization Particle size distribution shape Flotation bank air hold up profile Invisible losses tracking 

1 Introduction

The declining supplies of high-grade ores and increasing consumption of mineral and metal products have demanded higher operational efficiencies with minimum capital investments. The objective of copper flotation is typically to maximize the dollar return on the concentrate produced while minimizing the energy and other consumables. It is also essential to minimize the non-productive time that the process units are meeting production targets. The economic efficiency is maximized by manipulating the grinding and flotation circuits along the grade/recovery curve relationship.

To achieve such technical and economic objectives, improved stabilization of the grinding and flotation circuits is required. It is known that grinding circuits represent the largest consumption of electrical power and water in mineral processing [1]. Decreasing ore grades make it necessary to reduce the overall specific energy and water consumption in order to maintain operational economic parity.

For a given circuit, an optimal throughput is usually limited by the transport mechanisms in the mill. This is due to the complex rheology of the pulp at high percent solids. A change in ore hardness can alter the particle size distribution, changing the flow conditions in the mill causing it to choke and to start overflowing the grinding media. These are some of the reasons that operators always try to avoid these operating constraints. By operating closer to these constraints, considerable mill capacity is gained and proportional profit is made. This paper examines two novel strategies to improve the particle size distribution effects on grinding efficiency and rougher flotation optimization.

Flotation control technology has also matured considerably in the last decade. The large number of process variables in flotation circuits creates situations where it is complicated for the operator to know what action to take and if it is the right decision. Flotation disturbances can be classified as variations in the ore mineralogical properties, variations in the feed characteristics coming from the grinding circuits, and variations due to flotation circuit upsets.

The interaction of grinding circuit variations and how these affect the froth flotation process performance need to be understood for proper optimization.

Typical disturbances in the grinding circuits are:
  • Mill feed particle size distribution due to crusher circuit operation and bin or stockpile segregation

  • Ore hardness and mineralogical structure and composition

  • Pumping and classification limitations and equipment wear

It is due to these disturbances that an advanced grinding flotation management strategy is necessary.

A new control strategy would enable operators to track metal recovery and to define the right mill feed rate, particle size P80, particle size distribution shapes, flotation power intensity, pulp and froth levels, frother addition, and airflow rate profile. A grinding control strategy along with a flotation air hold up model is used to unify these hydrodynamic variables to find the best combination to improve the rougher metal recovery.

Typically, maximizing the recovery of the most valuable mineral is the predominant factor in the economic return. Thus, the grinding operation should be set accordingly. Figure 1 shows that for a given ore type there is unique milling rate that provides the optimum grind size that will yield maximum profit, that is, an optimal grind size that will maximize production at minimal costs. A higher milling rate might be achieved with a coarser particle size grind, but with profit offset by losses in the recovery due to poor liberation. A low milling rate could produce a fine particle size grind cut which, while yielding greater recovery, loses money because of throughput losses. Swings outside the safe profitable control band in either direction can produce a loss in profit [2].
Fig. 1

Profit Grinding Controls Strategy [2]

The profit of a given metallurgical operation can be estimated using a performance criterion of the form:
$$ \mathrm{Profit}=\mathrm{SUM}\ \mathrm{of}\ \left({\mathrm{Valuable}}_i\ast {\mathrm{Sales}}_i\right)-\mathrm{Variable}\ \mathrm{Costs}-\mathrm{Fixed}\ \mathrm{Costs} $$
where the variable i is the concentrate tonnage for each metal.

Variable Costs are electricity, water, reagents, and other consumables. The optimal economic milling rate can be obtained by finding the maximum profits from a profit model in terms of tonnage, energy, water, steel, and other consumables. The optimal economical operating conditions of the mill are affected by many disturbances and by the equipment availability.

A simple sensitivity analysis using Fig. 1 indicated that a profound effect of this optimal tonnage (TOP), i.e., grinding 5% below TOP costs X million/year while at 5% percent in excess can cost 1.5 X millions/year in lost profit. The difference in sensitivity above and below the TOP is a result of the gradual steepening of the slope of the recovery curves with the increased tonnage as showing in Fig. 1. As such, modeling each grinding line independently has been an excellent way to optimize the whole concentrator [2, 3, 4, 5].

1.1 Integrated Grinding/Flotation Optimization

To maximize the metal recovery and operating profit, the mill has to be operated at the optimal mill production target. Using data validation and classification algorithms enables an estimate of the rougher flotation metal recovery in real-time.

This paper describes the use of real-time data and events to transform data into operational insights for metal recovery optimization. Figure 2 shows the key objective of maximizing metal recovery and the major contributors to model this process.
Fig. 2

From operating insights to finding optimal particle size distribution for metal recovery

In the left side of Fig. 2, each unit is shown with the operating modes (On-target, Off-target, Down and Idle). A digital plant template can be used to transform the raw data into operational insights. A novel real-time analysis based on the production variance will be described. The time that the mill is operating at the operating target is called “Running OK”. Any other operating condition will result in losses. The key is to capture all consumables by process area when the units are operating in each of the following operating modes:
  • Running

  • Idle

  • Trouble, Invisible losses

  • Down

  • Maintenance

Then it is imperative to run every unit reducing off-target, down, and idle times. The generation of the events and the aggregation of the production and consumables losses are the first step in the quest to optimizing overall metal recovery. The event frame algorithms are used to aggregate the production and consumable information to assess production and operating variable information. The classification of operating mode equal to “Running OK” enables the creation of a data subset, which is used to generate soft sensors and to model process indicators. The center and right diagrams in Fig. 2 show the stabilization and reduction of the variability of the particle size distribution and the move towards the best P80 to optimize the overall metal recovery. Soft sensors can be used when process measurements are difficult or not available, for example, the cyclone overflow particle size measurement might have availability problems. As such, a soft sensor is built using the available operating variables. This soft sensor is calibrated using predictive analytics tools. The data subset is made available automatically to estimate the parameters.

The fishbone diagram (Fig. 3) shows the process variables captured in real time: the consumables (energy, water, reagents, etc.), the equipment operational modes for every section of the concentrator, the people, and the ore type quality.
Fig. 3

Fish bone diagram showing possible causes (events, consumables, and process variables) related to maximizing yields

The fishbone analysis shows the effect of the recovery grades and losses based on the operating parameters; the equipment events; the operating shifts; the material grades; and the amount of energy, water, and reagents used to achieve the recovery and grades. Classification of the operating data enables operators to build this predictive model using regression analysis and other models provided by the new software tools that are available. Once a training data set is obtained, a search for the best algorithm to fit the data can begin. To do so, one must have a good understanding of the business and the problem to be solved, and it is also necessary to understand the data and have proper preparation of the data. The key variables shown in the proposed fishbone cause-and-effect diagram are used in designing the predictive analytic model.

Improved particle size analysis enables finding the best particle size shape for the SAG mill feed. The ore feeders are balanced using the particle size distribution shape as the controlled variable. As such, the bin or stockpile natural segregation is balanced properly using this online estimate. A novel on-line method to estimate particle size distribution shape is presented in order to improve the overall grinding and optimize the particle size shape of the cyclone overflow. Having the right particle size feed to flotation improves the rougher flotation recovery.

In summary, there are four steps to the metal recovery performance monitoring and optimization:
  1. 1-

    A Digital Plant Template is used to organize the operating variables and to classify the operational states for further analysis and calculations. A process unit data model simplifies the configuration and generation of operational insights using real-time analytics.

  2. 2-

    The overall production effectiveness is used to define and evaluate the production and consumable losses when not operating at the production target. Real-time trends, alerts, and Business Intelligence (BI) dashboards are used to visualize and to analyze the operational data based on operational events.

  3. 3-

    Process Analytics. The Running OK operational state is used to calculate the particle size distribution shape of the grinding feed and products, and the P80 estimated grinding size is calculated based on soft sensor calculations using predictive analytics. The flotation recovery, concentrate, and tailing flows are calculated using a mass balance equation for the roughers, scavenger, and cleaner circuits based on the production feed rates and the metal assays. An air hold up model is used to combine the power, cell level, airflow rate, cell pulp/froth interface area, and frother addition operational variables. The operational models are derived with the Running OK data using predictive analytics models. A multilinear regression model is used to estimate the key variables when the process unit data variables are validated and under Running OK operating conditions.

  4. 4-

    Implementation is achieved using alerts and notifications that are generated when not operating at the desired conditions. The particle size distribution shapes are calculated using the Gaudin Schuman model, a regression model for online particle size p80, and grinding and rougher flotation models are used to guide the operations towards the best mill production flow rate. Optimized water additions, particle size, and air hold up maximize the overall recovery of the plant. At the same time, operational events such as off-target, down, and idle time are reduced.


2 Methods

Real-time streaming data is transformed into information by using the online analytics tool to classify operational events and aggregate the production and consumable data into improvement workflows based on current operational knowledge. The classification of the data allows the aggregation of data at the desired level of detail for determining where the improvement opportunities are. As such, collaboration between production, finance and planning, maintenance, and all the safety and environmental support become active and not passive as in the past.

The data hierarchy infrastructure is shown in Fig. 4 where the first level of raw data are captured by sensors through the diverse control systems. These are specialized data acquisitions and control devices that reside near the process equipment or in mobile equipment. Data validation is required to check the validity of the sensor signal. Data are classified to coordinate the integrated processes for overall plant optimization. A heuristic method defines the operating conditions of the process data and defines the event start and end times in order to transform the raw data into information. The resulting data can be used to develop empirical predictive analytics models and the process predictive model to be used within the right range. Data modeling is conducted when an operating mode is known to perform performance calculations, such as equipment condition alerts, process efficiencies, energy management, and estimation of inferred process variables based on line process models or real-time simulations.
Fig. 4

Data Hierarchy to transform raw data into operational insights and enable process analytics [6, 7, 8]

Process coordination is used to integrate the chain supply to extend the analysis from all processes (for example, as in a mine-to-mill or mill-to-port approach).

Once the process chain is well tuned, it is possible to identify opportunities to move closer to operating constraints. Operational (real-time) data can be used to explore new opportunities while using business analysis, visualization, and analysis of data and events.

2.1 Real-Time Operational Intelligence

A conceptual diagram of the process for detecting abnormal operating modes for continuous improvement and innovations is shown in Fig. 5. The schematic shows a process workflow that utilizes the targets from the daily plant schedule and the process inputs in a process analytics unit template, which classifies the operating modes of all the process units in an industrial plant. The variance is the difference between expected and actual results. The expected results are generally specified in the operational budget or the current production schedule [6]. The Digital Plant Template [6, 7] enables the transformation of data and events into operational insights. In essence, it is an innovative strategy that automates the Theory of Constraints for a Digital Plant Template [9].
Fig. 5

Digital Plant Template Classification of operational modes for all process units [6, 8]

An example of a dashboard is shown in Fig. 6 for Rougher Flotation operational modes showing the trouble operational event in critical state. The information shown is presented in real time using dashboards in PI Vision (Fig. 6) and published in MS Azure into Power BI in dashboard for personal consumption (Fig. 7). An example of the calculated Overall Production Performance for the entire mineral processing plant is shown in Fig. 7. The amount of time that the units are running under the production schedule or are running in trouble, idle, or in maintenance is displayed in Fig. 7 for the selected time period under analysis. The dashboards can be self-tailored for an Overall Production Effectiveness (OPE) or by specific disciplines such as Management, Operations, Maintenance and Planning, allowing benchmarking by unit, mode, and losses. Once PowerBI is running in MS Azure, Cortana Artificial Intelligence can assist in analyzing the operational data. Access to PowerBI dashboards using your devices such as your cellular phone becomes available. The created dataset can further be used to find insights via predictive analytics using machine learning tools (Running OK operational mode). This strategy lowers the bar for integrating the planning and execution goals. The access of real-time insights in the cloud from anywhere in the corporation is truly digital transformation. The digital plant template (DPT) contains the standard analytics and calculations to assess and analyze metrics of common interest, e.g., down time. The DPT simplifies a top down approach to digitize the plant. The Stockpile and Crusher, SAG and Ball Mill, Rougher Flotation, and Tailings sections were modeled as individual units, as shown in Fig. 6, where each section is modeled using the standard Process Unit template. The total feed, water, electricity, and reagent consumables were aggregated for each section, and main quality variables or KPI parameters are monitored.
Fig. 6

PI Vision Rougher Flotation production and operational events

Fig. 7

Power BI visualization of the process events for overall process effectiveness

Because the base template is not equipment- or process-specific, the real value of this approach comes with its scalability if applied across the organization to render a high-level overview of plant throughputs, consumables, recoveries, etc., for operations across the operation, and across the company.

3 Results and Discussion

Finding the optimum operating tonnage that provides the best particle size and particle size distribution shape (PSDS) is one of the keys to optimizing the process, grinding, and rougher flotation. The rougher flotation air hold up is estimated linking the power intensity in each cell, the pulp level, % solids, air flow rate, and frother addition.

3.1 Grinding Circuit Analysis and Modeling

The SAG mill feed particle size distribution was measured using a Split Engineering particle size analyzer and is shown in Fig. 8. The measured particle size distribution was modeled using a Gaudin Schuman model. An online linear regression algorithm was used to estimate the particle size parameter (k) and the particle size distribution shape modulus (a). This modulus has been found very useful in managing the particle size feed to the SAG mill by manipulating the percent of each feed rate drawn from the bottom of the stockpile.
Fig. 8

Particle size distribution and Gaudin Schumann model used to predict the PSD Shape of process streams

These PSDS values, “a” calculations, for the Sag mill feed and flotation feed are plotted in real time in Fig. 9.
Fig. 9

Particle size distribution shape indicator for SAG feed (bottom blue line) and cyclone overflow (top green line) measurements [4]

The SAG mill feed particle size distribution shape can be used to reduce the variation of the SAG mill feed disturbances by manipulating the stockpile feeder to achieve a better distribution shape by taking the segregated material as necessary to blend on line the material.

The following picture shows a Statistical Process Control Chart for a typical process size analyzer. Figure 10 shows a large particle size variability of the grinding process and the necessity for improved controls.
Fig. 10

Particle Size Statistical Process Control Chart

To improve the particle size measurement availability, a particle size soft sensor was built using operational data. PI Datalink was used to extract a data subset when the grinding mill was Running OK. The particle size estimate is based on SAG mill feed rate, grinding total electricity consumption, water flow rate additions, cyclone feed density, and cyclone overflow pressure. Microsoft Machine Learning Studio was used to review the data set and to obtain a Multilinear Regression Model with a PI Analytics model estimation of the model parameters. Fig. 11 shows the measured and estimated particle size (P80) comparison. The figure also shows the operational variables used in obtaining the multilinear regression. The featured operational variables are: total electricity consumption, total water consumption, feed density, and mill feed rate. The regression model with the R square higher than 95% was chosen. The resulting equation was configured in the Digital Plant Template for analysis and further use with the rougher flotation model.
Fig. 11

Real-time trend of measured particle size and predictive soft sensor variables [4]

3.2 Rougher Flotation Metal Recovery Analysis and Modeling

An integrated grinding flotation circuit using an online predictive model for recommendations and/or supervisory controls is shown in Fig. 12. A yield-based model can be derived from the fishbone analysis shown in Fig. 3. Online X-ray analyzer provides elemental concentrations to calculate the recovery in real time using the operating classification algorithm. The key is to use the right operating condition. In this case, while the process is in the Running OK condition, the recovery, tails, and concentrate flows can be estimated in real time after validation of the X-ray analysis. This on line calculation has proven to be a reliable way to model the metal recovery based on the grinding and flotation operating variables. Both measured disturbances and operating condition variables are used in developing the operational model. These variables are mill production rate, ore type, cyclone pressure, particle size (soft sensor), particle size shape (estimate), water additions, % solids, and metal grade in the feed, froth level, pulp level, power, aeration rate, frother, air holdup in the pulp (based in estimate).
Fig. 12

Integrated On-line estimation of grinding and flotation performance [8]

The hydrocyclone overflow product PSDS can be used in the flotation predictive model to understand the rougher flotation recovery. The grinding circuit can be manipulated to achieve the best PSDS to get the maximum recovery in real time. At the same time, the scavenger flotation cell is monitored for the % metal lost in the tailings in real time.

Modern flotation circuits include instrumentation to measure electrical power, frother height, pulp level, froth level, airflow rate, and frother flowrate addition. The rougher flotation metal recovery is estimated as a function of the hydrodynamic flotation operating variables. The air hold up is estimated using the correlation reported by Bascur [10].
$$ \%\mathrm{Air}\ \mathrm{HD}=\mathrm{k}3\left(\frac{\mathrm{Power}}{\mathrm{Pulp}\ \mathrm{Volume}}\right){.}^{.4}\left(\frac{\mathrm{Air}\ \mathrm{Flow}\ \mathrm{Rate}}{\mathrm{Cell}\ \mathrm{Area}1}\right){.}^{.6}\left(\mathrm{Frother}\ \mathrm{Flow}\right){.}^{.25} $$
The airflow rate to the flotation cell is a measured variable. The air flowrate divided by the cell area provides an estimate of the air velocity in the cell. The power measurement divided by the pulp volume is the energy intensity. This number is related to the attachment of bubbles and particles in the cell [10]. As such, the air hold up can be controlled using the airflow to the flotation cell. An air hold up profile can be defined and estimated as shown in Fig. 13. This number takes into account the energy intensity and the pulp level related to the residence time as shown in formula 2 [10]. The frother dosage is another important factor in the air hold up as shown in Fig. 14. The air hold up shows a linear relationship with the aeration rate and a nonlinear positive effect with the frother addition.
Fig. 13

Typical flotation bank percent air hold up estimates based on flotation sensors

Fig. 14

Percent Air Hold Up versus Air Flow Rate, Pulp Level, Frother Addition, and Power [10]

A recovery model and a grade-recovery model is obtained using the mill feed rate, particle size, particle size shape indicator, air hold up, froth height, and all the necessary process variables available. Recovery (X) is function of X = D (Cyclone Feed Flow, % Metal in Feed, Cyclone Overflow P80, Cyclone Overflow P80 Squares, Cyclone Overflow PSD Shape, etc.), M (Total Rougher Flotation Power, Total Rougher Water Addition, Pulp Level, Air hold up Rougher Cell, Reagent X to Rougher, Rougher Flotation Tails Flow, Rougher Flotation Concentration Flow, etc.). The key feature variables and coefficients that result from a Microsoft Machine Learning Batch Linear Regressor [11, 12] are:

$$ {\displaystyle \begin{array}{l}\mathrm{Recovery}=149.77\hbox{--} \mathrm{Hydrocyclone}\ \mathrm{Overflow}\ {\mathrm{PSDS}}^{\ast }\ 256.01+{\mathrm{Rougher}\mathrm{CopperFeed}}^{\ast }\ 83.5+\mathrm{Rougher}\\ {}\mathrm{Air}\ \mathrm{Hold}\ {\mathrm{Up}}^{\ast }\ 2.95\hbox{--} \mathrm{Hydrocyclone}\ \mathrm{Overflow}\ \mathrm{P}{80}^{\ast }\ 0.34\hbox{--} \mathrm{Rougher}\ {\mathrm{Flotation}\ \mathrm{Power}}^{\ast }\ 0.0414+\mathrm{Froth}\\ {}\mathrm{Height}\ {\mathrm{Rougher}\ \mathrm{Cell}}^{\ast }\ 0.041\hbox{--} \mathrm{Hydrocyclone}\ {\mathrm{Feed}\ \mathrm{flow}}^{\ast }\ 0.01+\mathrm{Reagent}\ \mathrm{Rougher}\ \mathrm{Cell}\ {2}^{\ast }\ 0.019.\end{array}} $$

The rougher recovery correlation finds the hydrocyclone PSDS (Gaudin Module estimate from the particle size distribution on line measurements) and the air hold up as notable feature variables. Major disturbances and manipulated variables provide a way to provide a way to drive the plant towards an optimal set of conditions depending on the feed grade. In the case presented here, the PSDS shape provides an indication of the ore hardness effect on the generation of fine particles. The preliminary results demonstrate the relevance of the particle size and shape effects on recovery. In addition, the air hold up metric is also a strong manipulated variable to move the metal recovery to the right direction. An ideal air hold up profile in a flotation bank will improve the overall recovery of metal into the concentrate. This critical variable can be used to optimize flotation with this approach. This is in accordance with semi-empirical hydrodynamic population balance model described in [10, 13].

The critical part of the presented methodology is the classification of operational data into running mode. The Running Ok operating condition state enables use of basic mass balance to estimate the metal recovery, concentrate flow, and tails flow in each of the flotation banks. The ability to have a good recovery estimate allows for the development of a recovery correlation with the enhanced particle size and shape soft sensors and with operational derived variables such as air holdup, energy intensity, and flotation bank profile of variables; however, additional work is required to build on this strategy.

There are many algorithms to choose from in modern machine learning tools [14]. The least squares multiple regression, neural networks, and random forest trees are the most traditional models used. These models are found in Microsoft Azure Machine Learning Studio [12]. Python and R are one of the most commonly used programming languages for predictive analytics [15]. They are not especially difficult to learn, but learning these programs may be more difficult for someone who has not been a process control engineer or process engineer. One can also use the Analysis ToolPak available in Excel to develop regression models.

4 Conclusions

The integration of grinding and flotation operational strategies is necessary for optimal metal recovery.

Using the Digital Plant Template simplifies the configuration of the data model; the metal recoveries for all flotation banks are calculated. The on-line recovery calculations are used to obtain a recovery model correlation with the featured operational variables as discussed. The manipulation of the air holdup profile in the cell becomes feasible. The aggregation of power, cell volume, air flow rate, and frother using [10] semi-empirical correlation provides a novel way to optimize the grinding and rougher flotation circuit.

The classification of the data into operating events for further analysis and process analytics is a fundamental strategy for Overall Performance Effectiveness using business intelligence tools such as Azure PowerBI. Current advances in technology, mineral processing online soft sensors, and machine learning algorithms enable new ways to push the envelope to understand and optimize the grinding and flotation processes. The online estimation of the particle size distribution shape can be used to tailor the SAG mill feed by manipulating the feeders. The particle size distribution shape can be used to model metal flotation recovery and optimize the water additions to the grinding and flotation circuits in order to improve recovery and operating profit.



The authors acknowledge the support of OSIsoft to publish this technical paper and the participation of many people that have contributed in this over the years.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.


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Copyright information

© Society for Mining, Metallurgy & Exploration Inc. 2019

Authors and Affiliations

  1. 1.OSIsoft, LLCHoustonUSA

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