Identification of the breakage rate and distribution parameters in a non-linear population balance model for batch milling

Document Type

Article

Publication Date

3-10-2011

Abstract

Non-linear population balance models (PBMs), which have been recently introduced due to the limitations of the classical linear time-invariant (LTINV) model, account for multi-particle interactions and thus are capable of predicting many types of complex non-first order breakage kinetics during size reduction operations. No attempt has been made in the literature to estimate the non-linear model parameters by fitting the model to experimental data and to discriminate various models based on statistical analysis. In this study, a fully numerical back-calculation method was developed in the Matlab environment to determine the model parameters of the non-linear PBM. Not only does the back-calculation method identify the parameters of complicated non-linear PBMs, but also it gives the goodness of fit and certainty of the parameters. The performance of the back-calculation method was first assessed on computer-generated batch milling data with and without random error. The back-calculation method was then applied to experimental batch milling data exhibiting non-first order effects using both the LTINV model and two separate non-linear models. The back-calculation method was able to correctly determine the model parameters of relatively small sets of batch milling data with random errors. Applied to experimental batch milling data, the back-calculation method with a two-parameter non-linear model yielded parameters with reasonable certainty and accurately predicted the slowing-down phenomenon during dry batch milling. This study encourages experimenters to use advanced non-linear population balance models along with the back-calculation method toward estimating the breakage rate and distribution parameters from dense batch milling data sets. © 2010 Elsevier B.V.

Identifier

79951682196 (Scopus)

Publication Title

Powder Technology

External Full Text Location

https://doi.org/10.1016/j.powtec.2010.12.019

ISSN

00325910

First Page

195

Last Page

204

Issue

1

Volume

208

Grant

EEC-0540855

Fund Ref

National Science Foundation

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