Development of Effective Voidage Correlations in Pilot-Scale Liquid–Solid Fluidized Bed Based on Data-Driven Modeling

Liquid–solid fluidized beds can meet many different demands from chemical, environmental, and pharmaceutical processes, and it is very crucial to accurately predict their voidages, which, however, are usually underestimated by the classical Richardson–Zaki equation. In this study, a data-driven modeling method was applied to develop the voidage correlation based on the experimental data from pilot-scale liquid–solid fluidized bed where the fluidization experiments of spherical glass beads were performed at different particle sizes, particle densities, liquid superficial velocities, and operating temperatures. By selecting different parametric spaces, various high-accuracy voidage correlations based on different dimensionless numbers (i.e., Re, Ret, Ar, Fr, St) were discovered and all of the values of R2were approximately 0.99. In comparison, the combination of Re and Ar numbers could better characterize the voidage and the mean square error was as low as 2.29 × 10–4. The proposed correlation also performed very well in predicting the voidage of the fluidization of irregular calcite pellets in a pilot-scale fluidized bed and the voidage of the fluidization of coarse coal particles in a laboratory-scale fluidized bed, thus indicating its universality.