A probability approach for investigation and determination of material slugs/air gap

In the past, pressure drop prediction models in low velocity dense-phase pneumatic conveying largely assumed steady-state conditions during conveying. However, the dense-phase flow regime is rather characterised by transient dunes or discrete full bore slug flows, which limit steady-state approaches in their ability to accurately describe these systems. Steady-state approaches as well as pressure drop prediction models for discontinuous slug flow depend on the total slug length - sum of all slugs in a pipeline - which can be related to the air-gap/slug-length ratio. As such, there is a need to accurately predict this ratio. This paper reports on investigations on describing slug length, air gap length and air-gap/slug-length ratio using a probabilistic approach. In particular, the primary variables of slug lengths and air gap lengths have been modelled under the assumption that their variations have logarithmic normal distributions. Subsequently, the probability distribution of air-gap/slug-length ratios has also been derived from the logarithmic distributions of these two basic variables. The resulting distribution models have been applied to compare experimental slug- and air gap length data observed from multi-slug conveying trails for polyethylene pellets, which showed a strong influence of the solid loading ratio. The derived probability model for the air-gap/slug-length ratio was also validated by the Kolmogorov-Smimov (K-S) test for goodness of fit.