RESEARCH ARTICLES CURRENT SCIENCE, VOL. 115, NO. 10, 25 NOVEMBER 2018 1904 *For correspondence. (e-mail: ss.tambe@ncl.res.in) Bubble size prediction in gas–solid fluidized beds using genetic programming R. R. Sonolikar 1 , M. P. Patil 1 , R. B. Mankar 2 , S. S. Tambe 3, * and B. D. Kulkarni 3 1 Solid and Hazardous Waste Management Division, CSIR-National Environmental Engineering Research Institute, Nehru Marg, Nagpur 440 020, India 2 Department of Chemical Engineering, Laxminarayan Institute of Technology, Amravati Road, Nagpur 440 033, India 3 Chemical Engineering and Process Development (CEPD) Division, CSIR-National Chemical Laboratory, Dr Homi Bhabha Road, Pune 411 008, India The hydrodynamics of a gas–solid fluidized bed (FB) is affected by the bubble diameter, which in turn strongly influences the performance of a fluidized bed reactor (FBR). Thus, determining the bubble diameter accurately is of crucial importance in the design and operation of an FBR. Various equations are available for calculating the bubble diameter in an FBR. It has been found in this study that these models show a large variation while predicting the experimentally measured bubble diameters. Accordingly, the present study proposes a new equation for computing the bubble diameter in a fluidized bed. This equation has been developed using an efficient, yet infrequently employed computational intelligence (CI)-based data- driven modelling method termed genetic programming (GP). The prediction and generalization performance of the GP-based equation has been compared with that of a number of currently available equations for computing the bubble diameter in a fluidized bed and the results obtained show a good performance by the newly developed equation. Keywords: Bubble diameter, bubble motion, fluidized bed, genetic programming. FLUIDIZED bed reactors (FBRs) are widely used in petro- leum, chemical, food, metallurgical, pharmaceutical and power generation industries 1 . The design of gas–solid fluidized reactors requires an understanding of the size and behaviour of bubbles therein. Despite widespread use of FBRs, their scale-up still depends on the empirical me- thods owing to the complicated nature of gas–solid flows inside the reactor. The formation and travel of bubbles play a crucial role in the hydrodynamic study of a flui- dized bed. Specifically, the size of a bubble decides the homogeneity, heterogeneity and slug formation in a flui- dized bed. There are four stages of bubble motion: forma- tion of bubble, its detachment from the orifice, travel in the bed and finally bursting. Harrison and Leung 2 , and Zenz 3 proposed equations for the formation of a bubble at the orifice. Bubble detachment time was studied 3–6 to propose equations for its prediction. A number of equa- tions have also been proposed for determining the bubble diameter while the bubble is in motion, as a function of the particle diameter and density, bed geometry, type of distributor and gas velocity. Previous work Major studies concerning the bubble travel are described here. A number of studies have proposed equations to model the bubble dynamics 7–21 . As suggested by Patil et al. 22 , the Darton’s model is based on the bubbles tending to rise in preferred paths and that the distance travelled by the two neighbouring bubbles before coalescence is proportional to their lateral separation. Farshi et al. 23 stu- died and compared the performance of a number of equa- tions with the experimental data and found that the equation by Rowe 15 fitted their experimental data the best. In the pilot scale study, the corresponding experi- mental data were well predicted by the equations of Rowe 15 and Darton et al. 8 . In a gas–solid bubbling flui- dized bed, Farshi et al. 23 suggested that the equations by Mori and Wen 16 and Rowe 15 possess a good bubble diameter predicting ability. Hilligard and Werther 7 per- formed experiments using quartz sand particles belonging to the Geldart’s Group B of 480 μm size and density equal to 2640 kg/m 3 . On the basis of these experiments, they proposed a relation for calculating the bubble diame- ter of the Geldart Group D particles. The two commonly used variables in all the equations for calculating the bubble diameter are, the ratio of injec- tion velocity (U) to minimum fluidization velocity (U mf ) and the bed height (h) of the bubble above the distributor (Table 1). The equations proposed 11,17 show that the diameter of the bubble (D b ) is proportional to the particle diameter (d p ), whereas Park et al. 13 reported D b to be pro- portional to 1.5 p ( ). d Similarly, D b is shown to be depen- dent on the density of the material 11,17 . The present study focuses on the behaviour of the bub- ble diameter since the hydrodynamics of a bubbling flui- dized bed strongly depends on the bubble characteristics. Owing to the variations found in the predictions of