Dynamic and perturbative system analysis of granular material's balance in a vibrating screen

In most particulate classification systems, feed rates in excess of 80% of the designed capacity leads to inefficiency and conversely feed rates below this value significantly diminishes the operational efficiencies. It therefore implies that maximum efficiency is only attainable at the expense of low capacity, and vice versa. This problem is caused by transience in granular flow due to start-ups and fluctuating feed-rates, in addition to fluctuations in feed material properties. If these variations are not checked, they cause instabilities, resulting in chaotic saddles responsible for in-process systemic error generation. These errors produce intermittent disruptions in production process and control. We have applied perturbation theory to study the effects of infinitesimal changes on the material balance analysis of the unit operation. The problem was identified as one of the highly multi-stable dynamic systems, characterized by ‘predator-prey’ phenomenon in dynamical systems theory. The study allowed formulation of optimal state equations, whose numerical solutions resulted in establishment of optimal operating conditions required to sustain stability, and consistently high tonnages and efficiency up to 99% simultaneously. The study also led to development of an optimization algorithm, which upon validation with experimental data showed a close relationship, with a minimal absolute error of 0.8 and a relative error of 6%. Finally, a representative case study was conducted on screen dimensioning, based on the determined parameters. Successful evolution of this methodology may be applied for up-scaling of real systems in future.