Quantifying Regularised Mining Dilution

Block model regularisation is a common tactic to model and apply mining dilution as part of a study or for operational planning. However, the impact of these changes to the block model is often only evaluated at surface level.

Regularisation of a block model to a selective mining unit (SMU) size is one of several ways to model mining dilution. SMU size is selected based on a variety of factors and often several sizes are tested as part of the model regularisation process. For a more general overview on SMU selection I would recommend the Deswik whitepaper “Block Model Knowledge for Mining Engineers – An Introduction”.

When a model is regularised all blocks are changed to match the size of the chosen SMU, smaller blocks are merged and grades and fields recalculated based on the values of the contributing blocks, larger blocks are split along the new block boundaries. This is a common task for a mining engineering consultant and most specialist software packages have a workflow for this purpose.

Typical evaluation of a regularised model would be to compare the tonnage and grade of the input model against the output. This is often done as a comparison of tonnage grade curves such as the one presented below for a Cu deposit which was regularised from a model with a smallest sub cell of X=0.625m and exact boundaries on the Y and Z blocks to a SMU size of X=5m, Y=2m and Z=2m.

At the breakeven cut-off grade (CoG) of 0.29% Cu there has been the following changes to tonnage, grade and contained metal.

With an additional tonnage above cut-off of ~210,000 tonnes in the SMU model it would be logical to assume a dilution of 39% has been modelled. However, this fails to account for the movement of previously above cut-off grade material into what is now a waste block.

To track material from the input model an additional field should be coded prior to model regularisation. For this example a field called DILUTION which is set to 0 in material greater than CoG and 1 in material below CoG will allow the tracking of dilution and ore loss into the final SMU model. When the model is regularised the DILUTION field should be treated the same as other grade fields and averaged by mass.

Once the model is regularised this DILUTION fields now represents the fraction of material above cut-off that was below cut-off in the original model. In blocks above the cut-off this is material is mining dilution.

Likewise in waste material, the inverse of this field represents the fraction of a waste block that was above cut-off in the original model. In blocks below the cut-off this material is one form of ore loss. You may still wish to apply additional ore loss factors.

If we re-evaluate the SMU model and report using the DILUTION field

250Kt of material that was originally below cut-off is now included as mining dilution in blocks that are above the 0.29% cut-off grade. 39kt of material that was originally above cut-off is now ore loss blocks that are below the 0.29% cut-off grade.

This represents a dilution of 50% and an ore loss of 7%. Significantly different to the 39% dilution calculated based on total tonnage.

This method can be applied across multiple regularisation scenarios to determine the sensitivity of a model to certain SMU dimensions. In the example below the Z, Y and Z axis have been flexed independently from a base case of 5 x 2 x 2 to determine the sensitivity of SMU changes on each axis.

I hope that this article was useful, hopefully there will be more to follow. If you have any questions or if you want to find how LS Mining could assist with your project then please get in touch via LinkedIn or the contact form on www.LS-Mining.com