Description
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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
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SysCAD
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References
- ↑ 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.