Grinding & Classification Circuits

Grinding & Classification Circuits

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Bond Work Index (Energy equation) (3 replies and 2 comments)

o
Okay
6 years ago
Okay 6 years ago

Hello Everyone,

I am dealing with the calculation of Bond Work Index. The flowsheet is attached. I have calculated primary ball mill bond index but for the calculation of second ball mill bond index I got trouble. In a bond energy equation,  where should I select tonnage ? and where should I pick P(80), F(80) values ? Thanks in advance.

flowsheet
https://www.911metallurgist.com/wp-content/uploads/2017/09/Flowsheet.png
Alex Doll
6 years ago
Alex Doll 6 years ago
1 like by David

You need a two-stage solution, first stage open-circuit mill and then second stage closed-circuit mill.

First stage, will be broken into two parts as well, you use a Bond rod mill work index for the coarse component of the ore (+2.1 mm) and the Bond ball mill work index for the fine component (-2.1 mm). It would look like this:

 

E_prim = [10*Wirm*(2100-0.5 - F80-0.5) + 10*Wibm*(T80-0.5 - 2100-0.5)]*EF2*EF4

E_sec = [10*Wibm*(P80-0.5 - T80-0.5)]*EF4*EF5

where:

E is the specific energy consumption, kWh/tonne, F80 is the feed size to the primary BM; T80 is the transfer size (prim mill product size), P80 is the final product (cyclone overflow).  The following "efficiency factors" may also apply, but they must be greater than 1.0 otherwise use 1.0: EF2 is the open-circuit correction factor, EF4 is the oversize feed factor, EF5 is the fine product factor.

To find the power at the mill pinion, multiply an E value by the circuit solids feed rate (feed rate of dry solids to primary mill or the dry solids flow rate of product in the cyclone overflow). 

Power as kW = E * (t/h dry solids)

A ball mill can safely operate at 90% of its motor rated power, so choose a motor size like this:

Motor size as kW = Power / 0.90

You will not get a circulating load prediction from a Bond calculation.  The assumption is that your secondary circuit is "efficient", whatever that might mean.  Typically this means circulating loads of 250%, but can go to over 400% for maximum classification efficiency.

o
Okay
6 years ago

Thank you sir, but I have calculated all of the stream tonnage and size distributions. However, my only confusion is while computing the second ball mill bond index, in which stream should I take P(80),F(80) and the tonnage for mill power estimation ? For example, for P(80), should I use hydrocyclone overflow or second mill product or whatever and also for F(80 should I select hydrocyclone underflow or whatever, and for tonnage which I use in mill energy calculation should I use fresh feed tonnage, circulation load or any other ?

M
BAUD
6 years ago
BAUD 6 years ago
1 like by David

BOND WORK INDEX

The Bond Work Index is a factor that measures the energy consumed in size reduction operation of the ore.

The  Bond's Work Index equation is:

W=WI* (10/√P80  -10/√F80)

where

W= the energy input (Work input) per ton, kwh/metric ton

WI= Work Index= specific energy per ton, kwh/metric ton (characterizes the ore)

F80 = 80% passing size of the circuit feed, in microns

P80 = 80% passing size of the circuit product, in microns.

Example

The dry feed of a ball mill circuit is 300 t/h.

The power at the pinion of the ball mill is 1800 kW.

F80 = 80% passing size of the circuit feed, in microns = 2500 um

P80 = 80% passing size of the circuit product, in microns = 225 um

  Solution

Work Input (Energy input): W= (1800 kw)/ 300 t/h=6.0 kwh/t

Then

WI = Work Index of this circuit

 W=WI*(10/√225  -10/√2500 )

6.0 kwh/t=WI*(10/15- 10/50)

WI = 12.86 kwh/ metric ton

Note:

-On your flow sheet, the feed of the second ball mill is the under flow of the cyclone.

-The F80 and P80 are obtained by a sieve size analysis of the ore sample respectively in the feed and in the product. This gives the mass fraction of the ore retained between successive sieve sizes.

-Construct the size distribution curves. Estimate the value size at 80% of passing on both curves for the feed and the product.

-The nominal power of an electric motor is not the power at the pinion.

 

o
Okay
6 years ago

Thank you sir, but I have calculated all of the stream tonnage and size distributions. However, my only confusion is while computing the second ball mill bond index, in which stream should I take P(80),F(80) and the tonnage for mill power estimation ? For example, for P(80), should I use hydrocyclone overflow or second mill product or whatever and also for F(80 should I select hydrocyclone underflow or whatever, and for tonnage which I use in mill energy calculation should I use fresh feed tonnage, circulation load or any other ?

Alex Doll
6 years ago
Alex Doll 6 years ago

F80 is the feed size to the primary BM; T80 is the transfer size (prim mill product size), P80 is the final product (cyclone overflow)

The F80 is the feed to the primary ball mill.

The T80 (is the P80 of the primary ball mill and the F80 to the secondary ball mill circuit) is measured at the pipe departing the primary ball mill.

The P80 is the product of the secondary ball mill circuit and is measured at the hydrocyclone overflow. 

The key: in a closed circuit ball mill circuit, you put a "black box" over the whole secondary circuit.  Ignore the hydrocyclone underflow and the secondary mill product, those are internal to the black box.  You only care what feed enters the secondary circuit (which is the primary mill product) and what product exits the secondary circuit (the hydrocyclone overflow).

Hope that helps.

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