Moisture measurement problem
By Prof Mark McGuinness
A chemical processing company brought an interesting challenge to the European Study Group with Industry held last year at the University of Limerick. They want to measure the moisture content of a crushed mineral ore in real time, on the conveyor belt as it is offloaded. The amount of water present has a strong effect on the weight and the consequent price paid. A microwave analyser that outputs a moisture content once every second has been tested with varying results, depending on whether the moisture levels are high or low.
We studied both the theory of how water molecules affect phase shift and attenuation of microwaves, and the data provided by the analyser and lab measurements of samples taken from the material. At first it seemed that all was well, and the analyser provides good estimates of moisture content to the desired accuracy, provided it is properly calibrated. The Study Group provided ways to improve the measurement of phase shift, applicable when phase changes by more than 360 degrees, and explored the significance of a characteristic geometric shape that is seen when phase is plotted against a shifted phase. Questions remained about the effect of changing the type of material, or how often the analyser should be calibrated.
Further communications with the company some months after the Study Group revealed that the analyser failed to properly respond when a very wet delivery of ore followed a relatively dry delivery of the same type of ore. Further investigation revealed that the signal to noise ratio seemed to be much worse for very wet material. One instinctive response to the apparent failure of the analyser was to consider the possibility of equipment failure (“a hardware problem”).
I am still having fun with this question – is it equipment failure, or is something else going on? The intriguing possibility is that when the amount of water in the porous medium (the milled ore under investigation) reaches a critical value, percolation theory tells us that it forms a connected network in the pores, with a resulting power-law behaviour for increasing conductivity to microwaves. The theory of a polarising dielectric underlying our analysis needs to be modified to account for the possibility of significant attenuation consequent on this critical phenomenon, possibly accounting for the high signal to noise ratio seen at higher moisture contents. Such understanding may point the way to improved measurement methods, possibly as simple as changing the operating frequency. This is work in progress. The interplay between theory and data remains crucial.
Mark Mc Guinness is a Professor of Applied Mathematics School of Mathematics and Statistics at the Victoria University of Wellington, New Zealand and an Adjunct Professor in the University of Limerick in Ireland