# Grinding & Classification Circuits

Grinding & Classification Circuits 2017-04-04T06:57:16+00:00
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## Understanding the JKMRC Model and breakage rate equation (5 replies)

JohnnyD
2 years ago
JohnnyD 2 years ago

The equation of the JKMRC breakage rate model published in papers is:

T/hr α r.s.(1-a)

There is no =

How should I read and understand this rock breakage rate equation?

David Kano
2 years ago
David Kano 2 years ago

I assume that the alpha (α) is a proportional sign and thus the equation needs no equals (=) sign. There will be, of course, a constant of proportionality in an equation with an equals sign.

For example, T/hr = r.s.(1-a).k (where k is the constant).

I am not big on equations with units (T/hr) in them unless they fix or imply the units of the other terms on the LHS of the equation.

JohnnyD
2 years ago
JohnnyD 2 years ago

The first time I saw the equation, I think the alpha is a proportional sign too. Maybe it does be. Now I feel I need to take more time to learn the JKMRC model. Really thanks.

Maya Rothman
2 years ago
Maya Rothman 2 years ago

The perfect mixing ball mill model to which you refer was first published by W.J. Whiten, 1976. "Ball mill simulation using small calculators", Proc. Australas. Inst. Min. Metall., No 258, June 1976. The paper describes the model in considerable detail. It is also described in the JKMRC Monograph, Mineral Comminution Circuits - Their Operation and Optimisation by Napier-Munn, Morrell, Morrison and Kojovic published by the JKMRC in 1996. The book is still available from the JKMRC. You can find details on their web site at https://www.jkmrc.uq.edu.au/jkmrc-mineral-comminution-circuits

John Koenig
2 years ago
John Koenig 2 years ago

First of all, you need to understand the concept under this expression. I recommended to do an "units evaluation" to corroborate the relationships. "s" represent the mass inside the mill (internal ore charge) with unit t and normally is treated like size distribution. "r" represents the grinding efficiency and has unit 1/s or 1/hr. For me, this is the essential parameter to represent the ball grinding process. "a" is a matrix that represent the percentage breakage from superior sizes, added to the current size. So, the unit result from your expression is t/h. OK from this point of view. Now, if you analyze the complete model the capacity treatment must be a proportional function of "amount that dissapear" (+, and represented by r) and the "amount of material from superior sizes" (-, represented by a). This approach it's similar considering the Americans models......the concept is the same

David
2 years ago
David 2 years ago

The 'equation' is a first-order rate relationship. The 'α' is a 'proportional to' symbol ( more correctly depicted as ∝)

Throughput (T/hr) is proportional to r.s.(1-a)

where, r = breakage rate, s = rock load mass, a = appearance function.

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