Template:BarrattEsagEquation

Barratt SAG Specific Energy Equation

This is a basic equation of the family of Bond/Barratt calculations. It describes specific energy requirement of a SAG (or Autogenous) mill Esag as a function of feed size F₈₀, transfer size T₈₀ and the work index values at three different sizes:

• Wi_C: the Bond low-energy impact crushing work index, covers 20 mm to 100 mm size range.
• Wi_RM: the Bond rod mill work index, covers 2 mm to 10 mm size range.
• Wi_BM: the Bond ball mill work index, less than 2 mm size range.

There are a series of calibration parameters that correspond to the size ranges listed above. It is useful to think of this model as a hypothetical 3-stage crushing — rod mill — ball mill circuit with a calibration adjustment (1.25) for SAG milling.

• P_C is the hypothetical tertiary crusher product size (default=18850 µm)
• P_R is the hypothetical rod mill product size (default=2100 µm)

Three Rowland Efficiency Factor adjustments are required:

• EF₄^RM is the oversize feed factor for rod milling, and is a function of the hypothetical crusher product size or the larger of work index for crushing and work index for rod milling.
• EF₄^BM is the oversize feed factor for ball milling, and is a function of the hypothetical rod mill product size and the work index for rod milling.

$</noinclude>{{{E|E_{SAG}}}} = \left [ {{{WiC|Wi_{C} }}} \times \left ( \frac {10}{\sqrt{ {{{Pc|P_{C} }}} }} - \frac {10}{\sqrt{ {{{F80|F_{80} }}} }} \right ) + {{{WiRM|Wi_{RM}}}} \times \left ( \frac {10}{\sqrt{ {{{Pr|P_{R} }}} }} - \frac {10}{\sqrt{ {{{Pc|P_{C} }}} }} \right ) \times EF_4^{RM} + {{{WiBM|Wi_{BM}}}} \times \left ( \frac {10}{\sqrt{110} } - \frac {10}{\sqrt{ {{{Pr|P_{R} }}} }} \right ) \times EF_4^{BM} \right ]\times 1.25 - {{{WiBM|Wi_{BM}}}} \times \left ( \frac {10}{\sqrt{ {110} }} - \frac {10}{\sqrt{ {{{T80|T_{80} }}} }} \right ) <noinclude>$

See list of pages that use this formula: