Your design P₈₀ just changed. Now what?

Projects evolve as they move from discovery to prefeasibility to final detailed design. Don't forget there is a couple of more stages between prefeasibility and detailed design if you want a robust projects, but that isn't today's topic.

What do you do when the first pass of grindability testing was based on a P₈₀ target that just got revised because of more testwork? Don't panic, this is perfectly normal and nearly all projects shift their target grind size as the test programs complete and the design evolves.

The first thing is to understand that Work Index changes as a function of size, so if your earlier grindability testing was all based at, for example, 135 µm target P₈₀ size, then the ball mill work index at your new target size of, for example, 180 µm might be a bit different. How the work index changes as a function of size is an ore characteristic that you have to measure, there is no magic formula that works for all ore types where you just "apply a factor". You need to compute the adjustment using Josefin's equation and a calibration ore sample where you have measured the ball mill work index at three (or more) different closing sizes. The tutorial video for how to perform this is available on my YouTube channel at this link: https://www.youtube.com/watch?v=1rA8gyy-nxE (21 min).

The second thing to know is that the power split between your SAG and ball mills are going to be different. The ball mill work load is different between the two P₈₀ sizes, which means the transfer size from the SAG mill might no longer be appropriate and you'll need to adjust the ratio of mill power between the SAG and ball mills. That means the mill sizes and motor sizes might need to be adjusted.

The target T₈₀ size for a typical SABC circuit is about 1.5 mm to 2.5 mm. If you had an initial design for P₈₀=135 µm with the following nicely balanced circuit:

and you just changed the P₈₀ without changing the geometry of the mills or the motor sizes, then the transfer size will adjust to balance the E_total = E_sag + E_ball, giving the following:

The transfer size required for efficiency operation has blown out to 2.8 mm as the model adjusts the duty done by the two mills to match the unchanged mill geometries. Both examples have 15,585 kW of SAG power and 21,998 kW of ball mill power (and total power of 37.6 MW) consumed because it is the geometry of the mills and their charges that determine the power draw, not the ore hardness or the particle sizes.

The mill sizes should be adjusted to get the T₈₀ back into the 1.5 mm to 2.5 mm size range, consuming the same amount of total power (37.6 MW). This means some of the excessive ball mill power should be adjusted to the SAG mill, so make the ball mills a bit smaller and the SAG mill a bit larger and see what the model gives you for the T₈₀. This example shows a larger SAG mill drawing 18 MW (versus 15.6 MW) and smaller ball mills drawing combined 19.6 MW (versus 22 MW). Yes, the tonnage goes up but that isn't today's topic, either.

The 1.5 mm to 2.5 mm rule-of-thumb I've offered is specific to a synthetic "Bond corrected" particle size distribution for the transfer size, the sort of thing you can compute using a "phantom cyclone" approach. The rule-of-thumb works for Bond-type models (like Barratt's SABC model in the example), but not for other models like SPI or Morrell Mi calculations – they have their own (possibly synthetic) T₈₀ calibration ranges. The T₈₀ you measure in a plant (as the screen undersize) will be coarser than these synthetic transfer sizes. A recent SAB circuit survey had a measured T₈₀ of 2.6 mm and a synthetic T₈₀ around 1.5 mm.

In conclusion:

1. Don't panic
2. Adjust your design ball mill work index using Josefin's correction, available here: https://www.sagmilling.com/articles/36/view/Correction%20of%20Bond%20Ball%20Mill%20Work%20Index%20Tests%20for%20Closing%20Sizes.pdf?s=1 (PDF 32 kb)
3. Adjust your mill sizes to keep the synthetic transfer size in an acceptable range for efficient operation. This will be an iterative calculation, but fortunately you charge the by hour. 😺