Chemical Engineering Journal 82 (2001) 247–257 Using CFD for scaling up gas–solid bubbling fluidised bed reactors with Geldart A powders R. Krishna ∗ , J.M. van Baten Department of Chemical Engineering, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands Received 2 May 2000; accepted 13 October 2000 Abstract The hydrodynamics of gas–solid fluidised bed are significantly affected by the scale of operation. This scale dependence is primarily caused by the scale dependence of the rise velocity of bubble swarms. Using the experimental data of Krishna et al. [Chem. Eng. Sci. 51 (1996) 2041–2050] for the bubble rise velocity, V b , in air–FCC fluid beds of 0.1, 0.19 and 0.38 m diameter we develop a model for V b using the Davies–Taylor–Collins relation as basis. This model is exactly analogous to that put forward earlier by Krishna et al. [Chem. Eng. Sci. 54 (1999) 171–183] for the rise of large bubble swarms in liquids. An Eulerian simulation model is developed for gas–solid fluid beds in which the drag between the (large) bubbles and the dense phase is calculated using the developed Davies–Taylor–Collins relations. Several simulations were carried out for columns ranging from 0.1 to 6 m in diameter. These simulations demonstrate the strong influence of column diameter on column hydrodynamics. The Eulerian simulation results rationalise the empirical correlation of Werther for the influence of column diameter on the bubble rise velocity V b . The Eulerian simulation results are used to estimate the axial dispersion coefficients of the dense (emulsion) phase for columns ranging to 6 m in diameter; these are in agreement with the trends observed in the literature. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Gas–solid bubbling; Fluidised bed reactors; Eulerian simulation model 1. Introduction Gas–solid fluidised beds are difficult to scale up because of the strong influence of column diameter on the hydrody- namics and existing scale up procedures in the literature are largely empirical in nature [1–4]. The primary cause of the scale dependence of gas–solid fluid beds is the fact that the bubble rise velocity, V b , is scale dependent. From the ex- perimental data on V b [1–4], it is clear that main factors in- fluencing V b are (a) average diameter of the bubble swarm, d b (b) column diameter, D T , and (c) height of the fluid bed, h. For a single, isolated, bubble of diameter d b the rise ve- locity V 0 b in a bed of powder is given by the Davies–Taylor relationship [5] V 0 b = 0.71  gd b (1) This relationship is equally valid for the rise of spheri- cal cap bubbles in liquids [6–11]. Due to the phenomenon of bubble growth, the average bubble diameter in a swarm increases with the height h above the distributor. Using a ∗ Corresponding author. Tel.: +31-20-525-7007; fax: +31-20-525-5604. E-mail address: krishna@its.chem.uva.nl (R. Krishna). bubble-growth model, Darton et al. [12] derived the follow- ing relationship for the bubble diameter d b = 0.54 (U − U df ) 2/5 (h + h 0 ) 4/5 g −1/5 (2) where U is the superficial gas velocity and U df is the ve- locity of gas through the dense (or emulsion) phase. The parameter h 0 characterises the distributor; for a porous plate distributor, for example, h 0 = 0.03 m. For fine Gel- dart A powders, the bubble growth does not take proceed indefinitely and the bubbles reach an equilibrium size, at a distance h ∗ above the distributor. The equilibration height h ∗ is determined inter alia by the particle size distribu- tion. For fluid cracking catalyst (d p ≈ 50 m), h ∗ has a value of about 0.5 m [13] and the superficial gas ve- locity through the dense phase U df has a value of about 2 mm/s, which is negligibly small in comparison with the operating gas velocities U used in this study. Clearly the phenomenon of bubble growth is important for short beds used in laboratory studies. In the experimental, and later computational, studies presented here we concentrate on the performance of fluid beds with dispersion heights ranging from 3 to 35m (see Table 1), far in excess of the equilibration height of 0.5 m. In such cases the as- sumption of constant bubble diameter is justified. Above 1385-8947/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved. PII:S1385-8947(00)00369-7