Model:Amelunxen SGI

Amelunxen SGI Model

This is a model that estimates the specific energy consumption of a SAG or AG mill plus ball mill circuit using the equation by Amelunxen (2014) for E_SAG and the classical Bond work index equation for E_ball substituting CF_ball in the place of the Rowland efficiency factors.

The model requires manual calibration factors for both equations (CF_SAG and CF_ball, respectively) and is very sensitive to the settings used for these factors.

Testwork Required

• SAG grindability index
• Bond ball mill work index

Required parameters

• F₈₀, µm is the 80% passing size of the fresh feed to the circuit (expected to be a Bond-compatible size distribution).
• P₈₀, µm is the 80% passing size of the circuit product (expected to be a Bond-compatible size distribution).
• Availability, expressed as a decimal (0.90 = 90% availability) is used to convert t/h to t/d.
• Ball mill Operating strategy when circuit is SAG-limited (note, fixed speed can only be vary P₈₀)

Optional parameters

• Description and Comment are optional text fields
• Maximum t/h limit is a t/h throughput limit above which the mills will turn down by, for example, grinding out.
• T₈₀ min and T₈₀ min override the transfer size restrictions built into the model
• Ball mill work index adjustment used to adjust Wi_BM for different P₈₀ sizes.
  • coefficient (a), the fitted Hukki coefficient to the adjustment equation (enter as a positive number)
• CFball calibration factor, model tuning factor for E_BM
• CFsag calibration factor, model tuning factor for E_ASAG

Formulae

$E_{SAG} = 5.9 \times SGI^{0.55} \times T_{80}^{-0.275} \times CFsag$^{Amelunxen, 2014}

$E_{ball} = W_i \times \left ( \tfrac {10}{\sqrt{ P_{80} }} - \tfrac {10}{\sqrt{ T_{80} }} \right ) \times CF_{ball}$^{Becerra & Amelunxen, 2012}

There is another model that has been published by F. Jorquera & M. Becerra (Procemin 2016) that was specifically calibrated to the El Soldado single-stage SAG mill (SS-SAG). They arrived at a 7% lower value for the coefficient (5.494 versus 5.9 in Amelunxen, 2014), and a slightly different exponent (0.563 versus 0.55 in Amelunxen). The exponent is within 2% of Amelunxen's value, and the model does not account for the way El Soldado rejects uncrushed pebbles from the SAG circuit, so the SGI of the feed is slightly harder than the actual work the mill is doing. Of interest is this single-stage SAG mill uses SGI to predict grinding down to about 200 µm with no need for a ball mill work index.

$E_\text{El Soldado} = 5.494 \times \left( \frac{SGI}{ \sqrt{T_{80}}} \right)^{0.5494} \times CFsag$

The Single Stage SAG model in SAGMILLING.COM uses Amelunxen's form of the equations as it is not normal to reject pebbles the way it is done at El Soldado. The pebble rejection probably reduces the E_SAG by about 10% at El Soldado versus what would be observed with pebble recycle.

CF_sag calibration factor

The CF_sag factor is used to reflect the effect of pebble crushing and pre-crushing on the overall circuit performance.

• Base value, SAB circuit (no pebble crushing, ~6 inch SAG feed), CF_sag = 1.00
• Pebble crushing, SABC circuit, CF_sag = 0.85
• Pre-crushing, (fine SAG feed, -120 mm SAG feed^{Custer et al, CMP 2001}), CF_sag = 0.90
• Pre-crushing and pebble crushing, CF_sag = 0.85 × 0.90 = 0.77

CF_ball calibration factor

The CF_ball is a manually picked value used to lump the phantom cyclone effect and the variety of Rowland efficiency factors into a single factor. This value is usually picked based on a mill survey, or taken from a diagram such as Figure 5 from Becerra & Amelunxen (2012)^Bibliography, reproduced below.

(CFnet is the term used by Becerra & Amelunxen for CF_ball)

If the CF_ball value is left blank, then the fitted "Los Bronces" curve is used (squares in the Becerra & Amelunxen diagram).

CF_ball = 2.35 - 0.29 × Ln(P₈₀)

Transfer size

The transfer size assumed in a Amelunxen SGI model is described as being "as would be measured in a plant survey" (uncorrected for the extra fines, meaning no allowance for the phantom cyclone effect is requried). This is different to the basis of the various Bond models where the transfer size is a synthetic value that implies the removal of the extra fines.

In practical terms, running an SGI model will require relaxing the upper T80 constraints (the default constraints are tuned to the Bond models). Upper limits of 5000 µm or 6000 µm are not uncommon when simulating Andean copper porphyry type ores in SAB or SABC-A configurations.