The grinding performance of a mill depends on the mill's instantaneous grinding rates and transport capacity, which are in turn influenced by the charge content of steel balls, the population of ore particles and water as illustrated in Figure 1.

Figure 1. Influence diagram for the key Dynamic Mill Charge Model parameters.

Controlling these three hold-ups can help with increasing the mill throughput and improving the quality of the mill’s product. However, these key mill charge properties are often not measured directly - and tracking them requires extensive mathematical modelling, combined with appropriate use of observed variables to ensure the models reflect the actual state of the mill.

Our Solution: Virtual Sensors's Grinding Application contains a Dynamic Mill Charge model, which combines a set of physics-based models that can the mill charge content in real-time. The Grinding Application delivers Virtual Sensors of the modelled variables, allowing for much-needed transparency on the mill charge and the grinding process that are normally left unobserved. The most important Virtual Sensors are described below. These can be directly used in the control and optimization of grinding mill circuits, regulating the mill's hold-ups and grinding performance.

Charge Volume

The Mill charge volume (Jt), traditionally cited as a % of total mill volume occupied by the charge, plays a key role in SAG mill performance. If this variable is higher than optimal, it leads to a reduction of energy transferred to the ore particles due to reduced media trajectory. This can lead to mill overloads. The mill charge volume is also required for the estimation of the charge's apparent density (see below)


The main factors that affect the mill charge load are:

  • Ball charge

  • Ore hardness

  • Feed size distribution

  • Mill transport properties

Charge Slurry Level & Density

The control of the density of the mill charge is critical for achieving optimal mill performance. High density leads to high slurry viscosity, which means that the mill charge is sticky, the impact is cushioned and residence time is increased. On the other hand, excessive dilution results in a coarser grind and a potential increase in liner and ball wear rates. While the precise adjustment of the mill charge density is clearly important, it is also very hard to measure directly.

This is now made possible by's Virtual Sensor.

Charge Trajectory

The Grinding Application consists of a trajectory model, which provides a Virtual Sensor on the trajectory of the charge in a rotating mill.

Knowing this trajectory in real-time allows Operators to adjust their ball charge, mill charge and mill speed (where available), such that they consistently achieve the desired impact zone in the mill. Hitting the right impact zone contributes to optimizing mill performance.

Ore Breakage & Particle Size Distribution

Modelling current ore breakage and transport is important for understanding the mill performance under various conditions.'s Grinding Application employs fundamental and machine learning models to deliver Virtual Sensors on the quantities of material in different size classes along the mill. These models are calibrated on historical plant data and then updated online to keep track of what is going on inside the mill.

Figure 2. An outline of the ore breakage and transport Virtual Sensors. The associated model’s inputs are feed particle size distribution, ore and water feed rates and mill weight dynamics. The model consists of a series of continuously stirred reactors.

If the relevant data is available from the plant, the ore breakage model is fitted to the feed and product size distributions. Regular samples of the mill product are used to keep it up-to-date.

For information on how to start using these Virtual Sensors on your own Grinding circuit, please reach out to us.

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