The work index value is useful to get down to a typical ball mill product size, such as 100 µm, but you can't use work index below about 50 µm because the exponent of -½ is wrong -- you need to use a model like Von Rittinger or a signature plot to get from 100 µm to 40 µm.  Break the equation into two parts, the "ball mill" portion modelled by Bond and the "fine grinding" portion modelled by a signature plot.

E_Bond = 10 × (Wi = 10.2) x (100^-½ - 4000^-½) = 8.59 kWh/t to get to 100 µm.

The signature plot for the Ernest Henry magnetite circuit in Australia is E_fine = 3×10⁶ × (40)^-3.1385
(Burford, MetPlant 2008).  The Ernest Henry tests were performed at about 100 µm feed to the vertical mill.

So using that equation, your specific energy requires E_fine = 3×10⁶ × (40)^-3.1385 = 28.12 kWh/t

Add the two values together for your whole specific energy requirement:

E = 8.59 + 28.12 = 36.71 kWh/t

To achieve your 115 tonnes/hour (metric tonnes, eh?), you need 36.71 kWh/t × 115 t/h = 4221 kW of power on the mill shaft.  Allowing for 10% losses and electromechanical inefficiency, 4221 ÷ 0.90 = 4690 kW.  You need a 5 MW motor to do your duty. A VTM 3000 has a 2.2 MW motor, so you need more than two of them to do this duty.

That's a pretty big number, so I encourage you to get a proper test done on your sample and don't rely on somebody else's testing to size your mill.  Burford's work, in particular, was performed by a vendor that sells a competitor to the VTM, so it is no surprise he finds the energy efficiency for a vertical mill is poor.

Hi Jose

I propose a metallurgical solution, may be your process don´t need too much ultra-fines below the 20 or 10 um that have a great energy consumption as indicate typical signature test. In such case you must replace the inefficient cyclones  by high frequency screens like Derrick equipment, in order to reduce the circulating load because the fines short-circuit. For instance using a 105 um slot screen (P100 105 um) is possible to get P80 40 um with a half of circulating load compared with cyclones, as is reported in many industrial cases.

In other side, I find too large the reduction ratio (4000/40 um) for this Vertimill application so with cyclones the overflow will report coarse particles with maximum size around 500 um (P100) which  content mainly silica compounds affecting iron concentrate quality.

Under this condition is possible to use the Bond equation adding a Benchmarking factor of 1.3 (own data), then we have:

SE 10x10.2x(1/40^0,5-1/4000^0.5)= 14.5 kwh/t

Factor 1.3

SE= 18.9 kwht

Motor= 2.2 Mw

10% losses

Throughput = 105 tph

I suggest contact Derrick copany for this application, they have lot experience in iron range mines.

Regards

LUIS BERNAL

Process Senior Consultant

PROCESS MINERALS CONSULTING

Jose,

read carefully what Alex gave you.  You need to do more tests regarding hardness and grindability. Your data appears limited and tower mill sizing to grind from 4mm to 40um in a single stage can be tricky. 4mm particles are best ground with a larger ball than the ball needed to grind to 40um. How with the vertimill manage the 4mm particles; will it sand-up? 'no lo se'...

Why not consider a 4000HP grate discharge ball mill for this?

In any case, just for interest, here is a case study for an expansion of a 2200 TPD SAG Mill operation.  The client wanted to increase the plant to 2700 TPD @ 30um.  Some plant samples were taken, work indexes obtained and data simulated. As it turns out a single 3000HP Vertimill would get that done "ON-PAPER".

The example was never put into action/production.

Summary: If this is a new installation = do more testing.

Good morning. Thanks a lot to David, Alex and Luis for such a quick, opportune  and right-exactly-to-the-point response to my problem. Definitely, 911 Metallurgist is a great,  highly useful tool for our Community.

José Antonio Ruiz