Estimation of the minimum spouting velocity in shallow spouted beds by intelligent approaches: Study of fine and coarse particles

The minimum spouting velocity, which is an essential parameter in the design and scale-up spouted beds, has been predicted by different intelligent methods for shallow spouted beds of fine and coarse dense-particles. Four important dimensionless moduli, namely, Ar, Hb/Do, Do/Dc, and tan(γ/2) have been taken as model inputs. A single correlation for the minimum spouting velocity in the whole range of dense particle diameter, i.e., fine and coarse, leads to a high average absolute relative error (AARE) in the estimation of Ums,o due to the effect of particle size on the hydrodynamics of these beds. Accordingly, two distinct range of data sets based on the particle size have been used in all calculations. Among the models used, Gaussian Process predicts the best results for both fine and coarse particles. The coefficients of best fit in the correlations have been optimized by the well-known optimization method of Imperialist Competition Algorithm (ICA). Finally, different empirical correlations have been analysed and their results compared with those calculated by the correlations proposed. A sensitivity analysis based on the Gaussian Process approach has been conducted in order to determine the most significant parameters affecting Ums,o in shallow spouted beds of fine/coarse particles. [Display omitted] •Ums was studied in shallow spouted beds for both fine and coarse heavy particles.•Two distinct equations was obtained by ICA to estimate Ums based on particle size.•Gaussian Process predicted the best results for both fine and coarse particles.•Different empirical correlations were analysed for both fine and coarse particles.•Sensitivity analysis was conducted to determine the important factors affecting UMS.