Energy efficiency of consecutive fragmentation processes

TL;DR

This paper analyzes the energy efficiency of using multiple fragmentation devices sequentially in the mining industry, providing asymptotic comparisons and conditions under which combined processes outperform individual ones.

Contribution

It introduces a model for the energy required in consecutive fragmentation processes and compares their efficiency to single-device processes asymptotically.

Findings

Consecutive fragmentation can be more energy-efficient than single processes under certain conditions.

The study provides asymptotic analysis as the fragment size approaches 0 or 1.

Conditions for efficiency depend on process parameters and energy cost-functions.

Abstract

We present a first study on the energy required to reduce a unit mass fragment by consecutively using several devices, as it happens in the mining industry. Two devices are considered, which we represent as different stochastic fragmentation processes. Following the self-similar energy model introduced by Bertoin and Martinez, we compute the average energy required to attain a size x with this two-device procedure. We then asymptotically compare, as x goes to 0 or 1, its energy requirement with that of individual fragmentation processes. In particular, we show that for certain range of parameters of the fragmentation processes and of their energy cost-functions, the consecutive use of two devices can be asymptotically more efficient than using each of them separately, or conversely.