Partitions: Difference between revisions

From Met Dynamics
Jump to navigation Jump to search
md>Scott.Munro
 
m (1 revision imported)
 
(4 intermediate revisions by 2 users not shown)
Line 14: Line 14:


:<math>\beta^* = \dfrac{\ln \big[ \exp (\alpha) + 2 \beta \beta^* (\exp (\alpha) - 1) \big]}{\alpha}</math>
:<math>\beta^* = \dfrac{\ln \big[ \exp (\alpha) + 2 \beta \beta^* (\exp (\alpha) - 1) \big]}{\alpha}</math>
When the value of <math>\beta</math> is zero, the Whiten-Beta equation reverts to:
:<math>E_{{\rm oa}i} = C \left [ \dfrac{ \exp (\alpha) - 1}{\exp \left ( \alpha \dfrac{\bar d_i}{d_{\rm 50c}} \right ) + \exp (\alpha) - 2} \right ]</math>


== Excel ==
== Excel ==

Latest revision as of 13:22, 2 March 2023

Description

Under construction icon-blue.svg.png This section is currently under construction. Please check back later for updates and revisions.

Model theory

Whiten-Beta

The Whiten-Beta expression for partition to overflow is:[1]

where:

  • is the index of the size interval, , is the number of size intervals
  • is the fraction of particles of size interval in the feed reporting to the overflow stream (frac)
  • is the geometric mean size of particles in size interval (mm)
  • is the corrected size at which 50% of the particle mass reports to underflow and 50% to overflow (mm)
  • is the fraction of feed liquids (or fines) split to overflow (frac)
  • is a parameter representing the sharpness of separation
  • is a term introduced to accommodate the so-called fish-hook effect, and controls the initial rise in the efficiency curve at finer sizes
  • is computed to ensure the Whiten-Beta function preserves the definition of in the presence of the fish-hook, i.e. at

The value of is not an input parameter and is computed numerically, by iteration, since by rearrangement:

When the value of is zero, the Whiten-Beta equation reverts to:

Excel

Under construction icon-blue.svg.png This section is currently under construction. Please check back later for updates and revisions.

SysCAD

Under construction icon-blue.svg.png This section is currently under construction. Please check back later for updates and revisions.

References

  1. Napier-Munn, T.J., Morrell, S., Morrison, R.D. and Kojovic, T., 1996. Mineral comminution circuits: their operation and optimisation. Julius Kruttschnitt Mineral Research Centre, Indooroopilly, QLD.