Assessing particle size distribution in suspensions through a multi-frequency ultrasonic backscatter approach

Abstract

Particle size is a critical parameter for calculating the solid phase holdup and settling velocity in pipeline suspensions. However, accurately determining solid holdup remains challenging due to the complexity and variability in multiphase suspensions, especially when the physical size of the suspended particles is unknown. We have developed a novel multi-frequency particle size measurement system that utilizes acoustic backscatter techniques. Furthermore, we propose a new particle size inversion algorithm that integrates Empirical Mode Decomposition (EMD) and the Pearson Correlation Coefficient (PCC) with traditional algorithms. By applying EMD, the raw echo signal is decomposed into Intrinsic Mode Functions (IMFs), allowing for effective noise separation. The PCC is subsequently used to determine correlations between IMFs, improving signal reconstruction accuracy. The minimum concentration gradient continuous inversion algorithm we proposed effectively solves the multi-solution problem of the energy ratio algorithm through the minimum concentration difference method. This algorithm innovatively employs sliding window technology to accurately assess the optimal particle size range of suspended particles in the ultrasonic measurement path. Experimental results indicate that the Mean Absolute Percentage Error (MAPE) for particle diameters in the ranges of 280–350 μm, 450–550 μm, and 760–880 μm are 7.16 %, 3.87 %, and 4.66 %, respectively. This method provides a precise and efficient solution for measuring particle size distribution in underground pipelines, with broad applications in pipeline maintenance, sediment transport modeling, and drainage system design.