* Corresponding author. Tel.: #31-20-525-7007; fax: #31-20-525- 5604. E-mail address: krishna@its.chem.uva.nl (R. Krishna). Chemical Engineering Science 56 (2001) 503}512 Eulerian simulations for determination of the axial dispersion of liquid and gas phases in bubble columns operating in the churn-turbulent regime J. M. van Baten, R. Krishna* Department of Chemical Engineering, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, Netherlands Abstract Fully three-dimensional (3D) transient simulations using computational #uid dynamics (CFD) have been carried out for bubble columns operating in the churn-turbulent #ow regime. The bubble column is considered to be made up of three phases: (1) liquid, (2) `smalla bubbles and (3) `largea bubbles and the Eulerian description is used for each of these phases. Interactions between both bubble populations and the liquid are taken into account in terms of momentum exchange, or drag, coe$cients, which di!er for the `smalla and `largea bubbles. Water and Tellus oil, with a viscosity 75 times that of water, were used as liquid phase and air as gaseous phase. The transient tracer responses in the gas and liquid phases were monitored at three di!erent stations in the column and the results analysed in terms of a one-dimensional axial dispersion model. The 3D simulation results for radial distribution of liquid velocity (<  (r)), centre-line liquid velocity (<  (0)), axial dispersion coe$cients of the liquid (D  ) and gas (D  ) phases, for columns of 0.174, 0.38 and 0.63 m in diameter were compared with experimental data generated in our laboratories and also literature correlations. There is good agreement between the values of <  (r), <  (0) and D  from 3D simulations with measured experimental data. The axial dispersion coe$cient of the small bubble population was almost the same as that of D  , whereas the dispersion of the large bubbles is signi"cantly lower in magnitude. It is concluded that 3D transient Eulerian simulations are potent tools for investigating the gas and liquid residence time distributions and have potential use as scale-up tools.  2001 Elsevier Science Ltd. All rights reserved. Keywords: Bubble columns; Large bubbles; Small bubbles; Churn-turbulent #ow regime; Radial velocity pro"les; Computational #uid dynamics; Axial dispersion 1. Introduction Bubble column reactors are attracting increasing aca- demic and industrial research interest in view of the many potential applications in natural gas conversion tech- nologies (Krishna, Ellenberger & Sie, 1996; Krishna & Sie, 2000). For the Fischer}Tropsch synthesis, for example, the bubble column slurry reactor is the most attractive reactor choice (Sie & Krishna, 1999). In view of the large gas throughputs involved in the process, the bubble column needs to be operated at high super"cial gas velocities, typically with ;"0.2}0.4 m/s, in the churn-turbulent #ow regime. For commercial viability of the Fischer}Tropsch process, gas-phase conversions in excess of 90% must be achieved (Maretto & Krishna, 1999). This requirement places severe demands on our capabilities to predict the hydrodynamic parameters (hold-up, mass transfer, axial dispersion of gas and liquid phases) for commercial scale reactors that could have diameters exceeding 6 m. Bearing in mind that cold-#ow hydrodynamics and mass transfer studies are often car- ried out in laboratory scale reactors with diameter small- er than say 0.5 m, there is a need for a systematic and scienti"c approach to scale up (Krishna, 2000). In this work we use computational #uid dynamics (CFD), in the Eulerian framework, to describe the hydro- dynamics of bubble columns reactors operating in the churn-turbulent #ow regime. Eulerian simulations are used to estimate the gas and liquid-phase dispersion characteristics. Validation of the Eulerian simulations is sought by comparison with the extensive data set gener- ated by our group in earlier work (Krishna, Urseanu, van Baten & Ellenberger, 1999b, 2000; Krishna, van Baten 0009-2509/01/$ - see front matter  2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 2 5 4 - 2