Stirred Mill (Power, Nitta): Difference between revisions

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== See also ==
== See also ==
* [[Mill (Herbst-Fuerstenau)]]
* [[Mill (Herbst-Fuerstenau)]]
* [[Ball Mill (Perfect Mixing)]]
* [[Stirred Mill (Perfect Mixing)]]
* [[Ball Mill (Perfect Mixing, Dynamic)]]
* [[Stirred Mill (Perfect Mixing, Dynamic)]]


== References ==
== References ==

Latest revision as of 02:30, 29 February 2024

Description

This article describes the Nitta method for estimating the power draw of a vertical stirred mill.[1]

Model theory

The Nitta approach computes mill power as:

where:

  • is the net power draw of the mill, i.e. excluding mill drive losses (kW)
  • is the gross power draw of the mill, i.e. including mill drive losses (kW)
  • is the mill drive efficiency (kW/kW)
  • is the power constant (kW), suggested.
  • is mill height (m)
  • is the fraction of mill volume occupied by the media charge, void space and stirrer below the charge level (v/v).
  • is the fraction of mill volume occupied by the stirrer below the level of the media charge (v/v).
  • is the diameter of the stirrer (m)
  • is the gap between the inside wall of the mill and the stirrer (m)
  • is the rotational speed of the stirrer (rps)

Adopting a similar approach as the Hogg and Fuerstenau tumbling mill power model, the net power draw, , may be separated into its contributing constituents:

where:

  • is the power drawn by the ball component of the mill load (kW)
  • is the power drawn by the interstitial slurry component of the mill load (kW)
  • is the volumetric fraction of interstitial void space in the charge (usually 0.4) (v/v)
  • is the density of balls (t/m3)

The apparent charge density, , may be computed as:

where is the density of slurry (t/m3).

The slurry density, , may be computed as:

where is the mass fraction of solids in the slurry (w/w), and is the densityy of solid ore particles (t/m3).

Additional notes

The Nitta model does not include a term for charge density, which may compromise its ability to predict mill power draw with alternative grinding media materials, ore densities or feed solids fractions.

Excel

The Nitta mill power model may be invoked from the Excel formula bar with the following function call:

=mdMillPower_Nitta(Parameters as Range)

Invoking the function with no arguments will print Help text associated with the model, including a link to this page.

The Parameters array and model results are defined below in matrix notation, along with an example image showing the selection of the same arrays in the Excel interface:


where:

  • is the volume of the charge (m3)
  • is the mass of balls in the mill (t)
  • is the mass of slurry in the interstitial charge void space (t)
Figure 1. Example showing the selection of the Parameters (blue frame), and Results (light blue frame) arrays in Excel.

SysCAD

The Nitta power model is an optional calculation for stirred mill units. If selected, the input and display parameters below are shown.

Tag (Long/Short) Input / Display Description/Calculated Variables/Options
Nitta
HelpLink ButtonModelHelp.png Opens a link to this page using the system default web browser. Note: Internet access is required.
MillDiameter Input/Display Diameter of the mill (inside liners).
MillHeight Input/Display Height of the mill.
ScrewDiameter Input/Display Diameter of the screw stirrer.
ScrewSpeed Input/Display Rotational speed of the screw stirrer.
ScrewVolFrac Input/Display Volume occupied by screw stirrer as a fraction of mill volume.
BallFilling Input/Display Volumetric fraction of the mill filled with balls, including slurry and interstitial voids between balls.
PowerConstant Input Coefficient of the power equation.
PowerLosses Input Fraction of power lost due to mill drive efficiency ().
SolidsFraction Display Mass fraction of solids in the slurry phase.
OreDensity Display Density of solids.
BallDensity Input/Display Density of balls.
ScrewWallGap Display Distance between mill wall and screw stirrer.
ChargeVolume Display Volume of media charge in the mill.
BallMass Display Mass of balls in the mill.
InterstitialSLMass Display Mass of slurry occupying charge void space.
RhoSlurry Display Density of slurry phase.
ApparentDensity Display Density of total charge (including balls, slurry and voids).
BallsPower Display Power drawn by the ball component of the mill load.
SlurryPower Display Power drawn by the interstitial slurry component of the mill load.
NetPower Display Net power drawn by the mill (excluding drive inefficiencies).
GrossPower Display Gross power drawn by the mill (including drive inefficiencies).

See also

References

  1. Nitta, S., Furuyama, T., Bissombolo, A. and Mori, S., 2006, September. Estimation of the motor power of the tower mill through dimensional analysis. In Proceedings of 23rd International Mineral Processing Congress (pp. 3-8).