Mill power draw models

Mill Power Draw Models

The mill power draw models are used to predict how much power will be consumed by a particular type of mill, mill geometry and set of mill operating conditions. This power is transferred to the ore and used to predict the throughput when combined with the specific energy consumption models. Models of this type do not predict the particle size distribution of a milled product — the more complicated population balance models are required for such modelling.

Several authors have offered different types of models, and all generally work for the particular class of equipment they were intended for. The classes of models, and the models in each class are:

• SAG mill models
  • Morrell C-models (phenomenological model with empirical fitting. Sub-divided into a simplified model with 'typical' defaults and full model with all parameters editable)
  • Loveday/Barratt model (uses an internal table of empirical "Power Numbers")
  • Austin SAG model (hybrid phenomenological and empirical model)
• Overflow ball mill models
  • Morrell C-models (phenomenological model with empirical fitting. Sub-divided into a simplified model with 'typical' defaults and full model with all parameters editable)
  • Nordberg model (largely empirical model)
• Grate ball mill models
  • Morrell C-models (phenomenological model with empirical fitting. Only the full model is available)
  • Nordberg model (largely empirical model)
• Other models
  • Cone crusher (secondary, tertiary or pebble crusher)

Comments on flow restrictions

All mill models deal strictly with the power that can be evolved from a particular mill geometry and operating condition. All models assume that there are no flow restrictions of any kind in the circuit and that only mill power will limit the throughput of a grinding circuit. In reality, grinding circuit throughput is frequently limited by the volumetric flow of a hydrocyclone feed pump or the pulp discharging capacity of a SAG mill.

These models give project designers clues as to "at what volumetric flow should I design my plant" by ignoring flow restrictions. A geometallurgy data set will demonstrate a range of circuit throughput that

The designer should check some basic rules of thumb (such as those in the SME Mineral Processing Handbook) against their design, including the range of circulating load in the ball mill and the superficial velocity of pulp through a ball mill.

Power at the mill shell

The mill power draw models used in SAGMILLING.COM all reference power as drawn at the mill shell. Most surveys report power values as they are measured in the plant distributed control system (DCS), which is usually relative to the motor input power. Refer to the Measurement of power article for description of how to convert DCS indicated power to mill power at the shell.

Note that modern wrap-around (gearless) mill drives do a software correction to report mill motor output power (which is the same as shell power). Therefore, new gearless mill drives do not require any correction when comparing DCS power measurements to model power draw predictions.

Liner and grate design

The design of mill liners and SAG mill discharge grates will have a large effect on how efficiently the mill operates and the circuit throughput. All models generally assume that a mill is fitted with "efficient" liners and that the grate design neither limits passage of pebbles (and pulp) nor permits re-circulation of pulp back into the mill.

Determining a correct liner and grate design is beyond the scope of the models hosted on SAGMILLING.COM, and there are specialized tools available to do such designs such as discrete element model (DEM) simulations and certain population balance models.