Grinding and Flotation Optimization Using Operational Intelligence
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Abstract
In recent years, metalproducing 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 realtime 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 online generation of insights to using operational intelligence tools is described. The implementation of a recovery/grind strategy with industrial examples in nonferrous mineral processing is presented.
Keywords
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 tracking1 Introduction
The declining supplies of highgrade 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 nonproductive 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.

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.
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 realtime.

Running

Idle

Trouble, Invisible losses

Down

Maintenance
Then it is imperative to run every unit reducing offtarget, 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 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 causeandeffect 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 online 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.
 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 realtime analytics.
 2
The overall production effectiveness is used to define and evaluate the production and consumable losses when not operating at the production target. Realtime trends, alerts, and Business Intelligence (BI) dashboards are used to visualize and to analyze the operational data based on operational events.
 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
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 offtarget, down, and idle time are reduced.
2 Methods
Realtime 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.
Process coordination is used to integrate the chain supply to extend the analysis from all processes (for example, as in a minetomill or milltoport approach).
Once the process chain is well tuned, it is possible to identify opportunities to move closer to operating constraints. Operational (realtime) data can be used to explore new opportunities while using business analysis, visualization, and analysis of data and events.
2.1 RealTime Operational Intelligence
Because the base template is not equipment or processspecific, the real value of this approach comes with its scalability if applied across the organization to render a highlevel 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 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.
3.2 Rougher Flotation Metal Recovery Analysis and Modeling
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.
A recovery model and a graderecovery 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:
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 semiempirical 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 online 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] semiempirical 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.
Notes
Acknowledgments
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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