The updated Benavente Correlation. 

An improved method for Estimating Grinding Media Consumption Rates

In 2007 Benavente established an empirical correlation for estimating grinding media consumption, based on operational parameters as well as Bond’s Abrasion Index.  Benavente’s correlation showed a substantial improvement in comparison with the results obtained via the use of the Bond Abrasion Index.

Carlos Rabanal, from Moly-Cop Perú describes the Updated Benavente Model and outlines why the model was improved and how it has resulted in a more accurate method for estimating grinding media consumption for existing or greenfield mineral processing operations.

Why the need to improve the current Benavente’s Empirical Correlation?

Based on the model originally developed by Benavente, a projection of grinding media consumption typically results in an error of approximately ± 12%, which until recently, was considered a satisfactory result given the lack of alternate methods to better predict consumption.

Grinding Media consumption is a significant expenditure item for any mineral processing operation, therefore the ability to accurately predict its consumption is an important capability for our customers.  So work was undertaken by Moly-Cop employees to try to reduce the error rate by improving the original Benavente’s Correlation through a detailed analysis of the drivers of grinding media consumption and the resulting coefficients in the equation.

As a result, a more robust correlation could be obtained, reducing
the average estimation error to ± 9% and a standard deviation of
5.5%.

The Updated Benevente Formula

Benevente1

Updated Benavente’s Empirical Correlation.

Research was conducted by Product Engineers from Moly-Cop Peru to further improve the capability of the empirical model originally developed by Benavente to estimate grinding media wear rates.  The work performed included analysis of operating performance data from 49 mills and included extensive determinations of the Bond Abrasion Index for different ore types.

For better understanding , the wear rate constant is directly related to the grinding media consumption rate expressed in grams of steel per kWh drawn by the mill, using the simple expression:

Benevente2

where dr represents the diameter of the new make-up balls periodically charged to the mill.

In an attempt to further improve the accuracy of the new correlation, additional variables such as mill diameter, speed (as a % of critical velocity) and product size (P80) were also considered and tested without significant improvement.

Moly-Cop Tools 3.0 Application

The use of the Updated Benevente Correlation for any particular operation is greatly facilitated by the inclusion of this formula in Moly-Cop Tools 3.0.  The new simulator can be seen opposite.

benevente3

Conclusion

The Updated Benavente Correlation is a powerful tool for budget projections in the case of greenfield or brownfield milling projects, as well as for the analysis of grinding media consumption rates in existing concentrators.

The Updated Benevente Correlation can be applied for the estimation of grinding media consumption rates with a much reduced average error rate of ± 9%.