Calculation of Particle Size Distributions from Ultrasonic Measurements: A Mineral Slurry Case Study

Ultrasonic transmission measurements have been used extensively to determine the particle size of solids in slurries. This case study examines the application of mathematical inversion techniques to the determination of the particle size distribution of a mineral slurry from data collected at a minerals processing plant. A new mathematical inversion technique, based on an extension of modified Chahine iteration combined with the principle of maximum entropy has been developed. Four algorithms were constructed and used to calculate particle size distributions from synthetic and raw plant data. These incorporated modified Chahine iteration and its extension, together with two different approaches to applying a density measurement constraint on the particle size distribution. In general the algorithms performed well with regression errors below 3 %. The correlation coefficients and slopes for this technique were 0.86 and 1.35 for the weight fraction of particles less than 75 microns when compared with the laser diffraction analysis. A better match was obtained for the plant data by using the new inversion technique, into which the principle of maximum entropy has been incorporated whereas this was not the case with the synthetic data, illustrating the need to match the inversion technique to the problem.