Sending microwaves through bauxite ore allows almost continuous measurement of moisture content during offload by conveyor belt from a ship. Data and results from a microwave analyser were brought to a European Study Group with Industry at the University of Limerick, with the over-arching question of whether the results are accurate enough. The analyser equipment uses linear regression against phase shifts and signal attenuation to infer moisture content in real time. Simple initial modelling conducted during the Study Group supports this use of linear regression for phase shift data. However, that work also revealed striking and puzzling differences between model and attenuation data.

We present an improved model that allows for multiple reflections of travelling microwaves within the bauxite and in the air above it. Our new model uses four differential equations to describe how electric fields change with distance in each of four layers. By solving these equations and taking reflections into account, we can accurately predict what the receiving antenna will pick up.

Our new solution provides much-improved matches to data from the microwave analyser, and indicates the deleterious effects of reflections. Modelled signal strength behaviour features a highly undesirable noninvertible dependence on bauxite mixture permittivity.

Practical measures that might be expected to reduce the effects of microwave reflections and improve the accuracy of microwave analyser results are suggested based on our improved model solution. This modelling approach and these results are anticipated to extend to the analysis of moisture content during transport on conveyor belts of other ores, slurries, coal, grains and pharmaceutical powders, especially when the depth of the conveyed material is variable.